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Iterative Approach for Tuning Multiple Converter-Integrated DER in Microgrids
Iterative Approach for Tuning Multiple Converter-Integrated DER in Microgrids
García-Ceballos, C.;Pérez-Londoño, S.;Mora-Flórez, J.
Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 1394096, 15 pages https://doi.org/10.1155/2022/1394096 Research Article Iterative Approach for Tuning Multiple Converter-Integrated DER in Microgrids C. Garcı ´a-Ceballos , S. Pe ´ rez-Londoño , and J. Mora-Flo ´ rez Department of Electric Power Engineering, Universidad Tecnolo´gica de Pereira, AA: 97-Post Code: 660003, Pereira, Colombia Correspondence should be addressed to J. Mora-Flo´rez; firstname.lastname@example.org Received 24 November 2021; Revised 22 February 2022; Accepted 1 March 2022; Published 11 April 2022 Academic Editor: Salvatore Favuzza Copyright © 2022 C. Garc´ıa-Ceballos et al. ,is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ,is paper proposes an iterative approach to adjust the control parameters of multiple power converters within a microgrid, which operates in grid-connected and grid-islanded modes. ,e adequate control parameters are determined using an op- timisation-based strategy, local measurements, and results obtained in previous algorithm iterations. ,e proposed objective function is based on the integral time-weighted absolute error (ITAE), modiﬁed to improve the microgrid control perfor- mance. ,e proposed approach addresses the control tuning complexity by considering an incremental strategy, starting from adjusting basic microgrids, continuing to the setting of intermediate microgrids, and ﬁnalising when the target microgrid control is ﬁne adjusted. ,e results obtained at the CIGRE LV benchmark microgrid validate the proposal, obtaining during faults, the maximum deviations from rated frequency around 2.2% and 0.3% in grid-islanded or grid-connected cases, re- spectively. Also, voltage and power references are adequately followed during steady-state regardless of the microgrid op- eration mode, where the steady voltage proﬁle is below 10% variation. ,e obtained results demonstrate the proposed approach advantages, which straightforwardly adjust multiple converters integrated into a microgrid. ,e main contributions are as follows: (a) the microgrid model is not required, and (b) only measurements at the point of common coupling of the distributed energy resource are used; consequently, the proposed tuning approach is especially applicable to complex microgrids. Finally, ﬁnely adjusted microgrids are required for further operation or protection studies where complex system conﬁgurations are commonly required. parameters are cautiously selected to obtain an adequate 1. Introduction microgrid behaviour [3, 6–12]. 1.1. Motivation. Distributed energy resources (DER) are On the other hand, operation or protection studies re- integrated into the electric network as these represent quire realistic microgrids, including several converter-in- technical and economic beneﬁts . Nevertheless, the study tegrated DER (CIDER), loads, and lines. Such microgrids of DER integration is an issue considering the compromise can be operated in grid-islanded and grid-connected modes, between the model detail and the system size; frequently, requiring the zero and the primary control layers. ,e latter when detailed representations are considered is at the ex- is used when the microgrid operates in grid-islanded mode, pense of the microgrid size [2–4]. while the former is required under grid-connected and grid- Power electronic devices such as the voltage source islanded cases. converter (VSC) are generally used to integrate DER into the As above exposed, the requirement of realistic size AC microgrid. ,e VSC is a nonlinear device that requires microgrids, which must be adequately controlled, is an issue several control layers, which are considered by the microgrid nowadays. Even though adjusting the PI control constants is hierarchical control . ,ese control schemes are usually considered in many proposals, a standard process is not based on proportional-integral (PI) strategies, whose available, which makes the microgrid adjustment from 2 International Transactions on Electrical Energy Systems Additionally, even though [16, 17] do not consider a scratch diﬃcult. Consequently, it is desirable to obtain a simpleand eﬀective methodthat allowsresearchers to design tuning technique, these references presented consider- ations for microgrid and VSC modelling; these are suit- and adjust multi-CIDER microgrids straightforwardly, and then deeper and detailed studies can be developed . able examples of how daunting, a time-consuming and In this way, this research is oriented to develop an oﬀ- challenging task is the adjusting of an adequate microgrid line approach to obtain adequate CIDER control parameters model. In , the VSC model was analysed, and a within a realistic size microgrid. ,e approach considers proposal for VSC 6th order model was validated through decentralised control strategies, several DER models, grid- the small-signal model and eigenvalue analysis. In , islanded and grid-connected modes, local measurements, the IEEE37 bus system was modiﬁed to include 7 VSCs; as and diﬀerent microgrid operating conditions. a result, the small-signal model of the whole microgrid reached 225th order, which was reduced to a 56-order system model. Finally, in , three types of controllers 1.2. State of the Art. Most of the proposed strategies to were tuned by using a small-signal model and the gravity determine the VSC control parameters aim for optimal centre of a stable area; however, only one VSC was tuning. ,ese can be divided into three approaches: considered in the test system. (a) ,ese that consider the physical model of the con- trolled system, where the control parameters are 1.2.2. Tuning Approaches considering the Transfer Function obtained using exact techniques or a combination of Equivalent Modelling of the Controlled System. ,is ap- exact and nonexact techniques. proach is usually applied due to the entire microgrid model (b) ,ese that use a transfer function equivalent model complexity; then, simpliﬁed transfer functions are consid- for the controlled system, where exact or nonexact ered. Usually, this tuning process does not include microgrid tuning techniques are predominant and mixed interaction or additional elements besides the VSC. More- techniques are also available. over, the simpliﬁcations to obtain TF equivalent make the obtained solutions inadequate for all operating conditions (c) ,ese where the controlled system model is not . considered and nonexact tuning techniques are ,erefore, the VSC can be modelled by an equivalent usually applied. ﬁrst-order transfer function (TF). ,is tuning approach is A tuning strategy based on the model is usually preferred considered in the following papers. In , a VSC dominant since the optimal solution is obtained; nonetheless, the pole TF and pole placement method were considered. Also, determination of VSC and microgrid dynamic models can in , a zero-level TF for the VSC zero control was be challenging in realistic size microgrids. As a consequence, complemented with fuzzy logic; then, the system response the last two approaches are widely considered. under small and large signal disturbances was enhanced. In , the state-space representation of the microgrid was simpliﬁed to a TF, and IMC was applied to obtain adequate 1.2.1. Tuning Approaches considering the Physical Compo- VSC behaviour under grid transition. In , the grid- nent Modelling of the Controlled System. In general, the forming mode of operation was studied, TFs and restrictions controlled system model has more parameters as the in the frequency domain (s) were applied to deﬁne complexity and size increase. In this approach, the models boundaries for the primary control parameters and also describe the behaviour of the components and consider at explored with diﬀerent primary control strategies. In , least the small-signal system model. Nonetheless, the model the simpliﬁed microgrid TFs and eigenvalue analysis was complexity is not always the same in microgrids since each carried away. However, it was remarked that a strict of these include diﬀerent considerations or components. ,e mathematical formulation of the optimisation problem was following paragraphs present some examples. In , a small- not acquirable, so the solution was obtained through a signal model (SSM) described a microgrid with three VSCs, genetic algorithm (GA) and validated through eigenvalues. which included 55 state variables and considered internal Additionally, even though the control parameters selection model control (IMC) complemented with particle swarm was not evident in , it considered the microgrid mod- optimisation (PSO). In , an eigenvalue analysis deﬁned elling using TFs, analysing stability issues and phase-locked the PSO objective function and state equations described the loop (PLL) bandwidth, and it also included multiple-input main elements of the microgrid; then  considers both multiple-output (MIMO) representation and parameters model and measures of the system. Finally,  propose a 2- boundaries. Finally, it was usual to validate the proposals VSCtestmicrogridrepresented by thestate-space model;the using a reduced and simpliﬁed test system in the references search space and objective function of a modiﬁed whale above. optimisation (WO) technique were obtained from the ei- genvalue analysis. In the two latter references, the optimi- sation strategy and the objective function deﬁnition were as 1.2.3. Tuning Approaches Which Do Not Require the Model of the Controlled System. As described in the two previous crucial as the modelling process. However, the system size and number of VSCs were small due to model size. Fur- tuning approaches (model-based approaches), the microgrid thermore, strong disturbances as short circuits were not model can diﬀer from one work to another, leading to deeply analysed. confusion when implementing and tuning a microgrid from International Transactions on Electrical Energy Systems 3 scratch. Moreover, even with the model acquirement, a adequate results with low modelling eﬀorts and can be nonexact technique was usually considered since the model straightforwardly implemented in several microgrids, regardless of the operating mode. used to determine the control parameters was quite complex in many cases. ,erefore, this third approachavoids the modelling stage 1.3. Contribution. ,e paper proposes a straightforward for the control tuning but requires the deﬁnition of an approach to deﬁne the control parameters, applied to tune optimisation function (OF). As the microgrid model is not realistic size microgrids with several CIDERs, operating in considered or is unknown, OF is based on the error in the grid-connected and grid-islanded modes. ,e considered signals of interest. Also, nonexact techniques are applied, CIDER representation includes the primary energy resource, which means that the obtained solution is the best from all the VSC, and the output ﬁlter. Additionally, as the microgrid explored solutions. As an advantage, this is a fast and model is not required, the proposed strategy can tune straightforward approach, where OF can be estimated using controls of complex microgrids. In the proposal, only local measurements. measurements at the CIDER point of common coupling On the other hand, nonexact techniques are a wide ﬁeld (PCC) are considered and compared with a reference signal of research in microgrid applications, especially when the to calculate OF, minimised through an iterative strategy system size conduces to a complex model. Among these based on an optimisation technique. ,ese measurements techniques,  presented a review of the operation cost, contain information about the CIDER’s behaviour and the concluding that swarm strategies had the best performance. remaining part of the microgrid. Other proposals, as presented in , applied PSO to adjust ,e proposed approach allows the tune of the control the primary level control for a simpliﬁed microgrid. Ad- parameters easily; besides, it can be applied to multiple ditionally, in , the grey wolf optimisation (GWO) ad- CIDER microgrids. As the used measurements contain the justed the control parameters for a wind turbine generator. microgrid response under diﬀerent disturbances, the In , the zero-level control for a simpliﬁed wind-battery obtained control parameters allow the stable behaviour microgrid was adjusted using GA. In , the PSO was for a wide range of operating conditions. ,is approach applied to train a modiﬁed fuzzy controller, where tests were speeds up other studies since an adequately tuned compared to PI controller regarding power-sharing and microgrid control is the base of upcoming operation or frequency regulation. protection analysis. As a result of state of the art, the main characteristics of references with control tuning strategies are summarised in Table 1. ,is table includes for comparison purposes the 1.4. Paper Organisation. ,is document is divided into ﬁve system model, the applied tuning technique, the adjusted sections. In Section 2, the required fundamental theoretical control, the signals used for control adjustment, commonly aspects related to the control of CIDERs are exposed, while power, voltage, and frequency; in some cases, also damping in Section 3, the proposed approach is described. Later, coeﬃcient ξ and the real part of eigenvalues Re(λ ) were also Section 4 presents the proposed tests, their results, and the used. Table 1 also includes the microgrid operating mode, corresponding analysis. Finally, Section 5 highlights the the test system size, and the proposal scalability. conclusions. From the comparison table, small test systems were noticed in most cases. Some approaches, as [28, 29], used large test systems, but the use of communication systems 2. Control of Converter-Interfaced Distributed jeopardised the overall microgrid behaviour. ,is last aspect Energy Resources is not considered in the proposal presented in this paper since primary and zero control layers are decentralised, no ,is section brieﬂy introduces the fundamental aspects of communication links are required, constituting an essential microgrid hierarchical control, which comprises four advantage by reducing costs and reliability issues. layers known as zero, primary, secondary, and tertiary ,e comparison in Table 1 allows concluding about [4, 5, 30, 31]. Zero layer control is the VSC local control, the proposal scalability, where qualitative labels, low, including the inner and outer loops. ,e primary level medium, or high, are considered. Low scalability means a controls the voltage, frequency, and power-sharing. ,e proposal that was not clearly validated nor presented to secondary level improves the quality of voltage and fre- be implemented in realistic size microgrids and also a quency and is in charge of islanding detection. ,e tertiary proposal that presents a high dependence of correct level deals with the optimal power ﬂow and the unit microgrid modelling. Medium scalability means a pro- commitment in microgrids. posal that addressed the tuning problem with a high Speciﬁcally, this proposal discusses the zero-level control potentiality for implementation on realistic size micro- for grid-following CIDERs, while the zero and primary level grids, mainly for the ﬂexibility to partially or totally controls are analysed in the grid-forming CIDERs. ,e zero- dismiss the microgrid model, which is complex to obtain level control for the grid-following CIDERs aims to deliver in realistic microgrids. High scalability is associated with the reference power imposed by the secondary and tertiary a proposal that addresses the tuning problem and can be control, while the microgrid is in grid-connected mode. ,e easily implemented in realistic size microgrids. Addi- zero-level control requires proportional and integral pa- tionally, the proposal presented in this paper has rameters (k , k ), asdepicted inFigure1.,e respective set P1 I1 4 International Transactions on Electrical Energy Systems Table 1: Comparison of some referenced microgrid tuning approaches. System Adjusted Signals for Microgrid Test system Reference Tuning technique Scalability model control level adjustment mode size Zero and 3 VSC-2  SSM IMC and PSO Q Islanded Low primary line P, U , U , 2 VSC-1 rms rms gen  None GWO Zero Connected Low and V line dc 2 VSC-2  TF Pole placement method Zero None Islanded Low line 2 VSC-0  None GA Zero ω Islanded Low gen line 3 VSC-2  SSM PSO Zero P and Re(λ ) Both Medium line 2 VSC-1  SSM Modiﬁed WO Zero Re(λ ) and ξ Islanded Low line 4 VSC-3  TF Fuzzy Zero to tertiary Q Both Medium line Zero and 1 VSC-1  TF IMC None Both Low primary line Deﬁnition of gain margins and 2 VSC-3  TF Primary Not clear Connected Low parameter ranges line SSM and Zero and 2 VSC-1  GA P and Q Islanded Medium TF primary line 2 VSC-2  None Fuzzy and PSO Primary P, Q, U, and f Islanded Low lines 7 VSC-10  None PSO and fuzzy Primary P and f Connected Medium line Modiﬁed ITAE index and Zero and 5 VSC-10 Proposal None i , i , u , u ,and f Both High d q d q metaheuristic optimisation primary line abc abc dq0 u Inner loop abc abc i + d ref dq0 θ k k P1, I1 - - Outer loop P ref Solve: ωL P=u i + u i d d q q dq0 Q ref CIDER abc u , u Q=u i - u i d q q d d q ωL k k P1, I1 q ref + Figure 1: Grid-following controller. of equations for the inner loop is presented in equation (1), where U and U are the dqvoltage references for the VSC, d q while the outer loop is represented by equation set (2). which at the same time are the output of the inner loop. Variables u , u and i , i are the dq voltages and currents d q d q measured at VSC PCC, which come from the Park U � u − ωLi + k + i − i , d d q P d d 1 ref transformation of u and i . ω is the system frequency abc abc (1) while θ is the angle reference for the Park transformation. L is the ﬁlter inductance. k and k are the proportional P I U � u + ωLi + k + i − i , 1 1 q q d P q q 1 ref and integral gains, respectively, for the PI controller. International Transactions on Electrical Energy Systems 5 Finally, i i and i are the dq currents used as a 3. Proposed Iterative and Incremental d d q ref ref ref reference for the inner loop, which at the same time are Approach for CIDER Tuning the output of the outer loop in ,is section presents a three-stage approach to adjust the P u + Q u ref d ref q i � , control parameters of several CIDERs within a target ref 2 2 u + u d q microgrid. Each CIDER uses the control scheme in Figures 1 (2) or 2 for grid-following and grid-forming operating modes, P u − Q u ref q ref d respectively. i � , 2 2 ref ,e structure of the proposed approach is presented in u + u d q Figure 3. It starts by identifying the target microgrid and deﬁning the basic microgrids as is presented in stage 1. ,e where i i and i are the dq references for the inner loop d d q ref ref ref and P and Q are the references of active and reactive target microgrid is deﬁned as the complex system of interest ref ref power for the outer loop, respectively. u and u are mea- to the network analyst, while the basic microgrids are d q surements as described for equation set (1). simpliﬁcations that consist of a single CIDER connected to a ,e grid-forming CIDER regulates frequency and load through a line, as presented in Figure 4. Next, in Stages voltage in grid-islanded mode. It requires three pairs of 2 and 3, the controls of basic microgrids are optimally parameters in the zero-level control, namely, (k , k ) for adjusted; then, these tuned microgrids are used to obtain P2 I2 the inner loop and (k , k ) for the outer loop. Additionally, intermediate microgrids by adding lines, loads, or CIDERs. P3 I3 the primary control requires the parameters related to active ,ese intermediate microgrids are iteratively enlarged and and reactive power (m , m ), as depicted in Figure 2. In the tuned, using an optimisation strategy based on the mea- p q case of the grid-forming CIDER, the set of equations for the surementsat theCIDER PCC.Finally, the targetmicrogridis obtained and tuned as a result of this iterative process. inner loop is the same as presented in (1), where the PI gains are now k and k ; the outer loop is represented by P I 2 2 equation set (3). Droop equations describe the primary 3.1. Stage 1: Identiﬁcation of the Target and Deﬁnition of the control in (4) and (5). Basic Microgrids. ,is stage is devoted to identifying the target microgrid’s characteristics and deﬁning the two basic i � i − ωCu + k + , u − u , d d q P d d ref 3 ref microgrids used for the CIDER control adjustment. ,us, (3) instead of initially handling the target microgrid, two basic 3 microgrids presented in Figure 4 are deﬁned in this stage. i � i + ωCu + k + , u − u , q q d P q q ref 3 ref ,e ﬁrst basic microgrid presented in Figure 4(a) operates in grid-connected mode and includes a single where C is the ﬁlter capacitance, k and k are the pro- P I grid-following CIDER. ,e second operates in grid-islanded 3 3 portional and integral gains, respectively, for the required PI mode and considers only one grid-forming CIDER, as controller, and u and u are the dq voltage references for d q depicted in Figure 4(b). ref ref the outer loop, so the voltage at the PCC is controlled, ,e size of the CIDER, line, and load in the basic andu comes from the droop control, whereas u is null. d q ref ref microgrids is deﬁned considering the target microgrid rated ,e remaining variables are already deﬁned in the previous values. ,ese basic microgrids are initially tuned as pre- set of equations. sented in stage two; next, these are used to deﬁne the in- termediate microgrids, as presented in stage three. u � u − m Q − Q , (4) d ref q ref ref ω � ω − m P − P , (5) ref p ref 3.2. Stage 2: Optimisation of the CIDER Control Parameters. Stage two focuses on determining the optimal control pa- where u is the voltage reference in the direct axis for the ref rameters for the CIDERs within a microgrid. In this stage, outer loop in (3), u is the voltage reference for the droop ref three main processes are proposed: (a) the objective function control, which is near 1 p.u. m is the proportional gain for (OF) is deﬁned, and an improvement criterion is also the droop control to regulate voltage; Q and Q are the ref established to evaluate the control parameters. (b) A control measured and reference values for the reactive power, re- parameter database is used to improve the odds of reaching a spectively. ω is the controlled frequency from the droop proper solution by the optimisation strategy. (c) ,e re- control, which allows obtaining θ for the Park transfor- quired microgrid control parameters are obtained from the mation adequate behaviour. ω is the reference of fre- ref execution of an optimisation process. quency for the VSC output, which is near 1 p.u. m is the proportional gain for the droop control to regulate fre- quency. Finally, P and P , are measured and reference ref values for the active power, respectively. 3.2.1. Deﬁnition of OF. ,e OF is deﬁned based on a As a result, two parameters have to be tuned for each modiﬁed ITAE index to consider evenly time-weighted grid-following CIDER (k and k k ), while six are re- measurements. ,e required variables are measured at the P1 I1 I1 quired for each grid-forming CIDER (k , k , k , k , m , CIDER PCC. ,is index is a robust alternative frequently P2 I2 P3 I3 q and m ). used for error estimation between two signals, which in this p 6 International Transactions on Electrical Energy Systems P , Q Outer loop ref ref Inner loop u , ω u i + ref ref d ref d ref + k , k k , k P3 I3 P2 I2 P, Q - - d i ωL ωC u = u – m (Q – Q ) d ref ref q ref dq0 CIDER ω = ω ref – m (P – P ref ) p abc ωC ωL Droop control q + + - - + + k , k k , k P3 I3 P2 I2 + q ref u + q ref + i u q q Figure 2: Grid-forming controller. Stage 1: Target microgrid Definition of target and Start (complex) basic microgrids n = 1 Grid-connected or grid- islanded basic microgrids Stage 2: Variable measurements Optimisation of the CIDER and OF calculation control parameters Control parameters Optimisation process database execution Best control Best OF parameters update Stage 3: n = n+1 Enlarging the basic microgrids Not n ≥ 2 Yes n = n+1 Not O.F > Y O.F best Yes Microgrid (n) = microgrid (n-1) + p-type elements Variable microgrid(n) is the target Not measurements and microgrid OF calculation Yes Final execution of the optimisation process Target microgrid best End control parameters Figure 3: Approach for tuning the CIDERs within a complex microgrid. International Transactions on Electrical Energy Systems 7 Tertiary or secondary Primary droop Voltage and frequency control, PQ references control references Zero level Zero level control control Load Load Main grid PCC PCC Line Line CIDER CIDER (a) (b) Figure 4: Basic microgrids. (a) Basic grid-connected microgrid. (b) Basic grid-islanded microgrid. case corresponds to the measured and the reference signals [32, 33]. Initially, for a single CIDER and a signal of interest (x), 0.5 the desired time window contains the microgrid response under a single disturbance, for example, short circuit and load change. ,is window is represented in Figure 5 and has t (k = 1) t + T (k = K) a ﬁxed time length (T); an initial time (t ), corresponding to time (s) the ﬁrst sample of interest (k � 1); and a total of K samples, Reference which are deﬁned according to the window length and the Measured sampling time (t ). smpl Figure 5: Considered time window for the measurements at the ,e ITAE index for the signals in Figure 5 is deﬁned as in CIDER PCC. equation ITAE � kt |Δx(k)|, (6) Finally, the ITAE is deﬁned as the OF and presented smpl total k�1 in (10), which allows comparing CIDERs behaviour. where Δx(k) � x(k) − x(k) . OF � ITAE reference measured total (10) Next, as several disturbances (d) are considered, the � αITAE + (1 − α)ITAE . form foll ITAE in equation (6) becomes D K In (10), α is an adjustable weighting factor that gives ITAE � kt |Δx(k, d)|, (7) relevance to either grid-forming or grid-following CIDERs, smpl d�1 k�1 considering values from 0 to 1. In the grid-islanded microgrid, the weighting factor emphasises the ﬁne pa- where D is the number of considered disturbances. rameter selection of the grid-forming CIDERs, while in the Additionally, several signals (s), such as voltage and grid-connected microgrid, the importance is focused on the current, are considered; then Δx contains a set of signals. grid-following CIDERs. Similarly, as the signals of interest diﬀer according to the CIDER operating mode, the average error per signal is preferred. ,ese considerations turn equation (7) into (8), 3.2.2. Deﬁnition of the Control Parameter Database. ,e which is obtained for each CIDER (c). purpose of the control parameter database is to initialise the S D K parameters for the CIDERs within the microgrid. ITAE � kt |Δx(k, d, s)|, (8) c smpl Initially, this database is empty; then, control parameters s�1 d�1 k�1 at ﬁrst executions of the optimisation process, which con- sider the basic microgrids, are obtained from empirical where S isthe numberof consideredsignals at each CIDER c. tuning methods or reported control parameters for similar After that, ITAE is estimated separately for the grid- applications, as these presented in [10, 12, 34]. After several forming (C ) and grid-following (C ) CIDERs. ,e form foll iterations, this database also contains parameters obtained evaluation of (9) is therefore performed. from the optimisation process, which is iteratively executed form 1 due to several intermediate microgrids being considered. It ITAE � ITAE ; form c is necessary to execute the optimisation process multiple form c�1 times since the CIDERs optimal control parameters are not (9) the same in each microgrid. ,en, the number of executions foll of the optimisation process is given by the criteria at stage 3 ITAE � ITAE . foll c foll c�1 as x (k) 8 International Transactions on Electrical Energy Systems ⎧ ⎪Continuetotheoptimisationprocessexecution, ∀ψ ≥ Y, OF (n) � ψ⇒ (11) OF ⎩ best Enlargetheintermediatemicrogrid, ∀ψ < Y, where Y is a positive integer greater than 1. microgrid. Here, p − type refers to an element as line-type, Finally, the parameters in the database are inputs for the load-type, or CIDER-type. optimisation strategy; then, as the information of previous Once these elements are added, the proposal veriﬁes solutions is available, the optimiser is more likely to ﬁnd a whether the obtained intermediate microgrid is the same as proper solution in the actual iteration. the target microgrid, the case in which the optimisation process is executed for the last time, and the best control parameters for the target microgrid are obtained. If the 3.2.3. Execution of the Optimisation Process. ,e considered intermediate microgrid diﬀers from the target microgrid, its optimisation problem is oriented to minimise the objective OF is calculated and compared to a limit value of Y times the function (OF), selecting adequate CIDER control param- best obtained OF, as in (11). When the limit value is sur- eters (par), as presented in passed, the optimisation process is once again executed. Otherwise, more elements are added to the actual microgrid, min αITAE + (1 − α)ITAE , par form foll and then another intermediate microgrid is generated. ,is s.t.par ∈ solutionspace, (12) iterative strategy continues until the target microgrid is adequately controlled. ξ ≥0. Figure 6 portrays the process to minimise the OF, as 4. Tests and Discussion proposed in (10). ,e initial set of parameters (par ) is obtained from the database, as previously described. ,e OF ,is section presents the test results that validate the proposed approach, aiming to adjust the CIDER control is estimated using these parameters at the CIDERs control and the measured signals of interest. ,e OF estimated in parameters within a complex microgrid. Measurements at the CIDERs PCC and PSO are used in this paper con- the internal iteration (i) is compared to the previous OF i−1 to calculate the tolerance. If the tolerance is lower than the sidering previous satisfactory results , although the desired value (ξ), then the best control parameters for the proposed approach allows other techniques as these presented in . CIDERs control are obtained (par ), which ends the best execution of the optimisation process. Otherwise, the op- Initially, the target and the basic microgrids are pre- sented; next, the results for the basic microgrid considering timisation strategy selects a new set of parameters to be evaluated in the CIDER control. two testing scenarios. After, the analysis of one of the in- termediate microgrids is presented, and ﬁnally, the last part Variable par is composed of two or six parameters for each grid-following or grid-forming CIDER, respectively. presents the result analysis of the target microgrid tuned using the proposed approach. Additionally, since the number of parameters increases with each CIDER in the microgrid, these are grouped, and each group uses the same control parameters. ,us, the 4.1. Test System. ,e target microgrid selected for tests is parameters sought by the optimisation strategy are given based on the CIGRE LV benchmark  and has 170kVA by (13). ,e CIDERs are grouped considering this dis- maximum load, operatingin islandedorconnected modesas tance to the main grid connection node in the grid- presented in Figure 7. ,e basic microgrids have a single connected case or to the grid-forming CIDER in the grid- 100kW CIDER (as CIDER 5), 2/0 AWG conductor, 100m islanded case. line, and 80kVA load. par � 2 Gr + 6 Gr , (13) foll form 4.2. Analysis of the Basic Microgrids where Gr and Gr are the number of groups for grid- foll form following and grid-forming CIDERs, respectively. 4.2.1. Testing Operating Conditions for the Basic Microgrids. ,e adequate signals used in evaluating the OF deﬁned in 3.3.Stage3:EnlargingtheBasicMicrogrids. ,is stage focuses (10) consider two testing scenarios in the case of basic microgrids. ,e ﬁrst testing scenario is oriented to evaluate on increasing the complexity of the deﬁned basic microgrids until they become the target microgrid. ,erefore, new the dq currents or voltages, considering the CIDER control microgrids, known as intermediate microgrids, are itera- based on the dq frame. On the other hand, as the mea- tively generated and used to increase the control parameters surements are in the abc frame, the second scenario con- database and analyse diﬀerent microgrid topology or CIDER siders the active and reactive power signals and the RMS operating modes. In that way, once stage 2 is completed, a voltage to evaluate the OF. Frequency is considered in both checkpoint veriﬁes whether the two basic microgrids are scenarios.Finally, the testing operating condition for basic already tuned, a case in which an intermediate microgrid is microgrids considers disturbances, including a three-phase generated by adding p − type elements to the actual fault (R � 1.0Ω) at 0.20s, and load changes of 15% and f International Transactions on Electrical Energy Systems 9 Start Control parameter i=1 database par (i) CIDER control Measure signals of yes par (best) = par (i) parameters are interest and calculate OF (i-1) - OF (i) < ξ par (i) OF (i) End i=i+1 Change par (i) according to optimisation strategy Figure 6: General scheme for the optimisation strategy execution. CIDER 5 40 kVA CIDER 1 15 kVA 100 kW 10 kW N6 4 AWG N10 30 m 14 AWG 2 AWG 30 m 105 m Main grid 2/0 AWG 2/0 AWG 2/0 AWG 2/0 AWG 2/0 AWG 400 V – 60 Hz 35 m 35 m 70 m 105 m 35 m sw N9 N4 N7 N1 N2 10 AWG 10 AWG 8 AWG 14 AWG 30 m 30 m 30 m 30 m N3 N5 N8 N11 CIDER 3 CIDER 2 CIDER 4 15 kVA 55 kVA 20 kW 45 kVA 20 kW 10 kW Figure 7: Target microgrid based on a CIGRE benchmark. 50% of the CIDER rated value at 0.56s for grid-islanded and 4.2.3. Results for Grid-Forming CIDER in the Basic Grid- grid-connected cases, respectively. Islanded Microgrid. ,e diﬀerencesbetweenscenarios in the grid-forming CIDER are bigger than in the grid-following case. ,erefore, in the dq frame scenario, the OF is 17.65 4.2.2. Results for Grid-Following CIDER in the Basic Grid- with u , u , and f, whereas it is 28.34 when u and f are d q rms Connected Microgrid. In this case, both scenarios behave used; on the other hand, the abc frame scenario has an OF of alike in the measured signals (i , i , P, and Q), which have d q 40.13 with u , u , and f, whereas it is 11.90 with u and f. d q rms a stable and ﬂawless response after the load change and the As a consequence, the dq frame scenario has slightly better fault clearance; then, no advantage of the dq frame sce- performance, as is presented in Figure 8. Also, it is shown nario over the abc frame scenario is noticed. For com- that the smaller diﬀerence is obtained for the i signal, which parison purposes, in the dq frame scenario, the OF best under fault has a slightly higher overshoot in the dq frame value is 5.13 when estimated using i and i i , whereas it is d q q scenario; however, it also recovers faster than the abc frame 208.4 when P and Q are used. In the abc frame scenario, scenario. Still, results from both scenarios enrich the control the OF is 5.91 when using i and i i , whereas it is 208.1 d q q parameter database. Finally, the best control parameters for with P and Q. ,en, the dq frame scenario is, on average, the CIDER in the basic grid-islanded microgrid are slightly better. [k , k ] � [0.082,0], [k , k ] � [8.657,6361.07], and P2 I2 P3 I3 −4 −5 Despite both scenarios being similar and valid to obtain [m , m ] � [4.291 × 10 ,3.173 × 10 ]. p q control parameters, the dq frame scenario is selected. Still, the best parameters obtained in both scenarios are used as nourishment for the control parameter database. ,e best 4.3.AnalysisoftheIntermediateMicrogrids. ,e evolution of control parameters for the CIDER in the basic grid-con- the two basic microgrids towards the target microgrid is nected microgrid are [k , k ] � [10.352421.962]. achieved at stage three of the proposed methodology. ,is P1 I1 not 10 International Transactions on Electrical Energy Systems 1.4 1.01 1.2 0.8 0.99 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 time (s) time (s) dq frame scenario rms dq frame scenario abc frame scenario rms abc frame scenario (a) (b) 0.6 0.3 −0.3 −0.6 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 time (s) u u d dq frame scenario q dq frame scenario u u d abc frame scenario q abc frame scenario (c) Figure 8: Comparison of the optimisation scenarios for the basic grid-islanded microgrid. (a)Basic microgrid frequency.(b) RMS voltage in the PCC. (c) Voltage in direct and quadrature axis at the PCC. stage is the most complex since it handles the microgrid Finally, the addition of CIDER-type elements causes enlarging by adding a line, load, and CIDER-type elements. drastic changes in OF that usually activate the optimisation Adding elements raises the microgrid’s complexity, process execution; that is, the associated OF is higher than 5 whose behaviour is mainly jeopardised by the CIDER-type times OF . For instance, in the intermediate microgrid, a best elements due to their nonlinear behaviour. As these el- second CIDER at N8 produces OF � 138.43, which is ements cause signiﬁcant increments in the OF, then one of around 27 times larger than the OF until the present best the intermediate microgrids obtained by adding line and iteration (OF until now results from the grid-connected best load-type elements and only the CIDER 5 to the basic basic microgrid and is 5.13), activating the optimisation grid-connected, resulting in the same topology presented process. ,e sequence mentioned above for intermediate in Figure 7, is here analysed as an example of the tuning microgrid deﬁnition and performance evaluation isexecuted process. In this case and using the same control param- until the target microgrid is obtained. eters as in the basic microgrid, the obtained OF value is 6.37. ,e OF is severely varied when changing the loca- 4.4. Analysis of Target Microgrid. ,is section summarises tion, rated power, and the number of CIDER-type ele- the optimisation process results for the CIDER control ments; for example, changing the CIDER location from parameters and the target microgrid overall behaviour. N6 to N5 causes an OF value of 9.06, while it rises to 94.85 or 268.11 when the CIDER rated power is reduced to 50 kW or 20 kW, respectively. Similar results are obtained 4.4.1. Control Parameters Obtained by the Optimisation from the intermediate microgrids based on the grid- Process. ,e target microgrid in Figure 7 operates in grid- islanded basic microgrid. A high OF is related to strong connected or grid-islanded modes. During grid-connected, and fast signal oscillations in both grid-islanded and grid- all CIDERs are grid-followers, while in grid-islanded, it has a connected cases. single grid-forming at node N6. ,e aspects mentioned above allow determining Y value. ,e best CIDER parameters for both microgrid oper- ,is is greater than 1, but not too small, never to stop the ating modes are diﬀerent, as presented in Tables 2 and 3. iteration process, and not too big that an intermediate Additionally, Gr � 2 and Gr � 1, and the criteria for foll form microgrid with lousy behaviour (high oscillations or low- assigning a CIDER to a certain group are related to the quality voltage or frequency signals) misses the optimisation distance from the slack node (N1 in grid-connected mode or process. A value of Y � 5 is considered. N6 in grid-islanded mode). u (p.u.) f (p.u.) dq u (p.u.) rms International Transactions on Electrical Energy Systems 11 Table 2: Best control parameters in the grid-islanded microgrid. Grid-islanded microgrid Group CIDER Parameters OF −5 m � 3.35 × 10 −6 m � 2.167 × 10 1 5 23.795 k , k �10.896, 0 P3 I3 k , k �2.012, 0 P2 I2 2 1 k , k �1.055, 1053 P1 I1 1.66 3 2, 3, and 4 k , k �0.241, 1742.6 P1 I1 Table 3: Best control parameters in the grid-connected microgrid. Grid-connected microgrid Group CIDER Parameters OF 1 1, 3, and 5 k , k �1.223, 3683.8 p1 i1 1.66 2 2 and 4 k , k �1.145, 3467 p1 i1 1.25 0.75 0.5 0.25 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 time (s) P P 1 4 P P 2 5 (a) 0.8 0.6 0.4 0.2 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 time (s) u u 1 4 u u 2 5 (b) Figure 9: Continued. P (p.u) u (p.u.) 12 International Transactions on Electrical Energy Systems 60.5 59.5 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 time s f f 1 4 f f 2 5 (c) Figure 9: CIDERs operation within the target microgrid. (a) Active power in CIDERs 1 to 5. (b) Voltage in CIDERs 1 to 5. (c) Frequency in CIDERs 1 to 5. 4.4.2. Testing Operating Conditions for Target Microgrid. As presented, the proposed approach is successfully Target microgrid contains intentional grid transition; then, applied and validated to adjust the control parameters of CIDER 5 is selected to operate in grid-forming and grid- several CIDERs within a complex microgrid and tested following modes according to the t state, while the under several disturbances, including intentional grid sw remaining CIDERs only operate in grid-following mode. transition. ,e best control parameters for grid-islanded and grid- connected modes are used while considering grid transition. 5. Conclusions Figures 9(a)–9(c) present the active power (P), voltage (u), and frequency (f) for each CIDER. ,e considered Nowadays, the modellingofrealistic sizemicrogrids requires operating conditions for tests include (a) operation starts in several studies. Nevertheless, the study of DER integration is grid-islanded mode, and grid-following CIDERs are com- an issue considering the compromise between the model pelled to deliver constant power; (b) two load increments of detail and the system size; frequently, the microgrid size is 15kVA in node N8 at 1.2s and 10kVA in node N6 at 1.4s; reduced when detailed representations are considered. (c) three-phase fault at node N4 with R � 1.01Ω and ,e proposed approach considers two basic microgrids duration of 0.3s at 1.8s and 3.1s3.1s; then disturbances are used to iteratively enlarge the system towards the desired included within the two microgrid operating modes; and (d) target microgrid. ,e approach helps to obtain an adequate intentional grid transition at 2.6s. microgrid behaviour because lines, loads, and CIDERs are As presented in Figure 9, the initial time instant of sequentially added; then, the control parameters are updated interest is 1s. ,is is because at any time earlier, the con- considering the settings in the previous iterations and a sidered CIDERs are in a start-up state, where grid-forming parameter database. CIDER starts ﬁrst, and grid-following CIDERs start se- ,e application of the proposed approach is quentially to reduce stability issues. ,e aforementioned straightforward, as it avoids detailed modelling of the start-up sequence is similar to a plug and plays capability in microgrid and the CIDER. As a consequence of simpli- the grid-following CIDERs. fying the modelling eﬀorts and reducing the computa- ,e main observations from the obtained results are as tional burden, suitable solutions for larger systems, follows: (a) CIDER 5 maintains frequency and voltage including several CIDERs, are obtained, which constitute during grid-islanded mode; (b) load changes during grid- relevant advantages of the proposal over those ap- islanded mode are adequately compensated by the grid- proaches usually addressed by the cited references. forming CIDER; (c) all CIDERs recover ﬂawlessly after the Moreover, the proposed objective function considers three-phase fault, including voltage sags and frequency measurements under diﬀerent system states; transient and small-signal stability is also addressed. variations regardless of the microgrid operative mode; however, disturbances are severer in the grid-islanded As demonstrated in the testing section, the proposal is mode; (d) the grid transition is supported by the validated and successfully applied to adjust the control microgrid, which forces CIDER 5 to follow power ref- parameters of several CIDERs in a complex microgrid, erence (Figure 9(a)) and voltage levels in all CIDERs are whose behaviour is analysed under small and strong dis- increased to slightly better values (Figure 9(b)). Addi- turbances, including load changes, faults, and intentional tionally, the highest frequency disturbance is caused by grid transition. Moreover, the proposed approach optimally the three-phase fault in the grid-islanded mode, followed adjusts CIDERs for operating under grid-connected or grid- by the grid transition as presented in Figure 9(c); however, islanded microgrid modes; consequently, considering the all CIDERs measurements are consistent and stable under observed results, the obtained microgrid and CIDER pa- the analysed time window. rameters conﬁguration adequately supports grid transition. f Hz International Transactions on Electrical Energy Systems 13 ,is corroborates the suitability of the proposed iterative K: Total of samples of the window to analyse and optimisation-driven approach. k : Proportional gain for grid-following inner loop P1 ,is proposal is also an integrated approach since it iter- control atively considers several systems prior to the target microgrid k : Proportionalgainforgrid-forminginnerloopcontrol P2 study. Also, the proposal considers parameter results from k : Proportionalgainforgrid-formingouterloopcontrol P3 other works or systems, which enables the proposal to embrace k : Integral gain for grid-following inner loop control I1 many other proposals as an initial point database. k : Integral gain for grid-forming inner loop control I2 Additionally, the ﬁne selection of the CIDER control k : Integral gain for grid-forming outer loop control I3 parameters in a target microgrid inﬂuences the system L: Filter inductance stability since, in the case of a deﬁcient adjustment process, m , m : Active and reactive gains for droop control p q high oscillations and time responses may lead to issues. In P, Q: Active and reactive power measures at PCC the performed tests, disturbances aﬀecting small-signal and par: Set of parameters to ﬁnd transient stability are indirectly considered by including the P : Reference of active power for VSC ref measured signals at the optimisation process. ,ese stability Q : Reference of reactive power for VSC ref studies are challenging to consider in other approaches due S: Number of considered signals at each CIDER c to the complexity of the system modelling; then, this fact T: Time length of window to analyse validates an additional demonstrated proposal advantage. t : Initial time of window to analyse Finally, the main contribution is to propose and validate an t : Sampling time for x signal smpl oﬀ-line approach to optimally adjust the control parameters of u : abc voltages at VSC PCC abc a multiple CIDER microgrid, considering only local mea- u , u : dq voltages measured at VSC PCC d q surements at the objective function. ,is function is evaluated u , dq voltage references for grid-forming outer loop ref considering several microgrid operating conditions such as u : ref grid transition, power system faults, and load changes. ,e U , U : dq voltage references for the VSC d q proposed approach accelerates microgrid studies since ﬁne Y: Limit value to compare the best objective function control adjustment is mandatory to obtain adequate test sys- at the optimisation process tems for studying further operation or protection issues. α: Relevance factor for grid-forming or grid- following CIDER ITAE Abbreviations Δx: Error between signal x reference and measure θ: Angle reference for the Park transformation AC: Alternating current ξ: Tolerance for the optimisation strategy CIDER: Converter-integrated distributed energy resource ω: System angular frequency DER: Distributed energy resource ω : Frequency reference for the VSC. ref GA: Genetic algorithm GWO: Grey wolf optimisation Data Availability IMC: Internal model control ITAE: Integral of time-weighted absolute error ,e data that support the ﬁndings of this study are available MIMO: Multiple-input multiple-output from the corresponding author upon reasonable request. 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International Transactions on Electrical Energy Systems
Hindawi Publishing Corporation
Iterative Approach for Tuning Multiple Converter-Integrated DER in Microgrids
International Transactions on Electrical Energy Systems
, Volume 2022 –
Apr 11, 2022
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