1 Introduction

Since the second and third industrial revolutions, the society experienced an impetuous advancement in technology as well as in economic sectors. The large traditional energy usage causes emissions of carbon, which affects global temperature to rise and form a shortage of fossil resources alongside. Renewable energy resources are abundant and have renewable properties. Therefore, the rational use of renewable energy will be the key to solve future energy shortages and protect the natural environment [1]. WTG has a good prospect of development and practical value. Electricity production is a gradual process. The planning, operation and control of the power grid are based on the principle of "balance between supply and demand." However, distributed generation based on wind turbines and photovoltaic power generation mainly depend on external conditions, which have fluctuations. It is difficult to regular and control them. This may lead to an unbalance between supply and demand. Large scale renewable energy generation connections in the power system will have a serious impact on the stable operation of the power system. To solve this problem, the multi-ESSs, which is system of WTG linked with each ESS, can be installed into the system. When the system is fully supplied, it will store energy and release it when the power system is stationary [2].

The power system reliability is the ability of the power system to continuously provide sufficient and high quality electricity to electricity power consumers. The reliability of power systems can be measured with reliability indicators. These indicators include the probability of failure, the frequency of the failure, and the time period of the failure. In addition, the expected power loss [MW] and expected electrical energy loss [MWh] caused by faults can also be used as indicators of power system reliability [3].

Probabilistic reliability evaluation of composite power systems including WTG [4] and effect of multi-BESS coordinated WTGs on power system reliability were studied by Prof. Jaeseok Choi (2017) [5]. In addition, the reliability evaluation of a single ESS model use MCS was studied by Dr. Po Hu (2009) [6]. Furthermore, the power system reliability impact of energy storage integration with intelligent operation strategy was studied by Prof. Chanan Singh (2014) [7].

The motive of this paper is to propose a model for the probabilistic reliability assessment of power systems with multi-ESSs installed in wind farms. In order to get the most optimized power system reliability solution, a multi-ESSs optimization operation problem was proposed in coordination with multi-WTGs in this paper. This algorithm is not only suitable for next-generation energy technologies with renewable energy resources, but also applicable to the feasibility and sensitivity analysis of conversion technologies.

2 Probabilistic Reliability Evaluation Method Using Monte Carlo Simulation

The MCS method is a calculation method based on the theoretical methods of probability and statistics. Considering the instability of renewable energy and the inherent uncertainty in the system, use MCS method can obtain the power system reliability coefficient through repeatedly and numerically generating a series of random numbers [8].

2.1 Generation Model

The two-state generator model include operating state (ON) and forced out of service state (OFF) as shown as Fig. 1a. In Fig. 1a, λ and μ are failure rate and repair rate respectively. They are calculated as like as Eqs. (1) and (2) [4].

$$\lambda = \frac{1}{MTTF}$$
(1)
$$\mu = \frac{1}{MTTR}$$
(2)
Fig. 1
figure 1

a Two-state generator model; b operating cycle of two-state generator model

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In the above equations, MTTF is mean time to failure and MTTR means mean time to repair. Sampling values of the time to failure (TTF) and time to repair (TTR) are shown in Fig. 1b. The relationship between TTF, TTR, and MTTF, MTTR can be obtained from the following equations [8].

$$MTTF_{i} = \sum\limits_{k = 1}^{{nY_{i} }} {TTF_{i,k} /nY_{i} }$$
(3)
$$MTTR_{i} = \sum\limits_{k = 1}^{{nY_{i} }} {TTR_{i,k} /nY_{i} }$$
(4)

where TTFi,k is time to failure of the ith generator at kth state [h], TTRi,k is time to repair of the ith generator at kth state [h]; MTTFi is mean time to failure of the ith generator [h]; MTTRi is mean time to repair of the ith generator [h]; nYi is Total operating years of the ith generator [years].

The chronological state transition process for a two-state generation is shown as Fig. 1b. The actual operating time in each generator unit maybe not be the same. So, it is impossible to apply the real operating results in a same time period. A virtual operation scenario for the same time period should be generated as shown as Fig. 2. The time period for each time regions with the MCS method is based on the forced outage rate (FOR) of the two-state model as shown as Eq. (5) [9].

$$FOR_{i} = \frac{{MTTR_{i} }}{{MTTF_{i} + MTTR_{i} }} = \frac{{\lambda_{i} }}{{\mu_{i} + \lambda_{i} }}$$
(5)

where FORi is forced outage rate at ith unit; λi is failure rate at ith unit; μi is repair rate at ith unit.

Fig. 2
figure 2

Available capacity of an example system

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From the chronological state transition process for a two-state generation, the operation history cycle for the virtual generators can be calculated by using following equations, Eqs. (6) and (7).

$$TTF_{i,k} = - MTTF_{i} \ln U_{k} = - \frac{1}{{\lambda_{i} }}\ln U_{k}$$
(6)
$$TTR_{i,k} = - MTTR_{i} \ln U_{k}^{{\prime}} = - \frac{1}{{\lambda_{i} }}\ln U_{k}^{{\prime}}$$
(7)

There the Uk and Uk' are the two uniformly distributed random number sequences between [0, 1] at the kth state. The total generator capacity in this research can be calculated using following Eq. (8).

$$TG_{k} = \sum\limits_{i \in NG}^{{}} {G_{i,k} \times ISK_{i,k} }$$
(8)
$$ISK_{i,k} = \left\{ {\begin{array}{*{20}c} 1 & {k \in \Omega {}_{{TTF_{i} }}} \\ 0 & {k \in \Omega_{{TTR_{i} }} } \\ \end{array} } \right.$$
(9)

where ISKi,k is the ith generator probability at kth state; TGk is total generation capacity at the kth state [MW]; NG is total generator unit; Gi,k is the ith generator capacity at the kth state [MW]; ΩTTFi is time to failure set at ith generator; ΩTTRi is time to repair set at ith generator.

In order to see the failure of the power system visually, the chronological load curve can be superimposed on the curve of the system's available capacity. Therefore, the available capacity of a system with load curve can be got as shown in Fig. 3.

Fig. 3
figure 3

Available capacity of a system with the load curve

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The reliability indices can be calculated using the following equations [10]. First, supply reserve power (SRP) can be calculated using Eq. (10). When the SRPk is negative, the not served energy (ENSk) arise. ENSk can be calculated using Eq. (11) as well. Thus, the reliability index expected energy not supplied (EENS) for a period is shown as Eq. (12).

$$SRP_{k} = TG_{k} + TW_{k} - PD_{k}$$
(10)
$$ENS_{k} = \left\{ {\begin{array}{*{20}l} {SRP_{k} } \hfill & {SRP < 0} \hfill \\ 0 \hfill & {SRP \ge 0} \hfill \\ \end{array} } \right.$$
(11)
$$EENS = \sum\limits_{k = 1}^{NSS} {ENS_{k} /NY}$$
(12)

where SRPk is supply reserve power at kth state [MW]; TGk is total conventional generator capacity at kth state [MW]; TWk is total wind turbine generator capacity at kth state [MW]; PDk is demand power at kth state [MW]; NSS is total number of states; NY is the period time in the MCS.

2.2 Wind Turbine Generator (WTG) Model

WTG systems are complex systems and generally include wind turbines, transmissions, generators, converters and corresponding support components, connection components and control components. WTG is an electrical equipment that converts wind resources into mechanical energy, thereby converting mechanical energy to electrical energy. The methodology for WTG model in this study is divided into two parts. Including the wind speed part and wind energy conversion system power generation part. The generation of hourly wind speed over a sufficiently long period of time is given site in this paper. The wind speed plays an important role in WTG output, there typical power curve of a WTG according to changing wind speed is shown in Fig. 4 [11].

Fig. 4
figure 4

WTG output curve

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As mentioned above, the WTG output (PW) depends on the wind speed. The PW according to changing wind speed can be calculated as follow equations.

$$P_{W} = 0,\;\;\;0 \le V \le V_{ci}$$
(13)
$$P_{W} = P_{R} \left( {A + B \times V + C \times V^{2} } \right),\;\;\;V_{ci} \le V \le V_{r}$$
(14)
$$P_{W} = P_{R} ,\;\;\;V_{r} \le V \le V_{co}$$
(15)
$$P_{W} = 0,\;\;\;V \ge V_{co}$$
(16)

The constants A, B, and C in Eq. (14) are depending on the cut-in wind speed (Vci), rated wind speed (Vr) and cut out wind speed (Vco) which can be determined as follow equations [12].

$$A = \frac{1}{{(V_{ci} - V_{r} )^{2} }}\left[ {V_{ci} (V_{ci} + V_{r} ) - 4(V_{ci} V_{r} )\left( {\frac{{V_{ci} + V_{r} }}{{2V_{r} }}} \right)^{3} } \right]$$
(17)
$$B = \frac{1}{{(V_{ci} - V_{r} )^{2} }}\left[ {4(V_{ci} V_{r} )\left( {\frac{{V_{ci} + V_{r} }}{{2V_{r} }}} \right)^{3} - \left( {3V_{ci} + V_{r} } \right)} \right]$$
(18)
$$C = \frac{1}{{(V_{ci} - V_{r} )^{2} }}\left[ {2 - 4\left( {\frac{{V_{ci} + V_{r} }}{{2V_{r} }}} \right)^{3} } \right]$$
(19)

Different places usually have different wind resources and the wind speed will not be the same. Even in the same area, the wind speed will change with the season and time. However, by observing the distribution of wind speed over a number of years in different regions, wind speeds in different regions will exhibit a similar Weibull probability distribution with a similar normal distribution. Combined with the wind output model mentioned above, the expected WTG output can be calculated using Eq. (20) [12].

$$EP_{{WTG_{k,t} }} = \sum\limits_{{i \in \rho_{kt} }} {\left( {PB_{swi} \times P_{swi} } \right)}$$
(20)

where EPWTGk,t is WTG expected output at time t of kth wind farm [MW]; PSWi is WTG expected output when the wind speed is SWi [MW]; PBSWi is probability when the wind speed is SWi; ρkt is the set of wind speeds on wind farm kth in a certain time t.

2.3 Multi-ESSs Model

This paper aims to develop a multi-ESSs model. This model requires each ESS to be connected to each wind farm to perform charging mode and discharging mode by using an appropriate control method. The basic model include multi-WTGs coordinated with multi-ESSs in power system is shown in Fig. 5.

Fig. 5
figure 5

Complete system with multi-ESSs model

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Where TGci is the ith conventional generator (CG) capacity [MW]; TGwi is the ith WTG capacity [MW]; SGwi is surplus output of ith WTG [MW]; qi is forced outage rate of ith CG; X% is percentage of a wind power dispatch restriction to supply load [pu]; Xi% is percentage of the ith WTG dispatch restriction to supply load [pu].

In the multi-ESSs model, the output WTG and ESS using to supply the load must obey the following rules [13].

WTG is using to supply the system load directly. If the wind resources are rich, the wind power is sufficient to supply demand. As a result, some of the surplus wind power can be stored in ESS. Once the wind speed is known, the total output of WTG can be calculated by using the WTG output curve. Then, use the wind power dispatch restriction parameter X% which is mentioned in the multi-ESSs model to calculate the surplus output of WTG (SGwi,k) as shown as Eq. (21). By the way, surplus output of CG (SGci,k) can be calculated use the total generator capacity of the conventional generating units minus the (1 − X%) total load as shown as Eq. (22).

$$SG_{wk} = \sum {TG_{wi,k} } - X_{i} \% \times L_{k} = \sum {SG_{wi,k} }$$
(21)
$$SG_{ck} = \sum {TG_{ci,k} } - (1 - X_{i} \% ) \times L_{k} = \sum {SG_{ci,k} }$$
(22)

where SGwk is total surplus output of the WTG at the kth state [MW]; SGci,k is total surplus output of the CG at the kth state [MW], TGwi,k is the ith WTG capacity at the kth state [MW]; TGci,k is the ith conventional generator capacity at the kth state [MW]; SGwi,k is surplus output of the ith WTG at the kth state [MW]; SGwi,k is surplus output of the ith WTG at the kth state [MW]; Lk is load at the kth state [MW]; Xi% is percentage of the ith WTG dispatch restriction to supply load [pu].

The energy storage time series for charging mode ESi,k, and the energy storage time series for discharging mode TGDi,k can be calculated in different conditions by using the following equations.

$$ES_{i,k + 1} = \left\{ {\begin{array}{*{20}l} {ES_{i,k} + SG_{wi,k} \times t_{k} } \hfill & {SG_{wi,k} \ge 0,\;SG_{ci,k} \ge 0} \hfill \\ {ES_{i,k} + SG_{ci,k} \times t_{k} } \hfill & {SG_{wi,k} \ge 0,\;SG_{ci,k} < 0} \hfill \\ {ES_{i,k} } \hfill & {SG_{wi,k} < 0,\;(SG_{wi,k} + SG_{ci,k} ) \ge 0} \hfill \\ {ES_{i,k} + (SG_{wi,k} + SG_{ci,k} ) \times t_{k} } \hfill & {SG_{wi,k} < 0,\;(SG_{wi,k} + SG_{ci,k} ) \le 0} \hfill \\ \end{array} } \right.$$
(23)
$$TG_{Di,k} = \left\{ {\begin{array}{*{20}l} 0 \hfill & {SG_{wi,k} \ge 0,\;SG_{ci,k} \ge 0} \hfill \\ { - SG_{ci,k} \times t_{k} } \hfill & {SG_{wi,k} \ge 0,\;SG_{ci,k} < 0} \hfill \\ 0 \hfill & {SG_{wi,k} < 0,\;(SG_{wi,k} + SG_{ci,k} ) \ge 0} \hfill \\ { - (SG_{wi,k} + SG_{ci,k} ) \times t_{k} } \hfill & {SG_{wi,k} < 0,\;(SG_{wi,k} + SG_{ci,k} ) < 0} \hfill \\ \end{array} } \right.$$
(24)

The ESS state of charge transition feature is shown as Fig. 6 [14]. If the SGwi,k is positive, the ESS should be charged. If the SGci,k is negative the ESS should be discharged. Therefore the control value of energy for ESS, EUi,k is proposed in this paper. In addition the state of energy ESi,k stored in the ESS is limited by a maximum value and minimum value as shown in following equations.

$$ES_{\min ,i} \le ES_{i,k} + EU_{i,k} \le ES_{\max ,i}$$
(25)
$$ES_{i,k} = ES_{i,k - 1} + EU_{i,k}$$
(26)
$$ES_{\min ,i} \le ES_{i,k} \le ES_{\max ,i}$$
(27)
Fig. 6
figure 6

ESS state of charge transition feature

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2.4 Multi-ESSs Operating Rule

The multi-ESSs model used in the power system aims to ensure reliable supply from each uncontrollable output of WTG. Therefore, the multi-ESSs operation rules is important to be determined as discharging mode and charging mode. As mentioned above, SGwk is a surplus output of WTG at kth state and SGck is surplus output of CG at kth state. There is new parameter SGk, shown as Eq. (28).

$$SG_{k} = SG_{wk} + SG_{ck}$$
(28)

As for operating rules, the proposed multi-ESSs model used the charging and discharging conditions as shown in Table 1.

Table 1 Charging and discharging rules
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As for discharging modes (II, IV), in the system with WTG connected multi-ESSs, if the total output of the existing conventional generators are less than (1 − X%) × Lk, ESS releases energy, as it is the discharge mode operates. In addition, if the total output of the existing conventional generators are less than (1 − X%) × Lk, and, at the same time the WTG's maximum permissible energy output is more than X% × Lk, in this time the ESS also discharge. In the power system with multi-ESSs, if only several ESSs used to supply the load can satisfy the demand, then the rest ESSs can be charged at the same time. However, if the power system only installed single ESS, it cannot operate charging mode at the same time with discharging mode. This is the reason why use the mark (★) in Table 1. As for charging mode (I), when the WTG's maximum permissible energy output is more than X% × Lk, at the same time the total output of WTG's maximum permissible energy output and the total output of the existing conventional generators are more than (1 − X%) × Lk, the ESS will save energy.

2.5 Reliability Evaluation Indices Calculation Method

In this study, a probabilistic method based on MCS is used in this paper through a simulation by repeatedly and numerically generating a series of random numbers. The reliability indices are calculated by summing and averaging the value of LOLE and EENS for every case. In addition, the energy index of reliability (EIR) is defined as follows [15].

  1. (1)

    Loss of Load Expectation (LOLE) [Hrs/yr]

    LOLE represents the average hours that the load value is expected to exceed the available system capacity in a time period tk.

    $$LOLE = \frac{1}{NY}\sum\limits_{{k \in \Omega_{D} }} {t_{k} }$$
    (29)

    where NY is simulation years; ΩD is a set of discharge modes.

  2. (2)

    Expected Energy not Served (EENS) [MWh/yr]

    When the power supply of the power system is less than the load demand, the shortage electricity of the power system can be defined as EENS. EENS can be obtained by the Eq. (30).

    $$EENS = \frac{1}{NY}\sum\limits_{{k \in \Omega_{D} }} {(TG_{Dk} + EU_{k} )}$$
    (30)

    where TGDk is discharge energy indispensable for eliminating any lack of supply for loads [MWh]; EUk is discharging control energy [MWh].

  3. (3)

    Energy Index of Reliability (EIR) [pu]

    $$EIR = 1 - \frac{EENS}{{TDE}}$$
    (31)

    where TDE is total demand energy [MWh].

2.6 Effective Load Carrying Capability (ELCC) and Capacity Credit (C.C.)

Using multi-ESSs model in a power system with distributed power sources can reduce the probability of insufficient power supply, thereby improving the reliability of the system. However, the actual reliable capacity of wind power will be less than its installed capacity. This chapter introduces the concept of actual reliable capacity of WTG and ESS. The capacity credit (C.C.) of the WTG is the ratio of its trusted capacity to its installed capacity [16].

  1. (1)

    Effective load carrying capability (ELCC) calculation method

    ELCC represents as "under the same stochastic target risk level, the ability of power system with supply load changes before and after expansion". The concept of ELCC as shown as Fig. 7 [16].

    Fig. 7
    figure 7

    Definition of ELCC

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    There, LOLE* is the same stochastic target risk level can be understood as same level of LOLE. The ELCC can be calculated using following equation.

    $$ELCC = PL_{ES}^{{LOLE^{*} }} - PL_{OS}^{{LOLE^{*} }}$$
    (32)

    where PLLOLE* ES is peak load of expanded system when the system LOLE is LOLE*. PLLOLE* OS is peak load of original system when the system LOLE is LOLE*.

  2. (2)

    Capacity credit (C.C.) calculation method

    C.C. is not only related to the expanded capacity in the power system, but also related to the economics of renewable energy generation. It is used as the index for valuation of renewable energy, which has much volatility. CA is total capacity of new generation.

    $$C.C. = \frac{ELCC}{{C_{A} }} \times 100\;[\% ]$$
    (33)

3 Case Study

The proposed method is applied to a power system of China-sized sample. According to the method mentioned above, using the input data from the similar China power system make a reliability evaluation for the power system. 1.36 billion people live within the 9,634,060 [km2] area in China. In 2016, power system installed capacity in China is shown in Table 2.

Table 2 Generator data of China power system in 2016
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In this case study, WTG in China's power system are integrated into three wind farms. Regionally divided into western wind area (WWA), eastern wind area (EWA) and southern wind area (SWA) shown as Fig. 8.

Fig. 8
figure 8

Regional wind farms in China

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There the WTG installed capacity in each wind areas shown as Table 3. In this table, the characteristic data include cut in wind speed, rated wind speed, cut out wind speed and average wind speed are also mentioned.

Table 3 WTG characteristic data of wind areas in China
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3.1 Basic Model of Reliability Evaluation

This paper aims to find the best way to improve the reliability of power system. That is using 3 kinds of different model systems for the following simulation (Fig. 9).

Fig. 9
figure 9

Three kinds of power systems in this paper

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In System C, the ESS specifications data with maximum ESS capacity is shown in Table 4.

Table 4 Multi-ESSs specifications in System C
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3.2 Basic Analysis of the Influence from Peak Load on System Reliability

After rapidly develop of China’s electrical industry over the last decade. The China’s electricity supply condition has been changed from a shortage electricity to an oversupply phenomenon. By the way, the imbalances in supply and demand condition are likely continue for the next decade.

Table 5 shows the reliability evaluation result of variation of LOLE, EENS and EIR of the model system according to changing of peak load in every model system. Max. ESS capacity in each wind farm in System C are shown as Table 4. Actually, China power system has already over capacity, and peak load is 980 [GW], at this point the reliability index is hardly change. In order to continue the research, choose the peak load as 1050 [GW] to continue the follow simulation (Figs. 10, 11).

Table 5 Reliability evaluation result in all of the systems
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Fig. 10
figure 10

LOLE with variation results under varying peak load

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Fig. 11
figure 11

EENS with variation results under varying peak load

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Above figures shows the reliability evaluation result of each system. There the peak load in these systems are 1050 [GW]. And the Max. ESS capacity in each wind area of systems are given in Table 6, System C is the most reliable.

Table 6 Reliability evaluation result for all systems
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3.3 Basic Analysis on the Impact of ESS Capacity on Reliability

In order to research the influence of ESS installed capacity on system reliability, 7 cases were proposed as shown in follow Table 7.

Table 7 Max. ESS characteristic data of cases
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Figure 12 shows the variation of LOLE and EENS of the model system according to changing of Max. ESS capacity in the 6 cases. It can easily see when the curve comes to Case D, the LOLE and EENS is decreased slowly. Compared Case E with Case F, the LOLE is hardly saturated. Therefore, in view point of reliability, it can be determined that optimal capacity of ESS is Case E (LOLE = 0.16 [Hrs/yr]).

Fig. 12
figure 12

Variation of reliability index of cases according to changing of ESS capacity

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3.4 Basic Analysis of WTG Dispatch Restriction to Supply Load (X% [pu])

4 cases are created to compare the variation of reliability index with the change of ESS capacity and the percentage of wind power dispatch restriction to supply load (X% [pu]). Got the result in each case as shown in Table 8.

  • Case 1: Without ESS

  • Case 2: ESS capacity are WWA: 36,960 MW, EWA: 23,750 MW, SWA: 13,630 MW.

  • Case 3: ESS capacity are WWA: 73,920 MW, EWA: 47,500 MW, SWA: 27,260 MW.

  • Case 4: ESS capacity are WWA: 184,800 MW, EWA: 118,750 MW, SWA: 68,150 MW.

Table 8 Reliability evaluation result according to changing of X% [pu]
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Results of system reliability changes as X% and Max. ESS Capacity changes as shown in Fig. 13. From this figure, after the curve arrived at the point X% = 0.3 [pu]. All of the cases have the same LOLE. It means added ESS or not is no influence for power system reliability, the ESS is not work. At the point X% = 0.1 [pu], WTG and multi-ESSs works flexible, efficient, every case has lowest LOLE. Therefore, the best reliability case can be Case 4 with the X% = 0.1 [pu].

Fig. 13
figure 13

Results of system reliability changes as X% and Max. ESS Capacity changes

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3.5 Effective Load Carrying Capability [ELCC] and Capacity Credit [C.C.] Calculation

Aimed to calculate the ELCC, there are 3 systems shown as Fig. 9 used in this part. Set a same LOLE level in each system and find the value of peak load. The input data in the model systems is shown in Table 9.

Table 9 Input data of model systems
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China power system's LOLE is around 8 [Hrs/yr] in 2016, Fig. 14 shows the variation of LOLE of the model systems when the peak load is changed used for calculating ELCC. It is set to the LOLE equal 8 [Hrs/yr] and find the value of peak load. By finding the result for the peak load corresponding to each system's LOLE equal to 8 [Hrs/yr], calculate the ELCC and C.C. shown as follow.

Fig. 14
figure 14

Reliability indices in advanced systems

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  1. (1)

    ELCC and C.C. calculation of system expanded WTGs

    As for System B, three wind farms were added based on System A, Thereby, the ELCC and C.C. of expanded WTGs can be calculated as:

    $$\begin{aligned} ELCC_{WTG} & = 1{,}072{,}600 - 1{,}049{,}400 = 23{,}200\;[{\text{MW}}] \\ C.C._{WTG} & = \frac{23{,}200}{{148{,}680}} \times 100\% = 15.6\% \\ \end{aligned}$$
  2. (2)

    ELCC and C.C. calculation of system expanded ESSs

    As for System C, three ESSs were added based on System B. Thus, the ELCC and C.C. of expanded ESS can be calculated as:

    $$\begin{aligned} ELCC_{ESS} & = 1{,}079{,}800 - 1{,}072{,}600 = 7200\;[{\text{MW}}] \\ C.C._{ESS} & = \frac{7200}{{37{,}170}} \times 100\% = 19.37\% \\ \end{aligned}$$
  3. (3)

    ELCC and C.C. calculation of system added WTGs and ESSs

    As for System C, three wind farms and multi-ESSs are added based on System A. Therefore, the ELCC and C.C. of expanded WTGs and multi-ESS can be calculated as:

    $$\begin{aligned} ELCC_{ESS + WTG} & = 1{,}079{,}800 - 1{,}049{,}400 = 30{,}400\;[{\text{MW}}] \\ C.C._{ESS + WTG} & = \frac{30{,}400}{{185{,}850}} \times 100\% = 16.36\% \\ \end{aligned}$$

After expanded WTGs and multi-ESSs in the power system, the ELCC has been increased from 23,200 to 30,400 [MW]. In addition, the C.C. has been increased. This means the multi-ESSs is helpful to increase the power system reliability (Table 10).

Table 10 Calculation result of ELCC and C.C.
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4 Conclusion

Sustainable energy system has been emphasized nowadays and many countries in the world will develop renewable energy as it can ease the contradiction of energy supply and address climate change. Thus, the energy structure will undergo major changes and the vast majority of the clean energy use of renewable energy will increasingly replace fossil energy for power generation. Therefore, how to effectively use distributed renewable energy to generate electricity without affecting the reliability of the power system is the primary task in the whole world.

First of all, multi-ESSs can maintain supply and demand balance by compensating for the uncertainty of power generation output from renewable energy. Secondly, the results of this research can provide reference opinions in the efficient and reliable application of distributed renewable energy in power systems.

Therefore, in order to avoid the uncertainty of WTG output and power fluctuations affecting the reliability of power systems, the application of multi-ESSs is a good method to ensure the reliability of power systems.

In this research, the reliability of a power system involving WTG and multi-ESSs can be evaluated using a basic model and algorithm. By using the proposed model, the reliability analysis of WTG with multi-ESSs can be obtained. Suitable capacity of WTG and multi-ESSs can be determined and used efficiently for a sensitivity analysis from the result. This research is helpful for future power system expansion planning.