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Optimal Energy Management of Virtual Power Plants with Storage Devices Using Teaching-and-Learning-Based Optimization Algorithm

Optimal Energy Management of Virtual Power Plants with Storage Devices Using... Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 1727524, 17 pages https://doi.org/10.1155/2022/1727524 Research Article OptimalEnergyManagementofVirtualPowerPlantswithStorage Devices Using Teaching-and-Learning-Based Optimization Algorithm Raji Krishna and S. Hemamalini School of Electrical Engineering, Vellore Institute of Technology, Chennai, Tamil Nadu 600127, India Correspondence should be addressed to S. Hemamalini; hemamalini.s@vit.ac.in Received 6 January 2022; Revised 29 May 2022; Accepted 15 June 2022; Published 29 August 2022 Academic Editor: Jaouher Ben Ali Copyright © 2022 Raji Krishna and S. Hemamalini. *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. In recent decades, Renewable Energy Sources (RES) have become more attractive due to the depleting fossil fuel resources and environmental issues such as global warming due to emissions from fossil fuel-based power plants. However, the intermittent nature of RES may cause a power imbalance between the generation and the demand. *e power imbalance is overcome with the help of Distributed Generators (DG), storage devices, and RES. *e aggregation of DGs, storage devices, and controllable loads that form a single virtual entity is called a Virtual Power Plant (VPP). In this article, the optimal scheduling of DGs in a VPP is done to minimize the generation cost. *e optimal scheduling of power is done by exchanging the power between the utility grid and the VPP with the help of storage devices based on the bidding price. In this work, the state of charge (SOC) of the batteries is also considered, which is a limiting factor for charging and discharging of the batteries. *is improves the lifetime of the batteries and their performance. Energy management of VPP using the teaching-and-learning-based optimization algorithm (TLBO) is proposed to minimize the total operating cost of VPP for 24 hours of the day. *e power loss in the VPP is also considered in this work. *e proposed methodology is validated for the IEEE 16-bus and IEEE 33-bus test systems for four different cases. *e results are compared with other evolutionary algorithms, like Artificial Bee Colony (ABC) algorithm and Ant Lion Optimization (ALO) algorithm. solutions [2] to enhance power quality and reliability. VPP is 1. Introduction a small, single imaginary power plant consisting of distrib- An increase in power demand and restrictions imposed on uted generators (DGs), energy storage devices, and con- fossil fuel usage to reduce power plant emissions have made trollable loads along with information and communication utilities look for alternate sources. Also, power distribution technologies that plan, monitor the operation and coordinate to remote locations is still a problem due to technical and the power flow between the components. Distributed gen- financial issues. To mitigate these problems, distributed erators consist of clean energy sources such as photovoltaic generators like wind, solar, fuel cells, and so on are used. *e (PV), wind, Micro Turbines (MT), Fuel Cells (FC), diesel government also announces useful schemes and policies generators, and Combined Heat Power Plants (CHPP). In such as Renewable Portfolio Standards (RPS) and different VPP, the storage devices (battery, electric vehicle, and bat- kinds of subsidies at different levels to encourage the usage of tery-based robots) play a major role in energy exchange renewable energy sources for power generation. *e global between the utility grid and VPP [3]. *ere are two types of VPP: commercial VPP and technical VPP. VPPs minimize power generation [1] using wind and solar energy has in- creased to 743GW and 874GW at the end of 2021, with an the generation costs, minimize emissions, maximize profit, 8% growth in renewable capacity. and enhance the trade in the electricity market. One of the Consumers need electrical energy at a cheaper cost, with main advantages of VPP is the integration of RES, which high reliability and high quality. VPP is one of the remarkable helps to reduce the deviation from the predicted generation 2 International Transactions on Electrical Energy Systems Energy storage devices play a vital role in maintaining the of electricity and associated penalties. *e other advantage is the integration of EVs, which can act as a storage device in the power balance in a VPP by selling or buying the power from the VPP [20]. Energy storage devices, like fuel cells and power system [4]. Even though RES helps to reduce the emission, RES is batteries, supply power to additional or instantaneous loads. not sufficient to meet the power demand and may fail to Regulation of SOC of battery is an important aspect to maintain the power balance between the generation and the enhance the proper power flow between the utility grid and load demand during peak hours. *is problem can be the VPP. A fuzzy-based control strategy [21] is applied for the overcome in VPPs, wherein the power generation from regulation of SOC and for controlling the power flow during other distributed resources and storage devices along with excess and insufficient conditions. *e concept of electric vehicles (EVs) to store energy to overcome the intermittent power generated from RES maintains the power balance [3]. During peak load, VPP can support the grid by supplying its supply of energy from the wind farms is discussed in [22]. *e metaheuristic techniques reduce computational reserves. Likewise, when the pricing of utility power is lesser than that of the VPP, VPP buys power from the utility grid. time compared with conventional methods [23]. Dimeas and Hatziargyriou used Multiagent System- (MAS-) based Optimal scheduling of each unit in a VPP is thereby im- portant for the economical operation. Various optimization control [24] for the optimal and effective control of a VPP. It techniques are used for the optimal operation of VPP [5, 6]. is claimed that in centralized systems, MAS provides a better For proper functioning of VPP, the Energy Management solution, but not an optimal solution. De Filippo et al. in- System (EMS) is responsible for controlling the flow of troduced a two-stage optimization model [25] for a VPP power between the generating units, controllable loads, and EMS, which decides the optimal planning of power flows for the storage devices. *ere are various challenges associated each time step at minimum cost. In this two-stage model, in the first stage, the prediction of uncertainty is modeled using with EMS of VPP, such as uncertainty of Renewable Energy Sources (RES), market price, power balancing, and inte- a robust approach to optimize the load demand shift and estimate the cost. In the second stage, an online greedy gration of all the units in VPP [7, 8]. Energy management in a VPP is done by replacing the optimization algorithm is implemented within the simulator that uses the optimal shift produced in the first stage to diesel generators with RESs and energy storage devices [9]. *e proper balance between the power generation and the minimize the operating cost. However, there is a loss of load demand is essential to avoid the instability problems in quality in the solution because of the greedy algorithm used the VPP operation. DG, being the peak load provider during in the second step. peak hours, helps to maintain the power balance between *e minimization of the total cost and thereby max- power generation and consumption [10]. *e penetration of imation of the profit is the major concept associated with various DGs, especially the RES, will bring more uncer- VPP. Profit maximization of VPP in a day-ahead market taking into account the uncertainty of RES is proposed [26]. tainties in the power system operation. Various mathe- matical methods are used in the literature to model the *e bidding strategy for a VPP is formulated as an opti- mization problem to maximize the profit using MILP. To uncertainty of RES. A Probabilistic Load Flow (PLF) using the unscented transformation (UT) method is introduced in reduce the operating cost while maintaining energy balance, [11] to analyze the system performance. *e increased system security, and system voltage level, a two-stage sto- utilization of PEVs along with the high penetration of RES chastic optimization model is introduced to address the will affect the optimal operation of the distribution feeder uncertainties in the wind power outputs and electricity reconfiguration (DFR) strategy in the smart grids. To mit- prices [27]. Results validated the reduction in operating costs igate this problem and to increase the efficiency of the while maintaining system reliability. An economic dispatch system, the V2G concept is proposed and the uncertainty of of VPP modeled using mixed-integer programming is RES is modeled with the UT method [12]. *e robust op- presented in [28]. Bilevel mathematical programming used to model the bidding strategy is proposed [29] to maximize timization model is used for calculating the generation cost of VPP on an hourly basis that is proposed in [13–16] while the profit and minimize the emission of VPPs. Computa- tional intelligence- (CI-) based metaheuristic techniques considering the uncertainty of PV and wind. A two-stage Stackelberg game is proposed for the day-ahead energy [30] are increasingly used for profit maximization in VPPs. management of VPP considering the uncertainty of RES and A trading model [31] of a VPP in a unified market is market price [17]. A combination of Stochastic Program- proposed and solved using the fruit fly algorithm (FFA) to ming and Adaptive Robust Optimization (ARO) based maximize the profit. approach is proposed to model the uncertainty of market However, most of these optimization techniques require price [18]. Integration of Electric vehicles (EVs) is a new algorithm parameters that need to be tuned to improve the performance of the techniques. Also, CI-based metaheuristic trend for power balancing in VPP. Integrating more and more uncertain sources of energy such as PV, wind, and methods are not efficient to handle uncertainty in real-time situations. All these disadvantages can be overcome using energy storage devices makes the system highly dynamic. *ereby, to maximize the profit of a VPP, Hybrid Levy the TLBO algorithm. In addition, the TLBO algorithm does not require any parameter to be tuned, which makes the Particle Swarm Variable Neighborhood Search Optimiza- tion (HL-PS-VNSO) [19] is suggested. *e uncertainties due implementation of TLBO much simpler. to plug-in-electric vehicles (PHEVs) in G2V (additional load In this paper, minimization of the operational cost of a to the grid) and market price are also considered. commercial VPP for 24 hours in a day is formulated as the International Transactions on Electrical Energy Systems 3 optimization problem. Power losses are also taken into VPP account. *e VPP consists of solar, wind, MT, FC, and FC MT battery as energy sources. VPP can supply or buy power from the utility grid depending upon the cost of power generation and load demand in the VPP and the utility price. Utility Grid *ough there are many techniques available in the literature Load Battery to solve this problem, in this paper, the TLBO algorithm is EMS used to solve the cost minimization problem by considering WT 4 different scenarios. Since the operating cost of RES is less PV compared to other generating units in the VPP, power output from the RES is utilized to the maximum. *e op- timal dispatch of generating units considering the power losses in the distribution system is done using backward- Figure 1: A virtual power plant (VPP) connected to a utility grid. forward sweep load flow analysis. SOC of batteries is also taken into account, which enhances the battery life and its performance. *is paper is organized as follows. In Section 2, the basic 2.1. Problem Formulation. *e main objective of the pro- structure of EMS for VPP, problem formulation, and the posed work is the optimal allocation of generating units and related constraints are discussed. An overview of the TLBO the storage devices to minimize the operational cost of VPP algorithm is presented in Section 3. In Section 4, the in 24 hours of a day using the TLBO algorithm. In addition, implementation of the TLBO algorithm for energy man- the operating limits of the storage device, say the battery, are agement in VPP is presented. Section 5 discusses the sim- also considered in this work. *e SOC of the battery is set to ulation results of 4 different cases and their comparison with operate in the range of 10% to 90% of the battery capacity. ABC and ALO algorithms. Finally, the conclusion and future *is will improve the performance and lifetime of the scope are discussed in Section 6. storage device. Depending upon the load demand and the price of generation, power can either be sold or purchased 2. Optimal Energy Management of Virtual from the main grid. Considering the hourly basis of usage, if Power Plants the per-unit cost of the utility grid is less than the cost of VPP power, buying the power from the utility grid is economical. *e objective of a VPP is to relieve the load on the grid by *e power bought from the utility grid is also stored in the smartly distributing the power generated by the individual storage devices. On the other hand, if the utility price is units during peak load. A VPP and its components con- more, then power from the VPP is sold to the utility. *e nected to a utility grid is represented in Figure 1. *e main objective function of the VPP is formulated to include the functionality of the EMS is to ensure proper power exchange cost of power purchase from the utility grid, the fuel cost of between the utility grid and the VPP through proper co- the DGs and storage devices, and the start-up/shutdown cost ordination between the DGs and the grid. Energy is ex- of the power sources in the VPP [32]. In addition, the cost of changed between the VPP and utility grid and thereby power losses is also taken into account. Power losses are trading is done. *is in turn can minimize the total operating calculated using the forward-backward sweep method [33]. cost or maximize the profit of a VPP. *e EMS continuously *e objective function for the problem statement monitors the status of each unit and sends suitable control mentioned above is given as follows. signals to control the operation of DGs, energy storage devices, and controllable loads in an economical manner. t t t t t t ⎧ ⎪ P × U × C + P × U × C + ⎫ ⎪ WT WT WT PV PV PV ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ t t t t t t ⎪ ⎪ ⎪ ⎪ P × U × C + P × U × C ⎪ ⎪ FC FC FC MT MT MT ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ g ⎪ ⎨ ⎬ t t−1 t t t Min(f(X)) � 􏽘 + 􏽘 S 􏼐U − U 􏼑 + U × P × C , (1) Gi i i ESS ESS ESS ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ t�1 i�1 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ s ⎪ ⎪ ⎪ ⎪ t t−1 t t t t ⎪ ⎪ ⎪ + 􏽘 S 􏼐U − U 􏼑 + P × C − P × C ⎪ ⎪ sj j j Grid Grid Losses Losses ⎩ ⎭ j�1 P + jQ i i I � 􏼠 􏼡 , (2) where P � 􏽐 (I ) R . Losses k k k�1 i 4 International Transactions on Electrical Energy Systems where I is the current flow in the kth branch, R is the k k P (t)≤ P ∗ Y(t), t �1,2, . . . T; X∈ [0,1], Discharge Dischargemax resistance of the kth branch, and M is the number of feeder t t t t t t (8) sections/branches. P , P , P , P , P , P ,and PV WT FC MT ESS Grid P are the available power from the PV, wind, turbine, Losses where SOC and SOC are the minimum and ESS,min ESS,max fuel cell, microturbine, storage devices, utility grid, and maximum state of charge of the storage device. *e dis- t t t t t power losses, respectively.C , C , C , C , C , and PV WT FC MT ESS charge efficiency is given as C are the bidding price of the PV, wind turbine, fuel cell, Grid microturbine, storage devices, and utility grid, respectively. η � . (9) Discharge C is the cost incurred towards the power losses. *e Charge Losses ON/OFF status of all the corresponding units is represented t t t t t *e storage devices cannot charge and discharge at the by U , U , U , U , and U . *e start-up or shutdown PV WT FC MT ESS same time and hence X(t) and Y(t) take values of either 0 or costs for the ith DGs and jth storage devices are given as 1. Bus voltage limit for the ith bus is given as S (t)and S (t), respectively. N and N are the numbers of Gi sj g distributed generators and the storage units, respectively. V ≤ V ≤ V , i ∈ {1,2, . . . N}, (10) min ,i i max ,i t t−1 U and U are the ON/OFF status of DG units and i i t t−1 U and U are the ON/OFF status of storage devices with where V and V are the minimum and maximum j j min ,i max ,i respect to time t and t − 1, respectively. voltage of the ith bus. *e current in each feeder should not exceed the maximum current carrying capacity of the branches. 􏼌 􏼌 2.2. Constraints. At any given time, the power generation 􏼌 􏼌 􏼌 􏼌 􏼌I 􏼌≤ I , k ∈ {1,2, . . . l}, (11) K max and the load demand in the VPP must be balanced; that is, the total power generation must equal the sum of load where l is the number of branches. *e maximum allowable demand and losses as expressed in active and reactive power injection of DGs are as follows. Ng N Ns Load P ≤ P ≤ P , DGmin DG DGmax 􏽘 P + 􏽘 P + P � 􏽘 P + P , (3) Gi Sj Grid Load,k Losses (12) i�1 j�1 k�1 Q ≤ Q ≤ Q , DGmin DG DGmax where N , N , and N are the numbers of distributed s load g where P and Q are the active and reactive powers of DG DG generators, the storage units, and loads, respectively. DGs, P and Q are the minimum allowable active DGmin DGmin *e power generation limits of DGs, storage devices, and and reactive powers of DGs, and P and Q are the DGmax DGmax utility grid are expressed as maximum allowable active and reactive powers of DGs. P ≤ P ≤ P , Gi,min Gi Gi,max 3. Overview of TLBO Algorithm P ≤ P ≤ P , (4) Sj,min Sj Sj,max *e Teaching-Learning-Based Optimization (TLBO) algo- P ≤ P ≤ P , Grid,min Grid Grid,max rithm is a new effective human population-based algorithm where P and P are the minimum and maximum proposed by Rao et al. *is algorithm resembles the Gi,min Gi,max allowable powers of DGs, P and P are the min- teaching-learning process of the instructor and students in a Sj,min Sj,max imum and maximum allowable power of the storage devices, lecture room. In this approach, a set of learners in a category and P and P are the minimum and maximum are considered as a population. Also, the number of subjects Grid,min Grid,max allowable powers of the utility grid. P , P ,and P are offered to the learners is the variables, the result of the Gi Sj Grid the available power from the DGs, storage devices, and learner is the fitness value, and the knowledge of the student utility grid, respectively. *e state of charge of the storage is the objective function. *e parameters considered in the device is expressed as objective function are the variables for the given problem and the best fitness value of the objective function is taken as SOC (t) � SOC (t −1) + η P (t)Δt ESS ESS Charge Charge the best solution. *e TLBO method is split into two phases: (5) the teacher phase and the learner phase. In the former phase, − η P (t)Δt, t �1,2, . . . T, Discharge Discharge the learners are learning from the teacher and in the latter Where SOC (t)and SOC (t − 1)aretheenergystoredin phase, the learners are learning by discussing with other Ess Ess the devices at time t and t– 1, respectively. P and learners [34, 35]. *e phases of TLBO are described as Charge P are the charging and discharging power at an follows. Discharge instant, Δt is a definite time, and η and η are Charge Discharge the efficiency during charging and discharging. *e SOC, 3.1. Teaching Phase. In this phase, the teacher continuously charging, and discharging limits of the storage devices are tries to improve the mean result of the class for his/her expressed as subject. *e best solution which is defined by the objective SOC ≤ SOC ≤ SOC , (6) ESS,min ESS ESS,max function is considered as the teacher in that population. *is phase starts with identifying the best solution. First, generate P (t)≤ P X(t), t �1,2, . . . T; X∈ [0,1], (7) a random population with N rows and S columns. N Charge Chargemax International Transactions on Electrical Energy Systems 5 represents the population size (number of learners in the Step 1. Initialization of Parameters class, i �1,2, . . ., N) and S represents the number of design Specify the input data of the VPP and TLBO algorithm. variables (number of subjects, j �1,2, . . ., S). *e jth variable *e VPP data includes generator bidding price, hourly utility of the ith learner is initialized randomly using grid price, load demand, and power limits of the renewable energy sources, storage devices, and distributed generation 1 min max min X � X + rand∗ X − X , (13) 􏼐 􏼑 i,j j j j units. Initialize the parameters of the TLBO algorithm, such aspopulationsize,designvariables,andstoppingcriteria.*e where rand is a uniformly distributed random number that population size corresponds to the number of students, the min max takes values between 0 and 1 and X and X represent j j numberofdesignvariablesorsubjectsofferedcorrespondsto the minimum and maximum values for the jth parameter. the number of generating units, and the stopping criterion is *e difference D between the best solution and the mean diff j chosen as the number of iterations. result of the class for the jth subject in the kth iteration is given by Step 2. Initialization of Population k k k D � rand􏼐X − T M 􏼑, (14) diff F j T,j j Generate a random population of dimension [N × S] according to the population size, N, and the number of where M is the mean result of the students for the subject j design variables, S. *e randomly generated population is and X represents the best solution for the subject j in the T,j mathematically expressed as X � [X , X , X . . . X ] , 1 2 3 N kth iteration. *e teaching factor T as given in (15) is in- where N is the number of solutions in the multidimensional dicative of the teaching ability of the teacher, depending on search space. Each solution X � [P , P , . . . , P . . . P ] is i i1 i2 ij iS which the mean result of the subject will change. Its value is represented by an S-dimensional vector, (i � 1,2,3, . . . N) selected as either 1 or 2. and (j � 1,2,3, . . . S), where S is the number of parameters T � round[1 + rand(0,1)]. (15) to be optimized. In this problem, S corresponds to the six DGs. *e elements of each solution vector (X ) represent ij *e solution for the problem is updated in each iteration the power output (P ) of distributed generation units that gi using can take values between the maximum and minimum generation limits as given in k k k X � X + D , (16) new,i,j old,i,j diff j P � P + rand(0,1)∗ 􏼐P − P 􏼑, (18) ij j, min jmax jmin where X is the new solution for the jth subject and new i,j X is the old solution for the jth subject in the previous where P and P are the minimum and maximum old i,j j min jmax iteration. If the updated solution is better than the previous power limits of each unit. For each interval in the scheduling one, it is an acceptable solution. *e accepted solution is the horizon, initialization of the population is done as given in input to the next phase. P P . . . P 11 12 1S ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ P P . . . P ⎥ ⎢ ⎥ ⎢ 21 22 2S ⎥ ⎢ ⎥ ⎢ ⎥ 3.2. Learner Phase. *is is the second phase of the algorithm ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ X � ⎢ ⎥, (19) ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⋮ ⋮ ⋱ ⋮ ⎥ in which the learners improve their knowledge through ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ mutual interaction. In this process, each learner will interact P P . . . P N1 N2 NS with other learners randomly to facilitate knowledge sharing depending on their knowledge level. *e solution to the where P is the real power output of the Sth generation unit NS problem is updated based on knowledge sharing. To rep- for the Nth individual, which should satisfy the constraint resent it mathematically, two learners are considered ran- given in (4). k k domly as X and X . *e updated solution can be (i) (r) expressed as follows. Step 3. Fitness Evaluation k k k k k ⎧ ⎪ ⎫ ⎪ Evaluate the generation cost as expressed in (1) for the X + rand × 􏼐X − X 􏼑 if 􏼐X < X 􏼑 ⎨ ⎬ i i r i r X � . (17) generated random population in (19) and calculate sum of new,i ⎪ ⎪ k k k ⎩ ⎭ th X + rand × X − X otherwise 􏼐 􏼑 the cost for all the generating units in the g iteration using i r i S � Sum􏼐X , X , . . . X 􏼑. (20) *e best solutions for the different subjects are accepted 1,j 2,j i,j at the end of this phase, and these solutions are the input for the teacher phase. Both the teacher and learner phases are repeated until the stopping criterion is met. In this work, the Step 4. Teacher Phase stopping criterion is the number of iterations. Based on the sum of the generation cost in (20), the minimum generating cost is selected as the best solution. *e best solution can be considered as a teacher as expressed in 3.3. Implementation of TLBO Algorithm for Energy Man- (21). Update the power generation matrix based on the best agement Problem. In this section, the implementation of the solution using (16). TLBO algorithm for the energy management of generating 􏼌 􏼌 􏼌 g 􏼌 units and load demand in a VPP is discussed. *e steps 􏼌 􏼌 X � X f(x) � min S 􏼁 . (21) 􏼌 􏼌 teacher involved in the implementation procedure are given below. 6 International Transactions on Electrical Energy Systems Utility grid 20 kV / 400 V Feeder 3 Feeder 1 Residential Load Commercial Load Feeder 2 14 13 9 Industrial Load 7 15 16 FC MT Wind 4 11 6 +– Battery PV Figure 2: Single-line diagram of IEEE-16-bus test system. FC 26 27 28 29 30 31 32 33 24 25 FC Battery 12 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 Utility MT 20 kV / 400 V Grid 19 20 21 22 WT 1 WT MT PV Figure 3: Single-line diagram of IEEE-33-bus test system. Step 5. Learner Phase and IEEE-33 [37] bus test systems shown in Figures 2 and 3 In this step, the best solution obtained in Step 4 is are considered in this paper. *ey comprise of wind, solar, considered as the input for the learner phase. *e solution is microturbine, and fuel cell as generating units, along with modified based on the mutual interaction among the the storage devices and loads. *e optimal load dispatch is learners and the solution matrix is updated using (17). done for 24 hours in a day, and the optimal power gener- ation is based on the utility price and the load demand at the particular hour. Programming is done in MATLAB for the Step 6. Repeat steps 3–5 until the stopping criterion is met, aforementioned problem and executed on Intel Core i7- which is the maximum number of iterations. 8550U, 8th Gen CPU @ 1.99GHz, 8.00GB RAM PC. *e power limits, bidding price, and start-up/shutdown cost of 4. Results and Discussions each generating unit for IEEE 16-bus and IEEE 33-bus test In this section, the cost minimization problem of a VPP is systems are given in Tables 1 and 2, respectively. *e load implemented using the TLBO algorithm. IEEE-16[32, 36] demand, utility market price, and forecasted power output International Transactions on Electrical Energy Systems 7 Table 1: Input data of IEEE-16-bus system. ID Type Minimum power (kW) Maximum power (kW) Bid (€ct/kWh) Start-up/shutdown cost (€ct) 1 MT 6 30 0.457 0.96 2 FC 3 30 0.294 1.65 3 PV 0 25 2.584 0 4 WT1 0 15 1.073 0 5 Battery −30 30 0.38 0 6 Utility −30 30 — 0 Table 2: Input data of IEEE-33-bus system. ID Type Minimum power (kW) Maximum power (kW) Bid (€ct/kWh) Start-up/shutdown cost (€ct) 1 MT1 6 30 0.457 0.96 2 FC1 3 30 0.294 1.65 3 PV 0 25 2.584 0 4 WT1 0 15 1.073 0 5 Battery −30 30 0.38 0 6 Utility −30 30 — 0 7 WT2 0 35 1.969 0 8 MT2 8 50 0.269 0.96 9 FC2 8 50 0.275 1.65 Table 3: Total load demand of IEEE-16-bus and IEEE-33-bus test Table 4: Utility price for IEEE 16-bus and IEEE 33-bus test systems. systems. Hr Utility price (€ct/kWh) IEEE-16-bus load 1 0.23 Hr IEEE-33-bus load demand (kW) demand (kW) 2 0.19 1 52 133.75 3 0.14 2 50 114.75 4 0.12 3 50 114.75 5 0.12 4 51 138.25 6 0.20 5 56 140.50 7 0.23 6 63 125.25 8 0.38 7 70 128.75 9 1.50 8 75 132.75 10 4.00 9 76 138.25 11 4.00 10 80 148.50 12 4.00 11 78 162.75 13 1.50 12 74 170.25 14 4.00 13 72 178.50 15 2.00 14 72 160.50 16 1.95 15 76 155.25 17 0.60 16 80 145.75 18 0.41 17 85 140.25 19 0.35 18 88 98.75 20 0.43 19 90 102.25 21 1.17 20 87 135.50 22 0.54 21 78 120.25 23 0.30 22 71 133.75 24 0.26 23 65 145.50 24 56 130.25 residential and commercial loads and 0.9 lagging for in- dustrial loads [38] for both IEEE 16- and IEEE 33-bus test [32] from PV, Wind1, and Wind2 are given in Tables 3–5, systems. *e optimization problem is solved for with and respectively. *e total load demand per day is taken as without losses for comparison purpose. In addition to the 1695kW and 3295kW for IEEE 16-bus and IEEE 33-bus test TLBO algorithm, ABC and ALO algorithms are also used in systems, respectively. *e power losses are computed using this paper to solve the problem statement and to validate the the forward-backward sweep method [33]. *e base power performance of the TLBO algorithm. and base voltage are taken as 100kVA and 400V, respec- *e parameters of the TLBO algorithm used in this tively, and the cost for the power losses is assumed as 0.19 problem are the population size, N taken as 100, maximum (€ct/kWh). *e power factor is taken as 0.85 lagging for iteration as 1000, and number of trials or runs as 20. *e 8 International Transactions on Electrical Energy Systems Table 5: Forecasted output of PV, WT1, and WT2. Hr PV (kW) WT1 (kW) WT2 (kW) 1 0 1.7850 4.165 2 0 1.7850 4.165 3 0 1.7850 4.165 4 0 1.7850 4.165 5 0 1.7850 4.165 6 0 0.9142 2.135 7 0 1.7850 4.165 8 0.1937 1.3017 3.045 9 3.7540 1.7850 4.165 10 7.5290 3.0854 7.210 11 10.4410 8.7724 20.475 12 11.9640 10.413 24.290 13 23.8930 3.9228 9.135 14 21.0490 2.3766 5.53 15 7.8647 1.7850 4.165 16 4.2208 1.3017 3.045 17 0.5389 1.7850 4.165 18 0 1.7850 4.165 19 0 1.3017 3.038 20 0 1.7850 4.165 21 0 1.3017 3.0345 22 0 1.3017 3.0345 23 0 0.9142 2.135 24 0 0.6124 1.435 Table 6: Optimal power dispatch using TLBO Case I. Hr MT (kW) FC (kW) PV (kW) WT1 (kW) Battery (kW) Utility (kW) SOC (kW) 1 6.000 16.563 0 1.7850 −2.348 30.0000 5.348 2 6.000 15.057 0 1.7850 −2.842 30.0000 8.190 3 6.000 15.654 0 1.7850 −3.439 30.0000 11.629 4 6.000 17.038 0 1.7850 −3.823 30.0000 15.452 5 6.000 22.342 0 1.7850 −4.127 30.0000 19.579 6 6.000 29.061 0 0.9142 −2.975 30.0000 22.554 7 10.709 30 0 1.7850 −2.494 30.0000 25.048 8 15.457 30 0.1937 1.3017 −1.952 30.0000 27.000 9 30.000 30 3.7540 1.7850 1.792 8.669 25.208 10 30.000 30 7.5290 3.0854 2.698 6.689 22.510 11 30.000 30 10.4410 8.7724 3.325 −4.538 19.185 12 30.000 30 11.9640 10.413 3.519 −11.896 15.666 13 30.000 30 23.8930 3.9228 1.414 −17.230 14.252 14 30.000 30 21.0490 2.3766 3.689 −15.115 10.563 15 30.000 30 7.8647 1.7850 2.384 3.966 8.179 16 30.000 30 4.2208 1.3017 1.548 12.930 6.631 17 30.000 30 0.5389 1.7850 1.468 21.208 5.163 18 24.828 30 0 1.7850 1.387 30.000 3.776 19 30.000 30 0 1.3017 −1.302 30.000 5.078 20 24.569 30 0 1.7850 0.646 30.000 4.432 21 30.000 30 0 1.3017 0.928 15.770 3.504 22 30.000 30 0 1.3017 0.501 9.197 3.003 23 6.000 30 0 0.9142 −1.154 29.240 4.157 24 6.000 20.715 0 0.6124 −1.327 30.0000 5.484 same parameters are used for ABC and ALO algorithms for utility grid. Whenever the bidding price of the DGs in the comparison. Four different cases are considered, and the VPP is less than that of the utility price, the generated VPP results are discussed in this section. power is used to meet the load demand. Also, the excess Power is exchanged between the VPP and the grid, based power generated and the energy stored in the storage devices on the bidding price of the generation units and that of the (discharging mode) are sold to the utility grid. If the bidding International Transactions on Electrical Energy Systems 9 0 4 8 12 16 20 24 –10 –20 Time in hour MT(kW) FC(kW) PV(kW) WT(kW) Battery(kW) Utility(kW) Figure 4: Optimal schedule of DGs and the utility–Case I. 0 4 8 12162024 Time (Hr) Figure 5: State of charge of battery–Case I. Table 7: Comparison of the total cost—Case I. Method Best solution (€ct) Worst solution (€ct) Mean (€ct) Simulation time (s) Without losses ABC 768.9008 773.4415 769.0444 7.998 ALO 767.6991 772.4553 767.8516 7.584 TLBO 765.2968 771.6939 765.4500 6.341 With losses ABC 761.9520 766.4927 762.0956 8.214 ALO 760.7503 765.5065 760.9028 7.982 TLBO 758.3480 764.7451 758.5042 6.587 price of the VPP is greater than that of the utility price, the power is bought from the utility grid and the same is stored in the storage devices (charging mode). In general, the power generated by the PV and wind is utilized based on their maximum availability. FC and MT are operated throughout the day because of lower bid costs. 4.1. Case I. In this case, all the generating units in the VPP 759 are in operation and they operate within their power limits. 758 *e VPP is connected to the utility grid. *e maximum 0 200 400 600 800 1000 power which can be exchanged between the VPP and the No.of Iterations utility grid is restricted to 30kW. All the DGs except PV are ABC in ON condition throughout the 24 hours. *e initial SOC of TLBO the storage device is taken as 3kW (i.e., 10% of the maxi- ALO mum capacity). *e optimal power dispatch for 24 hours of the day using the TLBO algorithm is given in Table 6. Each Figure 6: Comparison of convergence characteristics for Case I. Output Power (kW) Power (kW) Cost (€ct) 10 International Transactions on Electrical Energy Systems Table 8: Optimal power dispatch using TLBO algorithm—Case II. Hr MT (kW) FC (kW) PV (kW) WT1 (kW) Battery (kW) Utility (kW) SOC (kW) 1 6.000 3 0 1.7850 −2.213 43.428 5.213 2 6.000 3 0 1.7850 −2.742 41.957 7.955 3 6.000 3 0 1.7850 −3.514 42.729 11.469 4 6.000 3 0 1.7850 −3.867 44.082 15.336 5 6.000 3 0 1.7850 −4.315 49.53 19.651 6 6.000 3 0 0.9142 −2.813 55.899 22.464 7 6.000 3 0 1.7850 −2.584 61.799 25.048 8 6.000 30 0.1937 1.3017 −1.952 39.456 27.000 9 30.000 30 3.7540 1.7850 1.592 8.869 25.408 10 29.999 30 7.5290 3.0854 2.986 6.4007 22.422 11 29.999 30 10.4410 8.7724 3.821 −5.0344 18.601 12 29.990 30 11.9640 10.413 3.519 −11.8963 15.082 13 29.999 30 23.8930 3.9228 1.214 −17.0298 13.868 14 29.992 30 21.0490 2.3766 3.689 −15.1146 10.179 15 30.000 30 7.8647 1.7850 2.464 3.8863 7.715 16 29.999 30 4.2208 1.3017 1.548 12.9295 6.167 17 30.000 30 0.5389 1.7850 1.068 21.6081 5.099 18 25.128 30 0 1.7850 1.397 48.818 3.702 19 30.000 30 0 1.3017 −1.3017 54 5.004 20 26.538 30 0 1.7850 0.646 48.569 4.358 21 30.000 30 0 1.3017 0.839 15.8593 3.519 22 29.998 30 0 1.3017 0.519 9.1793 3.000 23 6.000 30 0 0.9142 −1.124 29.2098 4.124 24 6.000 3 0 0.6124 −1.243 47.6306 5.367 unit is optimally operated based on its bidding price and the load demand. During the first eight hours of the day, the bid cost of the utility is lesser than that of any of the DGs (except FC) in the VPP. *ereby, 30kW of power is purchased from the utility grid and the remaining load demand is supplied by the DGs in the VPP as shown in Figure 4. For instance, at the 8th 10 hour, the demand is 75kW. So, 30kW is purchased from the 0 0 4 8 12 16 20 24 –10 utility and the remaining 45kW is supplied by the DGs in –20 the VPP. As FC has the lowest bid cost, it supplies its –30 maximum capacity of 30kW, and the remaining 10kW is Time in hour supplied by PV, wind, MT, and battery. MT(kW) FC(kW) Also, the load demand is less during the first eight hours PV(kW) WT(kW) and thereby, the excess power generated in the VPP is stored Battery(kW) Utility(kW) in the battery. *e SOC of the battery is plotted in Figure 5. Figure 7: Optimal schedule of DGs and the utility—Case II. At the end of the 8th hour, the battery is charged to 90% of its maximum capacity (27kW). After the 8th hour, it can be observed that the utility grid price is higher than that of the other DGs (except PV) in the VPP. *e demand is also higher. Now, the local demand in the VPP is met by the DGs and the excess power generated is exported to the utility. *e battery is in discharging mode to meet the excess load demand. It is also observed from Figure 5 that at the end of the 18th hour of the day, the battery is discharged to 10% of its maximum capacity (3.776kW). For instance, at the 18th hour, the load demand is 88kW. *e available wind power is 1.7085kW, battery power of 1.387kW, and microturbine power of 24.828kW are used to 0 4 8 12162024 meet the demand along with the utility power and fuel cell Time in hour power of 30kW each. *ere is no PV power availability from the 18th hour. During these hours, the load demand in the Figure 8: State of charge of the battery—Case II. Output Power (kW) Power (kW) International Transactions on Electrical Energy Systems 11 Table 9: Comparison of the total cost—Case II. Method Best solution (€ct) Worst solution (€ct) Mean (€ct) Simulation time (s) Without losses ABC 748.8728 755.2788 749.1978 7.982 ALO 745.6808 756.0728 746.2068 7.245 TLBO 742.5108 753.2698 742.7778 6.153 With losses ABC 741.924 748.330 742.249 8.124 ALO 738.732 749.124 739.258 7.845 TLBO 735.562 746.321 735.829 6.524 VPP is met with the other sources based on their bidding price. During the last two hours of the day, the power de- mand is less and the excess power is stored in the battery. At 748 the end of the day, the SOC of the battery for Case I is 5.484kW. *e operating cost of VPP (with losses) for the Case I is obtained using the TLBO method and is compared with other metaheuristic techniques and is given in Table 7. It is evident from the results that TLBO is superior to other methods as it provides the minimum cost of €ct 758.348 for without losses and €ct 765.2968 for with losses. *e com- parison of convergence characteristics for the optimal op- 0 200 400 600 800 1000 erating cost for Case I is illustrated in Figure 6. It is observed No.of Iterations that the optimal solution is obtained within 100 iterations ABC when compared to the ABC and ALO methods. From Ta- TLBO ble 7, it can be observed that the time taken for the con- ALO vergence of optimal solution using the TLBO algorithm is Figure 9: Comparison of convergence characteristics—Case II. 6.587s, which is lesser than that of the other methods. 4.2. Case II. In this case, the DGs operate within their power the available power generation from the wind is utilized to limits and there is no restriction on the power exchange meet the load demand. Since the utility price is more than between the utility grid and the VPP. All the DGs are in ON the bidding price of MT and FC, these units are operating with their maximum capacity to meet the load demand. condition throughout the 24-hour time period except for PV. *e initial SOC of the storage device is 3kW, which is 10% of From the 18th to the 20th hours of the day, the load demand the maximum battery capacity. *e optimal power dispatch is high (peak load). During this period, PV power is not for 24 hours of the day using the TLBO algorithm is shown in available and also wind power availability is less. As the bid Table 8. In Figure 7, it is observed that for the first 7 hours of cost of fuel cell power is less, it is operated at its maximum the day, the utility grid price is low compared with the capacity. In addition, the utility power price is also less and bidding price of the DGs in the VPP. Hence, energy is thereby power is purchased from the utility. Power is also purchased from the utility grid without any restriction to stored in the storage devices during this interval. meet the load demand of VPP. *e power output from the *ediscussionsmadeforthe18thto20thhoursarevalidfor PV and wind turbine are used as per the availability. All other the23rdand24thhoursalso.Duringthe20thand22ndhoursof units of VPP are operating with minimum capacity due to the day, as the utility price is more than that of VPP, power is soldfromtheVPPtotheutilitygrid.Alltheunitsareoperating their higher bidding price compared to the utility price. During the first 8 hours, the load demand is less. with maximum capacity and the battery is also supplying the *erefore, the excess power is stored in the battery. At the power. On the 22nd hour, the battery has discharged to 3kW end of the 8th hour, the battery is charged to 90% of its (10%ofitsmaximumcapacity)asshowninFigure8.Duringthe maximum capacity (27kW) and is shown in Figure 8. *e last two hours of the day, the power demand is less and the load demand increases from the 9th hour of the day. *e excess power is stored in the battery. At the end of the day, the utility price is higher than that of the VPP bidding price from SOC of the battery for Case II is 5.367kW. the 9th to the 18th hour of the day. *ereby, power is sold to *e operating cost (with losses) for Case II using the the utility grid without any restrictions. *e battery is in TLBO algorithm is shown in Table 9 and is compared with discharging mode to meet the load demand. *e SOC of the the other metaheuristic techniques like ABC and ALO. From battery will change depending on the load demand and the Table 9, it is noticed that TLBO is better than other tech- niques in terms of convergence time and operating cost. *e bid cost. *e battery is discharged to 3.702kW (10% of its maximum capacity). During the 9th to 18th hour of the day, convergence graph for Case II is shown in Figure 9. It is Cost (€ct) 12 International Transactions on Electrical Energy Systems Table 10: Optimal power dispatch using TLBO algorithm—Case III. Hr Unit On/Off status MT (kW) FC (kW) PV (kW) WT1 (kW) Battery (kW) Utility (kW) SOC (kW) 1 010111 0 29.383 0 1.7850 −2.481 23.313 5.481 2 010111 0 26.241 0 1.7850 −3.042 25.016 8.523 3 110111 6.001 15.340 0 1.7850 −3.125 30.000 11.648 4 110111 6.003 17.232 0 1.7850 −4.018 29.999 15.666 5 010111 0 29.209 0 1.7850 −4.127 29.132 19.793 6 110111 6.000 28.999 0 0.9142 −2.912 29.999 22.705 7 110111 10.459 30 0 1.7850 −2.243 29.999 24.948 8 111111 15.557 30 0.194 1.3017 −2.052 30.000 27.000 9 111111 30.000 29.998 3.754 1.7850 1.568 8.895 25.432 10 111111 29.991 29.998 7.529 3.0854 2.995 6.403 22.437 11 111111 30.000 29.974 10.441 8.7724 3.448 −4.636 18.989 12 111111 29.999 29.997 11.964 10.413 4.212 −12.585 14.777 13 111111 29.962 29.999 23.893 3.9228 1.617 −17.393 13.160 14 111111 29.999 29.988 21.049 2.3766 3.571 −14.984 9.589 15 111111 29.996 29.999 7.8647 1.7850 2.786 3.609 6.803 16 111111 30.000 30 4.2208 1.3017 1.353 13.125 5.450 17 111111 30.000 30 0.5389 1.7850 1.363 21.313 4.087 18 110111 25.128 30 0 1.7850 1.087 30.000 3.000 19 110111 30.000 30 0 1.3017 −1.302 30.000 4.302 20 110111 26.414 30 0 1.7850 −1.198 30.000 5.500 21 110111 30.000 30 0 1.3017 1.288 15.411 4.212 22 110111 30.000 30.000 0 1.3017 1.211 8.488 3.001 23 110111 6.000 29.997 0 0.9142 −1.254 29.343 4.255 24 010111 0 29.448 0 0.6124 −1.927 27.868 6.182 evident from the characteristics that TLBO is faster than the other two methods. *e convergence time for this problem using TLBO is 6.524s. 0 4 8 12 16 20 24 4.3. Case III. In this case, all the generating units in the VPP –10 can switch between the ON/OFF modes and they operate –20 Time in hour within their power limits. *e initial SOC of the storage device is 3kW. *e VPP is connected to the utility grid. *e MT(kW) FC(kW) maximum power that can be exchanged between the VPP PV(kW) WT(kW) and the utility grid is restricted to 30kW. Battery(kW) Utility(kW) *e optimal power dispatch for 24 hours of the day using Figure 10: Optimal schedule of DGs and the utility—Case III. the TLBO algorithm is presented in Table 10. *e ON and OFF states of the MT, FC, PV, WT1, battery, and utility are represented by 1 and 0, respectively. From Figure 10, it is evident that, for the first 8 hours of the day, the utility grid price is low compared with the VPP bidding price. Hence, power is purchased from the utility grid to meet the load demand of VPP and the storage device is in charging mode. At the end of the 8th hour, the battery is charged to 90% of the maximum capacity; that is, the SOC is 27kW as depicted in Figure 11. During this period, the power output from the PV is zero. *e bidding price of FC is less compared to all the other units of VPP. Hence, FC is operating at its maximum capacity during this period. 0 4 8 12162024 Time in hour *e utility price is higher than that of the VPP bidding price from the 9th to 18th hours of the day. *ereby, the Figure 11: State of charge of the battery—Case III. power is sold to the utility grid by discharging the storage devices. *e battery is in discharging mode and discharged to 10% of its maximum capacity (i.e., 3.5kW during the 18th From the 19th and 20th hours of the day, the load hour as shown in the SOC plot in Figure 11). During this demand is high (peak load). During this period, the bidding duration, the power generation from the RES (PV and wind) price of FC is less and is operating with its maximum ca- are utilized as per the availability. pacity. Since the utility price is less compared to the VPP Output Power (kW) Power (kW) International Transactions on Electrical Energy Systems 13 Table 11: Comparison of the total cost—Case III. Best Method Worst solution (€ct) Mean (€ct) Simulation time (s) solution (€ct) Without losses ABC 766.4057 780.2791 767.0253 7.840 ALO 761.3383 779.1642 762.0748 7.568 TLBO 758.6558 777.9809 759.1309 6.548 With losses ABC 759.4569 773.3303 760.0765 8.012 ALO 754.3895 772.2154 755.1260 7.812 TLBO 751.707 771.0321 752.1821 6.987 bidding price, the grid power along with the power gen- 775 erated from the VPP is used to meet the peak load. Also, the storage device is in discharging mode. During the 21st and 22nd hours of the day, as the utility price is more than that of VPP, the power from VPP is sold to the utility grid. Since the bidding price of FC and MTis less compared with that of the utility price, these units are operating at their maximum capacity. *e battery is in discharging mode and discharged to 10% of maximum capacity (i.e., 3.122kW during the 18th hour as shown in the SOC plot in Figure 11). During the 23rd and 24th hours of the day, the utility price is less than that of VPP, so power is purchased from the utility to VPP 0 200 400 600 800 1000 and stored in the storage devices (charging mode). During No.of Iterations the last two hours of the day, the power demand is less and ABC the excess power is stored in the battery. *e operating cost TLBO (with losses) using the TLBO algorithm for Case III is ALO compared with the other metaheuristic techniques and is Figure 12: Comparison of convergence characteristics—Case III. given in Table 11. Minimum operating cost is obtained using the TLBO algorithm when compared with other methods. *e convergence characteristics with respect to the number *erefore 30kW of power is purchased from the utility, of iterations is plotted in Figure 12. It is observed that the while the remaining 98.75kW is supplied by the VPP units. optimal solution is obtained in minimum time and less As MT2 has the lowest bid cost, it supplies its maximum number of iterations using the TLBO algorithm. *e time capacity of 50kW and the remaining 48.75kW is supplied by taken for the convergence using the TLBO algorithm is other units. During the first 8 hours, the load demand is less. 6.987s. *erefore, the excess power is stored in the battery. *e SOC of the battery is plotted in Figure 14. At the end of the 8th 4.4. Case IV. In this case, the IEEE-33 bus test system is hour, the SOC of the battery is 90% of its maximum capacity considered. All the generating units of VPP are in ON (27.03kW) as displayed in Figure 14. condition and operating within their respective power limits. In general, the power generated by PV and wind is *e maximum amount of power that can be transferred utilized based on their maximum availability. MT2 is op- between the VPP and the utility grid is considered as 30kW. erated with its maximum capacity throughout the day be- *roughout the day, all DGs are available to meet the load cause of the lower bid cost. After the 7th hour, it can be observed that the utility grid price is more compared to the demand, except PV. *e initial SOC of the battery is as- sumed to be 3kW, which is 10% of its maximum capacity. other DG units in the VPP. *e demand is also higher. Now, *e optimal power dispatch for 24 hours of the day using the the local demand in the VPP is met by the DGs and the TLBO algorithm is shown in Table 12. Each unit is operated excess power generated is exported to the utility. From the within its capacity based on its bidding price and load 8th to 22nd hours of the day, FC1, MT2, and FC2 have lesser demand. Furthermore, power is transferred between the bid cost compared to the utility grid. Hence, these units are VPP and the utility grid based on the bidding price. operating at their maximum capacity during this period. *e From Figure 13, it can be observed that, during the first battery is in discharging mode to meet the excess load seven hours of the day, the bid cost of the utility is lesser than demand. It is also observed from Figure 14 that at the end of that of any of the DGs in VPP. As a result, 30kW of power is the 22nd hour of the day, the battery is discharged to 10% of bought from the utility grid and the remaining load demand its maximum capacity (3.071kW). For instance, at the 22nd hour, the load demand is 133.75kW. To meet this demand, is supplied by the DGs in the VPP based on their bid cost. For instance, at the 7th hour, the demand is 128.75kW. 4.337kW total available power from the RES, battery power Cost (€ct) 14 International Transactions on Electrical Energy Systems Table 12: Optimal power dispatch using TLBO algorithm—Case IV. Hr MT1 (kW) FC1 (kW) PV (kW) WT1 (kW) WT2 (kW) MT2 (kW) FC2 (kW) Bat (kW) Utility (kW) SOC (kW) 1 6 3 0 1.785 4.165 50 40.998 −2.198 30 5.198 2 6 3 0 1.785 4.165 50 22.767 −2.967 30 8.165 3 6 3 0 1.785 4.165 50 23.050 −3.250 30 11.415 4 6 3 0 1.785 4.165 50 47.123 −3.823 30 15.238 5 6 3.302 0 1.785 4.165 50 50.000 −4.752 30 19.99 6 6 3 0 0.914 2.135 50 35.946 −2.745 30 22.735 7 6 3 0 1.785 4.165 50 35.943 −2.143 30 24.878 8 6 30 0.194 1.302 3.045 50 50 −2.152 −5.638 27.03 9 26.888 30 3.754 1.785 4.165 50 50 1.658 −30 25.372 10 27.831 30 7.528 3.085 7.210 50 50 2.846 −30 22.526 11 19.794 30 10.441 8.772 20.475 50 50 3.268 −30 19.258 12 19.602 30 11.964 10.413 24.290 50 50 3.981 −30 15.277 13 30 30 23.893 3.923 9.135 50 50 1.864 −20.315 13.413 14 28.087 30 21.049 2.377 5.530 50 50 3.457 −30 9.956 15 30 30 7.865 1.785 4.165 50 50 2.876 −21.441 7.08 16 30 30 4.221 1.302 3.045 50 50 1.765 −24.583 5.315 17 30 30 0.539 1.785 4.165 50 50 1.212 −27.451 4.103 18 6 15.813 0 1.785 4.165 50 50 0.987 −30 3.116 19 6 24.755 0 1.302 3.038 50 50 −2.845 −30 5.961 20 6 30 0 1.785 4.165 50 50 0.885 −7.335 5.076 21 14.893 30 0 1.302 3.035 50 50 1.021 −30 4.055 22 28.430 30 0 1.302 3.035 50 50 0.984 −30 3.071 23 6 30 0 0.914 2.135 50 50 −1.216 7.667 4.287 24 6 3 0 0.612 1.435 50 40.715 −1.512 30 5.799 of 0.984kW, and 128.429kW of power from the other DGs are used and the excess power of 30kW is transferred to the utility grid during this hour. During the 23rd and 24th hours of the day, based on the utility price and power demand, DGs are operated and power is purchased from the utility to VPP. *e excess power generated in the VPP is stored in the 1 5 9 13 17 21 storage devices (charging mode). At the end of the day, the –10 SOC of the battery for Case IV is 5.799kW. –20 –30 *e operating cost (with losses) of VPP for Case IV –40 obtained using the TLBO method is compared with other Time in hour metaheuristic techniques and is given in Table 13. It is MT1(kW) Battery(kW) evident from the results that TLBO is superior to other WT1(kW) PV(kW) methods as it provides the minimum cost of €ct 797.0170 for FC2(kW) MT2(kW) without losses and €ct 780.5115 including losses. FC1(kW) Utility(kW) *e comparison of convergence characteristics for the WT2(kW) optimal operating cost for Case IV is illustrated in Figure 15. Figure 13: Optimal schedule of DGs and the utility—Case IV. It is observed that the optimal solution is obtained within 100 iterations when compared to the ABC and ALO methods. From Table 13, it can be observed that the time taken for the convergence of optimal solution using the TLBO algorithm is 30 7.895sec, which is lesser than the other methods. *rough the optimal dispatch of power from all the units of VPP using the TLBO algorithm, minimum generation cost is achieved. For the validation of the proposed meth- 15 odology, four different cases are considered for 2 different test systems and the total generation cost is computed and compared in Table 14. It is evident that, among the three cases for IEEE 16-bus system, Case II is more economical. *is is due to the unlimited power exchange option between 0 4 8 12162024 the VPP and the utility grid, wherein the low utility price Time (Hr) during off-peak hours is favorable for VPP to purchase Figure 14: State of charge of the battery—case IV. utility power and thereby minimize the generation cost. Power (kW) Output Power (kW) International Transactions on Electrical Energy Systems 15 Table 13: Comparison of the total cost—Case IV. Method Best solution (€ct) Worst solution (€ct) Mean (€ct) Simulation time (s) Without losses ABC 816.1944 845.6475 817.6637 9.987 ALO 805.5950 834.8358 806.9115 8.158 TLBO 797.0170 827.5376 797.5635 7.248 With losses ABC 799.6889 829.1420 801.1582 10.027 ALO 789.0895 818.3303 790.4060 8.954 TLBO 780.5115 811.0321 781.0580 7.895 0 200 400 600 800 1000 No.of Iteration ABC ALO TLBO Figure 15: Comparison of convergence characteristics—Case IV. Table 14: Comparison of the total generation cost—with losses. IEEE 16-bus system IEEE 33-bus system Cases Case I Case II Case III Case IV Generation cost (€ct) 758.348 735.562 751.707 780.511 In Case I, the maximum power exchange between the 5. Conclusion utility grid and the VPP is limited to 30 kW. All the units In this paper, the optimal energy management problem of of VPP including RES are in ON state in this case. VPP is formulated and implemented using the TLBO al- *erefore, the generation cost is higher than in the other 2 gorithm for 24 hours of the day. To evaluate the performance cases. In Case III, the maximum power exchange between of this optimization algorithm, four different cases are the utility grid and the VPP is limited to 30 kW. In ad- considered. *e power is exchanged between the utility grid dition to that, all the units of VPP are operating in an ON/ and the VPP based on their bidding price in all four cases. It OFF state based on the corresponding bidding price and is evident from the analysis that the operational cost of VPP start-up/shutdown cost. *erefore, the generation cost is is minimized by optimally scheduling the generation of each higher than that of Case II. It is observed from the unit of VPP. It is found that the cases with unlimited power abovementioned case studies that the generation cost of exchange between the utility grid and the VPP is more cases with limited power exchange between the utility grid economical compared to the cases with limited power ex- and the VPP is higher compared with the cases with change. Also, Case II is more feasible as it utilized the RES to unlimited power exchange. Case II is the most economical the maximum extent in spite of the higher bidding price to and feasible mode of operation. 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Optimal Energy Management of Virtual Power Plants with Storage Devices Using Teaching-and-Learning-Based Optimization Algorithm

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Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 1727524, 17 pages https://doi.org/10.1155/2022/1727524 Research Article OptimalEnergyManagementofVirtualPowerPlantswithStorage Devices Using Teaching-and-Learning-Based Optimization Algorithm Raji Krishna and S. Hemamalini School of Electrical Engineering, Vellore Institute of Technology, Chennai, Tamil Nadu 600127, India Correspondence should be addressed to S. Hemamalini; hemamalini.s@vit.ac.in Received 6 January 2022; Revised 29 May 2022; Accepted 15 June 2022; Published 29 August 2022 Academic Editor: Jaouher Ben Ali Copyright © 2022 Raji Krishna and S. Hemamalini. *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. In recent decades, Renewable Energy Sources (RES) have become more attractive due to the depleting fossil fuel resources and environmental issues such as global warming due to emissions from fossil fuel-based power plants. However, the intermittent nature of RES may cause a power imbalance between the generation and the demand. *e power imbalance is overcome with the help of Distributed Generators (DG), storage devices, and RES. *e aggregation of DGs, storage devices, and controllable loads that form a single virtual entity is called a Virtual Power Plant (VPP). In this article, the optimal scheduling of DGs in a VPP is done to minimize the generation cost. *e optimal scheduling of power is done by exchanging the power between the utility grid and the VPP with the help of storage devices based on the bidding price. In this work, the state of charge (SOC) of the batteries is also considered, which is a limiting factor for charging and discharging of the batteries. *is improves the lifetime of the batteries and their performance. Energy management of VPP using the teaching-and-learning-based optimization algorithm (TLBO) is proposed to minimize the total operating cost of VPP for 24 hours of the day. *e power loss in the VPP is also considered in this work. *e proposed methodology is validated for the IEEE 16-bus and IEEE 33-bus test systems for four different cases. *e results are compared with other evolutionary algorithms, like Artificial Bee Colony (ABC) algorithm and Ant Lion Optimization (ALO) algorithm. solutions [2] to enhance power quality and reliability. VPP is 1. Introduction a small, single imaginary power plant consisting of distrib- An increase in power demand and restrictions imposed on uted generators (DGs), energy storage devices, and con- fossil fuel usage to reduce power plant emissions have made trollable loads along with information and communication utilities look for alternate sources. Also, power distribution technologies that plan, monitor the operation and coordinate to remote locations is still a problem due to technical and the power flow between the components. Distributed gen- financial issues. To mitigate these problems, distributed erators consist of clean energy sources such as photovoltaic generators like wind, solar, fuel cells, and so on are used. *e (PV), wind, Micro Turbines (MT), Fuel Cells (FC), diesel government also announces useful schemes and policies generators, and Combined Heat Power Plants (CHPP). In such as Renewable Portfolio Standards (RPS) and different VPP, the storage devices (battery, electric vehicle, and bat- kinds of subsidies at different levels to encourage the usage of tery-based robots) play a major role in energy exchange renewable energy sources for power generation. *e global between the utility grid and VPP [3]. *ere are two types of VPP: commercial VPP and technical VPP. VPPs minimize power generation [1] using wind and solar energy has in- creased to 743GW and 874GW at the end of 2021, with an the generation costs, minimize emissions, maximize profit, 8% growth in renewable capacity. and enhance the trade in the electricity market. One of the Consumers need electrical energy at a cheaper cost, with main advantages of VPP is the integration of RES, which high reliability and high quality. VPP is one of the remarkable helps to reduce the deviation from the predicted generation 2 International Transactions on Electrical Energy Systems Energy storage devices play a vital role in maintaining the of electricity and associated penalties. *e other advantage is the integration of EVs, which can act as a storage device in the power balance in a VPP by selling or buying the power from the VPP [20]. Energy storage devices, like fuel cells and power system [4]. Even though RES helps to reduce the emission, RES is batteries, supply power to additional or instantaneous loads. not sufficient to meet the power demand and may fail to Regulation of SOC of battery is an important aspect to maintain the power balance between the generation and the enhance the proper power flow between the utility grid and load demand during peak hours. *is problem can be the VPP. A fuzzy-based control strategy [21] is applied for the overcome in VPPs, wherein the power generation from regulation of SOC and for controlling the power flow during other distributed resources and storage devices along with excess and insufficient conditions. *e concept of electric vehicles (EVs) to store energy to overcome the intermittent power generated from RES maintains the power balance [3]. During peak load, VPP can support the grid by supplying its supply of energy from the wind farms is discussed in [22]. *e metaheuristic techniques reduce computational reserves. Likewise, when the pricing of utility power is lesser than that of the VPP, VPP buys power from the utility grid. time compared with conventional methods [23]. Dimeas and Hatziargyriou used Multiagent System- (MAS-) based Optimal scheduling of each unit in a VPP is thereby im- portant for the economical operation. Various optimization control [24] for the optimal and effective control of a VPP. It techniques are used for the optimal operation of VPP [5, 6]. is claimed that in centralized systems, MAS provides a better For proper functioning of VPP, the Energy Management solution, but not an optimal solution. De Filippo et al. in- System (EMS) is responsible for controlling the flow of troduced a two-stage optimization model [25] for a VPP power between the generating units, controllable loads, and EMS, which decides the optimal planning of power flows for the storage devices. *ere are various challenges associated each time step at minimum cost. In this two-stage model, in the first stage, the prediction of uncertainty is modeled using with EMS of VPP, such as uncertainty of Renewable Energy Sources (RES), market price, power balancing, and inte- a robust approach to optimize the load demand shift and estimate the cost. In the second stage, an online greedy gration of all the units in VPP [7, 8]. Energy management in a VPP is done by replacing the optimization algorithm is implemented within the simulator that uses the optimal shift produced in the first stage to diesel generators with RESs and energy storage devices [9]. *e proper balance between the power generation and the minimize the operating cost. However, there is a loss of load demand is essential to avoid the instability problems in quality in the solution because of the greedy algorithm used the VPP operation. DG, being the peak load provider during in the second step. peak hours, helps to maintain the power balance between *e minimization of the total cost and thereby max- power generation and consumption [10]. *e penetration of imation of the profit is the major concept associated with various DGs, especially the RES, will bring more uncer- VPP. Profit maximization of VPP in a day-ahead market taking into account the uncertainty of RES is proposed [26]. tainties in the power system operation. Various mathe- matical methods are used in the literature to model the *e bidding strategy for a VPP is formulated as an opti- mization problem to maximize the profit using MILP. To uncertainty of RES. A Probabilistic Load Flow (PLF) using the unscented transformation (UT) method is introduced in reduce the operating cost while maintaining energy balance, [11] to analyze the system performance. *e increased system security, and system voltage level, a two-stage sto- utilization of PEVs along with the high penetration of RES chastic optimization model is introduced to address the will affect the optimal operation of the distribution feeder uncertainties in the wind power outputs and electricity reconfiguration (DFR) strategy in the smart grids. To mit- prices [27]. Results validated the reduction in operating costs igate this problem and to increase the efficiency of the while maintaining system reliability. An economic dispatch system, the V2G concept is proposed and the uncertainty of of VPP modeled using mixed-integer programming is RES is modeled with the UT method [12]. *e robust op- presented in [28]. Bilevel mathematical programming used to model the bidding strategy is proposed [29] to maximize timization model is used for calculating the generation cost of VPP on an hourly basis that is proposed in [13–16] while the profit and minimize the emission of VPPs. Computa- tional intelligence- (CI-) based metaheuristic techniques considering the uncertainty of PV and wind. A two-stage Stackelberg game is proposed for the day-ahead energy [30] are increasingly used for profit maximization in VPPs. management of VPP considering the uncertainty of RES and A trading model [31] of a VPP in a unified market is market price [17]. A combination of Stochastic Program- proposed and solved using the fruit fly algorithm (FFA) to ming and Adaptive Robust Optimization (ARO) based maximize the profit. approach is proposed to model the uncertainty of market However, most of these optimization techniques require price [18]. Integration of Electric vehicles (EVs) is a new algorithm parameters that need to be tuned to improve the performance of the techniques. Also, CI-based metaheuristic trend for power balancing in VPP. Integrating more and more uncertain sources of energy such as PV, wind, and methods are not efficient to handle uncertainty in real-time situations. All these disadvantages can be overcome using energy storage devices makes the system highly dynamic. *ereby, to maximize the profit of a VPP, Hybrid Levy the TLBO algorithm. In addition, the TLBO algorithm does not require any parameter to be tuned, which makes the Particle Swarm Variable Neighborhood Search Optimiza- tion (HL-PS-VNSO) [19] is suggested. *e uncertainties due implementation of TLBO much simpler. to plug-in-electric vehicles (PHEVs) in G2V (additional load In this paper, minimization of the operational cost of a to the grid) and market price are also considered. commercial VPP for 24 hours in a day is formulated as the International Transactions on Electrical Energy Systems 3 optimization problem. Power losses are also taken into VPP account. *e VPP consists of solar, wind, MT, FC, and FC MT battery as energy sources. VPP can supply or buy power from the utility grid depending upon the cost of power generation and load demand in the VPP and the utility price. Utility Grid *ough there are many techniques available in the literature Load Battery to solve this problem, in this paper, the TLBO algorithm is EMS used to solve the cost minimization problem by considering WT 4 different scenarios. Since the operating cost of RES is less PV compared to other generating units in the VPP, power output from the RES is utilized to the maximum. *e op- timal dispatch of generating units considering the power losses in the distribution system is done using backward- Figure 1: A virtual power plant (VPP) connected to a utility grid. forward sweep load flow analysis. SOC of batteries is also taken into account, which enhances the battery life and its performance. *is paper is organized as follows. In Section 2, the basic 2.1. Problem Formulation. *e main objective of the pro- structure of EMS for VPP, problem formulation, and the posed work is the optimal allocation of generating units and related constraints are discussed. An overview of the TLBO the storage devices to minimize the operational cost of VPP algorithm is presented in Section 3. In Section 4, the in 24 hours of a day using the TLBO algorithm. In addition, implementation of the TLBO algorithm for energy man- the operating limits of the storage device, say the battery, are agement in VPP is presented. Section 5 discusses the sim- also considered in this work. *e SOC of the battery is set to ulation results of 4 different cases and their comparison with operate in the range of 10% to 90% of the battery capacity. ABC and ALO algorithms. Finally, the conclusion and future *is will improve the performance and lifetime of the scope are discussed in Section 6. storage device. Depending upon the load demand and the price of generation, power can either be sold or purchased 2. Optimal Energy Management of Virtual from the main grid. Considering the hourly basis of usage, if Power Plants the per-unit cost of the utility grid is less than the cost of VPP power, buying the power from the utility grid is economical. *e objective of a VPP is to relieve the load on the grid by *e power bought from the utility grid is also stored in the smartly distributing the power generated by the individual storage devices. On the other hand, if the utility price is units during peak load. A VPP and its components con- more, then power from the VPP is sold to the utility. *e nected to a utility grid is represented in Figure 1. *e main objective function of the VPP is formulated to include the functionality of the EMS is to ensure proper power exchange cost of power purchase from the utility grid, the fuel cost of between the utility grid and the VPP through proper co- the DGs and storage devices, and the start-up/shutdown cost ordination between the DGs and the grid. Energy is ex- of the power sources in the VPP [32]. In addition, the cost of changed between the VPP and utility grid and thereby power losses is also taken into account. Power losses are trading is done. *is in turn can minimize the total operating calculated using the forward-backward sweep method [33]. cost or maximize the profit of a VPP. *e EMS continuously *e objective function for the problem statement monitors the status of each unit and sends suitable control mentioned above is given as follows. signals to control the operation of DGs, energy storage devices, and controllable loads in an economical manner. t t t t t t ⎧ ⎪ P × U × C + P × U × C + ⎫ ⎪ WT WT WT PV PV PV ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ t t t t t t ⎪ ⎪ ⎪ ⎪ P × U × C + P × U × C ⎪ ⎪ FC FC FC MT MT MT ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ g ⎪ ⎨ ⎬ t t−1 t t t Min(f(X)) � 􏽘 + 􏽘 S 􏼐U − U 􏼑 + U × P × C , (1) Gi i i ESS ESS ESS ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ t�1 i�1 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ s ⎪ ⎪ ⎪ ⎪ t t−1 t t t t ⎪ ⎪ ⎪ + 􏽘 S 􏼐U − U 􏼑 + P × C − P × C ⎪ ⎪ sj j j Grid Grid Losses Losses ⎩ ⎭ j�1 P + jQ i i I � 􏼠 􏼡 , (2) where P � 􏽐 (I ) R . Losses k k k�1 i 4 International Transactions on Electrical Energy Systems where I is the current flow in the kth branch, R is the k k P (t)≤ P ∗ Y(t), t �1,2, . . . T; X∈ [0,1], Discharge Dischargemax resistance of the kth branch, and M is the number of feeder t t t t t t (8) sections/branches. P , P , P , P , P , P ,and PV WT FC MT ESS Grid P are the available power from the PV, wind, turbine, Losses where SOC and SOC are the minimum and ESS,min ESS,max fuel cell, microturbine, storage devices, utility grid, and maximum state of charge of the storage device. *e dis- t t t t t power losses, respectively.C , C , C , C , C , and PV WT FC MT ESS charge efficiency is given as C are the bidding price of the PV, wind turbine, fuel cell, Grid microturbine, storage devices, and utility grid, respectively. η � . (9) Discharge C is the cost incurred towards the power losses. *e Charge Losses ON/OFF status of all the corresponding units is represented t t t t t *e storage devices cannot charge and discharge at the by U , U , U , U , and U . *e start-up or shutdown PV WT FC MT ESS same time and hence X(t) and Y(t) take values of either 0 or costs for the ith DGs and jth storage devices are given as 1. Bus voltage limit for the ith bus is given as S (t)and S (t), respectively. N and N are the numbers of Gi sj g distributed generators and the storage units, respectively. V ≤ V ≤ V , i ∈ {1,2, . . . N}, (10) min ,i i max ,i t t−1 U and U are the ON/OFF status of DG units and i i t t−1 U and U are the ON/OFF status of storage devices with where V and V are the minimum and maximum j j min ,i max ,i respect to time t and t − 1, respectively. voltage of the ith bus. *e current in each feeder should not exceed the maximum current carrying capacity of the branches. 􏼌 􏼌 2.2. Constraints. At any given time, the power generation 􏼌 􏼌 􏼌 􏼌 􏼌I 􏼌≤ I , k ∈ {1,2, . . . l}, (11) K max and the load demand in the VPP must be balanced; that is, the total power generation must equal the sum of load where l is the number of branches. *e maximum allowable demand and losses as expressed in active and reactive power injection of DGs are as follows. Ng N Ns Load P ≤ P ≤ P , DGmin DG DGmax 􏽘 P + 􏽘 P + P � 􏽘 P + P , (3) Gi Sj Grid Load,k Losses (12) i�1 j�1 k�1 Q ≤ Q ≤ Q , DGmin DG DGmax where N , N , and N are the numbers of distributed s load g where P and Q are the active and reactive powers of DG DG generators, the storage units, and loads, respectively. DGs, P and Q are the minimum allowable active DGmin DGmin *e power generation limits of DGs, storage devices, and and reactive powers of DGs, and P and Q are the DGmax DGmax utility grid are expressed as maximum allowable active and reactive powers of DGs. P ≤ P ≤ P , Gi,min Gi Gi,max 3. Overview of TLBO Algorithm P ≤ P ≤ P , (4) Sj,min Sj Sj,max *e Teaching-Learning-Based Optimization (TLBO) algo- P ≤ P ≤ P , Grid,min Grid Grid,max rithm is a new effective human population-based algorithm where P and P are the minimum and maximum proposed by Rao et al. *is algorithm resembles the Gi,min Gi,max allowable powers of DGs, P and P are the min- teaching-learning process of the instructor and students in a Sj,min Sj,max imum and maximum allowable power of the storage devices, lecture room. In this approach, a set of learners in a category and P and P are the minimum and maximum are considered as a population. Also, the number of subjects Grid,min Grid,max allowable powers of the utility grid. P , P ,and P are offered to the learners is the variables, the result of the Gi Sj Grid the available power from the DGs, storage devices, and learner is the fitness value, and the knowledge of the student utility grid, respectively. *e state of charge of the storage is the objective function. *e parameters considered in the device is expressed as objective function are the variables for the given problem and the best fitness value of the objective function is taken as SOC (t) � SOC (t −1) + η P (t)Δt ESS ESS Charge Charge the best solution. *e TLBO method is split into two phases: (5) the teacher phase and the learner phase. In the former phase, − η P (t)Δt, t �1,2, . . . T, Discharge Discharge the learners are learning from the teacher and in the latter Where SOC (t)and SOC (t − 1)aretheenergystoredin phase, the learners are learning by discussing with other Ess Ess the devices at time t and t– 1, respectively. P and learners [34, 35]. *e phases of TLBO are described as Charge P are the charging and discharging power at an follows. Discharge instant, Δt is a definite time, and η and η are Charge Discharge the efficiency during charging and discharging. *e SOC, 3.1. Teaching Phase. In this phase, the teacher continuously charging, and discharging limits of the storage devices are tries to improve the mean result of the class for his/her expressed as subject. *e best solution which is defined by the objective SOC ≤ SOC ≤ SOC , (6) ESS,min ESS ESS,max function is considered as the teacher in that population. *is phase starts with identifying the best solution. First, generate P (t)≤ P X(t), t �1,2, . . . T; X∈ [0,1], (7) a random population with N rows and S columns. N Charge Chargemax International Transactions on Electrical Energy Systems 5 represents the population size (number of learners in the Step 1. Initialization of Parameters class, i �1,2, . . ., N) and S represents the number of design Specify the input data of the VPP and TLBO algorithm. variables (number of subjects, j �1,2, . . ., S). *e jth variable *e VPP data includes generator bidding price, hourly utility of the ith learner is initialized randomly using grid price, load demand, and power limits of the renewable energy sources, storage devices, and distributed generation 1 min max min X � X + rand∗ X − X , (13) 􏼐 􏼑 i,j j j j units. Initialize the parameters of the TLBO algorithm, such aspopulationsize,designvariables,andstoppingcriteria.*e where rand is a uniformly distributed random number that population size corresponds to the number of students, the min max takes values between 0 and 1 and X and X represent j j numberofdesignvariablesorsubjectsofferedcorrespondsto the minimum and maximum values for the jth parameter. the number of generating units, and the stopping criterion is *e difference D between the best solution and the mean diff j chosen as the number of iterations. result of the class for the jth subject in the kth iteration is given by Step 2. Initialization of Population k k k D � rand􏼐X − T M 􏼑, (14) diff F j T,j j Generate a random population of dimension [N × S] according to the population size, N, and the number of where M is the mean result of the students for the subject j design variables, S. *e randomly generated population is and X represents the best solution for the subject j in the T,j mathematically expressed as X � [X , X , X . . . X ] , 1 2 3 N kth iteration. *e teaching factor T as given in (15) is in- where N is the number of solutions in the multidimensional dicative of the teaching ability of the teacher, depending on search space. Each solution X � [P , P , . . . , P . . . P ] is i i1 i2 ij iS which the mean result of the subject will change. Its value is represented by an S-dimensional vector, (i � 1,2,3, . . . N) selected as either 1 or 2. and (j � 1,2,3, . . . S), where S is the number of parameters T � round[1 + rand(0,1)]. (15) to be optimized. In this problem, S corresponds to the six DGs. *e elements of each solution vector (X ) represent ij *e solution for the problem is updated in each iteration the power output (P ) of distributed generation units that gi using can take values between the maximum and minimum generation limits as given in k k k X � X + D , (16) new,i,j old,i,j diff j P � P + rand(0,1)∗ 􏼐P − P 􏼑, (18) ij j, min jmax jmin where X is the new solution for the jth subject and new i,j X is the old solution for the jth subject in the previous where P and P are the minimum and maximum old i,j j min jmax iteration. If the updated solution is better than the previous power limits of each unit. For each interval in the scheduling one, it is an acceptable solution. *e accepted solution is the horizon, initialization of the population is done as given in input to the next phase. P P . . . P 11 12 1S ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ P P . . . P ⎥ ⎢ ⎥ ⎢ 21 22 2S ⎥ ⎢ ⎥ ⎢ ⎥ 3.2. Learner Phase. *is is the second phase of the algorithm ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ X � ⎢ ⎥, (19) ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⋮ ⋮ ⋱ ⋮ ⎥ in which the learners improve their knowledge through ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ mutual interaction. In this process, each learner will interact P P . . . P N1 N2 NS with other learners randomly to facilitate knowledge sharing depending on their knowledge level. *e solution to the where P is the real power output of the Sth generation unit NS problem is updated based on knowledge sharing. To rep- for the Nth individual, which should satisfy the constraint resent it mathematically, two learners are considered ran- given in (4). k k domly as X and X . *e updated solution can be (i) (r) expressed as follows. Step 3. Fitness Evaluation k k k k k ⎧ ⎪ ⎫ ⎪ Evaluate the generation cost as expressed in (1) for the X + rand × 􏼐X − X 􏼑 if 􏼐X < X 􏼑 ⎨ ⎬ i i r i r X � . (17) generated random population in (19) and calculate sum of new,i ⎪ ⎪ k k k ⎩ ⎭ th X + rand × X − X otherwise 􏼐 􏼑 the cost for all the generating units in the g iteration using i r i S � Sum􏼐X , X , . . . X 􏼑. (20) *e best solutions for the different subjects are accepted 1,j 2,j i,j at the end of this phase, and these solutions are the input for the teacher phase. Both the teacher and learner phases are repeated until the stopping criterion is met. In this work, the Step 4. Teacher Phase stopping criterion is the number of iterations. Based on the sum of the generation cost in (20), the minimum generating cost is selected as the best solution. *e best solution can be considered as a teacher as expressed in 3.3. Implementation of TLBO Algorithm for Energy Man- (21). Update the power generation matrix based on the best agement Problem. In this section, the implementation of the solution using (16). TLBO algorithm for the energy management of generating 􏼌 􏼌 􏼌 g 􏼌 units and load demand in a VPP is discussed. *e steps 􏼌 􏼌 X � X f(x) � min S 􏼁 . (21) 􏼌 􏼌 teacher involved in the implementation procedure are given below. 6 International Transactions on Electrical Energy Systems Utility grid 20 kV / 400 V Feeder 3 Feeder 1 Residential Load Commercial Load Feeder 2 14 13 9 Industrial Load 7 15 16 FC MT Wind 4 11 6 +– Battery PV Figure 2: Single-line diagram of IEEE-16-bus test system. FC 26 27 28 29 30 31 32 33 24 25 FC Battery 12 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 Utility MT 20 kV / 400 V Grid 19 20 21 22 WT 1 WT MT PV Figure 3: Single-line diagram of IEEE-33-bus test system. Step 5. Learner Phase and IEEE-33 [37] bus test systems shown in Figures 2 and 3 In this step, the best solution obtained in Step 4 is are considered in this paper. *ey comprise of wind, solar, considered as the input for the learner phase. *e solution is microturbine, and fuel cell as generating units, along with modified based on the mutual interaction among the the storage devices and loads. *e optimal load dispatch is learners and the solution matrix is updated using (17). done for 24 hours in a day, and the optimal power gener- ation is based on the utility price and the load demand at the particular hour. Programming is done in MATLAB for the Step 6. Repeat steps 3–5 until the stopping criterion is met, aforementioned problem and executed on Intel Core i7- which is the maximum number of iterations. 8550U, 8th Gen CPU @ 1.99GHz, 8.00GB RAM PC. *e power limits, bidding price, and start-up/shutdown cost of 4. Results and Discussions each generating unit for IEEE 16-bus and IEEE 33-bus test In this section, the cost minimization problem of a VPP is systems are given in Tables 1 and 2, respectively. *e load implemented using the TLBO algorithm. IEEE-16[32, 36] demand, utility market price, and forecasted power output International Transactions on Electrical Energy Systems 7 Table 1: Input data of IEEE-16-bus system. ID Type Minimum power (kW) Maximum power (kW) Bid (€ct/kWh) Start-up/shutdown cost (€ct) 1 MT 6 30 0.457 0.96 2 FC 3 30 0.294 1.65 3 PV 0 25 2.584 0 4 WT1 0 15 1.073 0 5 Battery −30 30 0.38 0 6 Utility −30 30 — 0 Table 2: Input data of IEEE-33-bus system. ID Type Minimum power (kW) Maximum power (kW) Bid (€ct/kWh) Start-up/shutdown cost (€ct) 1 MT1 6 30 0.457 0.96 2 FC1 3 30 0.294 1.65 3 PV 0 25 2.584 0 4 WT1 0 15 1.073 0 5 Battery −30 30 0.38 0 6 Utility −30 30 — 0 7 WT2 0 35 1.969 0 8 MT2 8 50 0.269 0.96 9 FC2 8 50 0.275 1.65 Table 3: Total load demand of IEEE-16-bus and IEEE-33-bus test Table 4: Utility price for IEEE 16-bus and IEEE 33-bus test systems. systems. Hr Utility price (€ct/kWh) IEEE-16-bus load 1 0.23 Hr IEEE-33-bus load demand (kW) demand (kW) 2 0.19 1 52 133.75 3 0.14 2 50 114.75 4 0.12 3 50 114.75 5 0.12 4 51 138.25 6 0.20 5 56 140.50 7 0.23 6 63 125.25 8 0.38 7 70 128.75 9 1.50 8 75 132.75 10 4.00 9 76 138.25 11 4.00 10 80 148.50 12 4.00 11 78 162.75 13 1.50 12 74 170.25 14 4.00 13 72 178.50 15 2.00 14 72 160.50 16 1.95 15 76 155.25 17 0.60 16 80 145.75 18 0.41 17 85 140.25 19 0.35 18 88 98.75 20 0.43 19 90 102.25 21 1.17 20 87 135.50 22 0.54 21 78 120.25 23 0.30 22 71 133.75 24 0.26 23 65 145.50 24 56 130.25 residential and commercial loads and 0.9 lagging for in- dustrial loads [38] for both IEEE 16- and IEEE 33-bus test [32] from PV, Wind1, and Wind2 are given in Tables 3–5, systems. *e optimization problem is solved for with and respectively. *e total load demand per day is taken as without losses for comparison purpose. In addition to the 1695kW and 3295kW for IEEE 16-bus and IEEE 33-bus test TLBO algorithm, ABC and ALO algorithms are also used in systems, respectively. *e power losses are computed using this paper to solve the problem statement and to validate the the forward-backward sweep method [33]. *e base power performance of the TLBO algorithm. and base voltage are taken as 100kVA and 400V, respec- *e parameters of the TLBO algorithm used in this tively, and the cost for the power losses is assumed as 0.19 problem are the population size, N taken as 100, maximum (€ct/kWh). *e power factor is taken as 0.85 lagging for iteration as 1000, and number of trials or runs as 20. *e 8 International Transactions on Electrical Energy Systems Table 5: Forecasted output of PV, WT1, and WT2. Hr PV (kW) WT1 (kW) WT2 (kW) 1 0 1.7850 4.165 2 0 1.7850 4.165 3 0 1.7850 4.165 4 0 1.7850 4.165 5 0 1.7850 4.165 6 0 0.9142 2.135 7 0 1.7850 4.165 8 0.1937 1.3017 3.045 9 3.7540 1.7850 4.165 10 7.5290 3.0854 7.210 11 10.4410 8.7724 20.475 12 11.9640 10.413 24.290 13 23.8930 3.9228 9.135 14 21.0490 2.3766 5.53 15 7.8647 1.7850 4.165 16 4.2208 1.3017 3.045 17 0.5389 1.7850 4.165 18 0 1.7850 4.165 19 0 1.3017 3.038 20 0 1.7850 4.165 21 0 1.3017 3.0345 22 0 1.3017 3.0345 23 0 0.9142 2.135 24 0 0.6124 1.435 Table 6: Optimal power dispatch using TLBO Case I. Hr MT (kW) FC (kW) PV (kW) WT1 (kW) Battery (kW) Utility (kW) SOC (kW) 1 6.000 16.563 0 1.7850 −2.348 30.0000 5.348 2 6.000 15.057 0 1.7850 −2.842 30.0000 8.190 3 6.000 15.654 0 1.7850 −3.439 30.0000 11.629 4 6.000 17.038 0 1.7850 −3.823 30.0000 15.452 5 6.000 22.342 0 1.7850 −4.127 30.0000 19.579 6 6.000 29.061 0 0.9142 −2.975 30.0000 22.554 7 10.709 30 0 1.7850 −2.494 30.0000 25.048 8 15.457 30 0.1937 1.3017 −1.952 30.0000 27.000 9 30.000 30 3.7540 1.7850 1.792 8.669 25.208 10 30.000 30 7.5290 3.0854 2.698 6.689 22.510 11 30.000 30 10.4410 8.7724 3.325 −4.538 19.185 12 30.000 30 11.9640 10.413 3.519 −11.896 15.666 13 30.000 30 23.8930 3.9228 1.414 −17.230 14.252 14 30.000 30 21.0490 2.3766 3.689 −15.115 10.563 15 30.000 30 7.8647 1.7850 2.384 3.966 8.179 16 30.000 30 4.2208 1.3017 1.548 12.930 6.631 17 30.000 30 0.5389 1.7850 1.468 21.208 5.163 18 24.828 30 0 1.7850 1.387 30.000 3.776 19 30.000 30 0 1.3017 −1.302 30.000 5.078 20 24.569 30 0 1.7850 0.646 30.000 4.432 21 30.000 30 0 1.3017 0.928 15.770 3.504 22 30.000 30 0 1.3017 0.501 9.197 3.003 23 6.000 30 0 0.9142 −1.154 29.240 4.157 24 6.000 20.715 0 0.6124 −1.327 30.0000 5.484 same parameters are used for ABC and ALO algorithms for utility grid. Whenever the bidding price of the DGs in the comparison. Four different cases are considered, and the VPP is less than that of the utility price, the generated VPP results are discussed in this section. power is used to meet the load demand. Also, the excess Power is exchanged between the VPP and the grid, based power generated and the energy stored in the storage devices on the bidding price of the generation units and that of the (discharging mode) are sold to the utility grid. If the bidding International Transactions on Electrical Energy Systems 9 0 4 8 12 16 20 24 –10 –20 Time in hour MT(kW) FC(kW) PV(kW) WT(kW) Battery(kW) Utility(kW) Figure 4: Optimal schedule of DGs and the utility–Case I. 0 4 8 12162024 Time (Hr) Figure 5: State of charge of battery–Case I. Table 7: Comparison of the total cost—Case I. Method Best solution (€ct) Worst solution (€ct) Mean (€ct) Simulation time (s) Without losses ABC 768.9008 773.4415 769.0444 7.998 ALO 767.6991 772.4553 767.8516 7.584 TLBO 765.2968 771.6939 765.4500 6.341 With losses ABC 761.9520 766.4927 762.0956 8.214 ALO 760.7503 765.5065 760.9028 7.982 TLBO 758.3480 764.7451 758.5042 6.587 price of the VPP is greater than that of the utility price, the power is bought from the utility grid and the same is stored in the storage devices (charging mode). In general, the power generated by the PV and wind is utilized based on their maximum availability. FC and MT are operated throughout the day because of lower bid costs. 4.1. Case I. In this case, all the generating units in the VPP 759 are in operation and they operate within their power limits. 758 *e VPP is connected to the utility grid. *e maximum 0 200 400 600 800 1000 power which can be exchanged between the VPP and the No.of Iterations utility grid is restricted to 30kW. All the DGs except PV are ABC in ON condition throughout the 24 hours. *e initial SOC of TLBO the storage device is taken as 3kW (i.e., 10% of the maxi- ALO mum capacity). *e optimal power dispatch for 24 hours of the day using the TLBO algorithm is given in Table 6. Each Figure 6: Comparison of convergence characteristics for Case I. Output Power (kW) Power (kW) Cost (€ct) 10 International Transactions on Electrical Energy Systems Table 8: Optimal power dispatch using TLBO algorithm—Case II. Hr MT (kW) FC (kW) PV (kW) WT1 (kW) Battery (kW) Utility (kW) SOC (kW) 1 6.000 3 0 1.7850 −2.213 43.428 5.213 2 6.000 3 0 1.7850 −2.742 41.957 7.955 3 6.000 3 0 1.7850 −3.514 42.729 11.469 4 6.000 3 0 1.7850 −3.867 44.082 15.336 5 6.000 3 0 1.7850 −4.315 49.53 19.651 6 6.000 3 0 0.9142 −2.813 55.899 22.464 7 6.000 3 0 1.7850 −2.584 61.799 25.048 8 6.000 30 0.1937 1.3017 −1.952 39.456 27.000 9 30.000 30 3.7540 1.7850 1.592 8.869 25.408 10 29.999 30 7.5290 3.0854 2.986 6.4007 22.422 11 29.999 30 10.4410 8.7724 3.821 −5.0344 18.601 12 29.990 30 11.9640 10.413 3.519 −11.8963 15.082 13 29.999 30 23.8930 3.9228 1.214 −17.0298 13.868 14 29.992 30 21.0490 2.3766 3.689 −15.1146 10.179 15 30.000 30 7.8647 1.7850 2.464 3.8863 7.715 16 29.999 30 4.2208 1.3017 1.548 12.9295 6.167 17 30.000 30 0.5389 1.7850 1.068 21.6081 5.099 18 25.128 30 0 1.7850 1.397 48.818 3.702 19 30.000 30 0 1.3017 −1.3017 54 5.004 20 26.538 30 0 1.7850 0.646 48.569 4.358 21 30.000 30 0 1.3017 0.839 15.8593 3.519 22 29.998 30 0 1.3017 0.519 9.1793 3.000 23 6.000 30 0 0.9142 −1.124 29.2098 4.124 24 6.000 3 0 0.6124 −1.243 47.6306 5.367 unit is optimally operated based on its bidding price and the load demand. During the first eight hours of the day, the bid cost of the utility is lesser than that of any of the DGs (except FC) in the VPP. *ereby, 30kW of power is purchased from the utility grid and the remaining load demand is supplied by the DGs in the VPP as shown in Figure 4. For instance, at the 8th 10 hour, the demand is 75kW. So, 30kW is purchased from the 0 0 4 8 12 16 20 24 –10 utility and the remaining 45kW is supplied by the DGs in –20 the VPP. As FC has the lowest bid cost, it supplies its –30 maximum capacity of 30kW, and the remaining 10kW is Time in hour supplied by PV, wind, MT, and battery. MT(kW) FC(kW) Also, the load demand is less during the first eight hours PV(kW) WT(kW) and thereby, the excess power generated in the VPP is stored Battery(kW) Utility(kW) in the battery. *e SOC of the battery is plotted in Figure 5. Figure 7: Optimal schedule of DGs and the utility—Case II. At the end of the 8th hour, the battery is charged to 90% of its maximum capacity (27kW). After the 8th hour, it can be observed that the utility grid price is higher than that of the other DGs (except PV) in the VPP. *e demand is also higher. Now, the local demand in the VPP is met by the DGs and the excess power generated is exported to the utility. *e battery is in discharging mode to meet the excess load demand. It is also observed from Figure 5 that at the end of the 18th hour of the day, the battery is discharged to 10% of its maximum capacity (3.776kW). For instance, at the 18th hour, the load demand is 88kW. *e available wind power is 1.7085kW, battery power of 1.387kW, and microturbine power of 24.828kW are used to 0 4 8 12162024 meet the demand along with the utility power and fuel cell Time in hour power of 30kW each. *ere is no PV power availability from the 18th hour. During these hours, the load demand in the Figure 8: State of charge of the battery—Case II. Output Power (kW) Power (kW) International Transactions on Electrical Energy Systems 11 Table 9: Comparison of the total cost—Case II. Method Best solution (€ct) Worst solution (€ct) Mean (€ct) Simulation time (s) Without losses ABC 748.8728 755.2788 749.1978 7.982 ALO 745.6808 756.0728 746.2068 7.245 TLBO 742.5108 753.2698 742.7778 6.153 With losses ABC 741.924 748.330 742.249 8.124 ALO 738.732 749.124 739.258 7.845 TLBO 735.562 746.321 735.829 6.524 VPP is met with the other sources based on their bidding price. During the last two hours of the day, the power de- mand is less and the excess power is stored in the battery. At 748 the end of the day, the SOC of the battery for Case I is 5.484kW. *e operating cost of VPP (with losses) for the Case I is obtained using the TLBO method and is compared with other metaheuristic techniques and is given in Table 7. It is evident from the results that TLBO is superior to other methods as it provides the minimum cost of €ct 758.348 for without losses and €ct 765.2968 for with losses. *e com- parison of convergence characteristics for the optimal op- 0 200 400 600 800 1000 erating cost for Case I is illustrated in Figure 6. It is observed No.of Iterations that the optimal solution is obtained within 100 iterations ABC when compared to the ABC and ALO methods. From Ta- TLBO ble 7, it can be observed that the time taken for the con- ALO vergence of optimal solution using the TLBO algorithm is Figure 9: Comparison of convergence characteristics—Case II. 6.587s, which is lesser than that of the other methods. 4.2. Case II. In this case, the DGs operate within their power the available power generation from the wind is utilized to limits and there is no restriction on the power exchange meet the load demand. Since the utility price is more than between the utility grid and the VPP. All the DGs are in ON the bidding price of MT and FC, these units are operating with their maximum capacity to meet the load demand. condition throughout the 24-hour time period except for PV. *e initial SOC of the storage device is 3kW, which is 10% of From the 18th to the 20th hours of the day, the load demand the maximum battery capacity. *e optimal power dispatch is high (peak load). During this period, PV power is not for 24 hours of the day using the TLBO algorithm is shown in available and also wind power availability is less. As the bid Table 8. In Figure 7, it is observed that for the first 7 hours of cost of fuel cell power is less, it is operated at its maximum the day, the utility grid price is low compared with the capacity. In addition, the utility power price is also less and bidding price of the DGs in the VPP. Hence, energy is thereby power is purchased from the utility. Power is also purchased from the utility grid without any restriction to stored in the storage devices during this interval. meet the load demand of VPP. *e power output from the *ediscussionsmadeforthe18thto20thhoursarevalidfor PV and wind turbine are used as per the availability. All other the23rdand24thhoursalso.Duringthe20thand22ndhoursof units of VPP are operating with minimum capacity due to the day, as the utility price is more than that of VPP, power is soldfromtheVPPtotheutilitygrid.Alltheunitsareoperating their higher bidding price compared to the utility price. During the first 8 hours, the load demand is less. with maximum capacity and the battery is also supplying the *erefore, the excess power is stored in the battery. At the power. On the 22nd hour, the battery has discharged to 3kW end of the 8th hour, the battery is charged to 90% of its (10%ofitsmaximumcapacity)asshowninFigure8.Duringthe maximum capacity (27kW) and is shown in Figure 8. *e last two hours of the day, the power demand is less and the load demand increases from the 9th hour of the day. *e excess power is stored in the battery. At the end of the day, the utility price is higher than that of the VPP bidding price from SOC of the battery for Case II is 5.367kW. the 9th to the 18th hour of the day. *ereby, power is sold to *e operating cost (with losses) for Case II using the the utility grid without any restrictions. *e battery is in TLBO algorithm is shown in Table 9 and is compared with discharging mode to meet the load demand. *e SOC of the the other metaheuristic techniques like ABC and ALO. From battery will change depending on the load demand and the Table 9, it is noticed that TLBO is better than other tech- niques in terms of convergence time and operating cost. *e bid cost. *e battery is discharged to 3.702kW (10% of its maximum capacity). During the 9th to 18th hour of the day, convergence graph for Case II is shown in Figure 9. It is Cost (€ct) 12 International Transactions on Electrical Energy Systems Table 10: Optimal power dispatch using TLBO algorithm—Case III. Hr Unit On/Off status MT (kW) FC (kW) PV (kW) WT1 (kW) Battery (kW) Utility (kW) SOC (kW) 1 010111 0 29.383 0 1.7850 −2.481 23.313 5.481 2 010111 0 26.241 0 1.7850 −3.042 25.016 8.523 3 110111 6.001 15.340 0 1.7850 −3.125 30.000 11.648 4 110111 6.003 17.232 0 1.7850 −4.018 29.999 15.666 5 010111 0 29.209 0 1.7850 −4.127 29.132 19.793 6 110111 6.000 28.999 0 0.9142 −2.912 29.999 22.705 7 110111 10.459 30 0 1.7850 −2.243 29.999 24.948 8 111111 15.557 30 0.194 1.3017 −2.052 30.000 27.000 9 111111 30.000 29.998 3.754 1.7850 1.568 8.895 25.432 10 111111 29.991 29.998 7.529 3.0854 2.995 6.403 22.437 11 111111 30.000 29.974 10.441 8.7724 3.448 −4.636 18.989 12 111111 29.999 29.997 11.964 10.413 4.212 −12.585 14.777 13 111111 29.962 29.999 23.893 3.9228 1.617 −17.393 13.160 14 111111 29.999 29.988 21.049 2.3766 3.571 −14.984 9.589 15 111111 29.996 29.999 7.8647 1.7850 2.786 3.609 6.803 16 111111 30.000 30 4.2208 1.3017 1.353 13.125 5.450 17 111111 30.000 30 0.5389 1.7850 1.363 21.313 4.087 18 110111 25.128 30 0 1.7850 1.087 30.000 3.000 19 110111 30.000 30 0 1.3017 −1.302 30.000 4.302 20 110111 26.414 30 0 1.7850 −1.198 30.000 5.500 21 110111 30.000 30 0 1.3017 1.288 15.411 4.212 22 110111 30.000 30.000 0 1.3017 1.211 8.488 3.001 23 110111 6.000 29.997 0 0.9142 −1.254 29.343 4.255 24 010111 0 29.448 0 0.6124 −1.927 27.868 6.182 evident from the characteristics that TLBO is faster than the other two methods. *e convergence time for this problem using TLBO is 6.524s. 0 4 8 12 16 20 24 4.3. Case III. In this case, all the generating units in the VPP –10 can switch between the ON/OFF modes and they operate –20 Time in hour within their power limits. *e initial SOC of the storage device is 3kW. *e VPP is connected to the utility grid. *e MT(kW) FC(kW) maximum power that can be exchanged between the VPP PV(kW) WT(kW) and the utility grid is restricted to 30kW. Battery(kW) Utility(kW) *e optimal power dispatch for 24 hours of the day using Figure 10: Optimal schedule of DGs and the utility—Case III. the TLBO algorithm is presented in Table 10. *e ON and OFF states of the MT, FC, PV, WT1, battery, and utility are represented by 1 and 0, respectively. From Figure 10, it is evident that, for the first 8 hours of the day, the utility grid price is low compared with the VPP bidding price. Hence, power is purchased from the utility grid to meet the load demand of VPP and the storage device is in charging mode. At the end of the 8th hour, the battery is charged to 90% of the maximum capacity; that is, the SOC is 27kW as depicted in Figure 11. During this period, the power output from the PV is zero. *e bidding price of FC is less compared to all the other units of VPP. Hence, FC is operating at its maximum capacity during this period. 0 4 8 12162024 Time in hour *e utility price is higher than that of the VPP bidding price from the 9th to 18th hours of the day. *ereby, the Figure 11: State of charge of the battery—Case III. power is sold to the utility grid by discharging the storage devices. *e battery is in discharging mode and discharged to 10% of its maximum capacity (i.e., 3.5kW during the 18th From the 19th and 20th hours of the day, the load hour as shown in the SOC plot in Figure 11). During this demand is high (peak load). During this period, the bidding duration, the power generation from the RES (PV and wind) price of FC is less and is operating with its maximum ca- are utilized as per the availability. pacity. Since the utility price is less compared to the VPP Output Power (kW) Power (kW) International Transactions on Electrical Energy Systems 13 Table 11: Comparison of the total cost—Case III. Best Method Worst solution (€ct) Mean (€ct) Simulation time (s) solution (€ct) Without losses ABC 766.4057 780.2791 767.0253 7.840 ALO 761.3383 779.1642 762.0748 7.568 TLBO 758.6558 777.9809 759.1309 6.548 With losses ABC 759.4569 773.3303 760.0765 8.012 ALO 754.3895 772.2154 755.1260 7.812 TLBO 751.707 771.0321 752.1821 6.987 bidding price, the grid power along with the power gen- 775 erated from the VPP is used to meet the peak load. Also, the storage device is in discharging mode. During the 21st and 22nd hours of the day, as the utility price is more than that of VPP, the power from VPP is sold to the utility grid. Since the bidding price of FC and MTis less compared with that of the utility price, these units are operating at their maximum capacity. *e battery is in discharging mode and discharged to 10% of maximum capacity (i.e., 3.122kW during the 18th hour as shown in the SOC plot in Figure 11). During the 23rd and 24th hours of the day, the utility price is less than that of VPP, so power is purchased from the utility to VPP 0 200 400 600 800 1000 and stored in the storage devices (charging mode). During No.of Iterations the last two hours of the day, the power demand is less and ABC the excess power is stored in the battery. *e operating cost TLBO (with losses) using the TLBO algorithm for Case III is ALO compared with the other metaheuristic techniques and is Figure 12: Comparison of convergence characteristics—Case III. given in Table 11. Minimum operating cost is obtained using the TLBO algorithm when compared with other methods. *e convergence characteristics with respect to the number *erefore 30kW of power is purchased from the utility, of iterations is plotted in Figure 12. It is observed that the while the remaining 98.75kW is supplied by the VPP units. optimal solution is obtained in minimum time and less As MT2 has the lowest bid cost, it supplies its maximum number of iterations using the TLBO algorithm. *e time capacity of 50kW and the remaining 48.75kW is supplied by taken for the convergence using the TLBO algorithm is other units. During the first 8 hours, the load demand is less. 6.987s. *erefore, the excess power is stored in the battery. *e SOC of the battery is plotted in Figure 14. At the end of the 8th 4.4. Case IV. In this case, the IEEE-33 bus test system is hour, the SOC of the battery is 90% of its maximum capacity considered. All the generating units of VPP are in ON (27.03kW) as displayed in Figure 14. condition and operating within their respective power limits. In general, the power generated by PV and wind is *e maximum amount of power that can be transferred utilized based on their maximum availability. MT2 is op- between the VPP and the utility grid is considered as 30kW. erated with its maximum capacity throughout the day be- *roughout the day, all DGs are available to meet the load cause of the lower bid cost. After the 7th hour, it can be observed that the utility grid price is more compared to the demand, except PV. *e initial SOC of the battery is as- sumed to be 3kW, which is 10% of its maximum capacity. other DG units in the VPP. *e demand is also higher. Now, *e optimal power dispatch for 24 hours of the day using the the local demand in the VPP is met by the DGs and the TLBO algorithm is shown in Table 12. Each unit is operated excess power generated is exported to the utility. From the within its capacity based on its bidding price and load 8th to 22nd hours of the day, FC1, MT2, and FC2 have lesser demand. Furthermore, power is transferred between the bid cost compared to the utility grid. Hence, these units are VPP and the utility grid based on the bidding price. operating at their maximum capacity during this period. *e From Figure 13, it can be observed that, during the first battery is in discharging mode to meet the excess load seven hours of the day, the bid cost of the utility is lesser than demand. It is also observed from Figure 14 that at the end of that of any of the DGs in VPP. As a result, 30kW of power is the 22nd hour of the day, the battery is discharged to 10% of bought from the utility grid and the remaining load demand its maximum capacity (3.071kW). For instance, at the 22nd hour, the load demand is 133.75kW. To meet this demand, is supplied by the DGs in the VPP based on their bid cost. For instance, at the 7th hour, the demand is 128.75kW. 4.337kW total available power from the RES, battery power Cost (€ct) 14 International Transactions on Electrical Energy Systems Table 12: Optimal power dispatch using TLBO algorithm—Case IV. Hr MT1 (kW) FC1 (kW) PV (kW) WT1 (kW) WT2 (kW) MT2 (kW) FC2 (kW) Bat (kW) Utility (kW) SOC (kW) 1 6 3 0 1.785 4.165 50 40.998 −2.198 30 5.198 2 6 3 0 1.785 4.165 50 22.767 −2.967 30 8.165 3 6 3 0 1.785 4.165 50 23.050 −3.250 30 11.415 4 6 3 0 1.785 4.165 50 47.123 −3.823 30 15.238 5 6 3.302 0 1.785 4.165 50 50.000 −4.752 30 19.99 6 6 3 0 0.914 2.135 50 35.946 −2.745 30 22.735 7 6 3 0 1.785 4.165 50 35.943 −2.143 30 24.878 8 6 30 0.194 1.302 3.045 50 50 −2.152 −5.638 27.03 9 26.888 30 3.754 1.785 4.165 50 50 1.658 −30 25.372 10 27.831 30 7.528 3.085 7.210 50 50 2.846 −30 22.526 11 19.794 30 10.441 8.772 20.475 50 50 3.268 −30 19.258 12 19.602 30 11.964 10.413 24.290 50 50 3.981 −30 15.277 13 30 30 23.893 3.923 9.135 50 50 1.864 −20.315 13.413 14 28.087 30 21.049 2.377 5.530 50 50 3.457 −30 9.956 15 30 30 7.865 1.785 4.165 50 50 2.876 −21.441 7.08 16 30 30 4.221 1.302 3.045 50 50 1.765 −24.583 5.315 17 30 30 0.539 1.785 4.165 50 50 1.212 −27.451 4.103 18 6 15.813 0 1.785 4.165 50 50 0.987 −30 3.116 19 6 24.755 0 1.302 3.038 50 50 −2.845 −30 5.961 20 6 30 0 1.785 4.165 50 50 0.885 −7.335 5.076 21 14.893 30 0 1.302 3.035 50 50 1.021 −30 4.055 22 28.430 30 0 1.302 3.035 50 50 0.984 −30 3.071 23 6 30 0 0.914 2.135 50 50 −1.216 7.667 4.287 24 6 3 0 0.612 1.435 50 40.715 −1.512 30 5.799 of 0.984kW, and 128.429kW of power from the other DGs are used and the excess power of 30kW is transferred to the utility grid during this hour. During the 23rd and 24th hours of the day, based on the utility price and power demand, DGs are operated and power is purchased from the utility to VPP. *e excess power generated in the VPP is stored in the 1 5 9 13 17 21 storage devices (charging mode). At the end of the day, the –10 SOC of the battery for Case IV is 5.799kW. –20 –30 *e operating cost (with losses) of VPP for Case IV –40 obtained using the TLBO method is compared with other Time in hour metaheuristic techniques and is given in Table 13. It is MT1(kW) Battery(kW) evident from the results that TLBO is superior to other WT1(kW) PV(kW) methods as it provides the minimum cost of €ct 797.0170 for FC2(kW) MT2(kW) without losses and €ct 780.5115 including losses. FC1(kW) Utility(kW) *e comparison of convergence characteristics for the WT2(kW) optimal operating cost for Case IV is illustrated in Figure 15. Figure 13: Optimal schedule of DGs and the utility—Case IV. It is observed that the optimal solution is obtained within 100 iterations when compared to the ABC and ALO methods. From Table 13, it can be observed that the time taken for the convergence of optimal solution using the TLBO algorithm is 30 7.895sec, which is lesser than the other methods. *rough the optimal dispatch of power from all the units of VPP using the TLBO algorithm, minimum generation cost is achieved. For the validation of the proposed meth- 15 odology, four different cases are considered for 2 different test systems and the total generation cost is computed and compared in Table 14. It is evident that, among the three cases for IEEE 16-bus system, Case II is more economical. *is is due to the unlimited power exchange option between 0 4 8 12162024 the VPP and the utility grid, wherein the low utility price Time (Hr) during off-peak hours is favorable for VPP to purchase Figure 14: State of charge of the battery—case IV. utility power and thereby minimize the generation cost. Power (kW) Output Power (kW) International Transactions on Electrical Energy Systems 15 Table 13: Comparison of the total cost—Case IV. Method Best solution (€ct) Worst solution (€ct) Mean (€ct) Simulation time (s) Without losses ABC 816.1944 845.6475 817.6637 9.987 ALO 805.5950 834.8358 806.9115 8.158 TLBO 797.0170 827.5376 797.5635 7.248 With losses ABC 799.6889 829.1420 801.1582 10.027 ALO 789.0895 818.3303 790.4060 8.954 TLBO 780.5115 811.0321 781.0580 7.895 0 200 400 600 800 1000 No.of Iteration ABC ALO TLBO Figure 15: Comparison of convergence characteristics—Case IV. Table 14: Comparison of the total generation cost—with losses. IEEE 16-bus system IEEE 33-bus system Cases Case I Case II Case III Case IV Generation cost (€ct) 758.348 735.562 751.707 780.511 In Case I, the maximum power exchange between the 5. Conclusion utility grid and the VPP is limited to 30 kW. All the units In this paper, the optimal energy management problem of of VPP including RES are in ON state in this case. VPP is formulated and implemented using the TLBO al- *erefore, the generation cost is higher than in the other 2 gorithm for 24 hours of the day. To evaluate the performance cases. In Case III, the maximum power exchange between of this optimization algorithm, four different cases are the utility grid and the VPP is limited to 30 kW. In ad- considered. *e power is exchanged between the utility grid dition to that, all the units of VPP are operating in an ON/ and the VPP based on their bidding price in all four cases. It OFF state based on the corresponding bidding price and is evident from the analysis that the operational cost of VPP start-up/shutdown cost. *erefore, the generation cost is is minimized by optimally scheduling the generation of each higher than that of Case II. It is observed from the unit of VPP. It is found that the cases with unlimited power abovementioned case studies that the generation cost of exchange between the utility grid and the VPP is more cases with limited power exchange between the utility grid economical compared to the cases with limited power ex- and the VPP is higher compared with the cases with change. Also, Case II is more feasible as it utilized the RES to unlimited power exchange. Case II is the most economical the maximum extent in spite of the higher bidding price to and feasible mode of operation. 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