Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Optimal coordination of unbalanced power distribution systems with integrated photovoltaic systems and semi‐fast electric vehicles charging stations

Optimal coordination of unbalanced power distribution systems with integrated photovoltaic... INTRODUCTIONThe utilisation of renewable energy technologies (RETs) such as photovoltaics (PVs) systems and electric vehicles (EVs) are expected to rise significantly in upcoming years as part of several measures being adopted by most governments to assist meet environmental goals.  For instance, the UK plans to ban all new internal‐combustion engine vehicles by 2040 to achieve its target of net‐zero emissions by 2050 [1]. It is also expected that the global installed capacity of solar PV systems will rise six‐fold by 2030 (compared with 2018) and reach 8519 GW by 2050 [2]. The massive growth of these technologies offers many opportunities, but they can pose several challenges for distribution system operators in regard to power quality. The uncertainty of the location and penetration of PV systems can raise the degree of voltage unbalance [3]. The connection of EVs on specific nodes and phases may further exacerbate the degree of voltage unbalance. Voltage unbalance can produce substantial unsymmetrical current flows in each phase, which can cause adverse impacts on the power distribution systems, including additional power losses and inefficient utilisation of network assets [4]. The first step to address this issue is to balance the residential loads across three‐phase feeders during the planning stage, but because of the uncertainties of load demand and PV generation and unpredicted EV charging behaviour, the typical power distribution systems are rarely balanced, particularly at the low voltage.Literature reviewAdvances in power electronics have helped researchers propose various effective methods to mitigate the problems arising from increased RETs integration. These include different autonomous control schemes for PV inverter [5], on‐load tap changers OLTC [6] and custom power devices [7, 8]. Although these local control approaches respond much faster at no additional cost, they can potentially lead to demand unnecessary reactive power compensation or insufficient voltage support, which may significantly increase power losses, especially at high PV penetration levels [9]. Moreover, the local control of these devices cannot effectively avoid frequent operation of a transformer, which may outweigh the benefits of RETs connection [10]. Most importantly, the influence of these devices on unbalanced voltage cannot be readily determined due to the inter‐phase coupling between distribution lines, which may deteriorate the voltage unbalance level [11]. Therefore, the integration of RETs requires transforming the current systems into coordinated supervisory control systems. Centralised control strategies allow effective control and operation of the network assets to mitigate voltage unbalance problem and achieve various objective functions such as minimising power losses.Many centralised control techniques have been proposed in the literature to minimise voltage rise and reduce voltage control devices’ operation in modern power distribution systems. In [12], an optimal operating of OLTC based on PV generation forecasts is proposed. A distribution static synchronous compensator (DSTATCOM) is coordinated with OLTC and distributed generation in [13] to control the voltage and minimise the power losses. A multi‐objective method for coordinating PV, battery storage systems, and OLTC is proposed in [14] based on forecasting data. These proposed optimisation problems are based on the assumption of balanced distribution network operation and forecasts PV generation and load data. This can lead to an inaccurate representation of the power distribution system operation, which is inherently unbalanced. Besides that, the RETs penetration is uncertain, their output cannot be forecasted accurately, and there may be discrepancies between the predicted and realised values.Several techniques considered the unbalanced operation of the power distribution system [15, 16]. Still, they did not consider minimising voltage unbalance in the optimisation problem. A coordinated control method of PVs, batteries and OLTC is suggested in [17] to mitigate both overvoltage and voltage unbalance in three‐phase unbalanced distribution networks. Voltage unbalance reduction during the daytime is suggested in [18] by optimally re‐phasing grid‐connected PV systems, which are limited to use single‐phase PV systems only. EVs’ potential to suppress the voltage rise resulting from high PV penetrations has recently attracted attention, and only a few studies have paid attention to the role of EVs on voltage unbalance reduction. In [19, 20], EVs are used as one of the control variables in the optimisation problem to limit the voltage unbalance by optimally selecting the state of EV, EV point of connection, and charging/discharging rating power. However, these methods affect customers’ comfort and demand monitoring and control infrastructure that outstripping the capability of the coordination scheme to reach hundreds to thousands of EVs in a given power distribution system.To satisfy the requirement of real‐time power distribution system operation, some authors choose to sacrifice accuracy to increase the computational performance of the optimisation algorithm. For example, in [21, 22], the authors ignore the discrete variables in the formulation, like OLTC and voltage regulators. They assumed a continuous tap of voltage regulation devices, and they had to round the optimal value to the closest integer number. There is no assurance that the rounded number is the correct optimal solution, especially if there is a very large step. A simplification is also adopted in [23, 24] to use a mixed‐integer linear programming to solve optimisation problems for the unbalanced power distribution system. One of the assumptions made is to ignore the inter‐phase coupling (i.e., Carson's line formulation and self and mutual conductors) to linearise the power flow equations. However, these simplifications often suffer from inaccuracies since power distribution systems are inherently nonlinear, which may not reflect the realistic outcome. Failure to consider mutual impedances can create off‐target control signals, which may inadvertently increase voltage unbalance.Novelty and contributionsThe incorporation of large‐scale RETs brings new challenges to the power distribution system operation, including exacerbation of voltage unbalance levels. Therefore, there is a demand for more effective control techniques and management strategies of various power distribution components. Motivated by the limitations described above, this paper proposes a comprehensive optimisation modelling framework incorporating voltage unbalance, voltage magnitude, and OLTC operation in a common platform to minimise power losses effectively through solving multi‐objective optimisation problem. The significance of the proposed optimisation scheme is the ability to determine the optimal tap position of OLTC, the amount of reactive power to be injected or absorbed by DSTATCOM and PV inverter, and EV point of connection (phase a, b, c) in near real‐time. Due to non‐convexity and non‐linearity of the problem, a meta‐heuristics method is advanced to solve the optimisation problem. Therefore, the main contribution and novelty of this article are as follows:proposing a novel mathematical framework for optimisation‐based coordination control scheme incorporating the natural intermittency and practical operation of unbalanced power distribution systems to achieve various objectives. The mathematical framework integrates robust, computationally efficient, and more accurate models (including realistic constraints and inter‐phase coupling) of the controllable devices, making them flexible, effective, and scalable for a practical operation of a power distribution system. The proposed optimisation platform also provides a pathway to consider other optimisation objectives and coordinated control of other technologies, including energy storage.proposing a novel control strategy for EVs charging stations and PV systems to effectively minimise the voltage unbalance, which is also incorporated into the proposed optimisation‐based coordination scheme. The proposed control strategy offers a reduction in supervision and control actions by reducing the search space of the control variable, which improves the convergence speed of the algorithm. This will help the utilities to leverage the large‐scale connection of RETs and allow them to be connected more into the network without concern about overvoltage or voltage unbalance problems.developing an advanced optimisation method combining two modified particle swarm optimisation (PSO) techniques. The advanced hybrid particle swarm optimisation (AHPSO) facilitates the proposed optimisation algorithm escaping from premature convergence and improving the local minimum problem, thereby improving the accuracy, convergence, and effectiveness of the proposed optimisation framework.Organisation of the articleThe rest of this article is organised as follows. Section 2 presents the problem description and the proposed strategies. Section 3 presents the mathematical formulation of the problem. Section 4 describes the proposed solution method used to solve the optimisation problem. Section 0 provides details of simulation results and analysis followed by conclusions in section 5.PROBLEM AND PROPOSED METHODOLOGYFigure 1a shows a simplified three‐phase modern distribution feeder connected to a substation through a transformer equipped with an OLTC. Voabc is the three‐phase voltage at the transformer's low voltage side, and Vsabc is the three‐phase voltage at the point of common coupling (PCC). Zabc is the self and mutual impedance of the distribution line, which reflect an accurate representation of an un‐transposed feeder without losing the explicit information about the neutral currents and voltages. The active power Ppv and reactive power Qpv production of each PV system are injected into nearby connected loads and EVs, and the net active power Pn and net reactive power Qn are fed into the grid. The PCC voltage in an unbalanced three‐phase system Vsabc can be determined using (1). Equation (1) shows that the increase of PCC voltage at phase p (a, b, c) is influenced by the impedances of distribution networks lines, the injected power, and the regulated voltage Voabc, while assuming grid voltage is constant.1Vsp=Vop+∑q=a,b,cZpqPnq+jQnqVsq∗.\begin{equation}V_s^p = V_o^p + {\sum_{q = a,b,c} {{Z^{pq}}\left( {\frac{{P_n^q + jQ_n^q}}{{V_s^q}}} \right)} ^*}.\end{equation}1FIGUREConceptual diagram of the proposed centralised controlIt is also evident from (1) that the injected power or connected EV in one phase can also affect the voltage magnitude of the other two phases because of the mutual impedance effect, making voltage control in an unbalanced network complicated. Also, due to unbalanced line coupling, load increases do not necessarily cause the voltage magnitude to decrease [11]. Therefore, the un‐coordinated operation of voltage control devices may provide a partial solution to the problem of overvoltage, but it can increase the unbalanced voltage and the total power losses on power distribution systems. In addition, due to the absence of online measurement and data monitoring in power distribution systems, operators may be unaware of this impact. To avoid such issues, it becomes an essential and vital part of active power distribution infrastructures to utilise a centralised control of different voltage control devices and make use of smart technology.This paper proposes a methodology for coordinating different voltage regulation devices in the power distribution systems integrated with PVs and EVs. The flow chart of the proposed coordination method is presented in Figure 1. The supervisory control systems coordinate four types of voltage regulation devices: OLTC, DSTATCOM, PV and EV. The suggested coordination scheme identifies the optimal values of the reactive power absorbed/injected from the PV inverters and DSTATCOM, the tap settings of the OLTC, and the phase connection of EV using real‐time data. These optimal control signals maintain the voltage magnitude range, limit voltage unbalance level, minimise the power losses and reduce the frequent operation of transformer OLTC. To avoid affecting customers’ comfort, like controlling their EV charging rate and state of charge, especially at charging stations, only switching the phase where EV should be connected is considered as a control variable. This will also reduce the required supervision and control facilities that go beyond the central controller capability to reach hundreds of EVs connected to the network. The low‐scale PV system can be excluded from central‐based control and can be locally controlled, while the large‐scale such as in industrial or commercial buildings (50 kW and above) are included in the optimisation model.The central unit receives the required network measurement such as PV and load profile and current setpoints of controllable devices at each control cycle (tcycle). An unbalanced three‐phase load flow is then performed to check for potential issues, such as thermal, voltages magnitude, or the voltage unbalances violation. After that, the optimisation model is exclusively applied when there is a constrain violation or after 1 h of the last control signal action. If the activating optimisation model's criteria are still not achieved, the unbalanced load flow is performed again for the next control cycle. The main components for deploying the proposed schemes are smart meters, sensors, controllers, and communication medium. Smart meters and sensors provide the necessary power consumption and voltage measurements. The controller can be a central controller where all information and measurement are processed to generate a control command to be sent to the controller installed at a controllable device. A static transfer switch is one of the controllable devices used at the charging stations to allow easy and flexible EV switching among the three phases. 5G is one of the communication methods that can be used in centralised control, which have already been utilised in power transmission and distribution systems [25].PROBLEM MODELLING AND FORMULATIONThe coordination between reactive power control capability of PV inverters, voltage control option of OLTC and DSTATCOM and phase switch of EV is an optimisation problem, and it has various operational goals as it must meet the various network operational constraints and component characteristics. The optimisation outcome minimises the power losses, the operational switching of OLTC, the voltage magnitude variation limit, and the voltage unbalance. Therefore, the objective function is constructed as a mixed‐integer nonlinear problem, which can be expressed as follows:2Minimise:fx,u,Subjectto:gx,u≤0hx,u=0,\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{3}{l}@{}} {{\rm{Minimise{:}}}\;f\left( {x,u} \right),}&{{\text{Subject to}}{:}}& \quad {g\left( {x,u} \right) \le 0}\\[6pt] \,&\,&\quad {h\left( {x,u} \right) = 0} \end{array} ,\end{equation}where f(x,u) is the objective function that requires to be minimised, x is the vector of dependent variables or the state variables. u is the vector of independent variables or the control variables used to achieve the optimisation problem. g(x,u) is the set inequality constraints, and h(x,u) is the equality system operating and control variable constraints.Objective functionThe main objectives of the optimisation model are to minimise the power losses, switch operation of OLTC and limit the unbalanced voltage while satisfying the operational constraints. The multi‐objective optimisation problem can be solved either by converting the multi‐objective function to a single objective function with different weighting factors or applying pareto‐based methods. Treating all objective functions as one objective function is commonly used because it has less computation burden than pareto‐based methods, and the optimisation of one objective function could be achieved without aggravation of another objective function. However, choosing an appropriate value for weighting factors could be challenging. To address this problem, some of the objective functions can be treated as a constraint in the optimisation problem by limiting their values except for the power losses, which cannot be limited. Therefore, the primary objective function is to minimise the total three‐phase power losses in a distribution network where the number of OLTC switches, voltage magnitude, and voltage unbalance factor is limited.Different formulations are used to describe the power losses in literature. Most of them are based on an approximation to reduce the complexity of the optimisation problem especially when analytical approaches are used. When metaheuristic optimisation techniques are used, any formulation can be used without approximation. Therefore, the difference between power generation (PG_ip$P_{G\_i}^p$) and loads (PL_ip$P_{L\_i}^p$) at each at phase p and node i is the most accurate representation of the total three‐phase power losses (fPL)${f^{PL}})$, and is computationally efficient. Thus, the objective function can be formulated as given in (3). It is calculated first by determining the total generated power, which is determined by running the load flow algorithm. The load flow calculation involves constructing a Y matrix that reflects the network per‐phase impedance, including Carson's line formulation. The detailed mathematical formulation of the three‐phase load flow calculation used to calculate the power losses can be found in [26].3fPL=∑i=1N∑p=a,b,cPG_ip−PL_ip.\begin{equation}{f^{PL}} = \mathop \sum \limits_{i = 1}^N \mathop \sum \limits_{p = a,b,c} \left(P_{G\_i}^p - P_{L\_i}^p\right).\end{equation}Equality constraintsEquality constraints represent the typical load flow equations. These constraints are strictly enforced during the load flow procedure if metaheuristic optimisation techniques are used, which are satisfied by performing load flow calculations to obtain the fitness function. Improved conventional Newton‐Raphson algorithm and Backward–Forward Sweep based algorithms are two common techniques employed for load flow calculation in unbalanced power distribution systems. Given its robustness and convergence speed, especially for ill‐conditioned systems, the former is used in this study. The new power and current injection method for balanced load flow calculation developed in [27] is extended by the authors in [26] to the unbalanced three‐phase power system, as shown in (4). The improved load flow algorithm presents a superior performance in convergence and computing time compared with other Newton‐Raphson methods. Full details of the improved three‐phase load flow and its performance can be found in [26].4ΔIxmabcΔIxrabc⋮⋮Δ(Py)abc⋮=−J·ΔVxrabcΔVxmabc⋮⋮Δ(δy)abc⋮,\begin{equation}\left[ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\Delta {{\left( {I_x^m} \right)}^{abc}}}\\[3pt] {\Delta {{\left( {I_x^r} \right)}^{abc}}}\\[3pt] \vdots \end{array} }\\[3pt] \vdots \\[3pt] { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\Delta {{({P_y})}^{abc}}}\\[3pt] \vdots \end{array} } \end{array} } \right] = - J \cdot \left[ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\Delta {{\left( {V_x^r} \right)}^{abc}}}\\[3pt] {\Delta {{\left( {V_x^m} \right)}^{abc}}}\\[3pt] \vdots \end{array} }\\[3pt] \vdots \\[3pt] { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\Delta {{({\delta _y})}^{abc}}}\\[3pt] \vdots \end{array} } \end{array} } \right],\end{equation}whereJ‐ represent the Jacobian matrixabc$abc$‐ represent the three phases (phase a, phase b, phase c)Ixr,Ixm,Vxr,Vxm$I_x^r,\;I_x^m,V_x^r,V_x^m$‐ are the real and imaginary part of the injection current and the voltage at bus xPy,δy${P_y},\;{\delta _y}$‐ real power injection and the voltage phase angle at bus yx,y$x,y$‐ represent the load buses and generator buses.Inequality constraintsState variablesThe state variables represent the power system operating limits as follows:Voltage Limit: voltage magnitude (Vip$V_i^p$) at all buses (i∈N)$( {i \in N} )$ and phases (p∈a,b,c)$( {p \in a,b,c} )$ in the power distribution system must be kept with the defined limit.5Viminp≤Vip≤Vimaxp.\begin{equation}V_{{i_{\min }}}^p \le V_i^p \le V_{{i_{\max }}}^p.\end{equation}Thermal Limit: the rated amount of current (|Iijp|$| {I_{ij}^p} |$) flow between any two nodes ij$ij$ or branch (NL)$( {NL} )\;$is restricted by the feeder thermal limit.6Iijp≤Iij_rated..\begin{equation}\left| {I_{ij}^p} \right| \le {I_{ij\_rated.}}.\end{equation}Voltage Unbalance: because it can produce undesirable operation conditions in the power distribution systems, the steady‐state voltage unbalance (VU%$VU\% $) at any bus i should be limited.7VU%i≤VU%Limit..\begin{equation}VU{\% _i} \le VU{\% _{Limit.}}.\end{equation}All these state variables are incorporated into the formation of the comprehensive objective function with penalty factors to maintain the state variables inside their allowable boundary and reject any infeasible solution. The penalty function can be specified by a quadratic term as follows.8F=fPL+k1∑i=1N∑p=a,b,c∇Vip+k2∑i=1Nl∑p=a,b,c∇Iip+k3∑i=1N∇VU%i,\begin{eqnarray} F &=& {f^{PL}} + {k_1}\sum_{i = 1}^N {\sum_{p = a,b,c} {\nabla V_i^p} } + {k_2}\sum_{i = 1}^{Nl} {\sum_{p = a,b,c} {\nabla I_i^p} }\nonumber\\ && +\; {k_3}\sum_{i = 1}^N {\nabla VU{\% _i}} ,\end{eqnarray}where9∇Vip=Vip−Vmin.2Vip<Vmin.0{Vmin.≤Vip≤Vmax.Vip−Vmax.2Vip>Vmax.,\begin{equation} \nabla V_i^p = \left\{ \def\eqcellsep{&}\begin{array}{ll} {{{\left( {\;V_i^p - {V_{min.}}} \right)}^2}}& {V_i^p &lt; {V_{min.}}}\\[3pt] 0& {\{V_{min.}} \le \;V_i^p \le {V_{max.}}\\[3pt] {{{\left( {\;V_i^p - {V_{max.}}} \right)}^2}} & {V_i^p &gt; {V_{max.}}} \end{array} \right.,\end{equation}10∇Iip=0Iijp≤Iij_limitpIijp−Iij_limitp2Iijp>Iij_limitp,\begin{equation} \nabla I_i^p = \left\{{ \def\eqcellsep{&}\begin{array}{ll} 0 &{I_{ij}^p \le I_{ij\_limit}^p}\\[3pt] {{{\left( {I_{ij}^p - I_{ij\_limit}^p} \right)}^2}} &{I_{ij}^p &gt; I_{ij\_limit}^p\;} \end{array} } \right.,\end{equation}11∇VU%i=0VU%i≤VU%limitVU%i−VU%limit2VU%i>VU%limit.\begin{eqnarray} \nabla VU{\% _i} = \left\{ { \def\eqcellsep{&}\begin{array}{ll} 0&{VU{\% _i} \le VU{\% _{limit}}}\\[3pt] {{{\left( {VU{\% _i} - VU{\% _{limit}}} \right)}^2}}&{VU{\% _i} &gt; VU{\% _{limit}}\;} \end{array} } \right..\nonumber\\ \end{eqnarray}Various definitions and standards were developed to evaluate the voltage unbalance level and its acceptable limits [3]. One of these definitions is based on IEEE Std. 141–1993 [28], and it is referred to as phase voltage unbalance (VU%). It is determined as the ratio between the maximum deviation of phase voltage magnitude (Vp,p∈{a,b,c})${V^p},\;p \in \;\{ {a,\;b,\;c} \})$ from average phase voltage magnitude and average phase voltage magnitude, as given in (12). Based on IEEE Std. 141–1993, VU% of 3.5% can cause 25% additional heating on the motors, and thus a voltage unbalance greater than 2% must be reduced. According to EN 50160 and ANSI C84.1‐2011 standards, the voltage magnitude variation limits are ±10% and ±5%, respectively [3]. Therefore, in this paper, VU%limit$VU{\% _{limit}}$ is restricted to 2%, and the voltage variation (Vmin.,Vmax.${V_{min.}},{V_{max.}}$) is limited to ±7%. k1,k2andk3${k_1},\;{k_2}\;and\;{k_3}$ represent penalty factors for voltage limit constraint (∇Vip$\nabla V_i^p$), thermal limit constraint (∇Iip$\nabla I_i^p$), and voltage unbalance limit constraint (∇VU%i$\nabla VU{\% _i}$), respectively. The penalty factors are chosen to be large number to avoid violation of relevant constraints.12VU%i=Max.Vabc−13∑p=a,b,cVp13∑p=a,b,cVp×100.\begin{equation}VU{\% _i} = \frac{{\left| {{\rm{Max}}.\left\{ {{V^{abc}} - \frac{1}{3}\mathop \sum \nolimits_{p = a,b,c} {V^p}} \right\}} \right|}}{{\frac{1}{3}\mathop \sum \nolimits_{p = a,b,c} {V^p}}} \times 100.\end{equation}Control variablesThe inequality constraints of the control variables are self‐limiting. The optimisation solver picks a feasible value for each control variable in the specified range. These control variables represent the control parameter of DSTATCOM, OLTC, PV Inverter and EV.DSTATCOMAccording to the operating concept of the DSTATCOM, the controllable voltage source (Vsh∠δsh${V_{sh}}\angle {\delta _{sh}}$) is used to control the rate of reactive power (Qshp)$Q_{sh}^p)$ to be injected or absorbed. Nevertheless, the magnitude of DSTATCOM voltage is constrained by the maximum and minimum values, while its phase angle can vary from 0 to 2π. Therefore, the control variable of DSTATCOM is constrained as follows:13Vsh−minp<Vshp<Vsh−maxpQsh−minp<Qshp<Qsh−maxp.\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {V_{sh - min}^p &lt; V_{sh}^p &lt; V_{sh - max}^p}\\[6pt] {Q_{sh - min}^p &lt; Q_{sh}^p &lt; Q_{sh - max}^p} \end{array} .\end{equation}DSTATCOM control parameters are considered as independent variables in most load flow calculation methods [29]. Therefore, several modifications are required to the existing load flow algorithms and sometimes cause convergence problems and demand high computation time. To address this problem, the author has proposed an innovative model of three‐phase DSTATCOM in [26], which can be used in unbalanced load flow calculation. In this paper, the developed DSTATCOM model will be used where its connected bus is modelled as a voltage‐controlled bus in load flow calculation with an identified voltage magnitude and zero active power exchange when it operates within limits. In the optimisation problem, the voltage magnitude is treated as a control variable, and then DSTATCOM model parameters for each phase can be calculated at the end of each iteration of the load flow calculation to check its limits. Full details of the developed DSTATCOM and its performance in terms of computation time and solution convergence can be found in [26].OLTCThree‐phase transformers are modelled in the three‐phase load flow calculation by an admittance matrix YTabc$Y_T^{abc}$, which depends upon the connection of the primary and secondary taps, and the leakage admittance.14YTabc=YppabcYpsabcYspabcYssabc,\begin{equation}Y_T^{abc} = \left[ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {Y_{pp}^{abc}}& \quad {Y_{ps}^{abc}}\\[6pt] {Y_{sp}^{abc}}&\quad {Y_{ss}^{abc}} \end{array} } \right],\end{equation}where Yppabc$Y_{pp}^{abc}$, Yssabc$Y_{ss}^{abc}$ are self‐admittance of the primary and secondary, respectively, and Yspabc$Y_{sp}^{abc}$, Ypsabc$Y_{ps}^{abc}$ are mutual admittances of the transformer. The transformer taps (Tap(t)$Tap( t )$) are assumed to be at the primary side, high voltage side and the transformer connection is Delta Wye‐G. The details of submatrices of the admittance matrix for different transformer connections and tap ratio and location can be found in [30]. A typical tap changing transformer has 21 discrete positions (nominal, 10 above and 10 below), and each tap has ±1% regulating range of voltage, therefore, the equivalent voltage ratio aT${a_T}$ is practically determined by the tap positions.15aTt=1+0.01×Tapt,\begin{equation}{a_T}\left( t \right) = 1 + 0.01 \times Tap\left( t \right),\end{equation}where Tap(t)$Tap( t )$ must be an integer value, and the limit on tap position of OLTC can be expressed by:16−10≤Tapt≤10.\begin{equation} - 10 \le Tap\left( t \right) \le 10.\end{equation}Regular OLTC tap position changing shortens their operation life and increases the associated maintenance costs because of the intermittent generation of PVs. Power system operators are usually interested in reducing the number of switches due to financial and technical considerations. These number depends on the switching type of OLTC (e.g., oil or vacuum) [31], which can vary between 600,000 and 1,000,000 switches [12]. According to [17], the maximum number of tap changes of the OLTC has been assumed equivalent to the typical value of 700,000 by the manufacturers without the need for maintenance. Taking into account this value and expected lifetime of 40 years, the maximum average number of tap changes per day must be restricted to 48 (700,000/(40 × 365). To satisfy this requirement and avoid unrealistic tap operation, the optimisation problem restricts the number of tap position changes between two consecutive times to be less than 3. Therefore, the constrain of tap position at each control cycle can be expressed by (17) considering the maximum and minimum tap position given by (16).17Tapt−1−3≤Tapt≤Tapt−1+3,\begin{equation}Ta{p_{t - 1}} - 3 \le Ta{p_t} \le Ta{p_{t - 1}} + 3,\end{equation}where Tapt$Ta{p_t}$ is the tap position at time step t and Tapt−1$Ta{p_{t - 1}}$ represent the previous tap position.PV InverterReactive power and active power control are different operation modes that can be integrated into PV inverters. Active power control is more effective in providing voltage regulation support than reactive power because of the high R/X ratio in the power distribution systems. Nevertheless, active power control is likely to be an unpreferable technique because of active power curtailment. For this reason, in this study, the reactive power control option of PV inverter is considered. There are various reactive power capability options available for PV inverters, which are normally defined by the country's standards and grid codes. Among them is to apply power factor (PF) adjustment according to the PV active power generation. PV inverters can provide reactive power at no solar input, however, this functionality is not standard in the industry [32]. Moreover, operating PV inverters at night will increase the inverter's operational stress and reduce their lifespan. Besides that, additional configuration of the PV inverter in the optimisation problem is required because the reactive power limitation needs to be recomputed at every period. Therefore, in this study, no reactive power support is considered while there is no solar power and accordingly, oversizing the inverter allows sufficient freedom of reactive power exchange, specifically on clear sky days. For this reason, the size of the inverters is increased by 25% of the rated active power of PV systems, allowing PV inverters to operate between 0.8 leading and 0.8 lagging power factor regardless of active power output [33]. This size of the inverter can be seen in some modern inverters, such as SMA Sunny Tripower Inverter [34].Normally, the three‐phase PV inverter is designed as a compact three‐phase unit. The generated active power is divided equally between the three phases, and the reactive power can be distributed among the PV inverter phases with different ratios depending on the assigned power factor (PFiabc$PF_i^{abc}$) value which is constrained by (18). Therefore, the bus (i) where the PV system is connected would be considered as a load bus in load flow calculation, where the active output power of PV (Ppv_iabc$P_{pv\_i}^{abc}$) is known, and the reactive power (Qpv_iabc$Q_{pv\_i}^{abc}$) can be calculated using (19). To design a reliable and realistic optimisation model, only large scale (> 50 kW) residential or commercial PV systems can be included in the optimisation model. This is to reduce the monitoring and control infrastructure required to reach the vast number of connected small‐scale PV inverters. Moreover, the small‐scale PV system has a local effect and can be controlled locally using droop control [33].180.8i−leadingabc<PFiabc<0.8i−laggingabc,\begin{equation}0.8_{i - leading}^{abc} &lt; PF_i^{abc} &lt; 0.8_{i - lagging}^{abc},\end{equation}19Qpv_iabc=Ppv_iabcPFabc×1−(PFabc)2.\begin{equation}Q_{pv\_i}^{abc} = \frac{{P_{pv\_i}^{abc}}}{{P{F^{abc}}}}\; \times \sqrt {1 - {{(P{F^{abc}})}^2}} .\end{equation}EVEVs have been recently involved in voltage management of smart power distribution systems by optimally controlling their charging rate, state of charge, and either charging or discharging. However, these control options may affect EV owners’ comfort level in charging stations or parking lots while they wait for their vehicle to charge. Moreover, nowadays, EV manufacturers are competing to provide fast charging facilities to their vehicles, making fast charging demand increase. This can be seen in public and workplace car parking, which are usually equipped with semi‐fast charging speed supplied by three‐phase feeders, and they are projected to represent the high portion of the overall charging stations [35]. The various control options of EV at home can be feasible; however, controlling many connected EVs makes the optimisation problem very complicated, and the time burden increases multifold. Therefore, in this paper, a charging station or parking lots equipped with semi‐fast charging facilities and a static transfer switch will be considered. One of the main features of a static transfer switch is to ensure instantaneous and quick load transfers without tolerating voltage disturbance limits. Many researchers identified static transfer switch as a possible cost‐effective solution to power quality problems in various applications such as dynamic switching residential customers among three‐phases and re‐phase of single‐phase PV system connection among the three phases [8]. The selection of the phase at which the EV should be connected will be used as a control variable. Each parking lot is represented by three variables despite the number of EVs connected at the parking site. Each variable identifies which phase that one‐third of the total number of EVs should be connected. Therefore, the control variables of parking lots are discrete variables, and their value represents as (20). In the load flow calculation, the bus with a charging station would be represented by constant load buses, and their loads depend on the number of vehicles connected at each phase and parking lots.20EVi13phase=0;phasea1;phaseb2;phasec,\begin{equation}EV_{i\frac{1}{3}}^{phase} = \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{2}{l}@{}} {0;\;}&\quad {phase\;a}\\[3pt] {1;\;}&\quad {phase\;b}\\[3pt] {2;}&\quad {\;phase\;c} \end{array} } \right.,\end{equation}where i express the first, second and third groups of the connected EV at each parking lot.PROPOSED SOLUTION OF ADVANCED HYBRID SWARM OPTIMISATION (AHPSO)The optimisation problem can be solved using some available techniques that may be classified as mathematical and meta‐heuristic approaches. Conventional (mathematical) optimisation techniques such as linear programming and nonlinear programming have achieved reasonable success in solving optimisation problems [36]. The major strengths of these methods are numerical stability and reliable convergence, but they are hard to handle discrete variables, exposed to get trapped in local minima solution, and highly sensitive to initial values [37]. These shortcomings can be overcome when meta‐heuristic methods, for example, particle swarm optimisation (PSO) and genetic algorithms (GA), are used to solve the optimisation problem with limited or fewer modifications in the original problem. However, their main concern is to achieve the global best solution in the shortest possible time because of the large number of load flows calculation needed in the solution process, limiting their use in on‐line applications. However, the problem of computation time is expected to be resolved by the next‐generation of software and hardware, taking into consideration the rapid advancement of computer technology. For instance, the limitation of using meta‐heuristic in on‐line applications was addressed in [38] and significantly accelerated the computations by operating the massively parallel architecture of graphics processing units (GPUs). The parallel computation allows all populations (e.g., 20 particles for the case of PSO) to perform the calculation at the same time, which all are independent of each other. On the other hand, conventional (mathematical) optimisation techniques cannot take advantage of parallel computation since each iteration relies on the previous iteration. Besides that, mathematical optimisation techniques cannot be properly used in the application of power distribution systems because of the massive number of complex assets (i.e., integer variables such as OLTC and EV connected phase) and unbalanced operation, which make the optimisation problem harder to be solved. Therefore, the development in computational intelligence with the advent of parallel processing capabilities and supercomputer use made meta‐heuristic methods possible for real‐time optimisation applications, such as [19, 39].Various meta‐heuristic methods and their variants have been proposed in the literature for solving the optimisation problem. PSO‐based approach is one of the most popular techniques due to its ability to deal with highly nonlinear and mixed‐integer problems. Yet, the original PSO sometimes requires more time to move into the solution space's effective area, depending on the case. For this reason, various versions of PSO were proposed and hybridised with other meta‐heuristics methods. For example, to alleviate the local minimum issue, a modification is applied to the PSO in [40], and the diversity of the optimisation variables is improved by employing GA mutation and crossover operators. A comparison investigation in [41], demonstrates that this modified variant of PSO outperforms other heuristic approaches with regard to accuracy, robustness and speed. Another version of PSO based on natural selection mechanism reported in [42], where the number of the best particle is increased while the worst particle is reduced at each generation. This allows low assessed agents to move to the best adequate area straight using the selection method, and concentrated search primarily in the current effective area is realised. Taking advantage of the two modified PSO proposed in [40] and [42] and to further improve the accuracy and prevent premature convergence of the solution, a combination of both these methods is proposed in this paper to solve the optimisation problem. The specific process related to the proposed optimisation technique (AHPSO) algorithm is given below and are presented in Figure 2.Initialise the parameter of PSO and GA and then the velocity Vi${V_i}$ and position Xi${X_i}$ of each particle are initialised randomly. Each particle is composed of several cells that represent the decision variables.Evaluate the objective function (8) of each particle after performing an unbalanced load flow calculation.Update personal best positions (pbest−i)${p_{best - i}})$ for each particle that has a new better objective value than the old personal best value and then updates the global best position (gbest)${{\rm{g}}_{best}})$ which represents the best ever solution achieved so far.Update the speed and position of the particle for the next iteration k+1 as follows:21Vik+1=χVik+c1r1pbest−i−Xik+c2r2gbest−Xik,\begin{equation}V_i^{k + 1} \,{=}\, \chi \left( {V_i^k \,{+}\, {c_1}{r_1}\left( {{{\rm{p}}_{best - i}} \,{-}\, X_i^k} \right) \,{+}\, {c_2}{r_2}\left( {{{\rm{g}}_{best}} \,{-}\, X_i^k} \right)} \right),\end{equation}22Xik+1=Xik+Vik+1,\begin{equation}X_i^{k + 1} = X_i^k + V_i^{k + 1},\end{equation}where χ is the constriction factor coefficient and is used to ensure the convergence of the search processes and produce better‐quality solutions than the standard PSO. c1,c2${c_1},\;{c_2}$ are the acceleration coefficients and, r1,r2${r_1},\;{r_2}$ are two random numbers with uniform distribution in the range of [0, 1]. In this paper, the acceleration coefficients are set c1=c1=2.05.${c_1} = {c_1}\; = \;2.05.$ The constriction factor coefficient (χ) is calculated as follows.23χ=22−φ−φ2−4φ,φ=c1+c2,φ>4.\begin{equation}\chi = \frac{2}{{\left| {2 - \varphi - \sqrt {{\varphi ^2} - 4\varphi } } \right|}},\quad \varphi = {c_1}\; + {c_2},\varphi &gt; 4.\end{equation}Apply crossover and mutation operators to half of the population members. Then check if the inequality constraints enforce the limits of positions. If not, then they are replaced by their respective boundaries. In this paper, the crossover and mutation rate are set as 1 and 0.1, respectively.Apply natural selection approach by sorting the practice according to their objective function values, and then only the speed and position of the worst half of the particles are replaced by the speed and position of the best half of the particles.Repeat steps 2–6 until a stopping criterion is achieved, which is reaching the maximum number of iterations or an adequately good fitness value is attained.2FIGUREThe flowchart of the proposed centralised control for case studiesCASE STUDIES AND ANALYSISIn order to verify the performance of the proposed optimal coordination algorithms, different scenarios are studied on the modified IEEE 37‐node and IEEE 123‐node test feeders [43], and the strength of the proposed method is evaluated in detail under various operating conditions. First, the contribution of the suggested control scheme on the unbalanced condition improvement and power losses reduction under different PV penetration levels is examined on the modified IEEE 37‐node test system. Then, the test cases are conducted on the IEEE 123‐node test system to confirm the proposed method's scalability on the severe unbalanced conditions. Three scenarios are adopted on each test network to analyse and compare the performance of the proposed optimisation model with an autonomous control scheme. The considered scenarios are:Scenario 1: network is operating without any voltage regulation devices (base case). There is no OLTC and DSTATCOM, and the PV inverters are operated at unity power factor. The EVs are connected equally among the three phases.Scenario 2: network is operating under the local control of connected voltage regulation devices. DSTATCOM and PV inverter are locally controlled, whereas the EVs are still connected equally among the three phases. The conventional rule‐based control method of OLTC is used, where tap position change to keep the deviation of the secondary bus voltage from the pre‐set reference with voltage regulation bandwidth is 0.012 pu.Scenario 3: network is operating with the proposed voltage regulation algorithm. All the voltage regulation devices and EVs’ connections are now controlled by the proposed optimisation model described in the flowchart shown in Figure 2. For case studies, the optimisation process has been performed over a period of 24‐h with a 10‐min time step. The initial value of OLTC tap, DSTATCOM Vsh and PV inverter PF was set at unity value, and the number of connected EV at each phase was set to be equal. Then unbalanced load flow is performed to check the operational constraints of the power distribution system. The optimisation model is then applied either if there is operational constraint violation (e.g., voltage unbalance level) or after 1 h of the last optimisation model being applied. The optimisation proposed a new setting of the coordinated devices that enforce the efficient operation of the power distribution system. These processes will be repeated every 10 min until the optimisation model has produced 24 h of operation.Finally, both test systems are used to evaluate the accuracy and robustness of the employed AHPSO. The proposed strategy and simulation were implemented in the MATLAB® (R2018a). The numerical experiments were conducted on a computer with an Intel computer i7‐6700 at 3.4 GHz CPU and 12GB RAM. For all case studies, the population size and maximum number generation are set to 20 and 100, respectively. For both local and proposed control (Scenario 2 and 3), the feeders’ voltage magnitude was within the limit, therefore the evolution of voltage unbalance and power losses would be the main interest in this study. Moreover, this study assumes that the size of feeders and transformer of the selected simulated network is designed to handle a high PV and EV charging station penetration level based on interconnection studies. Thus, the power loading of lines and transformers are within limits.IEEE‐37‐bus test systemFigure 3 shows the modified IEEE 37‐bus unbalanced radial distribution feeder [43]. In this test feeder, the loads are single‐phase, two‐phase and three‐phase, and the distribution lines are un‐transposed. All the three‐phase loads are assumed connected in a star configuration and are considered as a constant power load type where the given loads’ data are considered to be peak loads. For simplicity, each load bus represents a group of residential houses fed by a three‐phase feeder. To investigate the efficacy of the proposed method, it assumed that the substation transformer is equipped with OLTC. Two units of three‐phase PV generation systems are randomly connected to the tested feeder at buses 25 and 33. Two EV charging stations that emulate real parking are considered in this paper, and both are assumed to be commercial parking lots that provide a semi‐fast charging facility to EVs with a rating of 7.4 kW. The maximum number of connected EVs into EVs parking lots 1 and 2 are 20 and 15, respectively, which are connected into bus 20 and bus 9, respectively.3FIGUREModified IEEE 37‐bus test feederThe semi‐fast charging station is not yet common compared with slow (residential) or fast‐charging stations. In this type of charging station, the EVs are only charged during working hours, and the peak occurs between 12 pm and 2 pm. Figure 4 shows the total EVs at each time instant for the two parking lots, which are identical to the typical EVs parking lots profile used in [44]. A three‐phase DSTATCOM is installed at bus 8, having a capacity of 3 × 200 kVAr. The actual PV active power production on a sunny day, and a practical load profile of a three‐phase feeder throughout a day with a 10‐min of time resolution are shown in Figure 5. These data are recorded by HCT GreenNest Eco House [45]. The 24‐h load profile curve is incorporated into all load buses in the simulated network, considering various peak load levels and phases number. Although the measurements describe the active power load profile, they can be adopted to represent the reactive power profile. Several criteria were used in different studies to describe the PV penetration level [46], and the definition used in this paper is the ratio of the total three‐phase peak of PV active power to the total three‐phase peak load of the apparent power in the feeder.4FIGUREThe number of vehicles in parking lots5FIGUREThree‐phase load and PV power profileInitially, the simulated system is tested under a low PV penetration level (20%) to identify the system's detailed behaviour under various scenarios and point out the significance of the proposed optimisation model. The statistical analysis of voltage unbalance under the three scenarios for a period of 24 h at each bus are demonstrated through a standard box plot displayed in Figure 6. The line inside each box is the median, and the left and right edges of each box are the upper and lower quartiles, respectively. It shows that the voltage unbalance at the base case (Figure 6a) crossed the limit of 2% and reached up to 3.7% during some hours of the day. It evidences that most of the day, the voltage unbalance limits are violated at some buses, particularly bus 27 to bus 36. The operation of local control of voltage regulator devices representing scenario 2 manages to reduce the voltage unbalance to 2.6%, as shown in Figure 6b, but still, the network is suffering from voltage imbalance problems for a significant amount of time. Moreover, if the number of EVs connected at each phase are not assumed equal in the local control, the voltage unbalance level would be a catastrophe. After adopting the proposed optimisation model (scenario 3), the voltage unbalances are further minimised and maintained within standard limits, as shown in Figure 6c.6FIGUREVoltage unbalance for (a) Scenario 1, (b) Scenario 2, and (c) Scenario 3As far as scenario 3 is concerned, Figure 7 presents the related PF angle (δPFabc$\delta _{PF}^{abc}$) values of the two integrated PV inverters for each phase throughout the day, which reflect the rate of reactive power exchanged with the network. It can be noted that the PV inverters connected at bus‐33 most of its operating time absorb the reactive power at phase ‘b’ and supply it at the other two phases to reduce the voltage variation among the phases. This is due to the load is comparatively low at phase ‘b’ and high at phase ‘a’ and ‘c’, making the voltage unbalance level significant. It can also be observed from Figure 8 that most of the EVs are connected at phase ‘b’ to balance the power between the phases. The exclusion of EVs’ connections in the optimisation problem has increased the total energy losses per day by 6%. This is because the network is forced to absorb more reactive power to compensate the voltage unbalance, especially at a high penetration level. Involving EVs’ connections in the optimisation model may demand for oversizing the charging station infrastructure (sizing of each phase). However, shifting the car's load from one phase to other can reduce the overall loading to other phases in three‐phase systems. This is because the optimisation algorithm tries to minimise the loading difference in the three‐phase system, which consequently leads to maintain a reasonable feeder loading and hence, avoiding upgrading feeder size. For example, the loading of phase ‘c’ of the substation transformer is reduced from 120% to 105% (with respect to the transformer’ rating at each phase) after applying the proposed coordination scheme. To accommodate the voltage drop and reduce the power losses at peak load, the OLTC operates at tap position 3, and the DSTATCOM operates at the operating limit to inject reactive power, as shown in Figure 9. It is worth noting that the total number of taps changed during the day was 25, which is less than the maximum average number of tap changes per day (48 tap changes). Moreover, the loading of the substation transformer at peak load is reduced by 5% compared with the local control approach due to power losses and voltage unbalance reduction.7FIGURECorresponding PF angle of the connected PV inverter8FIGURENumber of connected EVs at each phase at the parking lots9FIGURETap position of OLTC and controllable voltage source of DSTATCOMTo examine the superiority of the proposed control approach at different PV penetration levels, the size of the integrated PV is increased to reach 100%. Figures 10 and 11 show the maximum voltage unbalance recorded and the total energy losses under various penetration levels. Although the support of PV active power between the phase is equal, the voltage unbalance reduces as the penetration level of PV increases. This is due to the inter‐phase coupling between the distribution line, causing different voltage drop at each phase, which might decrease the voltage unbalance. Injection of reactive power from PV inverter and DSTATCOM reduces the voltage unbalance significantly at high penetration level; however, the power losses increased significantly. For example, at 75% penetration level, the total energy losses rise by 45% to reduce the voltage unbalance from 3.12 to 2.29. In contrast to scenario 2, in the proposed optimisation model, the voltage unbalance reduces to 1.98, and the total energy losses reduce by 25%. This indicates that the lack of coordination between various voltage regulation devices can potentially reduce the severity of voltage unbalance with the cost of increasing network losses.10FIGUREComparison of maximum voltage unbalance11FIGUREComparison of total energy lossesFinally, the proposed control is tested under a different load profile to resemble a diverse situation of the power distribution system where the peak of load and PV generation is not synchronised. The new three‐phase load profile used in this case study is presented in Figure 12, which is based on real‐world data in Oman provided by Mazoon Electricity Company (MZEC). It can be seen from Figure 13 that at 20% of PV penetration level, the maximum voltage unbalance recorded throughout the day were 3.59 for scenario 1 and 3.31 and 2.09 for scenario 2 and 3, respectively. These values are the same for the different PV penetration levels because they occurred at the time of peak load (18:30), where the PV production is zero. Therefore, the PV generated power for this type of load profile does not influence the maximum voltage unbalance level but significantly impacts the overall energy losses. For example, at 100% penetration level, the energy losses per day is increased from 901 kWh to 1303 kWh when adopting the local control of voltage regulation devices, and after adopting the proposed control scheme, the energy losses is reduced to 769 kWh. By implementing the proposed coordination scheme, the voltage unbalance is maintained at the standard bounds regardless of PV generation, which concludes that the proposed coordination scheme can maintain the operational constraints limit in an unbalanced power distribution system under various load and PV generation profiles.12FIGUREDifferent three‐phase load profiles13FIGUREComparison of maximum voltage unbalance recorded during a dayIEEE‐123 test systemTo further verify the scalability of the proposed optimisation model on large‐scale power distribution systems, a modified IEEE123‐bus test system is adopted, as presented in Figure 14. In this test system, the voltage unbalance is relatively low compared with the IEEE37‐bus test system. For the purpose of the study, some loads were added in phase “a” to increase the percentage of voltage unbalance. All the four voltage regulators are replaced with two OLTC connected between bus 1 and 2 and between bus 65 and 73. All shunt capacitors are replaced with one three‐phase DSTATCOM connected at bus 103. The locations of the PV system and EVs are identified on the test system by square and triangle, respectively. All the assumptions and parameters of voltage control used previously are adopted here considering the same load, PV and EVs profile as shown in Figures 4 and 5.14FIGUREModified IEEE 123‐bus test feederIn this case study, the network was tested under a 30% PV penetration level. Without incorporating voltage regulator devices, it can be seen from Figures 15 and 16 that the voltage unbalance starts violating the limit from 8:30 until 14:30, with half of the network nodes in violation of limits. Even with incorporating voltage regulator devices that are controlled locally, more than 15 buses violated the standard limit of voltage unbalance. This makes mitigating the voltage unbalance in such a network challenging. To estimate the overall voltage unbalance of the whole system, the system voltage unbalance factor (VUFsys.$VU{F_{sys.}}$) is introduced as follows.24VUFsys.=∑i=1N=123∑t=024(VU%it)2\begin{equation}VU{F_{sys.}} = \sum_{i = 1}^{N = 123} {\sum_{t = 0}^{24} {{{(VU\% _i^t)}^2}} } \end{equation}15FIGUREComparison of maximum voltage unbalance recorded during the day16FIGUREComparison of maximum voltage unbalance recorded at each buswhere VU%it$VU\% _i^t$ is the voltage unbalance at time t and at bus i, which can be calculated using (12).Tables 1 and 2 show the reduction rate of energy losses and overall system voltage unbalance compared with the base case under 30% and 60% of PV penetration level. Compared with Scenario 1, the voltage unbalance factor for the whole system is reduced by 30.31% and 75.01% in Scenario 2 and Scenario 3, respectively at 30% penetration level and 41% and 80% at 60% PV penetration level. This shows that adopting the proposed optimisation control can significantly improve voltage unbalance, and can be twice as effective as local control. On the other hand, in Scenario 2, the network power losses increased in both penetration levels, whereas in Scenario 3, the power losses were reduced by more than 30%. This indicates that voltage unbalance can produce high power losses; however, minimising it does not always reduce power losses if coordination control is missing. It should be pointed out that for all the case studies performed, the corresponding daily average OLTC tap is at most half of the equivalent daily maximum average number of tap changes.1TABLEComparison of energy losses and VUFsys reduction rate under 30% PV penetration levelScenarioEnergy losses (kWh)Reduction rate of losses (%)VUFsys$VU{F_{sys}}$Reduction rate of VUFsys$VU{F_{sys}}$ (%)1265.78—1.4923—2267.76‐0.741.040030.313181.5031.710.373075.012TABLEComparison of energy losses and VUFsys reduction rate under 60% PV penetration levelScenarioEnergy losses (kWh)Reduction rate of losses (%)VUFsys$VU{F_{sys}}$Reduction rate of VUFsys$VU{F_{sys}}$ (%)1223.45—1.3973—2238.54‐6.750.816841.543138.8137.880.277780.13The findings presented in this research study emphasise that the unbalanced voltage level is considerably high in power distribution systems integrated with PVs and EVs. The contribution of high voltage unbalance on heightening the power losses can be identified as previously pointed out. However, its implications on equipment derating and ageing cannot be easily quantified and are excluded in this study. The detection of voltage unbalance is the first step in developing a practical solution to alleviate the unbalanced problem that cannot be achieved by autonomous‐based control. Moreover, minimising the voltage unbalance using a local control approach can sometimes increase the power losses, which can be significant under high PV penetration levels. Therefore, implementing centralised‐based control solutions becomes a critical part of active power distribution systems, enabling monitoring and efficient operation. The case studies demonstrate the central control's significance in reducing the power losses and voltage unbalance. The results also show the potential of EVs to collaborate with other equipment to manage voltage. The absence of optimal coordination of PVs and EVs can cause an excessive current flow in the neutral wire due to the increased level of voltage unbalance and thus increasing the overall energy losses, which negatively impacts the operational performance of a power distribution system.Different optimisation methodsTo evaluate the accuracy and robustness of the developed AHPSO, some well‐known optimisation techniques are used to solve the proposed optimisation problem. Since the proposed optimisation problem's nature is complex, analytical optimisation methods may not be reliable alternatives. Thus, three other versions of PSO, called pure standard PSO with constriction factor, hybrid PSO‐GA [40], and PSO based on natural selection PSO‐NS [42], are considered for verifying the performance of AHPSO method. A 100 trial runs based on various random initial values are conducted on both test systems, considering 20% of PV penetration level and the resulting average and standard deviation (SD) of objective function values are reported. Tables 3 and 4 show a comparison between the objective function values achieved by the different applied heuristic methods on the IEEE‐37 test system and the IEEE‐123 test system, respectively. The %RSD is the relative standard deviation of the samples and is calculated by dividing the standard deviation by the average value. It is used to check the robustness of methods, where the lower percentage values indicate the more robust a method will be. The %RSD value (i.e., Table 3) shows that the proposed AHPSO standard deviation is 0.545% of the average value, which is pretty small compared with other methods. In other words, the optimisation value is tightly clustered around the mean, which means that the optimisation solution will be almost the same at each solution process. On the other hand, if the percentage were large, this would indicate that the objective function value is more spread out.3TABLEComparison of objective values for different optimisation methods on the IEEE‐37 test systemPSOPSO‐NSPSO‐GAProposed AHPSOBest27.75127.75127.75127.751Worst31.35629.30729.11028.562Average28.33327.97527.90127.828SD0.8020.3650.3030.152%RSD2.8311.3071.0860.5454TABLEComparison of objective values for different optimisation methods on the IEEE‐123 test systemPSOPSO‐NSPSO‐GAProposed AHPSOBest24.16624.16624.16624.166Worst26.21425.01025.15424.490Average24.35824.27024.24024.197SD0.2680.1580.1430.062%RSD1.1020.6490.5890.258As observed from Table 3, the %RSD of the samples of the AHPSO (0.545%) is lower than other methods (2.831% for pure PSO, 1.307% for PSO‐NS, and 1.086% for PSO‐GA). Although the %RSD is relatively low for other methods, it can still compromise the network performance efficiency. For example, if we consider a large scale network with optimised minimum power losses of 6MW, the PSO‐GA method can bring an additional of 65.17 kW power losses because of its %RSD = 1.086%. This demonstrates the higher robustness of the AHPSO with respect to the changes in random initial values compared with the other three heuristic methods. It can also be noted for Table 4, that the average (24.197) value is very close to the best value (24.166) that was recorded during the whole trials, which also shows the superiority of the proposed method. Moreover, even at a large network scale, where the number of searching space and variables increase, the proposed optimisation solution method performs much better than other methods.CONCLUSIONWith a growing number of RET connections in the power distribution system, new control strategies are required to minimise the severity of voltage unbalance. This paper proposes an advanced coordination scheme between OLTC, DSTATCOM, PVs and EVs. A new advanced hybrid particle swarm optimisation is also proposed to solve the optimisation problem, and its robustness was verified. Different case studies using typical PV power generation and load demand data demonstrated the proposed approach's ability and scalability to alleviate voltage unbalance and reduce power losses under various PV penetration levels. The investigations argue that the proposed control scheme can significantly reduce unbalanced voltage and limit the OLTC actions considerably, allowing an increased lifetime for OLTC mechanisms. The study outcome further justified the strength of the approach compared with autonomously control schemes of voltage regulator devices in the streams of voltage unbalance reduction and power losses.The cost analysis of adopting the proposed coordination scheme was not the focus of this research study and was not conducted because, currently, some of the devices involved in centralised‐based control are not commercially available in the market. Moreover, the cost‐benefit resulting from minimising the voltage unbalance cannot accurately be quantified because of its long‐term impact. However, as the need for centralised‐based control devices rises and becomes available in the market, their prices will drop considerably. Moreover, as a result of providing a better power quality in the network and power losses reduction, the proposed centralised controls may become more cost‐effective by also considering the investment that has already been adopted on the widespread two‐way communication infrastructure and smart meters.CONFLICT OF INTERESTThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.FUNDING INFORMATIONThere is no funding.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.PERMISSION TO REPRODUCE MATERIALS FROM OTHER SOURCESNoneREFERENCESC. on C. Change: Net Zero: The UK's Contribution to Stopping Global Warming. Committee on Climate Change, London (2019)IRENA (2019): Future of Solar Photovoltaic: Deployment, Investment, Technology, Grid Integration and Socio‐Economic Aspects (A Global Energy Transformation: Paper). International Renewable Energy Agency, Abu Dhabi (2019)Kharrazi, A., Sreeram, V., Mishra, Y.: Assessment techniques of the impact of grid‐tied rooftop photovoltaic generation on the power quality of low voltage distribution network‐A review. Renew. Sustain. Energy Rev. 120, 109643 (2020)Islam, M.R., Lu, H., Hossain, M.J., Li, L.: Mitigating unbalance using distributed network reconfiguration techniques in distributed power generation grids with services for electric vehicles: A review. J. Clean. Prod. 239, 117932 (2019)Molina‐García, Á., Mastromauro, R.A., García‐Sánchez, T., Pugliese, S., Liserre, M., Stasi, S.: Reactive power flow control for PV inverters voltage support in LV distribution networks. IEEE Trans. Smart Grid 8(1), 447–456 (2016)Kraiczy, M., Stetz, T., Braun, M.: Parallel operation of transformers with on load tap changer and photovoltaic systems with reactive power control. IEEE Trans. Smart Grid 9(6), 6419–6428 (2017)Shahnia, F., Ghosh, A., Ledwich, G., Zare, F.: Voltage unbalance improvement in low voltage residential feeders with rooftop PVs using custom power devices. Int. J. Electr. Power Energy Syst. 55, 362–377 (2014)Heidari‐Akhijahani, A., Safdarian, A., Lehtonen, M.: Unbalance mitigation by optimal placement of static transfer switches in low voltage distribution feeders. IET Gener. Transm. Distrib. 14(20), 4612–4621 (2020)Alabri, W., Jayaweera, D.: Impact of Semi‐fast Charging Stations on Unbalanced Power Distribution Systems Integrated with PV Systems. In: 2021 IEEE PES Innovative Smart Grid Technologies Europe (ISGT‐Europe), pp. 1–5. IEEE, Piscataway (2021)Bai, F., Yan, R., Saha, T.K., Eghbal, D.: An excessive tap operation evaluation approach for unbalanced distribution networks with high PV penetration. IEEE Trans. Sustain. Energy 12(1), 169–178 (2020)Wang, L., Yan, R., Bai, F., Saha, T.K., Wang, K.: A Distributed inter‐phase coordination algorithm for voltage control with unbalanced PV integration in LV systems. IEEE Trans. Sustain. Energy 11(4), 2687–2697 (2020)Li, C., Disfani, V.R., Pecenak, Z.K., Mohajeryami, S., Kleissl, J.: Optimal OLTC voltage control scheme to enable high solar penetrations. Electr. Power Syst. Res. 160, 318–326 (2018)Murty, V.V.V.S.N., Sharma, A.K.: Optimal coordinate control of OLTC, DG, D‐STATCOM, and reconfiguration in distribution system for voltage control and loss minimization. Int. Trans. Electr. Energy Syst. 29(3), e2752 (2019)Hashemipour, N., et al.: Multi‐objective optimisation method for coordinating battery storage systems, photovoltaic inverters and tap changers. IET Renew. Power Gener. 14(3), 475–483 (2020)Meng, F., Chowdhury, B., Hossan, M.S.: Optimal integration of DER and SST in active distribution networks. Int. J. Electr. Power Energy Syst. 104, 626–634 (2019)Alboaouh, K., Mohagheghi, S.: Voltage, var and watt optimization for a distribution system with high PV penetration: A probabilistic study. Electr. Power Syst. Res. 180, 106159 (2020)Efkarpidis, N., De Rybel, T., Driesen, J.: Optimization control scheme utilizing small‐scale distributed generators and OLTC distribution transformers. Sustain. Energy, Grids Netw. 8, 74–84 (2016)Bandara, W.G.C., Godaliyadda, G., Ekanayake, M.P.B., J, B.: Ekanayake: Coordinated photovoltaic re‐phasing: A novel method to maximize renewable energy integration in low voltage networks by mitigating network unbalances. Appl. Energy 280, 116022 (2020)Jabalameli, N., Ghosh, A.: Online centralized coordination of charging and phase switching of PEVs in unbalanced LV networks with high PV penetrations. IEEE Syst. J. 15(1), 1015–1025 (2021)Islam, M.R., Lu, H., Hossain, J., Li, L.: Multiobjective optimization technique for mitigating unbalance and improving voltage considering higher penetration of electric vehicles and distributed generation. IEEE Syst. J. 14(3), 3676–3686 (2020)Daratha, N., Das, B., Sharma, J.: Coordination between OLTC and SVC for voltage regulation in unbalanced distribution system distributed generation. IEEE Trans. Power Syst. 29(1), 289–299 (2013)Zhao, F., Zhao, T., Ju, Y., Ma, K., Zhou, X.: Research on three‐phase optimal power flow for distribution networks based on constant Hessian matrix. IET Gener. Transm. Distrib. 12(1), 241–246 (2018)Li, C., Disfani, V.R., Haghi, H.V., Kleissl, J.: Coordination of OLTC and smart inverters for optimal voltage regulation of unbalanced distribution networks. Electr. Power Syst. Res. 187, 106498 (2020)Zeng, X.J., Zhai, H.F., Wang, M.X., Yang, M., Wang, M.Q.: A system optimization method for mitigating three‐phase imbalance in distribution network. Int. J. Electr. Power Energy Syst. 113, 618–633 (2019)Dileep, G.: A survey on smart grid technologies and applications. Renew. Energy 146, 2589–2625 (2020)Alabri, W., Jayaweera, D.: Unbalanced modelling of STATCOM and SVC in hybrid load flow method. In: 2019 IEEE PES Innovative Smart Grid Technologies Europe (ISGT‐Europe), pp. 1–5. IEEE, Piscataway (2019)Kamel, S., Abdel‐Akher, M., Jurado, F.: Improved NR current injection load flow using power mismatch representation of PV bus. Int. J. Electr. Power Energy Syst. 53, 64–68 (2013)I. S. Association: 141–1993. IEEE Recommended Practice for Electric Power Distribution for Industrial Plants (ANSI). IEEE Press, Piscataway (1994)Zhang, X.‐P., Rehtanz, C., Pal, B.: Flexible AC transmission systems: Modelling and control. Springer Science & Business Media, Berlin Heidelberg (2012)Arrillaga, J., Arnold, C.P.: Computer analysis of power systems. Analysis 9(7.8), 7–9 (1990)Ghazali, Y.Z.Y.: Managing on‐load tap changer life cycle in tenaga nasional berhad (TNB) distribution power transformers. CIRED‐Open Access Proc. J. 2017(1), 303–307 (2017)Olivier, F., Aristidou, P., Ernst, D., Van Cutsem, T.: Active Management of Low‐Voltage Networks for Mitigating Overvoltages Due to Photovoltaic Units. IEEE Trans. Smart Grid 7(2), 926–936 (2016)Alabri, W., Jayaweera, D.: Voltage regulation in unbalanced power distribution systems with residential PV systems. Int. J. Electr. Power Energy Syst. 131, 107036 (2021)SMA Solar Technology: Description of the Operating Parameters ‐ SUNNY TRIPOWER 60 /SUNNY HIGHPOWER PEAK1. http://www.windandsun.co.uk/media/995570/SMA‐Sunny‐Highpower‐PEAK1‐Description‐of‐the‐Operating‐Parameters.pdfChen, T., et al.: A review on electric vehicle charging infrastructure development in the uk. J. Mod. Power Syst. Clean Energy 8(2), 193–205 (2020)Abdi, H., Beigvand, S.D., La Scala, M.: A review of optimal power flow studies applied to smart grids and microgrids. Renew. Sustain. Energy Rev. 71, 742–766 (2017)Ebeed, M., Kamel, S., Jurado, F.: Optimal power flow using recent optimization techniques. Class. Recent Asp. Power Syst. Optim. 157–183 (2018)Roberge, V., Tarbouchi, M., Okou, F.: Optimal power flow based on parallel metaheuristics for graphics processing units. Electr. Power Syst. Res. 140, 344–353 (2016)Mehmood, K.K., Khan, S.U., Lee, S.‐J., Haider, Z.M., Rafique, M.K., Kim, C.‐H.: A real‐time optimal coordination scheme for the voltage regulation of a distribution network including an OLTC, capacitor banks, and multiple distributed energy resources. Int. J. Electr. Power Energy Syst. 94, 1–14 (2018)Juang, C.‐F.: A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Trans. Syst. Man, Cybern. Part B 34(2), 997–1006 (2004)Ziari, I., Ledwich, G., Ghosh, A., Platt, G.: Optimal distribution network reinforcement considering load growth, line loss, and reliability. IEEE Trans. Power Syst. 28(2), 587–597 (2012)Naka, S., Genji, T., Yura, T., Fukuyama, Y.: A hybrid particle swarm optimization for distribution state estimation. IEEE Trans. Power Syst. 18(1), 60–68 (2003)Kersting, W.H.: Radial distribution test feeders. IEEE Trans. Power Syst. 6(3), 975–985 (1991)Azzouz, M.A., Shaaban, M.F., El‐Saadany, E.F.: Real‐time optimal voltage regulation for distribution networks incorporating high penetration of PEVs. IEEE Trans. Power Syst. 30(6), 3234–3245 (2015)HCT GreenNest Eco House: AC Electric. https://dataloggers.livetozero.com/hct/index.html. Accessed 12 July 2019Olowu, T., Sundararajan, A., Moghaddami, M., Sarwat, A.: Future challenges and mitigation methods for high photovoltaic penetration: A survey. Energies 11(7), 1782 (2018) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "IET Generation, Transmission & Distribution" Wiley

Optimal coordination of unbalanced power distribution systems with integrated photovoltaic systems and semi‐fast electric vehicles charging stations

Download PDF
17 pages

Loading next page...
 
/lp/wiley/optimal-coordination-of-unbalanced-power-distribution-systems-with-N2Hbcj0gRw

References (45)

Publisher
Wiley
Copyright
© 2022 The Institution of Engineering and Technology.
eISSN
1751-8695
DOI
10.1049/gtd2.12458
Publisher site
See Article on Publisher Site

Abstract

INTRODUCTIONThe utilisation of renewable energy technologies (RETs) such as photovoltaics (PVs) systems and electric vehicles (EVs) are expected to rise significantly in upcoming years as part of several measures being adopted by most governments to assist meet environmental goals.  For instance, the UK plans to ban all new internal‐combustion engine vehicles by 2040 to achieve its target of net‐zero emissions by 2050 [1]. It is also expected that the global installed capacity of solar PV systems will rise six‐fold by 2030 (compared with 2018) and reach 8519 GW by 2050 [2]. The massive growth of these technologies offers many opportunities, but they can pose several challenges for distribution system operators in regard to power quality. The uncertainty of the location and penetration of PV systems can raise the degree of voltage unbalance [3]. The connection of EVs on specific nodes and phases may further exacerbate the degree of voltage unbalance. Voltage unbalance can produce substantial unsymmetrical current flows in each phase, which can cause adverse impacts on the power distribution systems, including additional power losses and inefficient utilisation of network assets [4]. The first step to address this issue is to balance the residential loads across three‐phase feeders during the planning stage, but because of the uncertainties of load demand and PV generation and unpredicted EV charging behaviour, the typical power distribution systems are rarely balanced, particularly at the low voltage.Literature reviewAdvances in power electronics have helped researchers propose various effective methods to mitigate the problems arising from increased RETs integration. These include different autonomous control schemes for PV inverter [5], on‐load tap changers OLTC [6] and custom power devices [7, 8]. Although these local control approaches respond much faster at no additional cost, they can potentially lead to demand unnecessary reactive power compensation or insufficient voltage support, which may significantly increase power losses, especially at high PV penetration levels [9]. Moreover, the local control of these devices cannot effectively avoid frequent operation of a transformer, which may outweigh the benefits of RETs connection [10]. Most importantly, the influence of these devices on unbalanced voltage cannot be readily determined due to the inter‐phase coupling between distribution lines, which may deteriorate the voltage unbalance level [11]. Therefore, the integration of RETs requires transforming the current systems into coordinated supervisory control systems. Centralised control strategies allow effective control and operation of the network assets to mitigate voltage unbalance problem and achieve various objective functions such as minimising power losses.Many centralised control techniques have been proposed in the literature to minimise voltage rise and reduce voltage control devices’ operation in modern power distribution systems. In [12], an optimal operating of OLTC based on PV generation forecasts is proposed. A distribution static synchronous compensator (DSTATCOM) is coordinated with OLTC and distributed generation in [13] to control the voltage and minimise the power losses. A multi‐objective method for coordinating PV, battery storage systems, and OLTC is proposed in [14] based on forecasting data. These proposed optimisation problems are based on the assumption of balanced distribution network operation and forecasts PV generation and load data. This can lead to an inaccurate representation of the power distribution system operation, which is inherently unbalanced. Besides that, the RETs penetration is uncertain, their output cannot be forecasted accurately, and there may be discrepancies between the predicted and realised values.Several techniques considered the unbalanced operation of the power distribution system [15, 16]. Still, they did not consider minimising voltage unbalance in the optimisation problem. A coordinated control method of PVs, batteries and OLTC is suggested in [17] to mitigate both overvoltage and voltage unbalance in three‐phase unbalanced distribution networks. Voltage unbalance reduction during the daytime is suggested in [18] by optimally re‐phasing grid‐connected PV systems, which are limited to use single‐phase PV systems only. EVs’ potential to suppress the voltage rise resulting from high PV penetrations has recently attracted attention, and only a few studies have paid attention to the role of EVs on voltage unbalance reduction. In [19, 20], EVs are used as one of the control variables in the optimisation problem to limit the voltage unbalance by optimally selecting the state of EV, EV point of connection, and charging/discharging rating power. However, these methods affect customers’ comfort and demand monitoring and control infrastructure that outstripping the capability of the coordination scheme to reach hundreds to thousands of EVs in a given power distribution system.To satisfy the requirement of real‐time power distribution system operation, some authors choose to sacrifice accuracy to increase the computational performance of the optimisation algorithm. For example, in [21, 22], the authors ignore the discrete variables in the formulation, like OLTC and voltage regulators. They assumed a continuous tap of voltage regulation devices, and they had to round the optimal value to the closest integer number. There is no assurance that the rounded number is the correct optimal solution, especially if there is a very large step. A simplification is also adopted in [23, 24] to use a mixed‐integer linear programming to solve optimisation problems for the unbalanced power distribution system. One of the assumptions made is to ignore the inter‐phase coupling (i.e., Carson's line formulation and self and mutual conductors) to linearise the power flow equations. However, these simplifications often suffer from inaccuracies since power distribution systems are inherently nonlinear, which may not reflect the realistic outcome. Failure to consider mutual impedances can create off‐target control signals, which may inadvertently increase voltage unbalance.Novelty and contributionsThe incorporation of large‐scale RETs brings new challenges to the power distribution system operation, including exacerbation of voltage unbalance levels. Therefore, there is a demand for more effective control techniques and management strategies of various power distribution components. Motivated by the limitations described above, this paper proposes a comprehensive optimisation modelling framework incorporating voltage unbalance, voltage magnitude, and OLTC operation in a common platform to minimise power losses effectively through solving multi‐objective optimisation problem. The significance of the proposed optimisation scheme is the ability to determine the optimal tap position of OLTC, the amount of reactive power to be injected or absorbed by DSTATCOM and PV inverter, and EV point of connection (phase a, b, c) in near real‐time. Due to non‐convexity and non‐linearity of the problem, a meta‐heuristics method is advanced to solve the optimisation problem. Therefore, the main contribution and novelty of this article are as follows:proposing a novel mathematical framework for optimisation‐based coordination control scheme incorporating the natural intermittency and practical operation of unbalanced power distribution systems to achieve various objectives. The mathematical framework integrates robust, computationally efficient, and more accurate models (including realistic constraints and inter‐phase coupling) of the controllable devices, making them flexible, effective, and scalable for a practical operation of a power distribution system. The proposed optimisation platform also provides a pathway to consider other optimisation objectives and coordinated control of other technologies, including energy storage.proposing a novel control strategy for EVs charging stations and PV systems to effectively minimise the voltage unbalance, which is also incorporated into the proposed optimisation‐based coordination scheme. The proposed control strategy offers a reduction in supervision and control actions by reducing the search space of the control variable, which improves the convergence speed of the algorithm. This will help the utilities to leverage the large‐scale connection of RETs and allow them to be connected more into the network without concern about overvoltage or voltage unbalance problems.developing an advanced optimisation method combining two modified particle swarm optimisation (PSO) techniques. The advanced hybrid particle swarm optimisation (AHPSO) facilitates the proposed optimisation algorithm escaping from premature convergence and improving the local minimum problem, thereby improving the accuracy, convergence, and effectiveness of the proposed optimisation framework.Organisation of the articleThe rest of this article is organised as follows. Section 2 presents the problem description and the proposed strategies. Section 3 presents the mathematical formulation of the problem. Section 4 describes the proposed solution method used to solve the optimisation problem. Section 0 provides details of simulation results and analysis followed by conclusions in section 5.PROBLEM AND PROPOSED METHODOLOGYFigure 1a shows a simplified three‐phase modern distribution feeder connected to a substation through a transformer equipped with an OLTC. Voabc is the three‐phase voltage at the transformer's low voltage side, and Vsabc is the three‐phase voltage at the point of common coupling (PCC). Zabc is the self and mutual impedance of the distribution line, which reflect an accurate representation of an un‐transposed feeder without losing the explicit information about the neutral currents and voltages. The active power Ppv and reactive power Qpv production of each PV system are injected into nearby connected loads and EVs, and the net active power Pn and net reactive power Qn are fed into the grid. The PCC voltage in an unbalanced three‐phase system Vsabc can be determined using (1). Equation (1) shows that the increase of PCC voltage at phase p (a, b, c) is influenced by the impedances of distribution networks lines, the injected power, and the regulated voltage Voabc, while assuming grid voltage is constant.1Vsp=Vop+∑q=a,b,cZpqPnq+jQnqVsq∗.\begin{equation}V_s^p = V_o^p + {\sum_{q = a,b,c} {{Z^{pq}}\left( {\frac{{P_n^q + jQ_n^q}}{{V_s^q}}} \right)} ^*}.\end{equation}1FIGUREConceptual diagram of the proposed centralised controlIt is also evident from (1) that the injected power or connected EV in one phase can also affect the voltage magnitude of the other two phases because of the mutual impedance effect, making voltage control in an unbalanced network complicated. Also, due to unbalanced line coupling, load increases do not necessarily cause the voltage magnitude to decrease [11]. Therefore, the un‐coordinated operation of voltage control devices may provide a partial solution to the problem of overvoltage, but it can increase the unbalanced voltage and the total power losses on power distribution systems. In addition, due to the absence of online measurement and data monitoring in power distribution systems, operators may be unaware of this impact. To avoid such issues, it becomes an essential and vital part of active power distribution infrastructures to utilise a centralised control of different voltage control devices and make use of smart technology.This paper proposes a methodology for coordinating different voltage regulation devices in the power distribution systems integrated with PVs and EVs. The flow chart of the proposed coordination method is presented in Figure 1. The supervisory control systems coordinate four types of voltage regulation devices: OLTC, DSTATCOM, PV and EV. The suggested coordination scheme identifies the optimal values of the reactive power absorbed/injected from the PV inverters and DSTATCOM, the tap settings of the OLTC, and the phase connection of EV using real‐time data. These optimal control signals maintain the voltage magnitude range, limit voltage unbalance level, minimise the power losses and reduce the frequent operation of transformer OLTC. To avoid affecting customers’ comfort, like controlling their EV charging rate and state of charge, especially at charging stations, only switching the phase where EV should be connected is considered as a control variable. This will also reduce the required supervision and control facilities that go beyond the central controller capability to reach hundreds of EVs connected to the network. The low‐scale PV system can be excluded from central‐based control and can be locally controlled, while the large‐scale such as in industrial or commercial buildings (50 kW and above) are included in the optimisation model.The central unit receives the required network measurement such as PV and load profile and current setpoints of controllable devices at each control cycle (tcycle). An unbalanced three‐phase load flow is then performed to check for potential issues, such as thermal, voltages magnitude, or the voltage unbalances violation. After that, the optimisation model is exclusively applied when there is a constrain violation or after 1 h of the last control signal action. If the activating optimisation model's criteria are still not achieved, the unbalanced load flow is performed again for the next control cycle. The main components for deploying the proposed schemes are smart meters, sensors, controllers, and communication medium. Smart meters and sensors provide the necessary power consumption and voltage measurements. The controller can be a central controller where all information and measurement are processed to generate a control command to be sent to the controller installed at a controllable device. A static transfer switch is one of the controllable devices used at the charging stations to allow easy and flexible EV switching among the three phases. 5G is one of the communication methods that can be used in centralised control, which have already been utilised in power transmission and distribution systems [25].PROBLEM MODELLING AND FORMULATIONThe coordination between reactive power control capability of PV inverters, voltage control option of OLTC and DSTATCOM and phase switch of EV is an optimisation problem, and it has various operational goals as it must meet the various network operational constraints and component characteristics. The optimisation outcome minimises the power losses, the operational switching of OLTC, the voltage magnitude variation limit, and the voltage unbalance. Therefore, the objective function is constructed as a mixed‐integer nonlinear problem, which can be expressed as follows:2Minimise:fx,u,Subjectto:gx,u≤0hx,u=0,\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{3}{l}@{}} {{\rm{Minimise{:}}}\;f\left( {x,u} \right),}&{{\text{Subject to}}{:}}& \quad {g\left( {x,u} \right) \le 0}\\[6pt] \,&\,&\quad {h\left( {x,u} \right) = 0} \end{array} ,\end{equation}where f(x,u) is the objective function that requires to be minimised, x is the vector of dependent variables or the state variables. u is the vector of independent variables or the control variables used to achieve the optimisation problem. g(x,u) is the set inequality constraints, and h(x,u) is the equality system operating and control variable constraints.Objective functionThe main objectives of the optimisation model are to minimise the power losses, switch operation of OLTC and limit the unbalanced voltage while satisfying the operational constraints. The multi‐objective optimisation problem can be solved either by converting the multi‐objective function to a single objective function with different weighting factors or applying pareto‐based methods. Treating all objective functions as one objective function is commonly used because it has less computation burden than pareto‐based methods, and the optimisation of one objective function could be achieved without aggravation of another objective function. However, choosing an appropriate value for weighting factors could be challenging. To address this problem, some of the objective functions can be treated as a constraint in the optimisation problem by limiting their values except for the power losses, which cannot be limited. Therefore, the primary objective function is to minimise the total three‐phase power losses in a distribution network where the number of OLTC switches, voltage magnitude, and voltage unbalance factor is limited.Different formulations are used to describe the power losses in literature. Most of them are based on an approximation to reduce the complexity of the optimisation problem especially when analytical approaches are used. When metaheuristic optimisation techniques are used, any formulation can be used without approximation. Therefore, the difference between power generation (PG_ip$P_{G\_i}^p$) and loads (PL_ip$P_{L\_i}^p$) at each at phase p and node i is the most accurate representation of the total three‐phase power losses (fPL)${f^{PL}})$, and is computationally efficient. Thus, the objective function can be formulated as given in (3). It is calculated first by determining the total generated power, which is determined by running the load flow algorithm. The load flow calculation involves constructing a Y matrix that reflects the network per‐phase impedance, including Carson's line formulation. The detailed mathematical formulation of the three‐phase load flow calculation used to calculate the power losses can be found in [26].3fPL=∑i=1N∑p=a,b,cPG_ip−PL_ip.\begin{equation}{f^{PL}} = \mathop \sum \limits_{i = 1}^N \mathop \sum \limits_{p = a,b,c} \left(P_{G\_i}^p - P_{L\_i}^p\right).\end{equation}Equality constraintsEquality constraints represent the typical load flow equations. These constraints are strictly enforced during the load flow procedure if metaheuristic optimisation techniques are used, which are satisfied by performing load flow calculations to obtain the fitness function. Improved conventional Newton‐Raphson algorithm and Backward–Forward Sweep based algorithms are two common techniques employed for load flow calculation in unbalanced power distribution systems. Given its robustness and convergence speed, especially for ill‐conditioned systems, the former is used in this study. The new power and current injection method for balanced load flow calculation developed in [27] is extended by the authors in [26] to the unbalanced three‐phase power system, as shown in (4). The improved load flow algorithm presents a superior performance in convergence and computing time compared with other Newton‐Raphson methods. Full details of the improved three‐phase load flow and its performance can be found in [26].4ΔIxmabcΔIxrabc⋮⋮Δ(Py)abc⋮=−J·ΔVxrabcΔVxmabc⋮⋮Δ(δy)abc⋮,\begin{equation}\left[ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\Delta {{\left( {I_x^m} \right)}^{abc}}}\\[3pt] {\Delta {{\left( {I_x^r} \right)}^{abc}}}\\[3pt] \vdots \end{array} }\\[3pt] \vdots \\[3pt] { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\Delta {{({P_y})}^{abc}}}\\[3pt] \vdots \end{array} } \end{array} } \right] = - J \cdot \left[ { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\Delta {{\left( {V_x^r} \right)}^{abc}}}\\[3pt] {\Delta {{\left( {V_x^m} \right)}^{abc}}}\\[3pt] \vdots \end{array} }\\[3pt] \vdots \\[3pt] { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\Delta {{({\delta _y})}^{abc}}}\\[3pt] \vdots \end{array} } \end{array} } \right],\end{equation}whereJ‐ represent the Jacobian matrixabc$abc$‐ represent the three phases (phase a, phase b, phase c)Ixr,Ixm,Vxr,Vxm$I_x^r,\;I_x^m,V_x^r,V_x^m$‐ are the real and imaginary part of the injection current and the voltage at bus xPy,δy${P_y},\;{\delta _y}$‐ real power injection and the voltage phase angle at bus yx,y$x,y$‐ represent the load buses and generator buses.Inequality constraintsState variablesThe state variables represent the power system operating limits as follows:Voltage Limit: voltage magnitude (Vip$V_i^p$) at all buses (i∈N)$( {i \in N} )$ and phases (p∈a,b,c)$( {p \in a,b,c} )$ in the power distribution system must be kept with the defined limit.5Viminp≤Vip≤Vimaxp.\begin{equation}V_{{i_{\min }}}^p \le V_i^p \le V_{{i_{\max }}}^p.\end{equation}Thermal Limit: the rated amount of current (|Iijp|$| {I_{ij}^p} |$) flow between any two nodes ij$ij$ or branch (NL)$( {NL} )\;$is restricted by the feeder thermal limit.6Iijp≤Iij_rated..\begin{equation}\left| {I_{ij}^p} \right| \le {I_{ij\_rated.}}.\end{equation}Voltage Unbalance: because it can produce undesirable operation conditions in the power distribution systems, the steady‐state voltage unbalance (VU%$VU\% $) at any bus i should be limited.7VU%i≤VU%Limit..\begin{equation}VU{\% _i} \le VU{\% _{Limit.}}.\end{equation}All these state variables are incorporated into the formation of the comprehensive objective function with penalty factors to maintain the state variables inside their allowable boundary and reject any infeasible solution. The penalty function can be specified by a quadratic term as follows.8F=fPL+k1∑i=1N∑p=a,b,c∇Vip+k2∑i=1Nl∑p=a,b,c∇Iip+k3∑i=1N∇VU%i,\begin{eqnarray} F &=& {f^{PL}} + {k_1}\sum_{i = 1}^N {\sum_{p = a,b,c} {\nabla V_i^p} } + {k_2}\sum_{i = 1}^{Nl} {\sum_{p = a,b,c} {\nabla I_i^p} }\nonumber\\ && +\; {k_3}\sum_{i = 1}^N {\nabla VU{\% _i}} ,\end{eqnarray}where9∇Vip=Vip−Vmin.2Vip<Vmin.0{Vmin.≤Vip≤Vmax.Vip−Vmax.2Vip>Vmax.,\begin{equation} \nabla V_i^p = \left\{ \def\eqcellsep{&}\begin{array}{ll} {{{\left( {\;V_i^p - {V_{min.}}} \right)}^2}}& {V_i^p &lt; {V_{min.}}}\\[3pt] 0& {\{V_{min.}} \le \;V_i^p \le {V_{max.}}\\[3pt] {{{\left( {\;V_i^p - {V_{max.}}} \right)}^2}} & {V_i^p &gt; {V_{max.}}} \end{array} \right.,\end{equation}10∇Iip=0Iijp≤Iij_limitpIijp−Iij_limitp2Iijp>Iij_limitp,\begin{equation} \nabla I_i^p = \left\{{ \def\eqcellsep{&}\begin{array}{ll} 0 &{I_{ij}^p \le I_{ij\_limit}^p}\\[3pt] {{{\left( {I_{ij}^p - I_{ij\_limit}^p} \right)}^2}} &{I_{ij}^p &gt; I_{ij\_limit}^p\;} \end{array} } \right.,\end{equation}11∇VU%i=0VU%i≤VU%limitVU%i−VU%limit2VU%i>VU%limit.\begin{eqnarray} \nabla VU{\% _i} = \left\{ { \def\eqcellsep{&}\begin{array}{ll} 0&{VU{\% _i} \le VU{\% _{limit}}}\\[3pt] {{{\left( {VU{\% _i} - VU{\% _{limit}}} \right)}^2}}&{VU{\% _i} &gt; VU{\% _{limit}}\;} \end{array} } \right..\nonumber\\ \end{eqnarray}Various definitions and standards were developed to evaluate the voltage unbalance level and its acceptable limits [3]. One of these definitions is based on IEEE Std. 141–1993 [28], and it is referred to as phase voltage unbalance (VU%). It is determined as the ratio between the maximum deviation of phase voltage magnitude (Vp,p∈{a,b,c})${V^p},\;p \in \;\{ {a,\;b,\;c} \})$ from average phase voltage magnitude and average phase voltage magnitude, as given in (12). Based on IEEE Std. 141–1993, VU% of 3.5% can cause 25% additional heating on the motors, and thus a voltage unbalance greater than 2% must be reduced. According to EN 50160 and ANSI C84.1‐2011 standards, the voltage magnitude variation limits are ±10% and ±5%, respectively [3]. Therefore, in this paper, VU%limit$VU{\% _{limit}}$ is restricted to 2%, and the voltage variation (Vmin.,Vmax.${V_{min.}},{V_{max.}}$) is limited to ±7%. k1,k2andk3${k_1},\;{k_2}\;and\;{k_3}$ represent penalty factors for voltage limit constraint (∇Vip$\nabla V_i^p$), thermal limit constraint (∇Iip$\nabla I_i^p$), and voltage unbalance limit constraint (∇VU%i$\nabla VU{\% _i}$), respectively. The penalty factors are chosen to be large number to avoid violation of relevant constraints.12VU%i=Max.Vabc−13∑p=a,b,cVp13∑p=a,b,cVp×100.\begin{equation}VU{\% _i} = \frac{{\left| {{\rm{Max}}.\left\{ {{V^{abc}} - \frac{1}{3}\mathop \sum \nolimits_{p = a,b,c} {V^p}} \right\}} \right|}}{{\frac{1}{3}\mathop \sum \nolimits_{p = a,b,c} {V^p}}} \times 100.\end{equation}Control variablesThe inequality constraints of the control variables are self‐limiting. The optimisation solver picks a feasible value for each control variable in the specified range. These control variables represent the control parameter of DSTATCOM, OLTC, PV Inverter and EV.DSTATCOMAccording to the operating concept of the DSTATCOM, the controllable voltage source (Vsh∠δsh${V_{sh}}\angle {\delta _{sh}}$) is used to control the rate of reactive power (Qshp)$Q_{sh}^p)$ to be injected or absorbed. Nevertheless, the magnitude of DSTATCOM voltage is constrained by the maximum and minimum values, while its phase angle can vary from 0 to 2π. Therefore, the control variable of DSTATCOM is constrained as follows:13Vsh−minp<Vshp<Vsh−maxpQsh−minp<Qshp<Qsh−maxp.\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {V_{sh - min}^p &lt; V_{sh}^p &lt; V_{sh - max}^p}\\[6pt] {Q_{sh - min}^p &lt; Q_{sh}^p &lt; Q_{sh - max}^p} \end{array} .\end{equation}DSTATCOM control parameters are considered as independent variables in most load flow calculation methods [29]. Therefore, several modifications are required to the existing load flow algorithms and sometimes cause convergence problems and demand high computation time. To address this problem, the author has proposed an innovative model of three‐phase DSTATCOM in [26], which can be used in unbalanced load flow calculation. In this paper, the developed DSTATCOM model will be used where its connected bus is modelled as a voltage‐controlled bus in load flow calculation with an identified voltage magnitude and zero active power exchange when it operates within limits. In the optimisation problem, the voltage magnitude is treated as a control variable, and then DSTATCOM model parameters for each phase can be calculated at the end of each iteration of the load flow calculation to check its limits. Full details of the developed DSTATCOM and its performance in terms of computation time and solution convergence can be found in [26].OLTCThree‐phase transformers are modelled in the three‐phase load flow calculation by an admittance matrix YTabc$Y_T^{abc}$, which depends upon the connection of the primary and secondary taps, and the leakage admittance.14YTabc=YppabcYpsabcYspabcYssabc,\begin{equation}Y_T^{abc} = \left[ { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} {Y_{pp}^{abc}}& \quad {Y_{ps}^{abc}}\\[6pt] {Y_{sp}^{abc}}&\quad {Y_{ss}^{abc}} \end{array} } \right],\end{equation}where Yppabc$Y_{pp}^{abc}$, Yssabc$Y_{ss}^{abc}$ are self‐admittance of the primary and secondary, respectively, and Yspabc$Y_{sp}^{abc}$, Ypsabc$Y_{ps}^{abc}$ are mutual admittances of the transformer. The transformer taps (Tap(t)$Tap( t )$) are assumed to be at the primary side, high voltage side and the transformer connection is Delta Wye‐G. The details of submatrices of the admittance matrix for different transformer connections and tap ratio and location can be found in [30]. A typical tap changing transformer has 21 discrete positions (nominal, 10 above and 10 below), and each tap has ±1% regulating range of voltage, therefore, the equivalent voltage ratio aT${a_T}$ is practically determined by the tap positions.15aTt=1+0.01×Tapt,\begin{equation}{a_T}\left( t \right) = 1 + 0.01 \times Tap\left( t \right),\end{equation}where Tap(t)$Tap( t )$ must be an integer value, and the limit on tap position of OLTC can be expressed by:16−10≤Tapt≤10.\begin{equation} - 10 \le Tap\left( t \right) \le 10.\end{equation}Regular OLTC tap position changing shortens their operation life and increases the associated maintenance costs because of the intermittent generation of PVs. Power system operators are usually interested in reducing the number of switches due to financial and technical considerations. These number depends on the switching type of OLTC (e.g., oil or vacuum) [31], which can vary between 600,000 and 1,000,000 switches [12]. According to [17], the maximum number of tap changes of the OLTC has been assumed equivalent to the typical value of 700,000 by the manufacturers without the need for maintenance. Taking into account this value and expected lifetime of 40 years, the maximum average number of tap changes per day must be restricted to 48 (700,000/(40 × 365). To satisfy this requirement and avoid unrealistic tap operation, the optimisation problem restricts the number of tap position changes between two consecutive times to be less than 3. Therefore, the constrain of tap position at each control cycle can be expressed by (17) considering the maximum and minimum tap position given by (16).17Tapt−1−3≤Tapt≤Tapt−1+3,\begin{equation}Ta{p_{t - 1}} - 3 \le Ta{p_t} \le Ta{p_{t - 1}} + 3,\end{equation}where Tapt$Ta{p_t}$ is the tap position at time step t and Tapt−1$Ta{p_{t - 1}}$ represent the previous tap position.PV InverterReactive power and active power control are different operation modes that can be integrated into PV inverters. Active power control is more effective in providing voltage regulation support than reactive power because of the high R/X ratio in the power distribution systems. Nevertheless, active power control is likely to be an unpreferable technique because of active power curtailment. For this reason, in this study, the reactive power control option of PV inverter is considered. There are various reactive power capability options available for PV inverters, which are normally defined by the country's standards and grid codes. Among them is to apply power factor (PF) adjustment according to the PV active power generation. PV inverters can provide reactive power at no solar input, however, this functionality is not standard in the industry [32]. Moreover, operating PV inverters at night will increase the inverter's operational stress and reduce their lifespan. Besides that, additional configuration of the PV inverter in the optimisation problem is required because the reactive power limitation needs to be recomputed at every period. Therefore, in this study, no reactive power support is considered while there is no solar power and accordingly, oversizing the inverter allows sufficient freedom of reactive power exchange, specifically on clear sky days. For this reason, the size of the inverters is increased by 25% of the rated active power of PV systems, allowing PV inverters to operate between 0.8 leading and 0.8 lagging power factor regardless of active power output [33]. This size of the inverter can be seen in some modern inverters, such as SMA Sunny Tripower Inverter [34].Normally, the three‐phase PV inverter is designed as a compact three‐phase unit. The generated active power is divided equally between the three phases, and the reactive power can be distributed among the PV inverter phases with different ratios depending on the assigned power factor (PFiabc$PF_i^{abc}$) value which is constrained by (18). Therefore, the bus (i) where the PV system is connected would be considered as a load bus in load flow calculation, where the active output power of PV (Ppv_iabc$P_{pv\_i}^{abc}$) is known, and the reactive power (Qpv_iabc$Q_{pv\_i}^{abc}$) can be calculated using (19). To design a reliable and realistic optimisation model, only large scale (> 50 kW) residential or commercial PV systems can be included in the optimisation model. This is to reduce the monitoring and control infrastructure required to reach the vast number of connected small‐scale PV inverters. Moreover, the small‐scale PV system has a local effect and can be controlled locally using droop control [33].180.8i−leadingabc<PFiabc<0.8i−laggingabc,\begin{equation}0.8_{i - leading}^{abc} &lt; PF_i^{abc} &lt; 0.8_{i - lagging}^{abc},\end{equation}19Qpv_iabc=Ppv_iabcPFabc×1−(PFabc)2.\begin{equation}Q_{pv\_i}^{abc} = \frac{{P_{pv\_i}^{abc}}}{{P{F^{abc}}}}\; \times \sqrt {1 - {{(P{F^{abc}})}^2}} .\end{equation}EVEVs have been recently involved in voltage management of smart power distribution systems by optimally controlling their charging rate, state of charge, and either charging or discharging. However, these control options may affect EV owners’ comfort level in charging stations or parking lots while they wait for their vehicle to charge. Moreover, nowadays, EV manufacturers are competing to provide fast charging facilities to their vehicles, making fast charging demand increase. This can be seen in public and workplace car parking, which are usually equipped with semi‐fast charging speed supplied by three‐phase feeders, and they are projected to represent the high portion of the overall charging stations [35]. The various control options of EV at home can be feasible; however, controlling many connected EVs makes the optimisation problem very complicated, and the time burden increases multifold. Therefore, in this paper, a charging station or parking lots equipped with semi‐fast charging facilities and a static transfer switch will be considered. One of the main features of a static transfer switch is to ensure instantaneous and quick load transfers without tolerating voltage disturbance limits. Many researchers identified static transfer switch as a possible cost‐effective solution to power quality problems in various applications such as dynamic switching residential customers among three‐phases and re‐phase of single‐phase PV system connection among the three phases [8]. The selection of the phase at which the EV should be connected will be used as a control variable. Each parking lot is represented by three variables despite the number of EVs connected at the parking site. Each variable identifies which phase that one‐third of the total number of EVs should be connected. Therefore, the control variables of parking lots are discrete variables, and their value represents as (20). In the load flow calculation, the bus with a charging station would be represented by constant load buses, and their loads depend on the number of vehicles connected at each phase and parking lots.20EVi13phase=0;phasea1;phaseb2;phasec,\begin{equation}EV_{i\frac{1}{3}}^{phase} = \left\{ { \def\eqcellsep{&}\begin{array}{@{}*{2}{l}@{}} {0;\;}&\quad {phase\;a}\\[3pt] {1;\;}&\quad {phase\;b}\\[3pt] {2;}&\quad {\;phase\;c} \end{array} } \right.,\end{equation}where i express the first, second and third groups of the connected EV at each parking lot.PROPOSED SOLUTION OF ADVANCED HYBRID SWARM OPTIMISATION (AHPSO)The optimisation problem can be solved using some available techniques that may be classified as mathematical and meta‐heuristic approaches. Conventional (mathematical) optimisation techniques such as linear programming and nonlinear programming have achieved reasonable success in solving optimisation problems [36]. The major strengths of these methods are numerical stability and reliable convergence, but they are hard to handle discrete variables, exposed to get trapped in local minima solution, and highly sensitive to initial values [37]. These shortcomings can be overcome when meta‐heuristic methods, for example, particle swarm optimisation (PSO) and genetic algorithms (GA), are used to solve the optimisation problem with limited or fewer modifications in the original problem. However, their main concern is to achieve the global best solution in the shortest possible time because of the large number of load flows calculation needed in the solution process, limiting their use in on‐line applications. However, the problem of computation time is expected to be resolved by the next‐generation of software and hardware, taking into consideration the rapid advancement of computer technology. For instance, the limitation of using meta‐heuristic in on‐line applications was addressed in [38] and significantly accelerated the computations by operating the massively parallel architecture of graphics processing units (GPUs). The parallel computation allows all populations (e.g., 20 particles for the case of PSO) to perform the calculation at the same time, which all are independent of each other. On the other hand, conventional (mathematical) optimisation techniques cannot take advantage of parallel computation since each iteration relies on the previous iteration. Besides that, mathematical optimisation techniques cannot be properly used in the application of power distribution systems because of the massive number of complex assets (i.e., integer variables such as OLTC and EV connected phase) and unbalanced operation, which make the optimisation problem harder to be solved. Therefore, the development in computational intelligence with the advent of parallel processing capabilities and supercomputer use made meta‐heuristic methods possible for real‐time optimisation applications, such as [19, 39].Various meta‐heuristic methods and their variants have been proposed in the literature for solving the optimisation problem. PSO‐based approach is one of the most popular techniques due to its ability to deal with highly nonlinear and mixed‐integer problems. Yet, the original PSO sometimes requires more time to move into the solution space's effective area, depending on the case. For this reason, various versions of PSO were proposed and hybridised with other meta‐heuristics methods. For example, to alleviate the local minimum issue, a modification is applied to the PSO in [40], and the diversity of the optimisation variables is improved by employing GA mutation and crossover operators. A comparison investigation in [41], demonstrates that this modified variant of PSO outperforms other heuristic approaches with regard to accuracy, robustness and speed. Another version of PSO based on natural selection mechanism reported in [42], where the number of the best particle is increased while the worst particle is reduced at each generation. This allows low assessed agents to move to the best adequate area straight using the selection method, and concentrated search primarily in the current effective area is realised. Taking advantage of the two modified PSO proposed in [40] and [42] and to further improve the accuracy and prevent premature convergence of the solution, a combination of both these methods is proposed in this paper to solve the optimisation problem. The specific process related to the proposed optimisation technique (AHPSO) algorithm is given below and are presented in Figure 2.Initialise the parameter of PSO and GA and then the velocity Vi${V_i}$ and position Xi${X_i}$ of each particle are initialised randomly. Each particle is composed of several cells that represent the decision variables.Evaluate the objective function (8) of each particle after performing an unbalanced load flow calculation.Update personal best positions (pbest−i)${p_{best - i}})$ for each particle that has a new better objective value than the old personal best value and then updates the global best position (gbest)${{\rm{g}}_{best}})$ which represents the best ever solution achieved so far.Update the speed and position of the particle for the next iteration k+1 as follows:21Vik+1=χVik+c1r1pbest−i−Xik+c2r2gbest−Xik,\begin{equation}V_i^{k + 1} \,{=}\, \chi \left( {V_i^k \,{+}\, {c_1}{r_1}\left( {{{\rm{p}}_{best - i}} \,{-}\, X_i^k} \right) \,{+}\, {c_2}{r_2}\left( {{{\rm{g}}_{best}} \,{-}\, X_i^k} \right)} \right),\end{equation}22Xik+1=Xik+Vik+1,\begin{equation}X_i^{k + 1} = X_i^k + V_i^{k + 1},\end{equation}where χ is the constriction factor coefficient and is used to ensure the convergence of the search processes and produce better‐quality solutions than the standard PSO. c1,c2${c_1},\;{c_2}$ are the acceleration coefficients and, r1,r2${r_1},\;{r_2}$ are two random numbers with uniform distribution in the range of [0, 1]. In this paper, the acceleration coefficients are set c1=c1=2.05.${c_1} = {c_1}\; = \;2.05.$ The constriction factor coefficient (χ) is calculated as follows.23χ=22−φ−φ2−4φ,φ=c1+c2,φ>4.\begin{equation}\chi = \frac{2}{{\left| {2 - \varphi - \sqrt {{\varphi ^2} - 4\varphi } } \right|}},\quad \varphi = {c_1}\; + {c_2},\varphi &gt; 4.\end{equation}Apply crossover and mutation operators to half of the population members. Then check if the inequality constraints enforce the limits of positions. If not, then they are replaced by their respective boundaries. In this paper, the crossover and mutation rate are set as 1 and 0.1, respectively.Apply natural selection approach by sorting the practice according to their objective function values, and then only the speed and position of the worst half of the particles are replaced by the speed and position of the best half of the particles.Repeat steps 2–6 until a stopping criterion is achieved, which is reaching the maximum number of iterations or an adequately good fitness value is attained.2FIGUREThe flowchart of the proposed centralised control for case studiesCASE STUDIES AND ANALYSISIn order to verify the performance of the proposed optimal coordination algorithms, different scenarios are studied on the modified IEEE 37‐node and IEEE 123‐node test feeders [43], and the strength of the proposed method is evaluated in detail under various operating conditions. First, the contribution of the suggested control scheme on the unbalanced condition improvement and power losses reduction under different PV penetration levels is examined on the modified IEEE 37‐node test system. Then, the test cases are conducted on the IEEE 123‐node test system to confirm the proposed method's scalability on the severe unbalanced conditions. Three scenarios are adopted on each test network to analyse and compare the performance of the proposed optimisation model with an autonomous control scheme. The considered scenarios are:Scenario 1: network is operating without any voltage regulation devices (base case). There is no OLTC and DSTATCOM, and the PV inverters are operated at unity power factor. The EVs are connected equally among the three phases.Scenario 2: network is operating under the local control of connected voltage regulation devices. DSTATCOM and PV inverter are locally controlled, whereas the EVs are still connected equally among the three phases. The conventional rule‐based control method of OLTC is used, where tap position change to keep the deviation of the secondary bus voltage from the pre‐set reference with voltage regulation bandwidth is 0.012 pu.Scenario 3: network is operating with the proposed voltage regulation algorithm. All the voltage regulation devices and EVs’ connections are now controlled by the proposed optimisation model described in the flowchart shown in Figure 2. For case studies, the optimisation process has been performed over a period of 24‐h with a 10‐min time step. The initial value of OLTC tap, DSTATCOM Vsh and PV inverter PF was set at unity value, and the number of connected EV at each phase was set to be equal. Then unbalanced load flow is performed to check the operational constraints of the power distribution system. The optimisation model is then applied either if there is operational constraint violation (e.g., voltage unbalance level) or after 1 h of the last optimisation model being applied. The optimisation proposed a new setting of the coordinated devices that enforce the efficient operation of the power distribution system. These processes will be repeated every 10 min until the optimisation model has produced 24 h of operation.Finally, both test systems are used to evaluate the accuracy and robustness of the employed AHPSO. The proposed strategy and simulation were implemented in the MATLAB® (R2018a). The numerical experiments were conducted on a computer with an Intel computer i7‐6700 at 3.4 GHz CPU and 12GB RAM. For all case studies, the population size and maximum number generation are set to 20 and 100, respectively. For both local and proposed control (Scenario 2 and 3), the feeders’ voltage magnitude was within the limit, therefore the evolution of voltage unbalance and power losses would be the main interest in this study. Moreover, this study assumes that the size of feeders and transformer of the selected simulated network is designed to handle a high PV and EV charging station penetration level based on interconnection studies. Thus, the power loading of lines and transformers are within limits.IEEE‐37‐bus test systemFigure 3 shows the modified IEEE 37‐bus unbalanced radial distribution feeder [43]. In this test feeder, the loads are single‐phase, two‐phase and three‐phase, and the distribution lines are un‐transposed. All the three‐phase loads are assumed connected in a star configuration and are considered as a constant power load type where the given loads’ data are considered to be peak loads. For simplicity, each load bus represents a group of residential houses fed by a three‐phase feeder. To investigate the efficacy of the proposed method, it assumed that the substation transformer is equipped with OLTC. Two units of three‐phase PV generation systems are randomly connected to the tested feeder at buses 25 and 33. Two EV charging stations that emulate real parking are considered in this paper, and both are assumed to be commercial parking lots that provide a semi‐fast charging facility to EVs with a rating of 7.4 kW. The maximum number of connected EVs into EVs parking lots 1 and 2 are 20 and 15, respectively, which are connected into bus 20 and bus 9, respectively.3FIGUREModified IEEE 37‐bus test feederThe semi‐fast charging station is not yet common compared with slow (residential) or fast‐charging stations. In this type of charging station, the EVs are only charged during working hours, and the peak occurs between 12 pm and 2 pm. Figure 4 shows the total EVs at each time instant for the two parking lots, which are identical to the typical EVs parking lots profile used in [44]. A three‐phase DSTATCOM is installed at bus 8, having a capacity of 3 × 200 kVAr. The actual PV active power production on a sunny day, and a practical load profile of a three‐phase feeder throughout a day with a 10‐min of time resolution are shown in Figure 5. These data are recorded by HCT GreenNest Eco House [45]. The 24‐h load profile curve is incorporated into all load buses in the simulated network, considering various peak load levels and phases number. Although the measurements describe the active power load profile, they can be adopted to represent the reactive power profile. Several criteria were used in different studies to describe the PV penetration level [46], and the definition used in this paper is the ratio of the total three‐phase peak of PV active power to the total three‐phase peak load of the apparent power in the feeder.4FIGUREThe number of vehicles in parking lots5FIGUREThree‐phase load and PV power profileInitially, the simulated system is tested under a low PV penetration level (20%) to identify the system's detailed behaviour under various scenarios and point out the significance of the proposed optimisation model. The statistical analysis of voltage unbalance under the three scenarios for a period of 24 h at each bus are demonstrated through a standard box plot displayed in Figure 6. The line inside each box is the median, and the left and right edges of each box are the upper and lower quartiles, respectively. It shows that the voltage unbalance at the base case (Figure 6a) crossed the limit of 2% and reached up to 3.7% during some hours of the day. It evidences that most of the day, the voltage unbalance limits are violated at some buses, particularly bus 27 to bus 36. The operation of local control of voltage regulator devices representing scenario 2 manages to reduce the voltage unbalance to 2.6%, as shown in Figure 6b, but still, the network is suffering from voltage imbalance problems for a significant amount of time. Moreover, if the number of EVs connected at each phase are not assumed equal in the local control, the voltage unbalance level would be a catastrophe. After adopting the proposed optimisation model (scenario 3), the voltage unbalances are further minimised and maintained within standard limits, as shown in Figure 6c.6FIGUREVoltage unbalance for (a) Scenario 1, (b) Scenario 2, and (c) Scenario 3As far as scenario 3 is concerned, Figure 7 presents the related PF angle (δPFabc$\delta _{PF}^{abc}$) values of the two integrated PV inverters for each phase throughout the day, which reflect the rate of reactive power exchanged with the network. It can be noted that the PV inverters connected at bus‐33 most of its operating time absorb the reactive power at phase ‘b’ and supply it at the other two phases to reduce the voltage variation among the phases. This is due to the load is comparatively low at phase ‘b’ and high at phase ‘a’ and ‘c’, making the voltage unbalance level significant. It can also be observed from Figure 8 that most of the EVs are connected at phase ‘b’ to balance the power between the phases. The exclusion of EVs’ connections in the optimisation problem has increased the total energy losses per day by 6%. This is because the network is forced to absorb more reactive power to compensate the voltage unbalance, especially at a high penetration level. Involving EVs’ connections in the optimisation model may demand for oversizing the charging station infrastructure (sizing of each phase). However, shifting the car's load from one phase to other can reduce the overall loading to other phases in three‐phase systems. This is because the optimisation algorithm tries to minimise the loading difference in the three‐phase system, which consequently leads to maintain a reasonable feeder loading and hence, avoiding upgrading feeder size. For example, the loading of phase ‘c’ of the substation transformer is reduced from 120% to 105% (with respect to the transformer’ rating at each phase) after applying the proposed coordination scheme. To accommodate the voltage drop and reduce the power losses at peak load, the OLTC operates at tap position 3, and the DSTATCOM operates at the operating limit to inject reactive power, as shown in Figure 9. It is worth noting that the total number of taps changed during the day was 25, which is less than the maximum average number of tap changes per day (48 tap changes). Moreover, the loading of the substation transformer at peak load is reduced by 5% compared with the local control approach due to power losses and voltage unbalance reduction.7FIGURECorresponding PF angle of the connected PV inverter8FIGURENumber of connected EVs at each phase at the parking lots9FIGURETap position of OLTC and controllable voltage source of DSTATCOMTo examine the superiority of the proposed control approach at different PV penetration levels, the size of the integrated PV is increased to reach 100%. Figures 10 and 11 show the maximum voltage unbalance recorded and the total energy losses under various penetration levels. Although the support of PV active power between the phase is equal, the voltage unbalance reduces as the penetration level of PV increases. This is due to the inter‐phase coupling between the distribution line, causing different voltage drop at each phase, which might decrease the voltage unbalance. Injection of reactive power from PV inverter and DSTATCOM reduces the voltage unbalance significantly at high penetration level; however, the power losses increased significantly. For example, at 75% penetration level, the total energy losses rise by 45% to reduce the voltage unbalance from 3.12 to 2.29. In contrast to scenario 2, in the proposed optimisation model, the voltage unbalance reduces to 1.98, and the total energy losses reduce by 25%. This indicates that the lack of coordination between various voltage regulation devices can potentially reduce the severity of voltage unbalance with the cost of increasing network losses.10FIGUREComparison of maximum voltage unbalance11FIGUREComparison of total energy lossesFinally, the proposed control is tested under a different load profile to resemble a diverse situation of the power distribution system where the peak of load and PV generation is not synchronised. The new three‐phase load profile used in this case study is presented in Figure 12, which is based on real‐world data in Oman provided by Mazoon Electricity Company (MZEC). It can be seen from Figure 13 that at 20% of PV penetration level, the maximum voltage unbalance recorded throughout the day were 3.59 for scenario 1 and 3.31 and 2.09 for scenario 2 and 3, respectively. These values are the same for the different PV penetration levels because they occurred at the time of peak load (18:30), where the PV production is zero. Therefore, the PV generated power for this type of load profile does not influence the maximum voltage unbalance level but significantly impacts the overall energy losses. For example, at 100% penetration level, the energy losses per day is increased from 901 kWh to 1303 kWh when adopting the local control of voltage regulation devices, and after adopting the proposed control scheme, the energy losses is reduced to 769 kWh. By implementing the proposed coordination scheme, the voltage unbalance is maintained at the standard bounds regardless of PV generation, which concludes that the proposed coordination scheme can maintain the operational constraints limit in an unbalanced power distribution system under various load and PV generation profiles.12FIGUREDifferent three‐phase load profiles13FIGUREComparison of maximum voltage unbalance recorded during a dayIEEE‐123 test systemTo further verify the scalability of the proposed optimisation model on large‐scale power distribution systems, a modified IEEE123‐bus test system is adopted, as presented in Figure 14. In this test system, the voltage unbalance is relatively low compared with the IEEE37‐bus test system. For the purpose of the study, some loads were added in phase “a” to increase the percentage of voltage unbalance. All the four voltage regulators are replaced with two OLTC connected between bus 1 and 2 and between bus 65 and 73. All shunt capacitors are replaced with one three‐phase DSTATCOM connected at bus 103. The locations of the PV system and EVs are identified on the test system by square and triangle, respectively. All the assumptions and parameters of voltage control used previously are adopted here considering the same load, PV and EVs profile as shown in Figures 4 and 5.14FIGUREModified IEEE 123‐bus test feederIn this case study, the network was tested under a 30% PV penetration level. Without incorporating voltage regulator devices, it can be seen from Figures 15 and 16 that the voltage unbalance starts violating the limit from 8:30 until 14:30, with half of the network nodes in violation of limits. Even with incorporating voltage regulator devices that are controlled locally, more than 15 buses violated the standard limit of voltage unbalance. This makes mitigating the voltage unbalance in such a network challenging. To estimate the overall voltage unbalance of the whole system, the system voltage unbalance factor (VUFsys.$VU{F_{sys.}}$) is introduced as follows.24VUFsys.=∑i=1N=123∑t=024(VU%it)2\begin{equation}VU{F_{sys.}} = \sum_{i = 1}^{N = 123} {\sum_{t = 0}^{24} {{{(VU\% _i^t)}^2}} } \end{equation}15FIGUREComparison of maximum voltage unbalance recorded during the day16FIGUREComparison of maximum voltage unbalance recorded at each buswhere VU%it$VU\% _i^t$ is the voltage unbalance at time t and at bus i, which can be calculated using (12).Tables 1 and 2 show the reduction rate of energy losses and overall system voltage unbalance compared with the base case under 30% and 60% of PV penetration level. Compared with Scenario 1, the voltage unbalance factor for the whole system is reduced by 30.31% and 75.01% in Scenario 2 and Scenario 3, respectively at 30% penetration level and 41% and 80% at 60% PV penetration level. This shows that adopting the proposed optimisation control can significantly improve voltage unbalance, and can be twice as effective as local control. On the other hand, in Scenario 2, the network power losses increased in both penetration levels, whereas in Scenario 3, the power losses were reduced by more than 30%. This indicates that voltage unbalance can produce high power losses; however, minimising it does not always reduce power losses if coordination control is missing. It should be pointed out that for all the case studies performed, the corresponding daily average OLTC tap is at most half of the equivalent daily maximum average number of tap changes.1TABLEComparison of energy losses and VUFsys reduction rate under 30% PV penetration levelScenarioEnergy losses (kWh)Reduction rate of losses (%)VUFsys$VU{F_{sys}}$Reduction rate of VUFsys$VU{F_{sys}}$ (%)1265.78—1.4923—2267.76‐0.741.040030.313181.5031.710.373075.012TABLEComparison of energy losses and VUFsys reduction rate under 60% PV penetration levelScenarioEnergy losses (kWh)Reduction rate of losses (%)VUFsys$VU{F_{sys}}$Reduction rate of VUFsys$VU{F_{sys}}$ (%)1223.45—1.3973—2238.54‐6.750.816841.543138.8137.880.277780.13The findings presented in this research study emphasise that the unbalanced voltage level is considerably high in power distribution systems integrated with PVs and EVs. The contribution of high voltage unbalance on heightening the power losses can be identified as previously pointed out. However, its implications on equipment derating and ageing cannot be easily quantified and are excluded in this study. The detection of voltage unbalance is the first step in developing a practical solution to alleviate the unbalanced problem that cannot be achieved by autonomous‐based control. Moreover, minimising the voltage unbalance using a local control approach can sometimes increase the power losses, which can be significant under high PV penetration levels. Therefore, implementing centralised‐based control solutions becomes a critical part of active power distribution systems, enabling monitoring and efficient operation. The case studies demonstrate the central control's significance in reducing the power losses and voltage unbalance. The results also show the potential of EVs to collaborate with other equipment to manage voltage. The absence of optimal coordination of PVs and EVs can cause an excessive current flow in the neutral wire due to the increased level of voltage unbalance and thus increasing the overall energy losses, which negatively impacts the operational performance of a power distribution system.Different optimisation methodsTo evaluate the accuracy and robustness of the developed AHPSO, some well‐known optimisation techniques are used to solve the proposed optimisation problem. Since the proposed optimisation problem's nature is complex, analytical optimisation methods may not be reliable alternatives. Thus, three other versions of PSO, called pure standard PSO with constriction factor, hybrid PSO‐GA [40], and PSO based on natural selection PSO‐NS [42], are considered for verifying the performance of AHPSO method. A 100 trial runs based on various random initial values are conducted on both test systems, considering 20% of PV penetration level and the resulting average and standard deviation (SD) of objective function values are reported. Tables 3 and 4 show a comparison between the objective function values achieved by the different applied heuristic methods on the IEEE‐37 test system and the IEEE‐123 test system, respectively. The %RSD is the relative standard deviation of the samples and is calculated by dividing the standard deviation by the average value. It is used to check the robustness of methods, where the lower percentage values indicate the more robust a method will be. The %RSD value (i.e., Table 3) shows that the proposed AHPSO standard deviation is 0.545% of the average value, which is pretty small compared with other methods. In other words, the optimisation value is tightly clustered around the mean, which means that the optimisation solution will be almost the same at each solution process. On the other hand, if the percentage were large, this would indicate that the objective function value is more spread out.3TABLEComparison of objective values for different optimisation methods on the IEEE‐37 test systemPSOPSO‐NSPSO‐GAProposed AHPSOBest27.75127.75127.75127.751Worst31.35629.30729.11028.562Average28.33327.97527.90127.828SD0.8020.3650.3030.152%RSD2.8311.3071.0860.5454TABLEComparison of objective values for different optimisation methods on the IEEE‐123 test systemPSOPSO‐NSPSO‐GAProposed AHPSOBest24.16624.16624.16624.166Worst26.21425.01025.15424.490Average24.35824.27024.24024.197SD0.2680.1580.1430.062%RSD1.1020.6490.5890.258As observed from Table 3, the %RSD of the samples of the AHPSO (0.545%) is lower than other methods (2.831% for pure PSO, 1.307% for PSO‐NS, and 1.086% for PSO‐GA). Although the %RSD is relatively low for other methods, it can still compromise the network performance efficiency. For example, if we consider a large scale network with optimised minimum power losses of 6MW, the PSO‐GA method can bring an additional of 65.17 kW power losses because of its %RSD = 1.086%. This demonstrates the higher robustness of the AHPSO with respect to the changes in random initial values compared with the other three heuristic methods. It can also be noted for Table 4, that the average (24.197) value is very close to the best value (24.166) that was recorded during the whole trials, which also shows the superiority of the proposed method. Moreover, even at a large network scale, where the number of searching space and variables increase, the proposed optimisation solution method performs much better than other methods.CONCLUSIONWith a growing number of RET connections in the power distribution system, new control strategies are required to minimise the severity of voltage unbalance. This paper proposes an advanced coordination scheme between OLTC, DSTATCOM, PVs and EVs. A new advanced hybrid particle swarm optimisation is also proposed to solve the optimisation problem, and its robustness was verified. Different case studies using typical PV power generation and load demand data demonstrated the proposed approach's ability and scalability to alleviate voltage unbalance and reduce power losses under various PV penetration levels. The investigations argue that the proposed control scheme can significantly reduce unbalanced voltage and limit the OLTC actions considerably, allowing an increased lifetime for OLTC mechanisms. The study outcome further justified the strength of the approach compared with autonomously control schemes of voltage regulator devices in the streams of voltage unbalance reduction and power losses.The cost analysis of adopting the proposed coordination scheme was not the focus of this research study and was not conducted because, currently, some of the devices involved in centralised‐based control are not commercially available in the market. Moreover, the cost‐benefit resulting from minimising the voltage unbalance cannot accurately be quantified because of its long‐term impact. However, as the need for centralised‐based control devices rises and becomes available in the market, their prices will drop considerably. Moreover, as a result of providing a better power quality in the network and power losses reduction, the proposed centralised controls may become more cost‐effective by also considering the investment that has already been adopted on the widespread two‐way communication infrastructure and smart meters.CONFLICT OF INTERESTThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.FUNDING INFORMATIONThere is no funding.DATA AVAILABILITY STATEMENTThe data that support the findings of this study are available from the corresponding author upon reasonable request.PERMISSION TO REPRODUCE MATERIALS FROM OTHER SOURCESNoneREFERENCESC. on C. Change: Net Zero: The UK's Contribution to Stopping Global Warming. Committee on Climate Change, London (2019)IRENA (2019): Future of Solar Photovoltaic: Deployment, Investment, Technology, Grid Integration and Socio‐Economic Aspects (A Global Energy Transformation: Paper). International Renewable Energy Agency, Abu Dhabi (2019)Kharrazi, A., Sreeram, V., Mishra, Y.: Assessment techniques of the impact of grid‐tied rooftop photovoltaic generation on the power quality of low voltage distribution network‐A review. Renew. Sustain. Energy Rev. 120, 109643 (2020)Islam, M.R., Lu, H., Hossain, M.J., Li, L.: Mitigating unbalance using distributed network reconfiguration techniques in distributed power generation grids with services for electric vehicles: A review. J. Clean. Prod. 239, 117932 (2019)Molina‐García, Á., Mastromauro, R.A., García‐Sánchez, T., Pugliese, S., Liserre, M., Stasi, S.: Reactive power flow control for PV inverters voltage support in LV distribution networks. IEEE Trans. Smart Grid 8(1), 447–456 (2016)Kraiczy, M., Stetz, T., Braun, M.: Parallel operation of transformers with on load tap changer and photovoltaic systems with reactive power control. IEEE Trans. Smart Grid 9(6), 6419–6428 (2017)Shahnia, F., Ghosh, A., Ledwich, G., Zare, F.: Voltage unbalance improvement in low voltage residential feeders with rooftop PVs using custom power devices. Int. J. Electr. Power Energy Syst. 55, 362–377 (2014)Heidari‐Akhijahani, A., Safdarian, A., Lehtonen, M.: Unbalance mitigation by optimal placement of static transfer switches in low voltage distribution feeders. IET Gener. Transm. Distrib. 14(20), 4612–4621 (2020)Alabri, W., Jayaweera, D.: Impact of Semi‐fast Charging Stations on Unbalanced Power Distribution Systems Integrated with PV Systems. In: 2021 IEEE PES Innovative Smart Grid Technologies Europe (ISGT‐Europe), pp. 1–5. IEEE, Piscataway (2021)Bai, F., Yan, R., Saha, T.K., Eghbal, D.: An excessive tap operation evaluation approach for unbalanced distribution networks with high PV penetration. IEEE Trans. Sustain. Energy 12(1), 169–178 (2020)Wang, L., Yan, R., Bai, F., Saha, T.K., Wang, K.: A Distributed inter‐phase coordination algorithm for voltage control with unbalanced PV integration in LV systems. IEEE Trans. Sustain. Energy 11(4), 2687–2697 (2020)Li, C., Disfani, V.R., Pecenak, Z.K., Mohajeryami, S., Kleissl, J.: Optimal OLTC voltage control scheme to enable high solar penetrations. Electr. Power Syst. Res. 160, 318–326 (2018)Murty, V.V.V.S.N., Sharma, A.K.: Optimal coordinate control of OLTC, DG, D‐STATCOM, and reconfiguration in distribution system for voltage control and loss minimization. Int. Trans. Electr. Energy Syst. 29(3), e2752 (2019)Hashemipour, N., et al.: Multi‐objective optimisation method for coordinating battery storage systems, photovoltaic inverters and tap changers. IET Renew. Power Gener. 14(3), 475–483 (2020)Meng, F., Chowdhury, B., Hossan, M.S.: Optimal integration of DER and SST in active distribution networks. Int. J. Electr. Power Energy Syst. 104, 626–634 (2019)Alboaouh, K., Mohagheghi, S.: Voltage, var and watt optimization for a distribution system with high PV penetration: A probabilistic study. Electr. Power Syst. Res. 180, 106159 (2020)Efkarpidis, N., De Rybel, T., Driesen, J.: Optimization control scheme utilizing small‐scale distributed generators and OLTC distribution transformers. Sustain. Energy, Grids Netw. 8, 74–84 (2016)Bandara, W.G.C., Godaliyadda, G., Ekanayake, M.P.B., J, B.: Ekanayake: Coordinated photovoltaic re‐phasing: A novel method to maximize renewable energy integration in low voltage networks by mitigating network unbalances. Appl. Energy 280, 116022 (2020)Jabalameli, N., Ghosh, A.: Online centralized coordination of charging and phase switching of PEVs in unbalanced LV networks with high PV penetrations. IEEE Syst. J. 15(1), 1015–1025 (2021)Islam, M.R., Lu, H., Hossain, J., Li, L.: Multiobjective optimization technique for mitigating unbalance and improving voltage considering higher penetration of electric vehicles and distributed generation. IEEE Syst. J. 14(3), 3676–3686 (2020)Daratha, N., Das, B., Sharma, J.: Coordination between OLTC and SVC for voltage regulation in unbalanced distribution system distributed generation. IEEE Trans. Power Syst. 29(1), 289–299 (2013)Zhao, F., Zhao, T., Ju, Y., Ma, K., Zhou, X.: Research on three‐phase optimal power flow for distribution networks based on constant Hessian matrix. IET Gener. Transm. Distrib. 12(1), 241–246 (2018)Li, C., Disfani, V.R., Haghi, H.V., Kleissl, J.: Coordination of OLTC and smart inverters for optimal voltage regulation of unbalanced distribution networks. Electr. Power Syst. Res. 187, 106498 (2020)Zeng, X.J., Zhai, H.F., Wang, M.X., Yang, M., Wang, M.Q.: A system optimization method for mitigating three‐phase imbalance in distribution network. Int. J. Electr. Power Energy Syst. 113, 618–633 (2019)Dileep, G.: A survey on smart grid technologies and applications. Renew. Energy 146, 2589–2625 (2020)Alabri, W., Jayaweera, D.: Unbalanced modelling of STATCOM and SVC in hybrid load flow method. In: 2019 IEEE PES Innovative Smart Grid Technologies Europe (ISGT‐Europe), pp. 1–5. IEEE, Piscataway (2019)Kamel, S., Abdel‐Akher, M., Jurado, F.: Improved NR current injection load flow using power mismatch representation of PV bus. Int. J. Electr. Power Energy Syst. 53, 64–68 (2013)I. S. Association: 141–1993. IEEE Recommended Practice for Electric Power Distribution for Industrial Plants (ANSI). IEEE Press, Piscataway (1994)Zhang, X.‐P., Rehtanz, C., Pal, B.: Flexible AC transmission systems: Modelling and control. Springer Science & Business Media, Berlin Heidelberg (2012)Arrillaga, J., Arnold, C.P.: Computer analysis of power systems. Analysis 9(7.8), 7–9 (1990)Ghazali, Y.Z.Y.: Managing on‐load tap changer life cycle in tenaga nasional berhad (TNB) distribution power transformers. CIRED‐Open Access Proc. J. 2017(1), 303–307 (2017)Olivier, F., Aristidou, P., Ernst, D., Van Cutsem, T.: Active Management of Low‐Voltage Networks for Mitigating Overvoltages Due to Photovoltaic Units. IEEE Trans. Smart Grid 7(2), 926–936 (2016)Alabri, W., Jayaweera, D.: Voltage regulation in unbalanced power distribution systems with residential PV systems. Int. J. Electr. Power Energy Syst. 131, 107036 (2021)SMA Solar Technology: Description of the Operating Parameters ‐ SUNNY TRIPOWER 60 /SUNNY HIGHPOWER PEAK1. http://www.windandsun.co.uk/media/995570/SMA‐Sunny‐Highpower‐PEAK1‐Description‐of‐the‐Operating‐Parameters.pdfChen, T., et al.: A review on electric vehicle charging infrastructure development in the uk. J. Mod. Power Syst. Clean Energy 8(2), 193–205 (2020)Abdi, H., Beigvand, S.D., La Scala, M.: A review of optimal power flow studies applied to smart grids and microgrids. Renew. Sustain. Energy Rev. 71, 742–766 (2017)Ebeed, M., Kamel, S., Jurado, F.: Optimal power flow using recent optimization techniques. Class. Recent Asp. Power Syst. Optim. 157–183 (2018)Roberge, V., Tarbouchi, M., Okou, F.: Optimal power flow based on parallel metaheuristics for graphics processing units. Electr. Power Syst. Res. 140, 344–353 (2016)Mehmood, K.K., Khan, S.U., Lee, S.‐J., Haider, Z.M., Rafique, M.K., Kim, C.‐H.: A real‐time optimal coordination scheme for the voltage regulation of a distribution network including an OLTC, capacitor banks, and multiple distributed energy resources. Int. J. Electr. Power Energy Syst. 94, 1–14 (2018)Juang, C.‐F.: A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Trans. Syst. Man, Cybern. Part B 34(2), 997–1006 (2004)Ziari, I., Ledwich, G., Ghosh, A., Platt, G.: Optimal distribution network reinforcement considering load growth, line loss, and reliability. IEEE Trans. Power Syst. 28(2), 587–597 (2012)Naka, S., Genji, T., Yura, T., Fukuyama, Y.: A hybrid particle swarm optimization for distribution state estimation. IEEE Trans. Power Syst. 18(1), 60–68 (2003)Kersting, W.H.: Radial distribution test feeders. IEEE Trans. Power Syst. 6(3), 975–985 (1991)Azzouz, M.A., Shaaban, M.F., El‐Saadany, E.F.: Real‐time optimal voltage regulation for distribution networks incorporating high penetration of PEVs. IEEE Trans. Power Syst. 30(6), 3234–3245 (2015)HCT GreenNest Eco House: AC Electric. https://dataloggers.livetozero.com/hct/index.html. Accessed 12 July 2019Olowu, T., Sundararajan, A., Moghaddami, M., Sarwat, A.: Future challenges and mitigation methods for high photovoltaic penetration: A survey. Energies 11(7), 1782 (2018)

Journal

"IET Generation, Transmission & Distribution" – Wiley

Published: Jun 1, 2022

There are no references for this article.