1

Abstract—This paper investigates the effect of energy storage systems on the availability of microgrids with different architectures in the presence of renewable energy sources (RESs). When RESs are used for power generation within a microgrid, its availability may be reduced due to the intermittent nature of RESs. Thus, energy storage systems may be used as a solution to improve microgrids availability. Therefore, it is important to have a realistic evaluation of microgrids availability and to determine how added energy storage affects microgrids. Since energy storage system is not just a one-time-use reserve, charging and discharging processes in energy storage need to be considered when their availability is evaluated. Thus, a Markov chain model is used in this paper to properly represent the charging and discharging processes of energy storage systems, and minimal cut sets method is used in order to evaluate the availability of different microgrid architectures. Using the proposed method, availabilities of radial, ring, and ladder type microgrid architectures are evaluated in the presence of RESs and energy storage systems, and results are discussed.

Index Terms—Availability, distributed power generation,

energy storage, Markov processes, microgrids, solar power generation.

I. INTRODUCTION NE of the expected advantages of microgrids is having a higher availability compared to the current electrical grid

[1, 2]. Microgrids use controlled distributed energy resources to generate power which makes isolated operation possible [3, 4], thus improving the local availability of energy supply. On the other hand, availability becomes more of an issue when a greater capacity of renewable energy sources (RESs) is used to generate power within microgrids [5, 6]. This is mostly because of highly variable and intermittent nature of power generation by RESs. Hence, it is necessary to maintain the advantage of high availability that microgrids have even when a large amount of RESs' generation takes place within microgrids.

This work was supported by NEC Laboratories America, INC. (NEC

Labs). J. Song and A. Kwasinski are with the Department of Electrical and

Computer Engineering, The University of Texas at Austin, TX 78712, USA (e-mail: {tedsong, akwasins}@mail.utexas.edu).

M. C. Bozchalui and R. Sharma are with the Energy Management Department, NEC Laboratories America, Inc., Cupertino, CA 95014, USA (e-mail: {mohammad, ratnesh}@sv.nec-labs.com).

There are various strategies to improve the availability when RESs are included to generate power; one of the strategies is to add energy storage [7-9]. When added, an energy storage system can immediately improve microgrids availability; however, calculating the amount of improved availability is not simple and easy. This is mainly due to the charging and discharging processes that take place in energy storage system, which makes it difficult to predict how much power is available from energy storage system during microgrids' operation. Some works have been reported in the literature on the evaluation of microgrids availability and/or reliability indices—availability and reliability are not equal since availability here represents the probability of the load being fully powered at any given time, whereas reliability represents the probability of a component carrying out an expected function for a given period of time [1]. For instance, [10] and [11] analyzed the reliability of distributed generation without including energy storage system in the study. In [12], the presented work includes energy storage system within microgrids, however, charging and discharging processes are not taken into account for the storage model, which is not realistic since energy storage system is not a one-time-use energy reserve. In [13], the authors propose a combined distributed generations (DGs) and energy storage model to evaluates the reliability of microgrids which includes the states of DGs, energy storage, and energy stored in the storage device without considering the effect of system architectures on the availability or reliability of microgrids.

This paper proposes a method for microgrids availability evaluation using a Markov chain energy storage model and minimal cut sets (MCS). The proposed method uses a Markov chain model to properly model the charging and discharging processes in energy storage system, which makes possible to understand how RESs and energy storage function together to provide power to the load and affect microgrids availability. This model also enables calculating the effect of energy storage system connected to a microgrid with multiple energy sources and loads. Considering the effect of system architectures on the availability of microgrids—which is another important factor that affects microgrids availability—this paper uses MCS method [1]. Using this approach, it can be seen that how energy storage system takes its role within

Microgrids Availability Evaluation using a Markov Chain Energy Storage Model:

a Comparison Study in System Architectures Junseok Song, Student Member, IEEE, Mohammad Chehreghani Bozchalui, Member, IEEE,

Alexis Kwasinski, Member, IEEE, and Ratnesh Sharma, Member, IEEE

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• When a short circuit failure of a CB occurs, the other CBs connected to that fault will operate (or be opened).

• MCS in Tables I to III are determined for the cases when Load #1 is not powered.

• When any load fails to be powered, it is considered as a system failure (Tables VI and VII).

• Power output of PV sources and energy storage devices is variable. Whenever they cannot produce enough power for all loads it is then assumed that they are in the failed state.

Both passive event—i.e. a component failure that does not have an impact on the remaining healthy part of the system—and active event—i.e. a component failure that cause the

TABLE I MCS DESCRIPTION, PROBABILITY, AND QUANTITY FOR

THE RADIAL-TYPE SYSTEM ARCHITECTURE SHOWN IN FIG. 2

# Minimal cut sets (Load #1) Quantity and probability of occurrence

1 {L1}

2 {CB1}, {CB2}, {CB3}, {CB4}, {CB5}, {CB6}, {CB7}, {CB8} (8)( )

3 {U2S2E} 4 {U2S1E, E1}, {U2S1E, E2} (2)( )5 {U2S0E, E1, E2} 6 {U1S2E, S1}, {U1S2E, S2} (2)( )7 {U1S1E, S1, E1}, {U1S1E, S1, E2},

{U1S1E, S2, E1}, {U1S1E, S2, E2} (4)( ) 8 {U1S0E, S1, E1, E2},

{U1S0E, S2, E1, E2} (2)( )

TABLE II MCS DESCRIPTION, PROBABILITY, AND QUANTITY FOR

THE RING-TYPE SYSTEM ARCHITECTURE SHOWN IN FIG. 3

# Minimal cut sets (Load #1) Quantity and probability of occurrence

1 {L1}

2 {CB1}, {CB2}, {CB3}, {CB4}, {CB5}, {CB10} (6)( )

3 {U2S2E} 4 {U2S1E, E1}, {U2S1E, E2} (2)( )5 {U2S0E, E1, E2} 6 {U1S2E, S1}, {U1S2E, S2} (2)( )7 {U1S1E, S1, E1}, {U1S1E, S1, E2},

{U1S1E, S2, E1}, {U1S1E, S2, E2} (4)( ) 8 {U1S0E, S1, E1, E2},

{U1S0E, S2, E1, E2} (2)( )

TABLE III MCS DESCRIPTION, PROBABILITY, AND QUANTITY FOR

THE LADDER-TYPE SYSTEM ARCHITECTURE SHOWN IN FIG. 4

# Minimal cut sets (Load #1) Quantity and probability of occurrence

1 {L4} 2 {L2, L3} 3 {CB2}, {CB3} (2)( )4 {U2S2E} 5 {U2S1E, E1}, {U2S1E, E2} (2)( )6 {U2S0E, E1, E2} 7 {U1S2E, S1}, {U1S2E, S2} (2)( )8 {U1S1E, S1, E1}, {U1S1E, S1, E2},

{U1S1E, S2, E1}, {U1S1E, S2, E2} (4)( ) 9 {U1S0E, S1, E1, E2},

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(3)( )

Fig. 2. A radial-type system architecture

Fig. 3. A ring-type system architecture

Fig. 4. A ladder-type system architecture

4

removal of other healthy components of the system—are considered in the calculation of reliability indices. In Fig. 2 to Fig. 4, Solar #1 & #2 represent the photovoltaic (PV) generation, and Storage #1 & #2 represent energy storage system. When demonstrating the simulations, both PV generations are assumed to have the same amount of generation capacity (1 MW), and both storages are assumed to have the same amount of capacity (1 MW) as well. Tables I to III present the MCS of the radial, ring, and ladder microgrid architectures, respectively. As mentioned earlier, MCS in each table are determined for Load #1 (Figs. 2 to 4). In other words, MCS are set for the case when the microgrid fails to supply Load #1. Then, the system availability can be evaluated after determining availabilities for every load in the system. This process is not a time consuming process since many MCS are redundant within the same architecture. As shown in Table I, there are 8 MCS for the radial-type system architecture which is shown in Fig. 1. MCS #1 represents the failure of a bus that connects all components in the shown radial-type system architecture. As it can be seen, the whole system fails when bus L1 fails. This means not a single generation nor storage device is able to be connected with any load due to the failure of bus L1. MCS #2 represents the failure of a single CB, which is the case a CB fails to open when there is a short circuit. Short circuit failure of a CB causes a voltage drop which introduces a system failure. Then, the other CBs connected to the fault may or may not be opened for the protection at that moment of failure. In either cases, i.e. other CBs operate to be opened or not, a short circuit failure of a CB in the radial-type architecture, then, is a single point of failure since no load is able to be powered with the presence of a short circuit failure. Therefore, the CB unavailability ( ) is multiplied by eight since MCS #2 considers the failures of all eight CBs in the system. MCS #3 represents the unavailability even when all components of the system are healthy and have no failure. In other words, MCS #3 does not describe the failure rates of component, however, describes the unavailability of power resources including energy storage system. For example, when there is no solar generation, or storage level is not enough to supply the load, the system is considered unavailable even there is no failure within the system. Hence, u2S2E of MCS #3 represents the unavailability when all components—two PV sources and two energy storage systems—are working in order but they cannot meet the power level required by load.

MCS #4 represents a case that one of the two energy storage systems is failed to operate as storage. In this case, the unavailability of power resources which includes two PV sources and one energy storage system is evaluated. This unavailability, u2S1E,—i.e. a case that one of two energy storage is failed to operate—will be greater than that of u2S2E because there is less amount of capacity to store the energy within the system. In addition, when any of two energy storages fail to operate, it is assumed that the CB connected to that storage opens to protect the system. In a same manner, the rest of unavailabilities can be found for other MCS shown in Table I and II. Particularly, Table III has different MCS from the previous ones. This is because ladder-type system architecture has a

different approach to connect power resources and loads. Unlike the other architectures, Load #1 can be disconnected from the rest of the system by CB2 and CB3, as shown in Fig. 4. This is represented as MCS #3. With this type of connection, the total number of CBs may be increased; however, this gives a lower possibility of a system failure to supply the load with regard to failures within microgrids. In addition, MCS #10 and #11 include unavailabilities with the information of how many loads are connected to that generation. This information is given only for the ladder-type architecture because when CBs that are connected to L1 and L2 fail to operate in a certain step, Load #1 is separated from the loads in other steps. For example, if CB #4 and #6 in Fig. 4 fail to operate, CB #1 and #3 will automatically be opened for the protection. Then, Solar #1 becomes the only power resource that powers Load #1 which is the only load that is connected to Solar #1. Since MCS are determined from the perspective of Load #1, the unavailability becomes u1S0E1L. As a result, u1S0E1L will be greater than u1S0E because u1S0E1L considers only a single load being powered instead of all four loads.

V. SIMULATION RESULTS Table IV shows the availability values that are used to conduct simulations. As mentioned, only short circuit failures were taken into account for CBs in the availability calculation. In addition, the availabilities of power generation with different amount of PV and energy storage are evaluated using two different energy storage system models: the Markov chain model and two-state—i.e. available or unavailable—energy storage model that is used in power system study traditionally. The Markov chain model, which was introduced in Section II,

TABLE IV AVAILABILITY VALUES OF COMPONENTS USED IN THE NUMERICAL

EXAMPLES

Item Availability ( ) Unavailability ( )Line [20] 0.99999714 Circuit Breaker [20] 0.99998858 Photovoltaic Moduleα [21] 0.99998965 Energy Storage (Battery) [22] 0.99996742 Power Generation (2S, 2E)β 0.99995859 Power Generation (2S, 2E)γ 0.99999102 Power Generation (2S, 1E)β 0.95661314 Power Generation (2S, 1E)γ 0.99999102 Power Generation (2S, 0E) 0.71430000 Power Generation (1S, 2E)β 0.97918508 Power Generation (1S, 2E)γ 0.99998437 Power Generation (1S, 1E)β 0.91262556 Power Generation (1S, 1E)γ 0.99998437 Power Generation (1S, 0E) 0.50250000 Power Generation (1S, 0E) - 1L 0.84270000

α Repair time was assumed to be 50 hours. β Acquired by the Markov chain model γ Acquired by the two-state model (0 or 1)

TABLE V SIMULATION INPUT INFORMATION

Item Capacity PV Generation Capacity (Ea.) 1000 kW (avg. generation = 317 kW) Energy Storage Capacity (Ea.) 1000 kWh Load (Ea.) 73 kW (avg.) / 153 kW (max.)

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TABLE VI ILITY RESULTS (M

Availability ( )0.99986111 0.99986111 0.99986111 0.99986111 0.99944444 0.99988395 0.99988395 0.99988395 0.99988395 0.99953580 0.99992253 0.99992253 0.99992253 0.99992253 0.99969015

TABLE VIIABILITY RESULTS (

Availability ( )0.99989680 0.99989680 0.99989680 0.99989680 0.99958721 0.99991964 0.99991964 0.99991964 0.99991964 0.99967857 0.99996532 0.99996532 0.99996532 0.99996532 0.99986129

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proposed method, a comparison study in the system architectures—which include radial, ring, and ladder configuration—is conducted. The results are presented using actual solar PV generation and load profile data. Simulation results show that the proposed method provides more realistic estimation of the system availability compared to the two-state model which may give overestimated availability values. In addition, further research may include the methodology about how to evaluate availability when microgrids are connected to grid.

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