A contingency based energy management strategy for multi-microgrids considering battery energy storage systems and electric vehicles

Journal of Energy Storage 27 (2020) 101087

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A contingency based energy management strategy for multi-microgrids considering battery energy storage systems and electric vehicles

T

Hossein Afrakhte, Peyman Bayat

⁎

Department of Electrical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran

ARTICLE INFO

ABSTRACT

Keywords: Energy management strategy Energy storage systems Electric vehicles (EVs) Multi-microgrid (MMG) Optimization Shuffled complex evolution

The emergence of microgrids along with extending the use of new energy resources, energy storage systems and electric vehicles at distribution level has changed traditional distribution systems into multi-microgrids (MMGs) which are usually more stable and reliable. For an MMG system, the probability of a fault occurrence at each time period makes the system operation process more complex. From this point of view, this paper aims at proposing a coordinated energy management strategy for optimal operation of MMG systems using a variable weighted multi-objective function. Based on this method, in the case of occurrence of a contingency problem, multiple operators are able to change the weight of functions depending on contingencies and are responsible for the proper use of energy storage systems and other distributed energy resources. Moreover, an efficient optimization algorithm called targeted search shuffled complex evolution is proposed to quickly optimize decision parameters during faulted and normal operation modes. Finally, a unified framework is presented to implement the proposed energy management strategy along with the reliability study of the intended test system, and the ability of the proposed approach is investigated in a modified reliability-based case study by considering different scenarios.

1. Introduction Microgrids (MGs) are the important parts of future power systems, enabling a fast pathway to more sustainable energy systems [1]. An MG can be defined as an active cell within the low voltage network consisting of a set of components, which are able to operate in grid-connected and islanded modes [2]. These components include loads, control devices and various distributed generation (DG) units used as renewable and non-renewable energy resources with or without consideration of energy storage units. Since the size of generation and energy storage is limited in a single MG, the development of an MG gradually tends to form a larger grid called multi-microgrid (MMG). As illustrated in Fig. 1, an MMG system is an entity containing multiple individual MGs. These individual MGs are geographically close and connected to the same distribution network (DN). Connecting individual MGs to a wider distribution system strengthens the system against unforeseen events (e.g., faults, extreme weather conditions, etc.) and improves the efficiency, resiliency and reliability of the entire grid, while still maintaining the stability of operation in the islanded mode and combining the benefits of MGs [3–5]. Therefore, interconnecting adjacent MGs through the point of common coupling (PCC) and building a resilient MMG system have ⁎

attracted great attention among researchers. In this context, the outage management and coordinated operation of MMGs are two important topics, which compared to the abundant literature on the energy management for a single MG, are rarely investigated. Moreover, only a handful of approaches are proposed for these two topics in the literature, which will be discussed further below. Coordinated operation of an MMG needs a holistic energy management strategy (HEMS) to meet certain operational objectives [5]. Indeed, MGs need to manage power flows by adjusting power imported/exported from/to their exterior space, dispatchable distributed energy resources (DERs), distributed energy storage systems and controllable loads. In this situation, each MG can be able to purchase power from a DN in the case of both normal operation and emergency events. Thus, sharing the power flow among MGs and DN on the one hand and sharing the power flow between DN and upstream network (UN) on the other are important issues. In retrospect, regarding the topic of energy management for an MMG system, based on the model complexity, existing approaches can be mainly categorized into three types: centralized, decentralized (distributed) and hybrid energy management. MGs and DNs in the centralized structure are coordinately controlled with the central controller, which can simplify the control

Corresponding author. E-mail address: [email protected] (P. Bayat).

https://doi.org/10.1016/j.est.2019.101087 Received 7 July 2019; Received in revised form 28 October 2019; Accepted 18 November 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

Nomenclature

Crupward/Crdownward upward/downward climbing rate of unit FBESS / EV the battery life depletion cost for set of FBESS/EV charging/discharging cost of FBESSs CFBESS CEV charging/discharging cost of EVs CDG, MGs operation cost of DGs which are located in the MGs CCut cost of paying for interruptible demands capacity CNID, MG selling price to the non-interruptible demands of MGs CNID, DN selling price to the consumer of DN CID, MG selling price to the interruptible demands of MGs CEx trading price between DNO and MGOs CDG, DN operation cost of DGs which are located in the DN trading price between DN and UN CUN state NFBESS / EV the limits of charging and discharging state conversion state (NFBESS / EV = 5) max/min SOCFBESS / EV maximum/minimum state of charge of FBESS/EV max min PEx / PEx upper/lower limit of exchange power between MGs and DN PRmax , QRmax upper power output of renewable energy units which are located in the MGs max min PDG , MGs / PDG, MGs maximum/minimum output active power of DGs max min QDG , MGs / QDG, MGs maximum/minimum output reactive power of DGs V max / V min upper/ lower limit of the voltage amplitude max PID maximum load curtailment capacity

(Indices and sets) nt, t m M σ j, k, n i L OF Nc

set and index for total number of time periods (h) index for MGs set containing all MGs in the MMG system index for weight factors index and set for total number of units and loadpoints index for number of nodes index for number of lines index for objective functions index for the number of customers

(Binary and ternary variables)

SFBESS , SEV ch / dch FBESS / EV

AEV

ACut c ADG , MGs

Ex

AEx

ADG, DN AUN

AFBESS y

ternary variable with three states as, −1 indicates discharging, +1 indicates charging and 0 indicates idle state charge/discharge binary indicators of FBESS/EV availability of electric vehicles in the parking lot, where 0 signifies unavailability and 1 indicates availability availability of interruptible demands, where 0 signifies unavailability and 1 indicates availability availability of DGs which are located in the MGs, where 0 signifies unavailability and 1 indicates availability binary variable, equal to 1 when MGs sale power to DN, while −1 means MGs purchase power from DN availability of MGs to exchange power with DN, where 0 signifies unavailability and 1 indicates availability availability of DGs which are located in the DN, where 0 signifies unavailability and 1 indicates availability availability of UN to exchange power with DN, where 0 signifies unavailability and 1 indicates availability availability of FBESSs for energy management, where 0 signifies unavailability and 1 indicates availability binary variable, determines whether each load is being supplied in the next timeslot (1), or not (0)

(variables) KW ratings of fixed battery energy storage systems KW ratings of EVs which are located in the MGs KW ratings of interruptible demands KW ratings of DGs which are located in the MGs reactive power output of DGs which are located in the MGs provided active power of non-interruptible demands of PNID, MG MGs provided active power of consumer of DN PCu, DN PLine active power flow on lines provided reactive power of interruptible demands of MGs QID, MG PID, MG provided active power of interruptible demands of MGs PEx exchange power between MGs and DN PDG, DN KW ratings of DGs which are located in the DN PUN exchange power between DN and UN PR KW ratings of renewable energy units (PVs+WTs) which are located in the MGs QR KVAR ratings of renewable energy units (WTs) which are located in the MGs QDG, MGs reactive power output of DGs which are located in the DN QLine reactive power flow on lines QNID, MG provided reactive power of non-interruptible demands of MGs SOCFBESS / EV state of charge of FBESS/EV

PFBESS PEV PCut PDG, MGs QDG, MGs

(Parameters) λ μ La U R X δ vbase

ch / dch FBESS / EV

v

failure rate of the components repair rate of the components average load connected to each loadpoint load curtailment duration line resistance between nodes line reactance between nodes criticality level of load points reference voltage the efficiencies of the FBESS/EV during the charge/discharge processes voltage magnitude of the load points

procedure. In other words, a central controller takes the entire responsibility of the system's operation and maintenance within time intervals. Although this structure can effectively guarantee a global optimal solution, it generally neglects local benefits from an individual viewpoint; this is in contrast with the profit-driven nature of microgrid operators (MGOs) [6]. Furthermore, a fault in the energy management system will affect the whole set of MGs. This architecture can have lower reliability, larger communication delay, and longer communication distance [7]. However, some researchers believe that this method is more applicable for outage management. Therefore, based on the centralized architecture, the reliability impacts of the coordinated outage management strategy in an MMG system are investigated in Ref.

[8], effectively coping with different contingencies and outage duration. According to the aforementioned problems, many researchers believe that having a centralized controller may not be the best way to control an MMG, because the system may suffer from disturbances [9]. Hence, a decentralized control would be more feasible. In decentralized structures, each MG separately schedules its activities based on the strategy of its operator with different rules, constraints, and objectives to maximize the local benefit [10]. Thus, initially in this structure, each MGO solves operation problems of its MG. However, the global optimal objective of the entire system is achieved when MGs are directly in touch with the distribution network operator (DNO) [11]. To reach this 2

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

Fig. 1. The diagram of an MMG system.

goal, each MG must have a sufficient generation and storage capacity to achieve an acceptable supply level during operation times. Many studies have proposed various distributed energy management schemes based on this architecture [12, 13]. The consensus-based algorithm (CbA) with the advantage of having a simple structure is one of the most widely used methods [14–16]. Based on this method, each MG adjusts its own parameters based on the information it receives from neighboring MGs. The authors in Ref. [14] formulated a decentralized twostage stochastic program of MG in a distribution system and used C-bA for power exchange between DNO and MGs with the purpose of MMG energy management. Moreover, a distributed power sharing method between MGs using average C-bA was presented in [15] to overcome emergency situations. Ref. [16] proposed a distributed coordinated control strategy based on multi-agent C-bA in order to manage MMGs for power-sharing. In the context of decentralized energy management, the other most frequently used method is the decomposition-based algorithm (D-bA) [17–19]. This method decomposes a global problem into n local sub-problems. In doing so, each n sub-problem is coordinately solved in order to achieve the global optimal solution. Specifically, based on this strategy, the authors of Ref. [17] proposed an optimal power flow by decoupling a system into multiple portions. In addition, a single-period energy trading algorithm based on a decomposition method was proposed in Ref. [20] to ensure the reliability of MMG systems and the speed of response. In the same way, by considering the uncertainty of resources and the volatility of energy among MGs, a robust optimization method with the ability to adapt to system conditions was proposed in Ref. [21] to optimize the overall operating cost of MMG systems. In doing so, an optimization problem was solved with D-bA to find optimum solutions. Further, a distributed method was proposed in Refs. [22, 23] to optimize the scheduling of an MMG system considering uncertainty in the real-time energy market. Based on the above-mentioned articles, D-bA is often robust, but with the disadvantage of complexity. The coordinated energy management of MMGs can be handled in a hybrid centralized-decentralized manner so that advantages of both centralized and decentralized methods can be incorporated. Based on this architecture, Ref. [24] proposed a hybrid EMS with the intention of solving the coordination problem of MGs in an MMG system for the purpose of higher computational efficiency. In doing so, the transaction power of a tie line, the exchange power of MGs and the output power of distributed generation (DGs) are regarded as control variables. In the same vein, in order to overcome the defects of centralized and decentralized methods (e.g., uncertainty between global and local optimum points) and with the purpose of total operation cost minimization, Ref. [25] proposed a cooperative game approach, aiming at implementing an MMG coordinated operation. It is worth mentioning that most of the above-mentioned articles considered only limiting constraints (e.g., voltage magnitude and power line transmission capacity) or the uncertainty of non-dispatchable units

and load consumption, while ignoring the failure probability of components. Accordingly, these studies failed to consider the reliability characteristics of main components (e.g., failure rate and repair rate). In addition, these researches did not address the type and length of lines. While, in an MMG operation, equipment failures not only cause challenges in maintaining the supply-demand balance, but also have a profound influence on energy scheduling results, which might pose various problems including low energy efficiency, high operation cost and frequent interaction with the grid. Since the failure rate and probability distribution of equipment are not the same, deterministic methods can be hardly used for the purpose of evaluating the system. Thus, further research has been carried out to use the Monte Carlo method in order to prevent random disturbance and equipment failure [26–28]. Based on this method, Ref. [28] investigated the reliability impacts of a coordinated outage management strategy in an MMG system and showed that it effectively coped with different contingencies and outage duration uncertainties. However, MGs are considered as a set and therefore the possibility of failure in the network environment of MGs has been ignored. Further, the study neglected reactive power and voltage levels. In a similar study, a hierarchical strategy related to outage management was proposed in Ref. [29] for MMGs for the purpose of enhancing power system resilience. To this end, a general optimization model was developed as a problem of mixed integer linear programming. Moreover, Ref. [30] proposed a strategy for the energy management of an MMG system, in which the contingency probability was considered and a DNO determined the optimum energy management for the following day, accordingly. Another study [31] proposed a method to use an outage model, quantifying the relationship between state variables and components’ outage rate, so that the influence of operating conditions could be investigated on an MMG system's reliability indices. In Ref. [32], an MMG system was presented with the aim of facilitating the service restoration in order to minimize the outage of customers while considering the uncertainty of loads and DGs. A common limitation to the above-mentioned articles is that the proposed schemes were based on the single objective or fixed-weighted multi objective functions. However, conventional functions need to be changed according to the network conditions and they cannot be used in all circumstances (e.g., outage time slots). Therefore, it is urgent to propose an effective energy management strategy in order to have a coordinated operation and overcome uncertain contingencies with the aim of filling the gaps mentioned in the literature. To this end, this study attempts to propose an efficient and robust approach for optimal MMG operation using a variable weighted multi-objective function. Based on this method, when a contingency problem occurs, multiple operators (MOs) are able to change the weight of the objective functions depending on contingencies. In doing so, MOs are responsible for an applicable energy supply to their various demands in different MMG system modes according to the type of faults and their locations. 3

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

Moreover, an efficient optimization algorithm is proposed based on the intelligent method to quickly optimize decision parameters during the fault periods and normal operation. The proposed optimization algorithm is based on the shuffled complex evolution (SCE) algorithm as an effective global optimization algorithm, which is called targeted search shuffled complex evolution (TSSCE). Furthermore, a unified framework is proposed for the reliability study of MMG systems, and the state transition sampling technique [33] is applied to address contingency in MMG systems. In addition, because of the difference between routine case studies and actual system operating conditions, a modified reliability-based case study with MMGs is used to evaluate the system performance under study. Finally, results are compared with those of other operation methods in different cases. The model robustness is also examined through sensitivity analysis. To summarize, the proposed HEMS has the following key features in comparison to other related works:

The rest of this paper is organized as follows. The structure of MMG under study is described in Section 2. The proposed HEMS is briefly introduced in Section 3, also, the proposed variable weighted multiobjective problem formulation and the proposed optimization algorithm called TSSCE are presented in this section. The present study is described with a unified general framework in Section 4. In Section 5 the superiority of the proposed HEMS is demonstrated based on simulation of different Cases. Finally, the conclusion and future works are outlined in Section 6. 2. Configuration of MMG system This section describes the configuration of a MMG system, as demonstrated in Fig. 2. This system consists of DN which can implement bidirectional energy trading with the isolated UN and N MGs; MGi= {MG1, MG2, …, MGN}. Based on the numerical values adopted in this study, all MGs have enough generation capacity to approximately supply their loads only in some circumstances, also they are interconnected and can exchange energy among their environment and DN as shown in Fig. 2. In retrospect, generally a low-voltage distribution system has a radial structure and similarly in the present article a radial DN is assumed. Furthermore, a radial structure is considered for all MGs. The MGs are geographically close which each integrates non-dispatchable DERs (e.g. photovoltaic (PV) cells and wind turbines (WTs)), dispatchable DERs (e.g. micro-turbines (MTs)), fixed battery energy storage systems (FBESSs) and mobile battery energy storage systems (MBESSs); e.g. EVs. Also, the demand side is composed of different types of loads (e.g. residential, agricultural, commercial, small industrial) which include non-interruptible and interruptible demands. FBESSs and MBESSs in each MG can be employed to store excess energy produced by non-dispatchable generation units in off-peak hours and then provide energy for loads in peak or emergency hours.

• A HEMS is introduced for the coordinated energy management of •

• •

•

poly-generation MMG systems with multiple resources, namely renewable and dispatchable DG units, fixed and mobile energy storage units (e.g., electric vehicles) as well as interruptible and non-interruptible demands. Based on both emergency and optimality conditions, the MMG system energy management is formulated as a variable weighted multi-objective function with the aim of solving both network and economic problems, while satisfying operation constraints of the system. Based on this architecture, when a contingency occurs, related operators attempt to provide a reliable power supply to their customers rather than increasing financial profits. An efficient optimization algorithm is proposed to resolve global optimization problems characterized by a large number of design variables. This algorithm is based on the SCE algorithm as an effective global optimization algorithm, which is called TSSCE. A comprehensive reliability assessment framework is developed to evaluate the impact of the proposed energy management method, and steps required for its successful implementation are introduced. The proposed framework makes it possible to evaluate and analyze the reliability indices of an MMG system. It can also determine the impact that different operating schemes have on the MMG system. An extensive modified reliability-based test system with MMGs is proposed to investigate the proposed method performance and feasibility. Moreover, sensitivity analysis is provided to explain how the method can be implemented under different operating conditions.

3. Proposed methodology In the common decentralized MMG energy management strategy, MGs are likely to be managed and operate under various ownerships and strategies, and can choose whether or not to join the MMG system at their own discretion. Therefore, any management scheme related to such a system needs to take into account the interests of each MGO and not to restrict their autonomy. Moreover, a DNO might be responsible for the operation of some DERs in a DN and takes the full responsibility of the DN management and control [10]. In order to achieve the global

Fig. 2. Configuration of a MMG system. 4

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

optimal objective, when the MG generation is limited, the DN sends the power flow to the MG; otherwise, MGs transfer their surplus power to the DN to keep it stable and reliable. For this purpose, the DNO adjusts optimal decisions for the DN based on the status of its local agencies and according to the MG limited or surplus power announced from the previous timeslot. Indeed, due to the failure rate and repair or the replacement time of components, different types of faults with various locations and durations can occur in MMG systems. In these situations, available resources must be dispatched to meet the needs of islanded portions. However, due to the different location and duration of each event, the network might be unable to supply customers with the required power. Consequently, the balance may not be maintained between the generated electric energy and the consumed electric energy in islanded portions. Thus, MGOs need to seriously consider this issue in their optimum energy management. To this end, failure probability is taken into consideration for the proposed energy management scheme of MMG systems, and operators determine their optimum energy management for the next timeslot with regard to fault situations. Based on this strategy, some objectives are superior over others during the fault operation mode. Accordingly, regional objectives must be prioritized by operators. For instance, when a fault occurs in a specific branch, power cannot pass through it. Moreover, economic issues (e.g., cost minimization) are less important than network issues (e.g., load curtailment minimization). Therefore, related operators are able to manage their network elements and change the weight of the objective functions depending on contingencies. However, during normal operation, the outage probability is reduced by considering the possibility of purchasing power from the UN; therefore, economic issues are a primary priority for operators. In order to achieve this goal, the MGO of each participating MG derives an optimal energy management solution for the system using a variable weighted multi-objective function, which is formulated in the next section. Therefore, the main advantage of the proposed method over the existing methods is that it can constantly update control actions of the next timeslot (one-hour intervals in this paper: ΔT=1 h).

As illustrated in Fig. 3, when a fault occurs on each side of the system, the related operators try to change their strategy by using proposed method and scheduling the available resources over next timeslots. It must be noticed that, when a contingency occurs in the current time slot, since coordination between operators (MGOs and DNO) requires enough time, related operator try to change their strategy for the next time slot and its effects in the current time slot have been ignored. However, for the grid connected portions, operators can use the real-time energy market. Therefore, in faulted operation modes, the actions related to the next timeslot are executed and this process continues until the related fault is totally removed. The general assumptions intended for this study are as follows:

• All MGs and the DN communicate with each other via commu• • • • • • •

nication network, which is assumed to be entirely reliable and secure. The operational costs of renewable energy resources (RERs) are ignored. A faulted component is repaired before a subsequent one occurs. Demand response is ignored in the present article, although it can be simultaneously considered in the problem formulation. The failure rate of the protective devices are neglected. One of the purposes of this study is to maximize total profits of MMG system, which basically depends on the active power, therefore, only active power is considered for cost minimization. Furthermore, active and reactive power losses are not considered in this study. The MMG system is assumed to be supplied from the UN through a single PCC and also each MG is assumed to be supplied from the DN through a single PCC. Some resources are not in the ownership of the MGs (e.g. FBESSs and MBESSs).

These assumptions are usually accepted in studies of distribution networks [28–32].

Fig. 3. Block-diagram routine representation of the hour-ahead scheduling timeline with consideration of the probability of failure modes effect. 5

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

3.1. Problem formulation

being supplied in the next timeslot, or not [14, 32]. Together with the objective functions, MGs operation should obey the following constraints to ensure feasible solutions:

In this section, the detailed formulation is presented. As taking into account only economic parameters might determine a feasible operating solution which does not solve outage problems of the MMG systems, both reliability and economic parameters are considered and a variable weighted multi-objective function is formulated. Since the proposed method is on the basis of decentralized architecture, the objective functions for MGs and DN are formulated separately, as follows:

■ Power balance constraints: The energy balance in the MGs has to be fulfilled. In this situations, the sum of the power purchased from DN, total power generated with local resources, charging/discharging power of FBESSs and EVs and curtailed load in the MGi must be balanced with local demand. Consequently, for each MG at each timeslot, the balance of energy can be seen as Eq. (6). It must be noticed that, if production is greater than consumption in the faulted portions of the MGs, MGOs can reduce some part of their production in order to maintain the balance.

3.1.1. Problem formulation for MGs Each MG in the present study try to maximize its own benefit considering the probability of equipment failure and the feasibility of bidirectional energy trading between itself and DN. Consequently, for each MG, maximize the served loads (OF1), minimize the total voltage variation (OF2), maximize the overall operation profit (OF3) and maximize profit of the resources which are not in the ownership of the MGs (OF4) are objective functions that have to be optimized simultaneously with equality and inequality constraints. The goal is to converge these four objective functions into one, using the variable weighted coefficients. Mathematically, the multi-objective function for different modes of MGs operation is formulated as follows:

max{OFt } =

11

12

13

14

21

22

23

24

31

32

34

:

:

:

:

i1

i2

i3

i4

nt

OF1: max

33

nLP

nt

1j

0

ij

1

&

2j ij

j, my j, m P j, m NID, MG (t )

{

m M t=1

OF1 OF2 , OF3 OF4

nID

j=1

1

= max

m M

OF3: Max

nt t=1 nt t=1

j=1

nt t=1

m M

(1

v j, m (t ))

(2)

v j , m (t ) > 1

nDG j =1

(CDG, MGs (t )

n ess j, m j, m j, m S (t ) PFBESS (t ) AFBESS (t )) j = 1 FBESS

j, m j, m PDG , MGs (t ) ADG, MGs (t ))

nID j, m P j, m (t ) Acut (t )) j = 1 cut

(Ccut (t )

ncu j=1

+CNID, MG (t )

m + (CEx (t )

j, m AFBESS (t )

+(CEV (t )

m M

nt t=1

{CFBESS (t )(

(1)

m PEx (t )

j, m,min PDG , MGs (t )

j, m PDG , MGs (t )

j, m,min QDG , MGs (t )

j, m QDG , MGs (t )

j, m PDG , MGs (t ) j, m PDG , MGs (t

ness j, m j, m j = 1 SFBESS (t ) PFBESS (t )

j, m FBESS (t )) n ev j, m j, m S j, m (t ) PEV (t ) AEV (t ) j = 1 EV

m,max PEx (t )

(7)

m, t

j, m,max PDG , MGs (t ) j, m,max QDG , MGs (t )

(8)

j, m, t

(9)

j, m, t

The downward and upward climbing rate of dispatchable DG units at each time period should satisfy the constraint as:

nID P j, m (t )} j = 1 ID, MG

(4)

OF4: Max

(6)

■ Ramp response constraints on dispatchable DG Units:

m m m Ex (t ) PEx (t ) AEx (t ))

j, m (y j, m PNID , MG (t )) + CID, MG (t )

j, m, t

For each MG, the power output of dispatchable DG units at each time period should satisfy the constraint as:

(3)

n ev j, m j, m S j, m (t ) PEV (t ) AEV (t )) j = 1 EV

+ (CEV (t )

nID P j , m (t ) j = 1 ID

■ Generation limits on dispatchable DG Units:

v j, m (t ) < 1

1)

ne j, m m (t ) PEx (t ) j = 1 Ex

j, m y j, m PNID , MG (t )

m,min PEx (t )

(v j, m (t )

{(CFBESS (t )

nCu j =1

j, m PDG , MGs (t )

Active power at the PCCs between each MG and DN must be limited to provide the real operation condition. In this context, the power exchange constraint between each MG and DN is as follows:

v j, m (t ) nLP j =1 nLP j =1

=

+

nDG j=1

MG2 operatingconditions : MGi operatingconditions

m M t=1 j =1 m M

nR P j , m (t ) j=1 R

+

■ Limit of power exchanged between MGs and DN:

nLP

OF2: Min

+

n ev j, m (t ) S j, m (t ) PEV j = 1 EV

+

MG1operatingconditions

j, m PID , MG (t )}

+

n ess j, m j, m (t ) PFBESS (t ) S j = 1 FBESS

j, m PDG , MGs (t

1)

1)

j, m PDG , MGs (t )

Crupward t

j, m, t

(10)

Crdownward t

j, m, t

(11)

■ Generation limits on RERs: j, m EV (t ))}

The amount of power absorbed by each RER must be bounded by the maximum available power as follows:

(5)

In which, σi1, σi2, σi3 and σi4 are weight coefficients for objective functions of OF1, OF2, OF3 and OF4 respectively. These coefficients are adjusted according to importance degree of objective functions considering the system status (faulted or un-faulted durations). It is worth mentioning that, in OF1, each MGO try to maximize the served loads based on the priority factor. In doing so, δj, mis the priority factor which is assigned to each non-interruptible load (critical loads have higher priority) within each MG . Also, with consideration of the δj, mand system status, yj, m as the binary factor determines whether each load is

0 0

PRj, m (t ) QRj, m (t )

PRj, m,max (t ) QRj, m,max (t )

j, m, t j, m, t

(12)

■ Power flow constraints: On the one hand, a power flow study is the most important and essential approach whose target is to determine the voltages, real and reactive power flows and etc., on the other hand, most commonly used 6

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

models (DC and AC power flow) have some disadvantages; e.g., reactive power and voltage levels are ignored in DC power flow and the AC power flow directly uses the conventional methods to solve the nonlinear equations which will increase complexity and computation time. Therefore, the linearized AC power flow model (called Distflow) is used in our problem formulation. Distflow equations have been used in many literatures for MGs and MMG systems [14, 32, 34]. Mathematically, the linearized power flow equations for a particular node i (see Fig. 4) are formulated as the following equations: L (i 1, i)

L, m PLine (t )

L (i, i + 1)

j, m,min SOCFBESS / EV (t )

j, m, ch FBESS / EV

24

L (i, i + 1)

i, m y i, m QNID , MG (t )

v i + 1, m (t ) = v i, m (t )

i, m, t

(15)

The limitation of voltage magnitude for each operation timeslot is considered as follows:

Vi (t )

Vimax (t )

nDG k=1

(

■ Battery capacity constraints on FBESSs and EVs [35]:

j, m, ch FBESS / EV

j, m, ch,max (t ) PFBESS / EV (t )

0

j, m, dch PFBESS / EV (t )

j, m, dch FBESS / EV

j, m, dch,max (t ) PFBESS / EV (t )

j, m , j , m, SOCFBESS / EV (t ) = SOCFBESS / EV (t

1

1) +

j, m, dch PFBESS / EV dch FBESS / EV

j, m, t j, m, t

j, m, ch ch FBESS / EV PFBESS / EV

(t ) t

state NFBESS / EV

j, m, t

(22)

j, m, t

(23)

j, m, t

nt t=1

[(

nMG k=1

k CEx (t )

K K k Ex (t ) PEx (t ) AEx (t ))

k k k CDG , DN (t ) PDG, DN (t ) ADG, DN (t ))

(CUN (t ) PUN (t ) AUN (t )) + CCu, DN (t )

nCu k=1

k (PCu , DN (t ))]

(24)

The energy management constraints for DN are intended as follows:

The scheduled power references for the batteries of FBESSs/ EVs at each timeslot (t), must be no greater than the maximum power that they can provide at each t. So, the limits for charging and discharging power are demonstrated in Eqs. (17) and (18). Additionally, the state of charge (SOC) which is related to the storage energy at each t, can be modeled as Eq. (19). Besides, the SOC at each t is bounded in the allowable range as Eq. (20). Also, Eq. (21) ensures that the batteries cannot charge and discharge simultaneously. On the other hand, The rechargeable battery employed within EVs and FBESSs is often characterized as having a useful life defined by the number of continuous charge/discharge cycles with respect to a given level of capacity fade; on the other word, cycle life is the number of discharge/charge cycles that the battery can experience before it fails to meet specific performance criteria. From this point of view, the number of alternative state change must be limited for each operation day to maximize the battery life time; consequently, from Eq. (22), the number of state conversion at the beginning and the end of time horizon per day (24-hours) should state not be greater than a predetermine value (NFBESS / EV ). Indeed, when a contingency fault occurs during the operation of each MG, this operating constraint has a direct influence on the capability of the different types of storage units (EVs and FBESSs) to contribute to the compensation of the outages [36]. j, m, ch PFBESS / EV (t )

1)

j,max PID (t )

ObjDNO : max

(16)

i, t

0

j, m, ch / dch FBESS / EV (t

3.1.2. Problem formulation for DN The operation management problem for DN can be formulated as an optimization procedure, involving the maximization of the overall operation profit. In this context, the operation cost of DN is composed of: power exchange cost between each MG and DN, power exchange cost between DN and UN and the cost of power generation through DGs which located in its own area. Also, the total revenue is obtained from selling power to each MG and its own consumers. Mathematically, the objective function for DN energy management is formulated as follows:

(14)

i, m , L , t

j, m PID (t )

0

■ Voltage magnitude limits:

Vimin (t )

(21)

j, m, t

For each interruptible demand, the amount of interruptible load should be lower than the maximum load curtailment capacity:

L, m L, m (RL PLine (t ) + XL QLine (t ))

/ vbase

1

■ Limits of load interruption:

i, m y i, m PNID , MG (t )

L, m i, m i, m QLine (t ) + QDG , MGs (t ) + QR (t )

i, m QID , MG (t ) = 0

j, m, ch / dch FBESS / EV (t )

(t )

also, 0 denotes idle state; meanwhile, in the present investigation state NFBESS / EV = 5.

i, m, t

L, m QLine (t )

j, m, t

ch Where, FBESS / EV represents the charging state, where 1 indicates dch charging; FBESS / EV is the discharging state, where 1 denotes discharging;

(13) L (i 1, i)

j, m, dch FBESS / EV

(t ) +

t=1

L, m i, m i, m PLine (t ) + SEV (t ) PEV (t )

i, m i, m +PDG , MGs (t ) + PR (t )

=0

j, m,max SOCFBESS / EV (t )

(20)

i, m i, m + SFBESS (t ) PFBESS (t )

i, m PID (t )

j, m SOCFBESS / EV (t )

■ Power balance constraints: The required power demand must be balanced by the total power generations of local resources along with the power purchased from UN and MGs in order to maintain reliable operation. Consequently, for DN at each timeslot, the balance of energy can be seen as: nDG

k PDG , DN (t ) +

k=1

nMG k=1

nCu

=

k PCu , DN (t )

K k Ex (t ) PEx (t )

+ PUN (t )

k, t

k=1

■ Limit of power exchanged between DN and UN:

(17) (18)

(t ) t (19)

Fig. 4. Simple node in the radial MG. 7

(25)

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

Active and reactive power at the PCC between DN and UN has to be in a limited bound, as: max PUN (t ) max QUN (t )

PUN (t ) QUN (t )

max PUN (t ) max QUN (t )

some portions which are not connected to DN might not be satisfied (see Fig. 5–Section 4, 5). Therefore MGOs have to determine the effective dispatch scheme of their own available recourses in islanded portion. That is why in the proposed method, the objectives are prioritized by the MGOs. On the other hand, when a fault occurs in the DN, the required power of some DN's portions which are connected to UN could be satisfied (see Fig. 5–Section 1). The customers within these sections would not be interrupted. Also, for the DN/islanded portion, DNO determines the optimum scheduling of its own grid after receiving the shortage or surplus power of the all MGs which are located in the islanded portion. (see Fig. 5–Section 2). b) Fully islanded: each MG might disconnect from the DN according to fault isolation, also DN might disconnect from UN (see Fig. 5section K and section 0, respectively). If any contingency occurs in the external grid which leads to isolation of the overall MMG system, MGs can be operated in island mode, because they have an ability to supplying their loads in some operation timeslots. Also, in DN, the power supplied by its local generations along with surplus power from each MG, may entirely remove this interruption, or, at least, may change the long interruption to a short or momentary one. In this case, economic issues are less important than network issues and the main objective is to maximize the served loads. Therefore, some objectives are privileged to other objectives and related operators must be able to change the weights of the functions according to the proposed approach. Motivated by above discusses, the weights of the functions are adjusted according to importance degree of objective functions during different situations which are listed in Table 1. These weights were

(26)

t t

(27)

■ Generation limits on dispatchable DG Units: same as the Eqs. (8, 9) ■ Ramp response constraints on dispatchable DG Units: same as the Eqs. (10, 11) ■ Limit of power exchanged between MGs and DN: same as the Eq. (7) ■ Power flow constraints: same as the Eqs. (13)–(15) ■ Voltage magnitude limits: same as the Eq. (16) 3.1.3. Weights adjustment In order to adjust the weights of the functions, all situations should be considered individually. Indeed, as demonstrated in Fig. 5, due to the repair time, replace time and failure rate of the system components, different types of faults (with various location and duration) can occur in the MMG systems which create different situations on each side of the system. These situations can be listed as follows: a) Hybrid (islanded/grid-connected): When a fault occurs in the MGs, related interconnection devices are used to isolate faulted section. In these circumstance, the required power of some portions which are connected to DN could be satisfied, also they have opportunity to send their surplus power to DN (see Fig. 5–Section 3, 6). According the ability of MGO to change its operating strategy, the customers within these sections would not be interrupted. But, the required power of

Fig. 5. MOs decisions for different types of faults with various locations and durations. 8

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

dimension, number of complexes and number of points in each complex, respectively. Step 1 (evaluation): Sample the population q1, q2 , …, qs within the feasible space [LB, UB]. Evaluate the performance of each member of the population in terms of related objective function value (Fi). If previous information was not available, use a uniform sampling distribution. Step 2 (sorting): Sort the s points in descending order based on their fitness. Store them in an arrayD = {qi , Fi , i = 1, ... , s} , this will result in the smallest criterion function value generating parameters at the bottom of the sampled parameter list. Step 3 (partitioning): Divide D into p complexes C1, …, C p with predefined size of the population. Each complex has m points, such that: C x = {qjx , F jx |qjx = qx + p (j 1), F jx = Fx+ p (j 1), j = 1, ... , m} . In this procedure, the first to p individual goes to the first to pth complex, therefore, individual (p + 1)th goes back to the first complex, etc. Step 4 (evolving): Evolve each complex Cx in parallel through a given fixed amount of the predefined number of times. The evolution of the complexes takes place using CCE algorithm (which is implemented in step 4.1–4.6) with three types of evolution steps, namely: reflection, contraction and mutation.

Table 1 Weights of the objective functions (Eqs. (2)-(5)) which must be adjusted by MGO for each timeslot. MGs operation modes Hybrid (islanded/gridconnected) Fully islanded Grid-connected

Grid-connected portions Islanded portions Due to the fault occurrence Optional islanded mode Optional grid-connected mode

σi1

σi2

σi3

σi4

0 0.8 0.6

0.25 0.2 0.4

0.6 0 0

0.15 0 0

0.2 0

0.2 0.25

0.4 0.6

0.2 0.15

determined with sensitivity analysis to diminish uncertainty and rank functions based on their contributive effects which is presented in last section. 3.2. Problem solution In some circumstances, due to the stochastic nature of the failures, related operators should act quickly to prevent disadvantage to their customer. For this purpose, this section has the aim of developing the accurate and efficient algorithm as an appropriate global optimization method to determine the best decision parameters of a MMG system for each timeslot. The proposed algorithm is based on the SCE algorithm as an effective global optimization algorithm which is called TSSCE. The essence of the proposed algorithm is as follows.

• Step 4.1: Initialize CCE parameters. In doing so, select w, α and β, where 2 ≤ w ≤ m, α ≥ 1and β ≥ 1. • Step 4.2: Calculate the probabilistic weights: assign a triangular probability distribution to Cx, which pi = m (m + 1) , i = 1, ..., m .According to the pi, the pointq1x has the highest probability, 2 in the same way, the pointqmx has the lowest probability, 2(m + 1

3.2.1. SCE SCE optimization algorithm is a relatively intelligent method consisting of the ability to cope with global optimization problems characterized by the large numbers of parameters, without the need of calculating any extra information; e.g. gradient or partial derivative information [37]. Motivated by the attractive features of SCE algorithm, nowadays, it has been used successfully for solving many problems in various fields with different multi-parameters and multi-objective functions [38–41]. This algorithm is a global search method comprising the tiers of population, simplex and complex. At first, the algorithm starts with a specified number of population, which are randomly distributed within the feasible bounded space. Then initial population is scattered equally into set number of complexes. These complexes are allowed to evolve independently from each other using the competitive complex evolution (CCE) procedure. Indeed, CCE procedure is used to change the simplex's worst vertex that help the search process into the best solution (evolving step). In doing so, a concept of the Nelder-Mead Simplex search strategy (concept of the reflection and contraction process) is used to continually evolve the individuals of a population toward better solutions in the pre-designated search space. It is worth mentioning that, in this step, if the results are not favorable, mutation process is implemented and the worst individual of the subcomplex gives its place to a new random solution taken from the feasible bounded solution space. After several generations, the complexes are mixed together, and new complexes are organized to share information which is obtained separately from each complex (shuffling step). So, it is inferred that SCE algorithm has the ability of powerful global searching. These two steps are repeated until certain convergence criteria are satisfied to achieve the best possible parameter in the feasible space. To sum up, SCE algorithm provides an applicable mechanism to merge benefits of both population-based evolution in stochastic manner and the direct-search in deterministic manner, but it does not guarantee to avoid being trapped into the local solution. The main steps considered for this algorithm are as follows.

2 ; m2 + m

• Step •

• • •

Step 0 (initialization): Select p ≥ 1and m n + 1to generate population (s = pm ) from the feasible space (using upper and lower bounds of the parameters; [LB, UB]), where n, p and m are

• 9

i)

m+1

4.3 (parents selection): Define a subcomplex: Randomly choose wseparate points u1, u2, ..., uw from Cx according to step 4.2. Save them in B which it is an array and define {ui , Fi , i = 1, ..., w} , where Fi the cost function value is related to point ui. Save in Cx in theL locations, then used them to create B; Step 4.4 (offspring production): Arrange w points by sorting B and w 1 L to increase function value. Use (1/(w 1) j = 1 uj ) to calculate the centroid g. Implement steps a-e, where, (a) Reflection step: find the reflection point using ur = 2g u w ; (b) If uris within [LB, UB], calculate Fr (function value of ur), then go to step c; otherwise, implement mutation step, in doing so, by considering into account the Cx, compute the smallest hypercube H⊂[LB, UB], then by considering H, randomly generate a mutation point z, calculate Fz (function value of z), set r and Fr to z and Fz, respectively; (c) IfFr < Fw, replace ur by uw, move to step e; otherwise implement contraction step, calculate uc = (g + u w )/2 and Fc(function value of uc); (d) Compare Fc with Fw, if Fw > Fc, replace uc by uw, move to step e; otherwise, implement mutation step for the second time, in doing so, randomly generate a mutation point (z) within H, replace uwby uz; (e) Repeat steps (a) to (d) in ψcycles (ψ > 1is a predefined parameter). It must be noticed that in each ψ, g must be calculated separately. Step 4.5: Relocate the parent's position (B) with the offspring, also arrange Cxto increase function value. Step 4.6: Repeat steps 4.1 to 4.5 in ζ cycles (ζ > 1is a predefined parameter). This step determines the number of offspring which should be generated to evolve all complexes. Step 5 (shuffling): Combine the evolved complexes from the step 4 into a single populationD = {C x , x = 1, ..., p} . Arrange D to increase criterion value. Step 6: If one of the convergence criteria is met then stop, else go to step 2, so finally, the process stops with the total-best solution.

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

3.2.2. Proposed TSSCE Motivated by the above motioned facts, unlike the conventional optimization methods (e.g. genetic algorithm (GA), particle swarm optimization (PSO)), SCE algorithm merges benefits of both populationbased evolution in stochastic manner and the direct-search in deterministic manner, which lead to have the ability of powerful global searching mechanism. These benefits are key features that have motivated the authors of the present article to modify the original SCE and make it become an appropriate optimization method for multi-objective problems with higher coverage rate and higher success rate of search. In retrospect, it is concluded that, behind the benefit of SCE algorithm there is a gap in this algorithm when it is unable to find an improved set of variables in CCE procedure [38, 42]; i.e., in the CCE procedure, updating of worst fitness is limited in the line segment between its current position and the average position of other individuals in its related complex without considering their function values. Thus in SCE algorithm, local search space is restricted during each complex evolution procedure and best individual of population has a less chance of evolution. This may lead to the improper searching process and results in premature convergence. Because of this, the algorithm may be trapped to unwanted local optima. To prevent such problem and increase the capability of local search of SCE algorithm, some researchers tried to improve the original SCE algorithm by adding the extra steps in CCE procedure [38]; This article assumed that the direction of search to find a best offspring can be determined by the more operations along with the reflection and inside contraction (expansion and outside contraction). Also, some tried to combine the SCE algorithm with other approaches [42]. These articles found creative ways to dominate shortcomings of traditional SCE algorithm, however, it may lead to increased complexity when confronting with multi-objective optimization problems. To this end, with the aim of simplicity and faster computation, the proposed SCE-based method is used to avoid the blindly search which is called TSSCE. Based on the TSSCE algorithm, it is possible to determine a much better search direction by combining the information of the function values of the populations in centroid g (step 4.4). Indeed, the present improved algorithm is similar to the original one except that it has to consider the function values of populations for its reflection and contraction steps. This mechanism increases the chances of producing offspring with high quality, thus may lead its convergence process in best directions. The flowchart of the proposed TSSCE algorithm is illustrated in Fig. 7. The main difference between presented TSSCE and original SCE algorithm is presented through the following steps:

rnew and Fr, new to z and Fz, respectively; (d') Compare Fr, new with Fw, if Fw > Fr, new, replace ur, newby uw, move to step f’; otherwise, implement new contraction step which it is based on g’ with considering the function values of the all populations, calculate uc, new = (g + u w )/2 and Fc, new(function value of uc, new); (e') Compare Fc, new with Fw, if Fw > Fc, new, replace uc, newby uw, move to step f’; implement mutation step for the second time, in doing so, randomly generate a mutation point (z) within H, replace uwby uz; (f') Repeat steps a’ to e’ in ψcycles, where ψ > 1is a predetermined parameter which set by user. 4. Proposed general framework As demonstrated in Fig. 8, the unified framework for implementing the proposed energy management strategy along with the reliability study of MMG systems, can be described as follows. Step 1: In this step, the main required data are collected. These data include: chronological information of controllable loads and noncontrollable Load, generation scenarios of DG and DERs, charging and discharging scenarios of FBESSs and EVs, network and conventional units’ constraints and the failure rate and repair or replace time of the main components within DN and MGs (including, lines, distribution transformers and etc.) Step 2: The network conditions are determined in this step, in doing so, the process of SST technique [33], is used to simulate fault conditions and generate a contingency event due to the failure rate (λ) and repair rate (μ) of the components. Quoting from Ref. [33], the operation procedure corresponding to the number of components decomposes into several states S(k). Some states in which contingency occurs, called off states, otherwise called on states. Each state has a probability density function fi (t ) = i exp( i t ) and it can transit to the next state S (k + 1) depending to the state duration T with the probability density function as Eq. (29). By considering that the MMG system contains m components, the transition rates of the components related to current state S(k) are δi (i =1, …, m). If the current state is up, then δi=λi, otherwise, δi=μi. Therefore, the state duration for state count k is calculated as Eq. (30). Then jth component which cause fault is detected with Eq. (31). Consequently, the location and outage duration of an unpredictable contingency event are detected based on this technique. Motivated by above discusses, for each timeslot, the status of the MMG system (each MG and DN) can be determined according to the concepts presented in Section 3.1.3.

Step 4.4′ (offspring production): Sort B and L so that the w number of populations are arranged in each complex. Then, imf . plement steps a (a') Calculate the function values (fj) of all populations in related complex, where j =1,…, w-1, then, compute the new centroid g′through Eq. (28). Based on this scheme, fitness values of all individuals are considered to find a much better search direction (see Fig. 6). Therefore, high quality individuals have more opportunities to become parents than low quality;

g =

w 1

1 w

1

j=1

fj fbest

uj

(28)

(b') Use the new centroid g′ to calculate the new point ur , new = 2g u w , which determined new reflection point and it is based on the function values of the all populations; (c') Check ur, new, if it is within feasible space [LB, UB], then calculate Fr,new, this function value for each step is likely better than Fr (for traditional SCE algorithm), this is due to the new best search direction. Go to Step d’; otherwise, implement mutation step and set

Fig. 6. New search direction in CCE procedure. 10

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

Fig. 7. Flowchart of the proposed TSSCE algorithm.

step. In doing so, the proposed energy management strategy is implemented during current timeslot and the principal decisions are made by the related operators (MGOs and DNO) for the next timeslot. Step 5: In this step, total curtailed load, unavailability or outage times and the number of customers affected at each load point are recorded to evaluate the reliability of customer load points in the system under study. In this context, the most widely used distribution system reliability indices are system average interruption duration index (SAIDI), system average interruption frequency index (SAIFI), customer average interruption duration index (CAIDI), average system unavailability index (ASUI), energy not supplied (ENS) and average energy not supplied (AENS) [45]. It should be emphasized, since the proposed method is based on the hour-ahead scheduling mechanism, the reliability indices must be updated in each timeslot. From this point of view, SAIDI and AENS are generalized in Ref. [28] for hour-ahead scheduling methodologies. The other indices (SAIFI, CAIDI and ASUI) are also generalized in present article for hour-ahead scheduling which are formulated as Eqs. (32)–(37). These generalized indices are used in this step for the purpose of MMG systems reliability evaluation.

m

f (t ) =

i (t )

ie

(29)

i=1

1

d (k ) =

Pj =

m i=1 i

j i=1 i

ln(rand )

if

rand

[0, 1]

0 < rand P1 P1 < rand P1 + P2 j 1 i = 1 Pi

< rand

j i = 1 Pi

(30)

then then then

P1 = failure component P2 = failure component Pj = failure component

(31) Step 3: For each timeslot, load profiles and the output power scenarios of RES units within the faulted and normal sections are sampled with predetermined scenarios which are presented in next section. Moreover, SOC and the number of EVs within the parking lots are determined with the stochastic energy modeling procedure of Ref. [43] and data of Ref. [44]. Also, SOC of FBESSs is updated according to the simulation of the previous timeslot. Step 4: Considering the outcome of previous step and status of the system, the weight of the objective functions are adjusted in this 11

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

Fig. 8. Proposed general framework.

SAIFI =

8760 t . Nt

Nc Nt c=1 t=1 Nc N c=1 c

c (t ) Nc

(Frequency /Customer . t . Nt )

Nc N c=1 c

t

ASUI = 1

× Nt

8760 t . Nt

Nc c=1

t

Nc N c=1 c

× Nt

Nt U (t ) Nc t=1 c

(35)

(32)

SAIDI =

8760 t . Nt

Nc Nt U (t ) Nc c=1 t=1 c Nc N c=1 c

ENS = (Hour / Customer . t . Nt )

8760 t . Nt

(33)

AENS =

CAIDI =

Nc c=1 Nc c=1

Nt U (t ) Nc t=1 c Nt (t ) Nc t=1 c

(Hour / Frequency )

8760 t . Nt

Nt

Lac (t ) Uc (t )

c =1 t=1

Nc c=1

Nt L c (t ) Uc (t ) t=1 a

Nc Nt )

(34)

Nc

(Watt. Hour/ t . Nt )

(36)

(Watt. Hour/Customer. t . (37)

Step 6: This process is iterated and the reliability indices are continuously updated until the convergence criteria are satisfied. 12

Journal of Energy Storage 27 (2020) 101087

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5. Numerical simulation results

Table 2 Detailed information of the test system.

5.1. Test system In this section, simulations are done in a modified version of reliability test system to demonstrate the effectiveness of the proposed HEMS. To this end, as illustrated in Fig. 9, the modified version of the distribution system of RBTS (Bus 6) [46] is used for the case study. The RBTS has useful advantages compared to the other test system, including the availability of reliability data for main components. The distribution network at bus 6 is a typical rural network with a total of 40 load points comprising commercial, small industrial, agricultural and residential customers. The modified version consists of 2938 customers which are decomposed into five separate sections with their own loads and distributed energy resources. This modified version is called MMG system which has four MGs (named MG1-MG4) and DN. Based on the numerical values adopted in this study, in normal operation and with consideration of the interruptible demand, all MGs have enough generation capacity to approximately supply their loads only in some circumstances, also they are interconnected and can exchange energy with DN according to the operation strategy and related operator's decision. Detailed test system information are shown in Table 2. The basic parameters for the test system and the lengths of the main lines (L1-L64) can be found in Ref. [46], also, the lengths of the other lines (La-Lk) are assumed about 0.6Km. Reliability data of dispatchable DG units is given from Ref. [47]. Also, failure rate of the transformer, distribution line repair time and transformer replace time are adopted from [48]. One can deduce from this paper that lines and cables have a failure rate which is significantly dependent on their length. Consequently, the main feeders (L1-L64) have a failure rate of (L × 0.065)f/yr for voltage level 11KV and (L × 0.046)f/yr for voltage level 33KV. On the other hand, the occurrence of a fault in the UN is inevitable, therefore, the values of MTTR and MTTF for UN are set to 2

Units

Load points

Customer type

Load level per load point (MW) Peak Average

Number of Customers

DN

14, 17 15 16 18, 23 19 20 21 22 24 25 26 27 1, 3 2, 4 5, 6 7, 8, 10 9 11 12, 13 28, 36 29, 39 30 37 38 40 31 32 33 34 35

Commercial Small industrial Small industrial Residential Residential Agricultural Agricultural Residential Agricultural Residential Agricultural Residential Residential Residential Residential Residential Residential Residential Residential Residential Residential Agricultural Agricultural Agricultural Agricultural Residential Agricultural Residential Agricultural Agricultural

0.8500 1.9670 1.0830 0.2964 0.3229 0.6517 0.6860 0.3698 0.7965 0.2776 0.7375 0.2831 0.3171 0.3229 0.3864 0.2964 0.3171 0.3229 0.3698 0.2776 0.2831 0.6517 0.5025 0.7375 0.7965 0.2776 0.5025 0.2831 0.6517 0.6860

10 1 1 147 126 1 1 132 1 79 1 76 138 126 118 147 138 126 132 79 76 1 1 1 1 79 1 76 1 1

MG1 MG2

MG3

MG4

Fig. 9. MMG system under study.

13

0.4697 1.6391 0.9025 0.1659 0.1808 0.2501 0.2633 0.2070 0.3057 0.1554 0.2831 0.1585 0.1775 0.1808 0.2163 0.1659 0.1775 0.1808 0 2070 0.1554 0.1585 0.2501 0 1929 0.2831 0.3057 0.1554 0.1929 0.1585 0.2501 0.2633

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

period is 7.2KW/h. Moreover, SOC and the number of EVs within the parking lots are determined with the stochastic energy modeling of Ref. [43] and data of Ref. [44]; then, the load caused by the EV charging time is determined after this procedure; for this work, the detailed information of the parking lots is presented in Table 4. The daily profiles for the studied loads are visualized in Fig. 12 [54, 55]. This figure is indicate that the profile is significantly different for the four types of loads, e.g. the system has higher agriculture demands in summer and spring months. In this study, interruptible demands are just available in two time intervals; 11:00AM to 2:00PM and 6:00PM to 9:00PM. Furthermore, 8% of residential demands for MG 1 and 2, and 4% of residential demands along with the 5% of agricultural demands for MG 3 and 4 are considered as interruptible demands, which the location of them are selected in a stochastic manner.

and 1460 h, respectively [28]. In the power systems, the protective devices have a higher precision and lower failure rate compared with the other devices; so, in many network reliability studies, protective devices are assumed to be fully reliable and functioning in the intended manner. These assumptions are commonly used and well accepted in network reliability studies [28, 29 and 43]. So, some of the components (e.g. protection device and etc.) that have not been taken into account are assumed to be 100% reliable. The line resistance and reactance of all MGs and DN are given from Ref. [49]. It must be considered that, in the power flow analysis, a power factor of 0.9 is considered for all mentioned loads, therefore reactive power of each load point is determined with information of Table 2 and Fig. 12 (see Section 5.2). According to the proposed scheme, each timeslot is set to 1 h and system operation was simulated in four seasons of the continuous months until convergence criteria were met. It is worth mentioning that, the simulation results are made by Matlab software on a professional computer with 4.2 GHz processor (intel core i7 7700k) and 32 GB of RAM.

5.3. Results and discussion To verify the superiority of the proposed energy management strategy, a comparison of the results of the following Cases is demonstrated clearly. It is worth mentioning that, for all Cases power transfer capacities of PCC1-PCC4 are considered: 1.2 MW, 1.8MW, 2.5 MW and 1.5 MW, respectively.

5.2. Input datas As illustrated in Fig. 10, in order to increase simulation accuracy and to capture the unpredictability and intermittent nature of renewable sources, three types of hourly wind speed models are used for each season. In other words, in each day of the seasons, one of the three samples is selected randomly for scheduling. For this work, wind data is acquired from Ref. [50]. Also, it is assumed that the WTs are the same type. Furthermore, for the sake of higher computational efficiency, two types of solar irradiation within a season are used for the studied MMGs system (see Fig. 11). It is worth mentioning that the RERs are assumed to work at maximum power point tracking mode with zero operating cost. It must be noticed that, in order to increase simulation accuracy, a white noise which refers to a statistical model for samples were added to make a change in the weather conditions. The parameters and rated capacities of dispatchable DERs, RERs and FBESSs are given in Table 3. Also, the hourly electricity price is obtained from Ref. [51] and operation cost of storage unit is adopted from Ref. [52]. In each parking lot, EVs are equipped with a 22 kWh battery pack according to the concept EV called Yoshita [53]. In this EV, the efficiencies of the battery and its charger are 0.9 and 0.964, respectively. The EV chargers are installed at a fixed parking lots and the charging and discharging power levels are also fixed according to certain standards. Indeed, the parking lots are considered as demand aggregators to find the total charging and discharging power of the EVs. In this context, for each EV, the maximum power transfer rate per each time

• Case 1: Optimal scheduling for just maximize the overall operation • • • •

profit in all conditions (SCE algorithm is used as the problem solution). Case 2: Optimal scheduling for both faulted and normal conditions based on fixed-weighted multi objective functions [σi1, σi2, σi3, σi4] =[0.3, 0.3, 0.3. 0.1] (SCE algorithm is used as the problem solution). Case 3: Optimal scheduling for both faulted and normal conditions based on the proposed HEMS using variable weighted multi-objective function and proposed problem solution (TSSCE algorithm). Case 4: Same as Case 3, except that SCE algorithm is used as the routine problem solution. Case 5: Same as Case 3, except that PSO algorithm is used as the routine problem solution.

The general framework presented in Section 4 is used to measure the reliability difference of the proposed HEMS (Case 3) along with other Cases. The major reliability indices for each section of the modified MMG test system for all Cases mentioned have been calculated and the results are summarized in Figs. 13–16 and Table 5. These results show that Case 3 has the greatest system availability, meaning when

Fig. 10. Hourly profiles of averaged wind speed (three sample for each season). 14

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Fig. 11. Hourly profiles of averaged solar irradiation (two sample for each season).

MMG system against unpredictable interruptions, also, it can reduce load curtailments in the entire system. From the results it is concluded that, the value of SAIFI is almost constant during operation, because this index is related to the system configuration (SAIFI=0.8967 Frequency/Customer.Year). In the other hand, there is a significant improve in SAIDI, CAIDI, ENS and AENS values. For the system, an improvement of 33% is achieved in the values of ENS from Case 1 to Case 3 and also, an improvement of 16.8% from Case 2 to Case 3. Also, SAIDI is reduced 28% from Case 1 to Case 3, thanks to the high percentage of served loads and thus the improve service availability (see Figs. 13 and 14). Also, it is expectable that, the improvement become clearer for larger systems. When contingency occurs in DN, during repair times of the faulted components, MGs, along with their local load points, can provide power supply for load points which are located in the DN. As a result, reliability indices in DN are also improved, however it has moderate improvement due to the system limitations. To sum up, the following conclusions can be extracted from the results shown in Figs. 13–16 and Table 5.

Table 3 DERs installed capacity in each MG and DN (it is assumed that all MTs and WTs generate power with 0.8 PF). Units

Type

Max Capacity (kW)

DN

MTs1 MTs2 MTs3 WTs PVs Each FBESS WTs WTs+ PVs FBESS MTs WTs PVs Each FBESS WTs+ PVs FBESS

600 800 1200 1100 600 200 850 500+400 400 1300 1100 700 150 1250+700 400

MG1 MG2 MG3

MG4

Table 4 Detailed information of the parking lots. Area

Maximum capacity number of PEV

Available Discharging Time

Available SOC (%) per each time slot

MG1

80

6:00–13:00 & 18:00–23:00

MG2

80

9:00–14:00 &17:00:24:00

MG3

60

08:00–24:00

MG4

45

08:00–24:00

10% 30% 30% 20% 10% 15% 20% 40% 20% 5% 10% 30% 30% 20% 10% 15% 20% 40% 20% 5%

(1) Proposed HEMS can enhance the reliability level of customers in the MMG system which can be confirmed by comparing the results presented in Figs. 13–16 and Table 5. This is due to the fact that considering the variable weighted multi-objective function in problem formulation, the local resources can be utilized with their high capacity in more contingencies, while the economic issues are neglected. Therefore, the system reliability indices are significantly improved by the proposed strategy (Case 3) compared with the other Cases, and it basically related to the reduction of system interruption and outage times. (2) The conventional problem formulation mainly used in MG systems presented in Case 1; compared with the proposed HEMS (Case 3) and Cases 4 and 5, it underestimates the probability of system component failures. Therefore, it achieves the cynical results about outage times, also, according to the numerical results, it is obvious that, all the reliability indices of Case 1 have deteriorated. As a result, more customers within the MMG system are exposed to higher risk of power outage as compared to Cases 3–5. Also, in Case 2, less attention has been paid to interruption durations due to the fact that in both faulted and un-faulted operations, the reliability issues are identical to the economic issues. (3) The obtained results confirm that the reliability improvement of load point inside DN varies with load point which are located in MGs. Indeed, load points located in MG 1, 2 and 4 can meet greater reliability improvement compared with other load points. (4) According to information of Table 3, the value of power output in

SOC<20 20≤SOC<30 30≤SOC<40 40≤SOC<50 SOC≥50 SOC<20 20≤SOC<30 30≤SOC<40 40≤SOC<50 SOC≥50 SOC<20 20≤SOC<30 30≤SOC<40 40≤SOC<50 SOC≥50 SOC<20 20≤SOC<30 30≤SOC<40 40≤SOC<50 SOC≥50

contingency occurs, power supply reliability of local loads can increase by the related MGOs decisions. From this point of view, as can be drawn from simulation results (see Figs. 13–16 and Table 5), implementation of the proposed HEMS can significantly improve the flexibility of the 15

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Fig. 12. Daily profiles for the four types of loads.

Fig. 13. Comparison of ASUI of each load point with varying Cases.

Fig. 14. Comparison of ASUI of each section with varying Cases.

each MG is available between 0 and 3.6 MW. Meanwhile, power transfer capacities of PCC1-PCC4 are considered between 1.2 to 2.5 MW. Hence, it is obvious that the power supply capability of MGs to external load points is limited. So, when a contingency occurs in

DN, this leads to a moderate improvement in reliability indices of the loads, which are located between other side of the fault and nearest MG. (5) AENS and ENS in Table 5 for Case 1 have a significant deviation 16

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Fig. 15. Comparison of SAIDI of each section with varying Cases.

Fig. 16. Comparison of CAIDI of each section with varying Cases.

compared to the other Cases, because the scheduling is just based on the normal operation. Also, ENS is at its lowest value for Case 3 when compared to other Cases.

algorithm. It is noteworthy to remark that, since the operation cost of RERs are neglected in the present article, some MGs have high profits compared to DN. Furthermore, for the same day, Fig. 17 shows the lowest and highest voltages level of the served load in all sections. It can be seen that in Case 3, the lowest and highest voltage levels are within the safest range of fluctuation compared to the other Cases. In order to show the impact of the different energy management strategy (Case 1–5) on the charging/discharging profile of EVs, for the same day and same contingency (in L35, at 11:30 AM), the values of charging and discharging profiles of EVs (for MG3 and MG4) were extracted with Case 1 to Case5, and the results are shown in Figs. 18 and 19. These results demonstrate that the charging/discharging process can be non-continuous and occur any time within the entire duration considering the total available capacity of parked EVs in each parking lot. Also, for MG3 and MG4, regarding the system operation mode, the charging/discharging profiles of each FBESS were studied and the results are presented in Figs. 20 and 21, respectively. Furthermore, the general impact of the various energy management strategies (Cases1-5) on the SOC of FBESSs can be seen in Figs. 22 and 23. In all Cases, the initial SOC for MG3 and MG4 are 48 and 37.5 respectively. The impact of the different charging/discharging profiles on the SOC of FBESSs can be seen clearly in the initial faulted operation time intervals (11:30 AM), where the aggregate SOC rises sharply for the Case3. Indeed, for each FBESS, the value of SOC changes based on the extracted decision variables (charge and discharge status) as well as

For the typical day in summer which the system experience a contingency in L35 (at 11:30 AM), the values of DN and each MG profits are extracted with Case 1 to Case5 and listed in Table 6. When the economic issue is at the highest priority for operators and the probability of a fault occurrence in each side of the system is not considered (Case 1), the total profits of the MG3 and MG4 are $307.509 and $1375.044, respectively. When economic and reliability objectives are prioritized by the operators, the associated values are $49.183 and $1073.081, respectively. From the results it can be concluded that the system reliability is improved when considering the proposed HEMS (Case3), but at the expense of a slight decrease in total profits. Also, the associated value for Case 2 is reduced severely due to the fact that in both faulted and un-faulted operations times, the reliability issues have an identical weight with the economic issues. Therefore, by considering the proposed HEMS, the reliability level increase significantly, while, the total operation profits may decrease slightly, which can reflect the influence of the variable weighted multi-objective function on the scheduling results. As illustrated in Tables 5 and 6, the results from Case 3 is close to the results from Cases 4 and 5, however, the difference is not neglectable, which verifies the superiority of the proposed problem solution (TSSCE algorithm) when compared with the SCE and PSO 17

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Table 5 Comparison of ENS and AENS of each section with varying Cases. Units

ENS (MWH/Year)

AENS (MWH/Customer.Year) Customer type Case 1

Case 2

Case 3

Case 4

Case 5

DN

Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case

Commercial Small industrial Residential Agricultural

0.3393 1.0607 0.0203 0.7140

0.3055 1.0039 0.0182 0.6527

0.2775 0.8280 0.0179 0.5403

0.2890 0.8870 0.0181 0.5588

0.2913 0.9450 0.0181 0.5685

Commercial Small industrial Residential Agricultural

– – 0.0177 –

– – 0.0131 –

– – 0.0109 –

– – 0.0118 –

– – 0.0121 –

Commercial Small industrial Residential Agricultural

– – 0.0144 –

– – 0.0120 –

– – 0.0093 –

– – 0.0099 –

– – 0.0103 –

Commercial Small industrial Residential Agricultural

– – 0.0187 0.8851

– – 0.0127 0.7999

– – 0.0088 0.5708

– – 0.0090 0.6022

– – 0.0095 0.6042

Commercial Small industrial Residential Agricultural

– – 0.0334 1.3119

– – 0.0277 1.1415

– – 0.0183 0.4356

– – 0.0188 0.4671

– – 0.0197 0.5326

Commercial Small industrial Residential Agricultural

0.3393 1.0607 0.0182 0.9393

0.3055 1.0039 0.0147 0.8396

0.2775 0.8280 0.0123 0.5228

0.2890 0.8870 0.0128 0.5533

0.2913 0.9450 0.0131 0.5716

MG1

MG2

MG3

MG4

System

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

22.923 20.734 19.453 19.902 20.034 13.525 10.032 8.334 8.993 9.255 14.001 11.667 9.010 9.625 9.982 9.3250 7.1298 5.0031 5.2005 5.3714 9.1185 7.7254 4.1416 4.3174 4.6551 68.8925 57.2882 46.1391 48.0379 49.2975

the efficiency of the batteries. Further, it would be interesting to show the superiority of the proposed optimization algorithm in term of CPU time compared with other algorithms. The proposed energy management strategy developed in this article determines the optimal hour-by-hour (hour-ahead) scheduling for the MMG system; therefore, for each day, the optimization process will be repeated 24 times. Consequently, the computational

time of the optimization process is strongly important if we need to optimize both the energy cost and the reliability of the system over a complete year. In that case, the CPU time related to the (24×365) successive operating steps can reach with measurements of TTotal, 24 × 365 where, TTotal = i = 1 Ti . Clearly, one of the aims of the present article is to address this concern by developing a faster optimization algorithm. From this point of view, the proposed optimization algorithm

Table 6 Total profits ($) of each section. Units

Cases

DN

Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case Case

MG1

MG2

MG3

MG4

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

Self-generation cost

Cost of buying power from MGs/DN/UN

Cost of interruptible demands

Revenue from the sale of power to MGs/DN/UN

Revenue from the sale of power to noninterruptible and interruptible demands

Value of profits

8650.3 8747.1 8963.0 8990.8 8998.3 265.3 280 293.7 295.1 296.9 342.5 355.1 367.0 369.3 370.5 3536.6 3649.7 4052.2 4063.1 4101.5 437.6 441.1 456.9 457.9 459

20030.6 19954.3 19866.3 19997.0 20101.1 3650.0 3671.3 3536.1 3644.2 3745.6 3821.0 3844.2 3800.9 3841.1 3877.8 3089.9 2967.3 2908.1 2914.7 2918.7 3535.2 3642.6 3600.1 3661.4 3679.3

– – – – – 466.2 468.9 507.0 456.5 493.7 478.2 483.1 513.5 469.8 502.9 461 482 509.7 491.5 488 466.2 588.7 507.4 500.3 493.5

3954.3 3870.5 3547.2 3611.5 3700.4 398.9 331.8 307.1 381.3 367.9 401.5 337.6 315.9 392.4 377.3 498.7 331.2 597.6 581.8 567.3 244.4 175 245.5 227.9 219.4

26009.1 25880.5 26482.2 26563.5 26568.3 5547.7 5502.1 5530.9 5511.5 5507.1 5764.5 5721.3 5751.3 5730.5 5728.3 6796.3 6600.1 6921.7 6862.4 6856.1 5569.7 5324.1 5391.9 5413.5 5408.1

1282.4 1049.4 1199.9 1187.1 1169.3 1865.1 1713.7 1801.2 1796.9 1638.8 1824.3 1676.4 1685.6 1742.6 1654.4 307.5 −167.7 49.2 −25.2 −84.7 1375 826.7 1073.1 1021.7 995.6

18

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Fig. 17. Highest and lowest voltage levels of load points in each section.

Fig. 18. Charging/discharging profiles of EVs for MG3.

developed in this investigation leads to a better compromise in terms of convergence speed by converging close to the optimal solution, which reduces the CPU time dramatically compared to conventional methods (SCE and PSO) without compromising on the quality of the solution. Indeed, the proposed optimization algorithm (TSSCE) is faster in terms of computational time than SCE algorithm since the new searching method is used to avoid the blindly search. From this point of view, the CPU times taken by three separate tests (Cases 3 to 5) were extracted and the results are demonstrated in Table 7. The given times correspond to the total time required to run proposed TSSCE, SCE and PSO until each MG and DN reach global

optimality (considering system constraints, power flow constraints and generation units’ constraints). As can be seen from the Table 7, for each operation time slot (1 h) taking into account the different operation modes (as described in Section 3.1.3), the CPU times for Case 3, vary from 101.34 s to 121.04 s that are lower than those of Cases 4 and 5 values. Thus, the CPU times of the proposed optimization method (TSSCE) decrease significantly compared with the results of Cases 4 and 5. Consequently, from the results, it can be concluded that, standard SCE has the shortcomings that the calculation time is too long and it is easy to fall into local optimal solution.

Fig. 19. Charging/discharging profiles of EVs for MG4. 19

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

Fig. 20. Charging/discharging profiles of FBESS for MG3.

Fig. 21. Charging/discharging profiles of FBESS for MG4.

Fig. 22. SOC of FBESS for MG3.

5.4. Sensitivity analysis

considering different weights for objective functions. As an example, for MG4 which is located in the islanded portion, with the increase in weight coefficient of OF3, since less attention paid to problems associated with served loads, ENS increases. On the other hand, excessive increases in the weight coefficient of OF1 would reduce the value of ENS, but at the expense of an excessive decrease in total profits (see Fig. 24(a) and (b)). Therefore by considering the operation modes (faulted or un-faulted timeslots), it is necessary to rank four objectives (which are presented in Section 3.1.1) based on their contributive effects. From this point of view, according to the importance degree of objective functions and simulation results, these objective functions are prioritized and the weight coefficients of them are presented in Table 1

The aim of this section is to explore the viability of implementing proposed HEMS in a typical MMG system. Indeed, the viability of implementing proposed HEMS is sensitive to a weight coefficient of each objective function. Understanding how weight coefficients affect the proposed HEMS implementation is critical to determining whether the energy management will be profitable. The trade-off between total operation cost and load served is the main factor that have a significant effect on the profitability of the energy management. For the typical day in summer with a contingency in L35, the results have a wide diversion compared to aforementioned results, when 20

Journal of Energy Storage 27 (2020) 101087

H. Afrakhte and P. Bayat

Fig. 23. SOC of FBESS for MG4. Table 7 CPU time comparison; TS= Min., Max. and average CPU times for the optimization process of each operation time slot (1 h) in one day operation of the system (a typical day in summer which the system experience a contingency in L35 (at 11:30 AM)). Cases

Optimization method

Pop. size

Algorithm termination

CPU time (TS (s)) Min.

Max.

Ave.

3 4 5

TSSCE SCE PSO

150 150 150

Maximum number of generation (80) Maximum number of generation (80) Maximum number of generation (80)

101.34 173.67 119.71

121.04s 198.97 143.75

112.55 188.04 134.25

Fig. 24. The effects of different weight coefficients on: (a) profit and (b) ENS; (where Sigma is weighting factor (σ)).

(see Section 3.1.3). It must be noticed that, according to the various configuration of MG and MMG systems and different system operation strategies, operators can choose different [σi1, σi2, σi3, σi4] to achieve their purposes.

reliability conditions, particularly in MGs and DNs, and also in MMG systems with radial configuration. In addition, the results indicate the improved system reliability after considering the proposed HEMS, but at the expense of a slight decrease in total profits. There exist some limitations in the present study, which should be further investigated. First, demand response is ignored, although it can be simultaneously considered in the problem formulation. Second, the failure rate of protective devices is also neglected. It can be commented that the performance of protective devices can have influence on reliability indices. Third, although the CPU times of the proposed optimization method (TSSCE) decrease significantly compared with the results of original SCE and some other algorithms, but, the extracted results should be compared with the results of the other solvers (e.g. GAMS software) in the future works.

6. Conclusion and future works This study introduces a HEMS for MMG systems, consisting of the proposed problem formulation and solution. Based on both emergency and optimality conditions, the MMG system energy management is formulated as a variable weighted multi-objective function with the purpose of solving both network and economic problems, while satisfying operation constraints of the system. Moreover, a comprehensive reliability assessment framework along with the modified reliabilitybased MMG test system is developed to investigate the impact and feasibility of the proposed HEMS. The numerical results are encouraging, showing that the reliability performance of the MMG system can be significantly improved by the proposed HEMS and that it is possible to effectively minimize the outage time of customers with poor

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to 21

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influence the work reported in this paper. Supplementary materials

[28]

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.est.2019.101087.

[29] [30]

References

[31]

[1] K. Karabiber, Controllable AC/DC integration for power quality improvement in microgrids, Adv. Electric. Comp. Eng. 19 (2) (2019) 97–104. [2] P.B. Nempu, J.N. Sabhahit, Stochastic algorithms for controller optimization of grid tied hybrid AC/DC microgrid with multiple renewable sources, Adv. Electric. Comp. Eng. 19 (2) (2019) 53–60. [3] Z. Xua, P. Yanga, C. Zhenga, Y. Zhanga, J. Penga, Z. Zenga, Analysis on the organization and development of multi-microgrids, Renew. Sustain. Energy Rev. 81 (2018) 2204–2216. [4] D. Ming, M. Kai, B. Rui, Energy coordination control of multi-microgrid based on multi-agent system, Power Syst. Protect. Control 41 (24) (2013) 1–8. [5] S.A. Arefifar, M. Ordonez, Y.A.R.I. Mohamed, Energy management in multi-microgrid systems: development and assessment, IEEE Trans. Power Syst. 32 (2) (2017) 910–922. [6] W. Shi, X. Xie, C.C. Chu, R. Gadh, Distributed optimal energy management in microgrid, IEEE Trans. Smart Grid 6 (3) (2015) 1137–1146. [7] H.M. Kim, Y. Lim, T Kinoshita, An intelligent multiagent system for autonomous microgrid operation, Energies 5 (9) (2012) 3347–3362. [8] S.A. Arefifar, Y.A.R.I. Mohamed, T. El-Fouly, Optimized multiple microgrid-based clustering of active distribution systems considering communication and control requirements, IEEE Trans. Indust. Electron. 62 (2) (2015) 711–723. [9] Y. Liu, Y. Li, H.B. Gooi, Y. Jian, H. Xin, X. Jiang, J. Pan, Distributed robust energy management of a multi-microgrid system in the real-time energy market, IEEE Trans. Sustain. Energy 10 (1) (2019) 396–406. [10] A. Kargarian, M. Rahmani, Multi-microgrid energy systems operationin corporating distribution-interline power flow controller, Electric Power Syst. Res. 129 (2015) 208–216. [11] F.H. Aghdam, S. Ghaemi, N.T. Kalantari, Evaluation of loss minimization on the energy management of multi-microgrid based smart distribution network in the presence of emission constraints and clean productions, J. Clean. Prod. 196 (2018) 185–201. [12] Z. Wang, B. Chen, J. Wang, Coordinated energy management of networked microgrids in distribution systems, IEEE Trans. Smart Grid 6 (1) (2015) 45–53. [13] B. Zhao, X. Wang, D. Lin, M.M. Calvin, J.C. Morgan, R. Qin, C. Wang, Energy management of multiple microgrids based on a system of systems architecture, IEEE Trans. Power Syst. 33 (6) (2018) 6410–6421. [14] Z. Wang, B. Chen, J. Wang, J. kim, Decentralized energy management system for networked microgrids in grid-connected and islanded modes, IEEE Trans. Smart Grid 7 (2) (2016) 1097–1105. [15] Z. Wang, B. Chen, J. Wang, C. Chen, Networked microgrids for self-healing power systems”, IEEE Trans. Smart Grid 7 (1) (2016) 310–319. [16] Q. Sun, R. Han, H. Zhang, J. Zhou, J.M. Guerrero, A multi agent based consensus algorithm for distributed coordinated control of distributed generators in the energy internet, IEEE Trans. Smart Grid 6 (6) (2015) 3006–3019. [17] T. Erseghe, Distributed optimal power flow using ADMM, IEEE Trans. Power Syst. 29 (5) (2014) 2370–2380. [18] E. Loukarakis, J.W. Bialek, C.J. Dent, Investigation of maximum possible OPF problem decomposition degree for decentralized energy markets, IEEE Trans. Power Syst. 30 (5) (2015) 2566–2578. [19] E. Loukarakis, C.J. Dent, J.W. Bialek, Decentralized multi-period economic dispatch for real-time flexible demand management, IEEE Trans. Power Syst. 31 (1) (2016) 672–684. [20] D. Gregoratti, J. Matamoros, Distributed energy trading: the multiple-microgrid case, IEEE Trans. Indust. Electron. 62 (4) (2015) 2551–2559. [21] B. Zhanga, Q. Lia, L. Wangb, W. Fengc, Robust optimization for energy transactions in multi-microgrids under uncertainty, Appl. Energy 217 (2018) 346–360. [22] B. Gaurav, P.S. Bhanu, K. Rajesh, Strategic optimisation of microgrid by evolving a unitised regenerative fuel cell system operational criterion, Int. J. Sustain. Energy 35 (8) (2016) 722–733. [23] Y. Liu, H.B. Gooi, H. Xin, Distributed energy management for the multi-microgrid system based on ADMM, IEEE Power Energy Soc. Gen. Meet. (2017). [24] M. Mao, Y. Wang, L. Chang, Y. Du, Operation optimization for multi-microgrids based on centralized-decentralized hybrid hierarchical energy management, IEEE Energy Convers. Congr. Expos. (ECCE) (2017). [25] Y. Dua, Z. Wangb, G. Liub, X. Chenb, H. Yuanc, Y. Weid, F. Lia, A cooperative game approach for coordinating multi-microgrid operation within distribution systems, Appl. Energy 222 (2018) 383–395. [26] M.M. Ghahderijani, S.M. Barakati, S Tavakoli, Reliability evaluation of stand-alone hybrid microgrid using sequential Monte-Carlo simulation, Iranian Conference on Renewable Energy and Distributed Gen, 2012. [27] Y. Duan, Y. Gong, X. Tan, H. Wang, Q. Li, Probabilistic power flow calculation in

[32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]

[45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55]

22

microgrid based on Monte-Carlo simulation, Trans. China Electro Tech. Soc. 26 (1) (2011) 274–278. H. Farzin, M. Fotuhi-Firuzabad, M. Moeini-Aghtaie, Role of outage management strategy in reliability performance of multi-microgrid distribution systems, IEEE Trans. Power Syst. 33 (3) (2018) 2359–2369. H. Farzin, M. Fotuhi-Firuzabad, M. Moeini-Aghtaie, Enhancing power system resilience through hierarchical outage management in multi-microgrids, IEEE Trans. Smart Grid 7 (6) (2017) 2869–2879. F. Hamzeh Aghdam, J. Salehi, S. Ghaemi, Contingency based energy management of multi-microgrid based distribution network, Sustain. Cities Soc. 41 (2018) 265–274. X. Xu, J. Mitra, T. Wang, L. Mu, Evaluation of operational reliability of a microgrid using a short-term outage model, IEEE Trans. Power Syst. 29 (5) (2014) 2238–2247. A. Arif, Z. Wang, Networked microgrids for service restoration in resilient distribution systems, IET Gen. Trans. Distribut. 11 (14) (2017) 3612–3619. R. Billinton, A. Sankarakrishnan, A system state transition sampling technique for reliability evaluation, Reliab. Eng. Syst. Safe 44 (1994) 131–134. M. Baran, F. Wu, Optimal capacitor placement on radial distribution systems, IEEE Trans. Power Deliver. 4 (1) (1989) 725–734. F. Xiao, Q. Ai, New modeling framework considering economy, uncertainty, and security for estimating the dynamic interchange capability of multi-microgrids, Electric Power Syst. Res. 152 (2017) 237–248. M. Xie, X. Ji, X. Hu, P. Cheng, Y. Du, M Liu, Autonomous optimized economic dispatch of active distribution system with multi-microgrids, Energy 153 (2018) 479–489. Q.Y. Duan, V.K. Gupta, S. Sorooshian, Shuffled complex evolution approach for effective and efficient global minimization, J. Optim. Theory Appl. 76 (1993) 501–521. X. Gao, Y. Cui, J. Hu, G. Xu, Z. Wang, J. Qu, H. Wang, Parameter extraction of solar cell models using improved shuffled complex evolution algorithm, Energy Convers. Manage. 157 (2018) 460–479. Y. Ding, C. Wang, M. Chaos, R. Chen, S. Lu, Estimation of beech pyrolysis kinetic parameters by shuffled complex evolution, Bioresour. Technol. 200 (2016) 658–665. L. Hasalová, J. Ira, M. Jahoda, Practical observations on the use of shuffled complex evolution (SCE) algorithm for kinetic parameters estimation in pyrolysis modeling, Fire Saf. J. 80 (2016) 71–82. R. Carlos, M. Gomes, M.A. Vitorino, M. Beltrao, D.R. Correa, D.A. Fernandes, R. Wang, Shuffled complex evolution on photovoltaic parameter extraction: a comparative analysis, IEEE Trans. Sustain. Energy 8 (2) (2017) 805–815. V.C. Mariani, L.D.S. Coelho, A hybrid shuffled complex evolution approach with pattern search for unconstrained optimization, Math. Comput. Simul. 81 (2011) 1901–1909. H. Farzin, M. Fotuhi-Firuzabad, M. Moeini-Aghtaie, Reliability studies of modern distribution systems integrated with renewable generation and parking lots, IEEE Trans. Sustain. Energy 8 (1) (2017) 431–440. P. Bayat, H. Afrakhte, P. Bayat, A hybrid shuffled frog leaping algorithm and intelligent water drops optimization for efficiency maximization in smart microgrids considering EV energy storage state of health, J. Intell. Fuzzy Syst. 35 (5) (2018) 5619–5634. R. Billinton, R.N. Allan, Reliability Evaluation of Power Systems 2 Plenum press, New York, 1984. R. Billinton, S. Jonnavithula, A test system for teaching overall power system reliability assessment, IEEE Trans. Power Syst. 11 (4) (1996) 1670–1676. R. Karki, R. Billinton, Reliability/cost implications of PV and wind energy utilization in small isolated power systems, IEEE Trans. Energy Convers. 16 (2001) 368–373. R.N. Allan, R. Billinton, I. Sjarief, L. Goel, K.S. So, A reliability test system for educational purposes-basic distribution system data and results, IEEE Trans. Power Syst. 6 (2) (1991) 813–820. B.R. Sathyanarayana, Sensitivity-based Pricing and Multiobjective Control for Energy Management in Power Distribution Systems, PhD thesis Arizona state university, 2012. Jager D., Andreas A.NREL national wind technology center (NWTC): M2 Tower; Boulder, Colorado (Data). NREL Report No. DA-5500-56489. https://midcdmz.nrel. gov/nwtc_m2/. M. Jalali, K. Zare, H Seyedi, Strategic decision-making of distribution network operator with multi-microgrids considering demand response program, Energy 141 (2017) 1059–1071. H. Farzin, M. Fotuhi-Firuzabad, M. Moeini-Aghtaie, Stochastic energy management of microgrids during unscheduled islanding period, IEEE Trans. Ind. Inf. 13 (3) (2017) 1079–1087. P. Bayat, A. Baghramian, P. Bayat, Implementation of hybrid electric vehicle energy management system for two input power sources, J. Energy Storage 17 (2018) 423–440. J. Zhu, W. Gu, P. Jiang, S. Song, H. Liu, H. Liang, M. Wu, Dynamic island partition for distribution system with renewable energy to decrease customer interruption cost, J. Electr. Eng. Technol. 12 (6) (2017) 2146–2156. J.A. Jardini, C.M.V. Tahan, M.R. Gouvea, S.U. Ahn, F.M. Figueiredo, Daily load profiles for residential, commercial and industrial low voltage consumers, IEEE Trans. Power Deliver. 15 (1) (2000) 375–380.