Optimal Technical and Economical Operation of Microgrids through the Implementation of Sequential Quadratic Programming Algorithm
1 Abstract -- In this paper, the optimal operation of a microgrid is investigated when the network is connected at a 24-hour interval for a specific day. For the optimal operation, some criteria, such as the simultaneous reduction in operation costs, losses, and voltage deviations, as well as the increase in reliability are taken into consideration. Given the capacity of the installed units, a part of the load of the demanded energy is always supplied by the grid. In line with the objectives set, planning for the charge and discharge of storage systems as well as the interaction among distributed power generators are investigated. The operation process is considered as an optimization problem, and the created problem is solved by the Sequential Quadratic Programming (SQP) algorithm. In addition, by implementing the Demand Response (DR) program in the optimal operation, the acquired results are compared with those obtained when this strategy is not employed. Simulation results indicate that the utilization of the Demand Response (DR) program in the optimal operation of the microgrid leads to a number of improvements. To elucidate it more, in addition to the decrease in the operation costs of the microgrid, the voltage deviation indices, reliability, and losses are improved contrary to non-DR schemes.
Index Terms -- Optimal operation; Microgrid, Storage, Distributed generation resources, Demand respond, Sequential Quadratic Programming (SQP).
I. I
NTRODUCTION
OWADAYS, many researchers and countries pay special attention to the utilization of renewable energies because fossil fuels are about to run out. The utilization of renewable resources in different forms leads to a decrease in losses, generation costs, and pollution, an increase in system reliability, and an improvement in voltage deviations [1]. Owing to the widespread use of distributed generation units in electric distribution systems, it is vital to take microgrids into account. The proper implementation of microgrids leads to less losses and environmental pollution in one hand, with fewer transmission lines being required to be built, on the other hand [2,3]. The main problem of renewable distributed generation units in electric distribution systems is their uncertainty, which is resolved well by energy storage units [4]. Due to the high cost of energy storage units, combining them with demand-side management will result in more reliability [5]. With the demand
The authors are with Department of Electrical Engineering, Yazd University, Iran (e-mail: [email protected]; [email protected]; [email protected]) side response not taken into account, loads are required to be supplied fully at any moment of the day with any magnitudes, regardless of the power system efficiency. However, new methods reduce load variations to improve power system efficiency as much as possible [6]. All microgrids are required to possess a central management part to monitor loads and generation units so as to make appropriate decisions about the restrictions and goals of the power system operation [7]. Since a microgrid has a nonlinear and discrete identity, the presence of a suitable optimization algorithm is required to come up with a satisfactory solution [5]. The benefits of a central supervising unit for devising a coordinated scheme have been discussed [8]. Genetic algorithm (GA) is an optimization algorithm employed [9] to establish a smart energy management system for the operation of a power system. In order of minimizing the operation costs of microgrids, linear planning (LP) has been employed to optimize the charge and discharge of energy storage units [10]. In addition, the role of a management center aimed at optimizing operations has been investigated by considering power exchanges with an upstream power network [11]. Particle swarm and LP optimization methods could be employed to optimize the operation costs of a microgrid with energy storage units [12]. In the same vein, the energy management of a microgrid can be optimized by the Adaptive Modified Particle Swarm Optimization (AMPSO) method [13]. The Honey Bee Mating Optimization (HBMO) method can be used to optimize the energy management of a power distribution system, which contains fuel cells, wind, and solar generation units [14]. The optimal management strategy of distributed batteries in distribution systems with a high level of solar energy penetration has been discussed [15]. Demand side response can be used to reduce the losses of distribution systems [16]. Various optimizing algorithms [17], such as genetic algorithm [18, 9], particle swarm optimization [19], and an algorithm based on differential evolutions [20] are employed to enhance the operation of microgrids. The amount of the power dedicated to each distributed generation unit and its variations in accordance with each hour of the day have direct impacts on the losses of a microgrid. Therefore, the consideration of losses in load flow calculations is vital. This paper aims to minimize the operation costs of
Optimal Technical and Economical Operation of Microgrids through the Implementation of Sequential Quadratic Programming Algorithm
Ali Montazeri, Alireza Sedighi Anaraki,
Member IEEE , Shahab Aref N microgrids, improve their reliability, reduce losses, and modify voltage deviations. The contribution level of each distributed generation unit, the power exchange circumstance with the upstream network, the charge and discharge planning of energy storage units, as well as the losses of microgrids are considered in this paper to optimize the operation of microgrids. The objective functions are scrutinized exclusively, and their coefficients are determined by their importance level. In order to optimize the objective function, GA and Sequential Quadratic Programming (SQP) are employed, which are appropriate for the numerical solution of nonlinear optimization problems. The mathematical model of the problem is presented in section Ⅱ, and the solution algorithm is explained in section Ⅲ. Section Ⅳ describes the studied system, and in the end, the simulation algorithm and the results are presented in section Ⅴ. II. MATHEMATICAL MODELING
To present a mathematical model for a microgrid connected to a power distribution network, it is essential to consider the constraints of each equipment utilized in the microgrid. The constraints must be defined so that the final optimization problem would be simple and practical. In this paper, the objective function is comprised of four main parts, with each of which having different features. However, each part is normalized and then converted into a single function by employing weighting coefficients. It is worth noting that the model presented in this paper is considered for a specific day and could be applicable to all other days of the year. Since the model presented is comprehensive, it could be utilized in other case studies. A. Operation Cost Function
An operation cost function consists of the cost of power generation by distributed power generation resources as well as the cost of utilizing batteries and the energy received from the upstream distribution network, which is modeled by (1), (2) [13,15] as follows: ( ) ( ( )) ( ). ( ) ( ). i T N i g Grid Ggrid S St i
F P B P t P t B t P t B = = = + + (1) ( ( )) . ( ) = + i i i g i g i
B P t b P t C (2) where T represents the duration considered for the investigation, N denotes the number of active distributed power generation resources in the network, P gi denotes the active generated power of the i th power source in terms of kW, and P Grid (t) is the active power received from the network in the t th hour in terms of kW. In addition, P s (t) indicates the active power of the charge and discharge of the energy storage system in the network at the t th hour in terms of kW. B Grid (t) implies the price of the energy per hour in the network in €ct. B S represents the coefficient of the cost function of using batteries in terms of €ct/kWh. B i (P gi (t)) is the offered price for the i th distributed power generation unit for generating P gi kilowatt of power in the t th hour in terms of €ct. In the end, c i and b i are the coefficients of the cost function for the i th unit in terms of €ct/kWh and €ct/h as illustrated in Table Ⅰ. TABLE Ⅰ
The information of active distributed generation unites in microgrids [9].
Type Pmin (Kw)
Pmax (Kw) Bi (€ct/kwh) Ci (€ct/h) PV1 0 3 54.84 0 PV2 0 10 54.84 0 WT 0 15 10.63 0 MT 6 30 4.37 85.06 FC 3 30 2.86 255.8 B. Loss function
Economic consequences and heavy costs paid for power losses have made this topic be regarded more than ever in today’s electrical engineering community of the world. It is axiomatic that the amount of the power loss of the network is influenced by the amount of the distributed generation sources and batteries. One of other main objectives of this paper is to minimize the power loss according to the optimal dispatch of the distribution generation power, which is stated by (3) [21] as follows:
24 2,1 1 ( ) ( ) r N i T iT i
I R
F P = = = (3) where R i represents the branch resistor of B, I i, T is the current of branch B at time T, N r denotes the total number of the branches, and F is the entire loss of the whole network in an entire 24-hour day in terms of kW. It is evident that the value of the current of the branches is dependent on the power of DGs, batteries, and the strength of the interaction with the upstream network. C. Cost Function of Unsupplied Energy
One of the main purposes of the optimal operation in the microgrid considered is to improve reliability. To evaluate system reliability, there exist various indices, among which the cost of unsupplied energy is chosen, which occurs according to the error occurrence of the HV/MV transformer or MV feeders. After the occurrence of the error, the faulty equipment is separated from the network by opening some switches which are closed normally. Next, the disconnected loads are supplied by the utilization of DGs and island-made batteries in case such utilization is technically feasible. Therefore, the power distribution of DGs and the state of the charge (SOC) in batteries must be in such a way that the unsupplied energy, as one of the objective functions, would be minimized. The objective function of the unsupplied energy is stated by (4) [22, 23]:
243 1 ( ) ( ) ( ) ( ) EV OUT RDG RSTj j j jt j A
F OC S t S t S t T P = = − − (4) where F represents the function of the unsupplied energy, OC is the outage cost, j denotes the failure rate of the j th occurrence in each hour, and ( ) OUTj
S t denotes the power of the load disconnected by the j th occurrence at hour t. In addition, ( ) RDGj
S t indicates the restored power by the DG units after the j th occurrence in hour t, ( ) RSTj
S t represents the restored power by the batteries after the j th occurrence in hour t, and Δt is the time required for either repairing or replacing the equipment. In (4), the OC value is a function of the disconnected load type and the duration of the outage. This determines the type and amount of the supplied load by means of DGs at the time of the occurrence of the error and the islanding of a part of the network [23]. D. Voltage Deviation Function
One of the objective functions considered is the voltage deviation function, which is modeled by (5) as [24]:
244 ,1 1 ( ) = = = − r N ref i TT i
F P V V (5) where V ref is the reference voltage being equal to 1, and V i,T denotes the voltage value for load points at time T. It is obvious that the voltage value at the load points is dependent on the power of DGs and batteries. E. System Constraints and Restrictions • Power balance
System constraints include the power balance constraint in busbars and the technical constraints related to each equipment employed in the microgrid. In (6), the power balance constraint is observed in the busbar connected to the main network. Considering this constraint, the constraint of DG generation planning and management of energy exchange with the distribution network (including electricity, charge and discharge of batteries in each hour, as well as losses in each hour) must be in such a way that the energy demanded by the load would be always supplied. This constraint is considered by (6), as follows: ( ) ( ) ( ) ( ) ( ) i N g Grid D S Lossi
P t P t P t P t P t = + = + (6) where P D (t) represents the demanded power in each hour, and P S (t) is the power of the energy storage system, which could be marked differently according to the charge and discharge status of the batteries in each hour. Thus, when batteries are being charged, the demanded load must be increased. In the same vein, when batteries are being discharged, the demanded load must be decreased. By so doing, power generation sources will supply more loads at the charge time and less loads at the discharge time. P Loss (t) is the power loss of the microgrid in 24 hours, which is calculated using the backward-forward load distribution approach, at the presence of the batteries. It is clear that the amount of the power loss in the network is influenced by the values of DGs and batteries. That is the reason why (6) is a complex and non-linear constraint, which is solvable through the implementation of SQP algorithm. • Power Generation and Voltage Restriction
The active power allocated to each source should fall within the permitted generation range of that source. In addition, the voltage magnitude of all busbars must fall within the allowed range. In other words, the required energy of the loads must be supplied normally. Such restrictions are expressed by (7) and (8) as [15]: min max i i i g g g
P P P (7) min , max i t
V V V (8) • Storage system
The stored energy in the batteries of a microgrid can supply uninterruptable loads when required. This necessitates the restriction that the amount of the stored energy in batteries must not be lower than a specific level. In this way, the state of charge (SOC) of batteries can be stated by (9) as [15]: arg ( ) ( -1)(1- ( )) max(0, ( )) ch e B
SOC t SOC t t P t t = + arg
Bdisch e
P t t + (9) where SOC (t) and SOC (t-1) represent the stored energy at times t and t-1, respectively. In addition, η indicates the efficiency of the charge and discharge of batteries, and δ is the inner discharge coefficient of the storage system, which is dependent on battery parameters, with some of which being stated in [25]. Besides, Δt is the duration of the time interval, which is considered one hour in this paper. The charge status of batteries in each hour as well as the amount of their charge and discharge in each hour are the two constraints stated in (10) and (11) as follows: maxmin ( )
SOC SOC t SOC (10) max ( )
B B
P t P (11) where values SOC min , SOC max , and P Bmax are considered 16 kWh, 40 kWh, and 4 kWh, respectively [15]. • Power system
The restriction of the maximum exchangeable power between the microgrid and the global network could be modeled by (12) as follows: max ( ) ( )
Grid Grid
P t P t (12) P Gridmax is considered 300 kW [26]. III.
SIMULATION ALGORITHM
The optimal operation of microgrids has been modeled by (1) – (6) in section Ⅱ. In other words, the optimal operation is considered an optimization problem, with the main purpose of which being to minimize different objective functions, while a number of technical and economic constraints are present. In this paper, a combination of the two algorithms of genetic algorithm and sequential quadratic programming (SQP) has been employed. Fig. 1 demonstrates the diagram of the problem-solving approach. SQP, being one of the most proper, repetitive, and instrumental schemes, is a highly popular and powerful scheme used for numerical problem solving in non-linear optimization problems. Starting from a point, this algorithm reaches an acceptable response using the gradient of the provided data. It must be noted that SQP requires a reasonable initial point to reach a reliable response. If the optimization problem had no constraint or restriction, SQP would be reduced into a newton approach. Genetic algorithm (GA) is employed to reach the initial point of SQP algorithm. In fact, the output of GA, which is a relative optimal response, is utilized as the input of SQP algorithm to reach a more proper response. SQP utilizes the estimation of the Lagrange function in each repetition. In addition, it solves the problem by quadratic programming (QP). This quadratic program is a repetitive approach whose answer is offered in the K th reiteration of QP. The solving approach of SQP is presented as (13) [27]: min 0.5 ( ) t tk k imize d H d f x d + : ( ) ( ) 0, 1,..., ti k i k subject to h x d h x i p + = = (13) ( ) ( ) 0, 1,..., ti k i k g x d g x i p + = = According to (14), the final X
K+1 is obtained in the K th repetition. k k k k X x d + = + (14) IV. THE STUDIED SYSTEM
In this paper, the studied system is a low-voltage network with three feeders to supply domestic, industrial, and commercial loads. There are different types of DGs, including photovoltaic, fuel cells, wind turbines, micro turbines, and storage units in the simulated microgrid, with the structural information of which presented in [11]. The power factor of all DGs is assumed to be one, so no reactive power is either generated or consumed. Fig. 2 shows the studied microgrid.
Fig. 1. Problem-solving approach Fig. 2. The structure of studied microgrid [11].
Figs. 3 and 4 show the price of the electricity market for a 24-hour period [13] and the load variation diagram of the microgrid [11]. The generation rate of the solar and wind units are presented in [13]. V. SIMULATION AND RESULTS
First of all, to investigate the optimal management of a microgrid, its load is supposed to be supplied by an upstream network, with all DGs and batteries being disconnected. Table Ⅱ presents operation costs, losses, unsupplied energy, and voltage deviations according to the load profile of the microgrid as presented in Fig. 3. The received active power from the upstream power system is shown in Fig. 5. In addition, Fig. 6 shows the power loss of a microgrid for a 24-hour period. Next sections are related to the effectiveness of DGs, their optimum generation plan, storage systems, as well as their charge and discharge schedules, according to the optimal planning of the objective function in the operation of a microgrid. This situation is compared with the initial state in which DGs and storage systems are not considered in the network.
A. The first scenario: the operation optimization of the microgrid to minimize operating costs
This section aims to reduce the operating costs of microgrids using the interaction among DGs, batteries, and the upstream power system. Fig. 7 shows the optimization results of this scenario. In addition, Fig. 8 shows the power exchanged among the studied network, the upstream grid, and the power loss in a 24-hour period in the initial state.
According to Fig. 8 and Table Ⅲ, when scenario 1 is applied, a number of factors are decreased in comparison with the initial state, including 11.82% in costs, 22.59% in losses, 28.19% in
Fig 3. Proposed price of market for 24 hours [13]. Fig. 4. Load profile of microgrid [11]. TABLE Ⅱ
Results of optimum operation in initial state
Cost (€) 533.21 Losses (kW) 85.501 Cost of unsupplied energy (€) 35.05 Voltage deviation 2.2915 5 Fig. 5. Active power received Fig. 6. Loss power of network from upstream network in initial state in initial state the reliability index, and 11.04% in voltage deviations. According to Fig. 8, the optimal planning of the generation leads to a reduction in the active power exchanged with the upstream network which entails a reduction in the maximum power consumed. Based on this scenario, power losses decrease and lead to a drop in costs.
B. The second scenario: the operation optimization of the microgrid to reduce power losses
Power generation costs are excluded in this section. Hence, the contribution level of DGs, the amount of the power exchanged with the upstream network, as well as the charge and discharge plan of batteries are considered to reduce power losses in the studied system. Fig. 9 demonstrates the results of this scenario. The power exchanged between the microgrid and the upstream network as well as the 24-hour power losses of this scenario are compared with the initial state. Fig. 10 shows
Fig. 7. Dedicated active power to DGs and charge and discharge of batteries
Fig. 8. Comparison between first scenario and initial state in terms of the active power exchanged between microgrid and upstream network and hourly loss power TABLE Ⅲ
Results of optimum operation due to first scenario
Cost (€) Losses (kW) Cost of unsupplied energy (€)
Voltage deviation index
Initial state 533.21 85.501 36.04 2.2915 First scenario 470.18 66.187 25.88 2.0386 the results of this comparison. According to table Ⅳ, after the implementation of the second scenario, a number of factors decreased in comparison with the initial state, including 3.6% in costs, 35.99% in losses, and 30.47% in the costs of unsupplied energy, but the voltage deviation index increased about 4.49%. According to Fig. 10, the losses and the power exchanged with the upstream network decreased significantly, which resulted in a reduction in the maximum load in the power system.
C. The third scenario: the operation optimization of the microgrid to reduce the cost of the unsupplied energy
This scenario is based on the fact that the required loads of the network are supplied so that the costs of unsupplied energy are minimized. Hence, the contribution level of DGs in electricity generation, power exchange with the upstream network, as well as the charge and discharge plan of batteries are considered to minimize the cost of unsupplied energy. Fig. 11 shows the results of this scenario. According to Fig. 12 and Table Ⅴ, the implementation of the third scenario decreased some factors, including 1.36% in costs, 23.9% in losses, and 34.4% in the reliability index, but voltage deviations increased by about 0.2%. The optimal generation planning reduced the power exchanged with the upstream network and resulted in a decrease in the consumed load peak
Fig. 9. Devoted power to generation units, and charge and discharge plan of batteries
Fig. 10. Comparison between second scenario and initial state in terms of the active power exchanged between microgrid and upstream network and hourly loss power
TABLE Ⅳ
Results of optimum operation due to second scenario
Cost (€) Losses (kW) Cost of unsupplied energy (€) Voltage deviation index Initial state 533.21 85.501 36.04 2.2915 Second scenario 513.93 54.73 25.06 2.3944 6 of the network. The costs are reduced in this scenario due to the loss reduction.
D. The forth scenario: the operation optimization of the microgrid to reduce voltage deviations
The main purpose of this scenario is to reduce voltage deviations. Hence, the contribution level of DGs in electricity generation, power exchanged with the upstream network, as well as the charge and discharge plan of batteries are considered to reduce voltage deviations. Fig. 13 shows the results of this scenario. According to Fig. 14 and Table Ⅵ, the forth scenario reduced some factors in comparison with the initial state, including 0.42% in costs, 2.96% in losses, 26.8% in the reliability index, as well as 31.92% in voltage deviations. Just like previous generation planning, this scheme reduces power exchanged with the upstream network and decreases the consumed load peak of the network as well.
E. The fifth scenario: the optimal operation of the microgrid
The purpose of the optimal operation in this section is to reduce operation costs, power losses, voltage deviations, and the cost of unsupplied energy simultaneously. In previous scenarios, each of these parameters was optimized individually. Four objective functions are combined to create the primary
TABLE Ⅴ
Results of optimum operation due to third scenario
Cost (€) Losses (kW) Cost of unsupplied energy (€) Voltage deviation index Initial state 533.21 85.501 36.04 2.2915 Third scenario 525.95 65.063 23.64 2.2962 objective function. To this end, objective functions are normalized, and then using suitable weighting coefficients, one function is obtained from all other functions, as Eq. 15 shows:
F F F FF W WF F F F − −= + − − (15)
F F F FW WF F F F − −+ + − − where the minimum value of each function is its singular optimal value, and the maximum value of each function is the value of the function before executing the program. It must be noted that i W denotes the importance of each function. This value is determined using an AHP process. VI. THE ANALYTICAL HIERARCHY PROCESS
As already noted, for the optimal operation of the micro-grid, the weighted sum of the single objective functions was used to turn the multi-objective function into a single one. To determine the weighting coefficients, different methods such as goal attainment and the fuzzy approach were used. One of the most efficient techniques for weighting multi-objective functions is the Analytical Hierarchy Process (AHP). This technique was introduced by Thomas L. Saati (1980), and it has been the focus of attention in scientific circles for the past
Fig. 13. Devoted power to generation units, and charge and discharge plan of batteries
Fig. 14. Comparison between forth scenario and initial state in terms of the active power exchanged between microgrid and upstream network and hourly loss power
TABLE Ⅵ
Results of optimum operation due to forth scenario
Cost (€) Losses (kW) Cost of unsupplied energy (€) Voltage deviation index Initial state 533.21 85.501 36.04 2.2915 Forth scenario 530.95 82.97 26.38 1.5601
Fig. 11. Devoted power to generation units, and charge and discharge plan of batteries
Fig. 12. Comparison between third scenario and initial state in terms of the active power exchanged between microgrid and upstream network and hourly loss power
20 years. In this paper, the Analytical Hierarchy Process has been used to weight multi-objective functions. The weighted coefficients of the multi-objective function were determined in accordance with the descriptions offered in [28], by the Expert Choice software. The objective function weighting coefficients obtained by the Analytical Hierarchy Process using the Expert Choice software are presented in Eq. 16.
F F F FF F F F F − − − − = + (16) F F F FF F F F − −+ + − −
The results of this scenario are presented in Fig. 15. According to Fig. 16 and the results of comparing scenario 5 and the base mode in Table Ⅶ, costs, losses, the reliability index, and voltage deviations are decreased by 11.21%, 27.68%, 32.05%, and 11.89%, respectively, by applying the results of scenario 5. In addition, according to Fig. 16, optimal production scheduling reduces the power exchanged with the upstream network, thereby resulting in a reduction in the total network consumption peak. Load management is a method employed by system operators, in which they encourage consumers to reduce their load at peak or expensive times and shift consumption to off-peak hours. In this method, apart from reducing the costs for consumers, the benefits of operating a micro-grid are increased. By applying the load demand response strategy (DR), which is a method of load management, the obtained results are compared with those of the case in which this strategy is not applied to optimize the operation of the micro-grid. Fig. 17 shows the results obtained from applying consumed load management to the optimal operation. As Table Ⅷ shows, by the simultaneous applying of load management to the optimal operation, it is observed that all parameters studied in this paper are reduced significantly. Fig. 15. Devoted power to generation units, and charge and discharge plan of batteries
Fig. 16. Comparison between first scenario and initial state in terms of the active power exchanged between microgrid and upstream network and hourly loss power
TABLE Ⅶ
Results of optimum operation due to fifth scenario
Cost (€) Losses (kW) Cost of unsupplied energy (€)
Voltage deviation index
Initial state 533.21 85.501 36.04 2.2915 Fifth scenario 473.46 61.588 24.49 2.0191
Fig. 17. Devoted power to generation units, and charge and discharge plan of batteries
Fig. 18. Comparison between active power exchanged between microgrid and upstream network and hourly loss power
TABLE Ⅷ
Comparison between optimum operation results
Cost (€) Losses (kW) Cost of unsupplied energy (€)
Voltage deviation index
Initial state 533.21 85.501 36.04 2.2915 Fifth scenario without DR 473.46 61.588 24.49 2.0191 Fifth scenario with DR 393.95 52.67 24.17 1.9673
Figs. 19 illustrate the power exchanged with the grid and the consumed load before and after DR implementation.
Fig. 19. Power exchanged with the grid before and after DR and The consumed load of grid before and after DR 8
VII.
CONCLUSION
In this paper, after modeling objective functions and introducing the studied system, the optimal operation of microgrids was examined at the presence of distributed generation sources as well as the storage system in various scenarios. In this study, both the amount of cooperation and the way batteries are charged and discharged are analyzed, with the operation duration of the microgrid considered to be 24 hours. SQP was the utilized algorithm, being a fast algorithm in reaching the final solution. An initial supposed value was also determined to solve the problem by Genetic algorithm in a way that the convergence of the solution would occur more quickly. In addition, the results obtained from the optimization process, including the way of supplying the load demand in the distributed generation source, the scheduling of the charge and discharge of batteries, and the received power from the distribution network were presented. The results were compared with conditions before utilizing optimal programming. In addition, the impact of using DR was investigated. According to the results obtained, the simultaneous implementation of optimal programming and the demand response (DR) culminated in interesting results; in other words, during the low loading time intervals, when the expense of purchasing electricity from the upstream network is low, the required power of the microgrid is mostly acquired from the upstream network. In addition, during the peak load period when the price of purchasing electricity from the upstream network is high, distributed generation sources play the major role in supplying the required load of the network. Batteries are charged and discharged in a way that when acting addition, in the period of the peak load when electricity is expensive, the power of batteries is injected into the network to decrease the operating price in the whole microgrid. VIII.
REFERENCES [1]
Y.M. Atwa, E.F. El-Saadany, M.M. A. Salama, R. Seethapathy, M. Assam and S. Conti, “Adequacy evaluation of distribution system including wind/solar DG during different modes of operation,”
IEEE Trans. on Power System , vol. 26, pp. 1945-1952, 2011. [2]
F. Katiraei, R. Iravani, N. Hatziargyriou and A. Dimeas, “Microgrids management,”
IEEE Power and Energy Magazine , vol. 6, no. 3, pp. 54–65, 2008. [3]
S.M. Tabatabaei and B. Vahidi, “Optimum management of hybrid distributed generations in microgrid using bacterial foraging solution,”
Science International Journal , vol. 25, pp. 417-496, 2013. [4]
B. Bahmani-Firouzi and R. Azizipanah-Abarghooee, “Optimal sizing of battery energy storage for micro-grid operation management using a new improved bat algorithm,”
Electrical Power and Energy Systems , vol. 56, pp. 42–54, 2014. [5]
M. Marzband, A. Sumper, J.L. Domínguez-García and R. Gumara-Ferret, “Experimental validation of a real time energy management system for microgrids in islanded mode using a local day-ahead electricity market and MINLP,”
Energy Conversion and Management , vol. 76, pp. 314-22, 2013. [6]
J. Mohammadi, A. Rahimi-Kian and M.S. Ghazizadeh, “Aggregated wind power and flexible load offering strategy”,
IET Renewable Power Generation , vol. 5, pp. 439–447, 2011. [7]
H.A. Shayanfar, G. Derakhshan and A. Ameli, “Optimal operation of microgrids using renewable energy resources”,
International Journal on Technical and Physical Problems of Engineering (IJTPE) , vol. 4, no. 1, pp. 97-112, 2012. [8]
N.D. Hatziargyriou, A.G. Anastasiadis, J. Vasiljevska and A.G. Tsika lakis, “Quantification of economic, environmental and operational benefits of microgrids,” in 2009
IEEE Bucharest PowerTech : Innovative Ideas Toward the Electrical Grid of the Future , 2009. [9]
C. Chen, S. Duan, T. Cai, B. Liu and G. Hu, “Smart energy management system for optimal microgrid economic operation,”
Renewable Power Generation, IET , vol. 5, pp. 258-267, 2011. [10]
S. Chakraborty, M.D. Weiss and M.G. Simoes, “Distributed intelligent energy management system for a single-phase high frequency AC microgrid”,
IEEE Transactions on Industrial Electronics , vol. 54, pp. 97–109, 2007. [11]
A.G. Tsikalakis, and N.D. Hatziargyriou, “Centralized control for optimizing microgrids operation’,
IEEE Transactions on Energy Conversion , Vol. 23, pp. 241–248, 2008. [12]
E. Sortomme and M.A. El-Sharkawi, “Optimal power flow for a system of microgrids with controllable loads and battery storage,” in
IEEE/PES Power Systems Conference and Exposition (PSCE '09), pp. 1–5, 2009. [13]
A.A. Moghaddam, A. Seifi, T. Niknam and M.R. Pahlavani, “Multi-objective operation management of a renewable MG (micro-grid) with back-up micro-turbine/fuel cell/battery hybrid power source,”
Energy , vol. 36, pp. 6490–6507, 2011. [14]
L.H. Wua, Y.N. Wanga, X.F. Yuan and S.W. Zhou, “Environmental/economic power dispatch problem using multi-objective differential evolution algorithm,”
Electric Power Systems Research , vol. 84, pp. 1171–1181, 2010. [15]
N. Bazmohammadi, A. Karimpour, S. Bazmohammadi, “Optimal operation management of a microgrid based on MOPSO and Differential Evolution algorithms,” , 2012. [16]
R. Shawa, M. Attreea, T. Jacksonb and M. Kay, “The value of reducing distribution losses by domestic load-shifting: a network perspective,”
Energy Policy, Elsevier , vol. 37, pp.3159-3167, 2009. [17]
N. Nouri, P. Rafiee and A. Tadaion, "NOMA-Based Energy-Delay Trade-Off For Mobile Edge Computation Offloading in 5G Networks," , Tehran, Iran, 2018, pp. 522-527. [18]
S. Obara and A.G. El-Sayed, “Compound microgrid installation operation planning of a PEFC and photovoltaics with prediction of electricity production using GA and numerical weather information,”
Int. J. hydrogen energy , vol. 34, pp. 8213–8222, 2009. [19]
I. S. Bae and J.O. Kim, “Phasor discrete particle swarm optimization algorithm to configure micro-grids,”
Journal of Electrical Engineering & Technology , vol. 7, no. 1, pp. 9-16, 2012. [20]
M. Hemmati, N. Amjady and M. Ehsan, “System modeling and optimization for islanded micro-grid using multi-cross learning-based chaotic differential evolution algorithm,”
Int. J. Electrical Power & Energy Systems , vol. 56, pp. 349-360, 2014. [21]
T. Niknama, A. Kavousifard, S. Tabatabaei and J. Aghaeia, “Optimal operation management of fuel cell/wind/photovoltaic power sources connected to distribution networks,”
Journal of Power Sources , vol. 196, pp. 8881–8896, 2011. [22]
A. Ahmadian, M. Sedghi, and A.A. Golkar, "Optimal operation distribution network with island mode operation capability and considering wind generation, storage and plug-in electric vehicles,"
Iranian Electric Industry Journal of Quality and Productivity (IEIJQP) , Vol. 3, Issue 6, pp. 20-32, 2015. [23]
M. Sedghi, M. Aliakbar-Golkar and M.R. Haghifam, “Distribution network expansion considering distributed generation and storage units using modified PSO algorithm,”
International Journal of Electrical Power & Energy Systems , vol. 52, pp. 221–230, 2013. [24]
H. Singh and L. Srivastava, “Multi-objective reactive power management using differential evolution,” , pp. 1 – 6, 2012. [25]
Y. Bao, X. Chen, H. Wang and B. Wang, “Genetic algorithm based optimal capacity allocation for an independent wind/PV/diesel/ battery power generation system,”
Journal of Information & Computational Science , vol. 10, no. 14, pp 4581-4592, 2013. [26]
E. Mashhour and S.M. Moghaddas Tafreshi, ”Integration of distributed energy resources into low voltage grid: A market-based multi period optimization model,”
Electric Power Systems Research , vol. 80, pp 473-411, 2010. [27]
W. Sheng, K.Y. Liu and S. Sheng, “A trust region SQP method for coordinated voltage control in smart distribution grid,”
IEEE Transactions on Smart Grid , vol. 7, no. 1, pp. 381-391, 2016. [28]
S. H. Ghodsypour, “Analytical hierarchy process (AHP),” 2 ndnd