Battery Energy Storage System Strategy for Island System Based on Reliability Assessment

Abstract

To meet the targets of the 2030 agenda of the United Nations (UN) to reduce CO₂ emissions, various small-scale renewable generation sources have been integrated into electricity systems to maintain decarbonisation and reduce the use of thermal generation, aiming to achieve the sustainable development of electricity generation. In this context, this paper introduces a battery-based strategy with the integration of small-scale renewable generation sources. This is evaluated through an analysis of the reliability of transmission lines, considering contingencies of the orders of N-1 and N-2 to identify cases where there are isolated nodes and to visualise the cases with maximum load shedding in the system, indirectly affecting nodes close to the isolated nodes. The proposed strategy is analysed in a six-node RBTS and adapted to the IEEE 118-node system, obtaining energy-efficient results and a reduction in reliability indices.

1. Introduction

The growing environmental crisis due to climate change and greenhouse gas emissions has led to a shift towards renewable energy sources and clean energy generation to reduce greenhouse gas emissions and reduce dependence on fossil fuels.

The main generation technologies that stand out as very useful for generating clean energy are solar and wind sources. Due to their intermittent nature, it is necessary to include Battery-Based Energy Storage Systems (BESSs) to guarantee energy supply when there is no availability of generation with a high level of uncertainty, such as wind generation.

With the large-scale integration of renewable energies, the operating conditions of the power systems (PSs) present a high variability in energy supply, so the System Operator (SO) must perform reliability assessments with greater precision in their short-term planning schemes, a strategy that has been gaining greater relevance in recent decades [1].

In this respect, the need to store energy has driven the development of storage technologies since 1980, when it was too expensive and inefficient to purchase and operate. However, BESS technology around the world has grown exponentially, being economically and technologically viable [2], to take advantage of the energy matrix and the resources available to generate energy in several regions and countries worldwide.

As such, large-scale energy storage technologies such as batteries are presented as a viable option due to their specific power, energy density, and charging and discharging efficiency, making them cost-effective and reliable [3].

The reliability evaluation of PSs considering BESSs is considered in [4], and the estimated configuration provides applications that batteries can have in power systems. These applications range from frequency regulation, as addressed in [5,6], to voltage regulation [7], which is modelled in the hybrid battery systems of different technologies and for which different controls and the State of Charge (SoC) per battery array are available. The authors study the reliability of the BESS from the perspective of the battery and its integration into the grid; however, they do not establish energy-harnessing strategies due to the intermittency of renewable generation. In the evaluation of the reliability of the PS, they use indices that show the performance of the systems in the face of disturbances in previous events and from which probabilistic analyses can be performed [8]. Reliability indices have proven useful for evaluating the inclusion of renewable energy, as shown in [9]. The Expected Energy Not Supplied (EENS) index is used to indicate the missing energy when adding wind generation sources. It has also been adapted for the integration of photovoltaic generation, where the surplus energy is stored in a BESS [10]. When assessing the reliability of a power system, the analysis of contingencies N-1 and N-2 depends on the level of reliability that needs to be assessed, and the system is analysed in each case with different ratings and indices, as in [11], where a voltage and frequency analysis was performed for each contingency.

In [12], an optimisation model was used for a system with both wind and PV generation, as well as a BESS and the Demand Response–Time-Of-Use programme, using the Loss Of Load Probability (LOLP) index; however, no contingency analysis was performed to determine the impact of the sudden output of each element.

Meanwhile, in [13], a BESS in conjunction with the demand response (DR) was studied in a Direct-Current Optimal Power Flow (DCOPF) using the EENS index, which showed the capabilities of these to improve the state of the system, but no contingency analysis was performed.

The DR programmes addressed in [14] present a model that makes use of the EENS index but without performing a contingency analysis.

A reliability assessment for a multiple-element (N-2) output was reviewed in [15], focusing on transmission lines using an annualised demand curve, as well as DR programmes, without considering renewable generation sources or BESSs.

In [16], EENS and LOLP reliability indices were studied in a system featuring renewable energy sources, BESSs, and DR programmes. Alternative indices such as failure frequency, recovery time, or availability factors have been considered for distribution networks [17].

In [18], the authors used dynamic thermal rate system analysis on transmission lines to assess the reliability of lines. They modelled weather conditions in an uncertain manner through the Monte Carlo method, mainly to integrate renewable generation sources and their impact on the integration of the BESS into the grid, without emphasising contingency analysis. Their contribution is given as the integration of a thermal measurement system in the lines.

The authors of [19] performed a reliability analysis of a PS considering N-1 and N-2 contingencies as well as generation reserves to identify various demand response schedules, providing expected nodal prices for different scenarios.

Reliability studies in PSs are important for both the planning and operation of the grid. In recent decades, PSs have included new generation technologies, with increasing integration of intermittent renewable generation into the grid; however, there are few studies that include BESSs or DR and focus on reliability analysis.

In [20,21], the importance of electricity supply through renewable energies is mentioned as presenting a high risk of energy supply to users. However, the use of storage technologies improves reliability rates.

In [22], they perform a study to assess the contributions of a BESS to system generation insufficiency, considering the integration of renewable generation, using a Monte Carlo technique to assess reliability. However, the authors do not perform detailed strategies for isolated nodes, avoiding these configurations (isolated grids) in their final indices.

Finally, the authors in this review of the state of the art focus their studies on various indices and integration of intermittent generation sources; however, the effect of the intermittency of generation elements is not studied. Furthermore, no strategies for BESS operation in the face of isolated nodes and their effect on reliability indices are established. Few references study the integration of BESSs for N-1 and N-2 criteria in contingency analysis or its impact on reliability indices.

This paper presents a strategy that considers a BESS for isolated nodes using reliability assessment. Forced outage rates of transmission lines are considered to establish parameters of the availability and unavailability of the element, to integrate the probabilities of occurrence of a fault. The probabilistic reliability indices are obtained using a demand duration curve, referencing the integration of the BESS and renewable energy sources (RES) such as wind turbines and photovoltaic generation. This proposal is evaluated in the 6-node RBTS and the 118-node IEEE.

2. Mathematical Modelling of RES in DC OPF

Analysis of Optimal Power Flows (OPF) is the best way to assess reliability in electrical power systems. In addition, the integration of renewable energy sources (RES) in the model is sought; therefore, the following elements are considered as part of the Generation Powers (PG).

2.1. RES

In today’s electricity systems, renewables are being connected to the grid and promise to play an important role in complementing fossil fuel generation.

2.1.1. Wind Energy

The power output of a wind turbine is highly dependent on the wind speed as well as the performance and efficiency characteristics of the generator. A table is used to convert wind speed to available electrical power using the wind turbine power curve according to the following:

$$P{G}^{WT}=\left\{\begin{array}{cc}0& 0\le S{W}_i<V_{ci}\\ P_r\left(\alpha +\beta S{W}_i+\gamma S{W}_i^2\right)& V_{ci}\le S{W}_i<V_r\\ P_r& V_r\le S{W}_i<V_{co}\\ 0& S{W}_i>V_{co}\end{array}\right.$$

(1)

where $S{W}_i$ is the wind speed, $V_{ci}$ is the wind speed for operation input, $V_r$ is the nominal wind speed, $V_{co}$ is the wind speed for operation output, and $P_r$ is the nominal power output $\alpha ,\beta ,\gamma$.

The constants $\alpha ,\beta ,\gamma$ depend on $V_{ci}$, $V_r$, $V_{co}$, as expressed in Equation (2):

$$\begin{gathered} \alpha ={\displaystyle \frac{1}{{\left(V_{ci}-V_r\right)}^2}}\left\{V_{ci}\left(V_{ci}+V_r\right)-4V_{ci}{V}_r{\left[{\displaystyle \frac{V_{ci}+V_r}{2V_r}}\right]}^2\right\} \\ \beta ={\displaystyle \frac{1}{{\left(V_{ci}-V_r\right)}^2}}\left\{4\left(V_{ci}+V_r\right){\left[{\displaystyle \frac{V_{ci}+V_r}{2V_r}}\right]}^2-\left(3V_{ci}+V_r\right)\right\} \\ \gamma ={\displaystyle \frac{1}{{\left(V_{ci}-V_r\right)}^2}}\left\{2-4{\left[{\displaystyle \frac{V_{ci}+V_r}{2V_r}}\right]}^2\right\} \end{gathered}$$

(2)

2.1.2. Photovoltaic Energy

The photovoltaic (PV) energy connected to the power system is an electrical generation unit that uses a PV array as the main source of electricity generation and is designed to operate synchronously and in parallel with the AC grid. These systems can include battery storage and other generation sources to supply loads during grid outages and peak load hours [3,23].

The hourly output of a PV generating unit varies over time. The hourly output of a PV panel can be calculated from the total incident radiation on the solar panel [24] as follows:

$${PG}_{PV}={\displaystyle \frac{V_{ref}{I}_{ref}}{H_{TR}Ap}}{H}_T$$

(3)

where $V_{ref}$ is the reference voltage of the PV array, $I_{ref}$ is the reference current of the PV array, $H_{TR}$ is the nominal solar insolation, $H_T$ is the actual solar insolation, and $Ap$ is the area of the PV array.

2.1.3. BESS

The energy storage limits of the battery when charging and discharging are considered in (4) and (7), where $P_{jt}^{usr}/P_{jt}^{dsr}$ is the charge and discharge schedule of the unit within t periods of the system. In (8), the charging and discharging event is prevented within the same period t, where $I_{jt}^{DeBatt}/I_{jt}^{ChBatt}$ is the discharging/charging status of the BESS, respectively. In (9), the minimum and maximum storage levels in period t are considered.

$$-P{R}_j\le {PB}_j\le {PR}_j;j\in {\Omega }_B$$

(4)

$$E_{jt}^{Batt}=E_{j(t-1)}^{Batt}+n_{Ch}\left(P_{jt}^{ChBatt}+P_{jt}^{dsr}\right)-n_{DeCh}\left(P_{jt}^{DeBatt}+P_{jt}^{usr}\right)$$

(5)

$$0\le P_{jt}^{ChBatt}+P_{jt}^{dsr}\le P_j^{ChBatt, max}{I}_{jt}^{ChBatt}$$

(6)

$$0\le P_{jt}^{DeBatt}+P_{jt}^{usr}\le P_j^{DeBatt, max}{I}_{jt}^{DeBatt}$$

(7)

$$I_{jt}^{DeBatt}+I_{jt}^{ChBatt}\le 1$$

(8)

$$E_j^{Batt,min}\le E_{jt}^{Batt}\le E_j^{Batt,max}$$

(9)

2.2. DC OPF

The DCOPF for each model of period t can be described as follows:

The objective function minimises the cost of operation added to the Value Of Lost Load (VOLL) and is expressed using Equation (10):

$$Min\sum _{t=24}^{N_t}\sum _{i=1}^{N_g}\left[C_i\left({PG}_{i,t}\right)\right]+\sum _{i=1}^{N_B}{VOLL}_i\left({ENS}_{i,t}\right)$$

(10)

where $C_i\left({PG}_i\right)$ is the curve production cost, subject to the ${PG}_i$ power generation of element i, the ${VOLL}_i(EN{S}_i$) Value of Lost Load, and the ENS of bus i.

The constraints of the DCOPF are subject to the following:

The Nodal Balance equation: Constraint (11) presents the system balance of generation–demand, which takes the generated power of the set of generators of RES described in Section 2.1, and the conventional (thermal, nuclear) generator of the system, the BESS contribution of energy, the power flow of the transmission lines, and the ENS to satisfy the demand of period t:

$$\sum _{\mathrm{g}⋲{\mathsf{\Omega }}_{\mathrm{G}}}\mathrm{P}{\mathrm{G}}_{\mathrm{g},\mathrm{t}}+\sum _{\mathrm{j}⋲{\mathsf{\Omega }}_{\mathrm{B}}}\mathrm{P}{\mathrm{B}}_{\mathrm{j},\mathrm{t}}-\sum _{\mathrm{j}⋲{\mathsf{\Omega }}_{\mathrm{N}\mathrm{T}\mathrm{L}}}{\mathrm{P}\mathrm{f}}_{\mathrm{i}\mathrm{m}}=\sum _{\mathrm{l}⋲{\mathsf{\Omega }}_{\mathrm{L}\mathrm{B}}}\mathrm{P}{\mathrm{D}}_{\mathrm{l},\mathrm{t}}-\sum _{\mathrm{i}⋲{\mathsf{\Omega }}_{\mathrm{N}\mathrm{B}}}{\mathrm{E}\mathrm{N}\mathrm{S}}_{\mathrm{i},\mathrm{t}}$$

(11)

where $PD$ is the power demand, ${Pf}_{im}$ is the power flow transmission of the element connected in node i-m, and ${PB}_j$ is the injection of storage energy in bus i.

Generation physical constraints: Constraint (12) considers the minimum and maximum limits of the connected generators in the power system:

$${PG}_i^{min}\le {PG}_i\le {PG}_i^{max};i\in {\Omega }_G$$

(12)

Limits ${PG}_i^{min}$ and ${PG}_i^{max}$ are the minimum and maximum power generation of element i.

The BESS: Constraints (13)–(18) represent the limits of the BESS, described in Section 2.1.3:

$$-P{R}_j\le {PB}_j\le {PR}_j;j\in {\Omega }_B$$

(13)

$$E_{jt}^{Batt}=E_{j(t-1)}^{Batt}+n_{Ch}\left(P_{jt}^{ChBatt}+P_{jt}^{dsr}\right)-n_{DeCh}\left(P_{jt}^{DeBatt}+P_{jt}^{usr}\right)$$

(14)

$$0\le P_{jt}^{ChBatt}+P_{jt}^{dsr}\le P_j^{ChBatt, max}{I}_{jt}^{ChBatt}$$

(15)

$$0\le P_{jt}^{DeBatt}+P_{jt}^{usr}\le P_j^{DeBatt, max}{I}_{jt}^{DeBatt}$$

(16)

$$I_{jt}^{DeBatt}+I_{jt}^{ChBatt}\le 1$$

(17)

$$E_j^{Batt,min}\le E_{jt}^{Batt}\le E_j^{Batt,max}$$

(18)

Physical limits of transmission power flow: Constraint (19) represents the physical limits of the transmission lines through the minimum and maximum flows:

$${-Pf}_{im}^{max}\le {Pf}_{im}\le {Pf}_{im}^{max};m{\Omega }_{LT}$$

(19)

The parameter ${Pf}_{im}^{max}$ is the maximum power flow transmission of the element connected in node i to node− m.

ENS constraints: Constraint (20) represents the ENS of the node for the period t, which represents the load curtailment in bus i to satisfy the energy balance:

$${ENS}_i\le {ENS}_i^{max};i\in {\Omega }_{NB}$$

(20)

where ${ENS}_i$ is the Energy Not Supplied, and ${ENS}_i^{max}$ is the maximum Energy Not Supplied in node i.

The purpose of the DCOPF is to evaluate each outage transmission line for N-1 contingency states as for the N-2 contingencies, and the expected value of the sum of the contingencies to be evaluated in the system will be obtained, including the RES of the section and the BESS, to evaluate the reliability assessment. The optimisation problem is formulated as a Linear Programming Problem (LP) with a linear objective function with linear constraints. The model is solved with the interior point method [25], programmed with MATLAB R2023b code and solved through CPLEX [26].

3. Reliability Assessment

This section presents the concepts used to evaluate the reliability of the PS. The unavailability (Uc) of the element c is computed by (21):

$$U_c=\left({\displaystyle \frac{{\lambda }_c}{{\mu }_c}}\right)$$

(21)

where ${\lambda }_c$ is the failure rate of the connected element and ${\mu }_c$ is the number of annual repairs of such an element. The availability of component Ac is calculated by Equation (22):

$$A_c=1-U_c$$

(22)

Considering a power system with Nc independent components, Equation (23) determines the probability for every state j in the contingency with exactly b failed components:

$$p_j=\underset{c=1}{\overset{b}{\Pi }}{U}_c\underset{c=b+1}{\overset{Nc}{\Pi }}{A}_c$$

(23)

Equation (22) uses availability and unavailability parameters associated with independent elements in the system; therefore, it calculates the probabilities of system elements associated with each other.

Nodal Energy Not Supplied (NENS) is defined by (24), where NL is the number of load nodes:

$$NEN{S}_j^i=\sum _{i=1}^{NL}EN{S}_i$$

(24)

The Expected Nodal Energy Not Supplied ENENS is shown in (25):

$$ENEN{S}_j^i=\sum _{i=1}^{NL}{p}_j^i\times NEN{S}_j^i$$

(25)

The EENS is the sum of all nodes in the system, with the ENENS being multiplied by the period t to be considered.

4. Isolated Node Analysis Strategy

The purpose of battery-based storage systems is to contain as much energy available from generation sources and/or the grid as possible. In this sense, the aim is to make better use of the BESS to meet the system’s operational constraints and ensure its operation to maintain a reliable power system and continuous supply, even in the event of severe contingencies or power outage.

Strategy 1: The contingency analysis is performed, as can be observed in Figure 1, and the network status for contingency (j) is checked. If there is no isolated node, strategy 1 is reviewed. Strategy 1: If there are no islands, review the conditions of the RES. If the BESS is loading, consider Pd = PD_i − BESS_i, and run the DCOPF to check reliability indices. If the BESS is not loading, take Pg_i + BESS_i and run the DCOPF and calculate the reliability indices. If there is an isolated node, check strategy 2.

Strategy 2: If there are islands, check if the BESS is loading and if it checks the ENS. If the ENS is present (PD_i > Pg), run the DCOPF on the rest of the system and take the ENS. If there is no ENS, run the DCOPF for the rest of the system, and calculate reliability indices. If there are no islands, run the DCOPF for the rest of the system. The strategy proposed can be observed in Figure 2.

If all states have been reviewed and all reliability indices are quantified, the case goes back to contingency review (j).

In this context, this article proposes two strategies for the penetration of intermittent generation sources to increase the reliability of the system. The total contingency evaluation of the island nodes-based strategy methodology is shown in Figure 3.

The application of the strategy for isolated nodes begins. Identifying the number of contingencies to be evaluated (j), a review of the network is performed to identify the isolated nodes generated. The conditions of each isolated node are reviewed, and the strategy to be applied is evaluated according to the BESS conditions. The same process is carried out for the total number of islands caused by the output of the transmission elements, as well as the total number of hours to be evaluated.

5. Numerical Examples

This section considers the experimental part to validate the proposed improvements of the BESS strategies. CPLEX is used with MATLAB code to formulate the DCOPF considering renewable generation sources and the BESS as part of the optimisation model. The calculations are carried out on an Intel Core i5, 3.1 GHz, with 12 GB RAM and a Windows 10 personal computer Lenovo in Mexico City. For the experimental section, two test systems are used: a six-bus RBTS to demonstrate the proposed methodology and IEEE 118 nodes to test and validate the scalability of the proposal in larger networks. The VOLL is 10,000 [$/MWh], the limit of the ENS is ${ENS}_i^{MAx}$ = PDi, and the maximum ENS is equal to the power demand at the load node.

Figure 4 shows the flow chart used to solve the contingency analysis. First, the demand data and technical parameters are required. Then, the total number of contingencies to be evaluated is identified. Each contingency is solved using the DCOPF, identifying the optimal solution for the respective network state, satisfying the constraints proposed in Section 2, and defining the ENS for each contingency. Once all the contingencies have been evaluated, an expected value solution (global solution) of the network state is obtained and the reliability indices of Section 3 are printed.

5.1. Six-Bus RBTS

Figure 5 presents a diagram of the test system. The system is composed of six nodes and nine transmission lines, as well as two generation plants. This PS considers the generation of two RES, solar and wind, connected to batteries. This was modified from the original system to demonstrate the proposed solution.

Table 1. Generator data of the RBTS.

PG	Bus	PGMin [MW]	PGMax [MW]	C(PG) [$/MWh]	Type
1	1	0	110	12	Thermal
2	2	0	130	0.5	Thermal
3	5	0	25	NA	Wind
4	6	0	15	NA	Wind
5	6	0	2.5	NA	Solar

presents the main generation data to be used in the test system [27]. The capacity of the batteries is limited to the sum of the maximum generation power of the renewable generation. The location of the BESS is proposed for radial lines. For the six-node RBTS, BESS₁ = 25 [MW] and BESS₂ = 17.5 [MW].

Table 2. Transmission data of the RBTS.

Line	From	To	Capacity [MW]	r [p.u.]	x [p.u]	Ac	Uc
L1	1	3	85	0.0342	0.18	0.998288	0.0017123
L2	2	4	71	0.114	0.6	0.994292	0.0057078
L3	1	2	71	0.0912	0.48	0.995434	0.0045662
L4	3	4	71	0.0228	0.12	0.998858	0.0011416
L5	3	5	71	0.0228	0.12	0.998858	0.0011416
L6	1	3	85	0.0342	0.18	0.998288	0.0017123
L7	2	4	71	0.114	0.6	0.994292	0.0057078
L8	4	5	71	0.0228	0.12	0.998858	0.0011416
L9	5	6	71	0.0228	0.12	0.998858	0.0011416

shows the data of the transmission lines, parameters, and line capacity, as well as the main statistical characteristics, all taken from [27].

Figure 6 presents the demand behaviour for one day, taken from [28].

The PD in the peak demand period associated with the nodes is shown in

Table 3. Max demand reference.

Bus	PD [MW]
2	40
3	85
4	40
5	20
6	20

.

For the six-bus RBTS, the following case studies will be analysed:

Case 1: Base case without a BESS and without strategy;

Case 2: Integration of BESS RES without strategy;

Case 3: Integration of BESS-RES with isolated node strategies.

5.1.1. Case 1

This first case will be taken as a base case to provide a reference in subsequent cases. Here, the N-2 contingency study will be carried out as proposed in [29]. The data of the transmission lines and demand behaviour are shown in Table 2 and Table 3 and Figure 6. To have comparable data between cases, it is considered that the generation of the nodes with renewable energy is equally distributed between the two original generation nodes: $0\le P{G}_1\le 131.25$ and $0\le P{G}_2\le 151.25$.

To demonstrate the reliability assessment step by step, the output is considered as a transmission element, in this case, L9 (N-1), and the probability of occurrence is calculated with (9):

$$P\left(L9\right)=A_{L1} A_{L2}{A}_{L3}{A}_{L4}{A}_{L5}{A}_{L6}{A}_{L7}{A}_{L8}{U}_{L9}$$

$$\begin{gathered} P\left(L9\right)=\left(0.998288\right)\left(0.994292\right)\left(0.995434\right)\left(0.998858\right)\left(0.998858\right)\left(0.998288\right) \\ \left(0.994292\right)\left(0.998858\right)\left(0.0011416\right) = \mathrm{0.00111573}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \end{gathered}$$

In this context, the probability of the occurrence of line 9 is 0.0011573. This procedure applies to all the lines of the system up to contingencies of order N-2. Subsequently, the contingency analysis based on [30] is carried out to identify the EENS and ENENS.

Table 4. Islanded nodes generated by the reliability assessment.

Outage	Island Nodes	Pj	ENS [MW]	Time [s]	Solution Value [$]	Convergence
0	NA	0.9763	0	2.43	1978.72	Optimal
L5	NA	0.0017	0	2.86	1978.73	Optimal
L9	N6	0.00111573	20	4.31	62,016.21	Global
L5 L8	N5, N6	1.91 × 10−6	40	12.04	124,001.30	Global
L5 L9	N6	1.91 × 10−6	20	12.21	162,016.21	Global
L8 L9	N6	1.27 × 10−6	20	12.16	162,016.72	Global

presents the isolated nodes once the contingency analysis is developed for the peak demand period and case 1. Nodes 5 and 6 are the isolated nodes for the system contingencies. In this research, the ENS reaches 40 MW for the sum of both nodal loads, while the NENS (Equation (13)) is 0.669 [MWh/yr].

Table 4 shows the optimal and global convergence cases. The optimal cases have simulation times close to 2 s and lower operating costs and all the restrictions are met, reaching the best solution for the scenario analysed. The cases with global solutions present times of up to 12 s and high costs, due to the activation of restrictions such as the ENS, which indicates that it is necessary to cut energy to reach a solution.

Figure 7 presents the EENS of the system for the 24 time periods. The highest EENS of 9555.40 [MWh/yr] is presented for the periods of maximum demand. In this study, the behaviour of the EENS in the periods of lower demand reaches 3061 [MWh/yr] at 07:00 h.

An analysis is performed for the peak demand period.

Table 5. ENENS for case 1.

Bus	ENENS [MW/yr]
2	3.65
3	10.43
4	9.89
5	11.28
6	29.07

presents the ENENS. It can be observed that nodes 5 and 6 are the nodes with the highest ENENS, forming islands even in simple contingencies on L9. It is also identified that node 6 presents an ENENS of up to 29.07 [MW/yr].

In this case, the analysis obtains the EENS and ENENS reference indices for the integration of RES and the BESS in the contingency analysis.

5.1.2. Case 2

In this case, the integration of the BESS and RES is presented, and strategies are not considered. Figure 8 presents the wind and sun behaviour data to simulate PG^wt and PG_PV generation output behaviour patterns for nodes 5 and 6 [29]. The capacity of the BESS at node 5 is 25 [MW], and the BESS capacity at node 6 is 20 [MW].

Figure 9 presents the EENS of the system for the 24 time periods. The highest EENS, 8450 [MWh/yr], is presented for the periods of maximum demand. In this case, the behaviour of the EENS in the periods of lower demand reaches 2320 [MWh/yr] at 11:00 h.

An analysis is performed for the peak demand period.

Table 6. ENENS for case 2.

Node	ENENS [MW/yr]
2	2.83
3	6.35
4	5.69
5	6.09
6	26.94

presents the ENENS, and it is observed that, by integrating RES with a BESS in the contingency analysis, the ENENS is reduced by 25.51% compared to case 1. Node 6 has an ENENS of 26.94 [MW/yr] because it is a node that forms islands in the event of contingencies of the order N-1.

5.1.3. Case 3

Case 3 presents a study of the reliability assessment applying the considerations described at the beginning of Section 5 and the strategies proposed in this work. In Figure 10, the EENS is presented for case 3. The major EENS is 7904 [MWh/yr], and is presented in the peak demand period, a reduction of 546 [MWh/yr] compared to case 2.

Additionally, for periods of minimum demand, there is a reduction of 2% compared with case 2. Figure 11 shows the behaviour of the BESS with the implementation of the strategies detailed in Section 4. The behaviour of the BESS with both strategies can be seen, and the BESS with strategy 2 is the one that injects more power in the event of various contingencies. However, in the period of maximum demand, BESS 1 is the one that injects more energy in the event of the contingencies being present in the system.

In addition, Figure 12 shows the behaviour of the BESS in the face of the various strategies at node 6. In contrast to at node 5, BESS 1 is the one that discharges in the period of maximum demand when evaluating the contingencies in the system.

Figure 13 presents a comparison between cases 1, 2, and 3. The EENS for a 24 h horizon is observed. According to this figure, the EENS decrease is due to the integration of the strategies into the BESS in the system.

In this analysis, a reduction between cases 2 and 3 is present due to the integration of the BESS. Case 3 presents a 30% reduction in ENENS at the system level, while the difference between case 2 and 3 is 6.49%. This is due to the integration of the battery strategies that allow discharging in a sudden event and reduce the ENENS in the presence of isolated nodes.

Once cases 1, 2, and 3 were reviewed, the research in this study concluded that the integration of BESS strategies in the power system allows a reduction in EENS because these considerations allow the BESS to unload in the event of a contingency in the grid and recharge again, taking advantage of the availability of energy generated by the RES.

Table 7. ENENS comparison for 6-bus RBTS.

	Case 1	Case 2	Case 3
Bus	ENENS [MW/yr]
2	3.65	2.83	2.64
3	10.43	6.35	5.93
4	11.28	5.69	5.31
5	9.89	6.09	5.69
6	29.07	26.94	25.16

present the ENENS comparison.

5.2. 118-Bus System

To demonstrate the scalability of the proposal, the 118-bus test system is considered. The data used for the analysis are taken from [31]. Additionally, the RES are integrated into the network according to the data shown in

Table 8. Data generator of 118-bus system.

Bus	PGMin [MW]	PGMax [MW]	C(PG) [$/MWh]	Type
2	0	25	NA	PV
33	0	15	NA	Wt
117	0	2.5	NA	PV

. The N-1 and N-2 contingencies are evaluated to identify isolated nodes in the system. The behavioural patterns of demand and the RES are implemented in this new case. The capacity of the BESS is comparable to the previous case.

Table 9. Most representative contingencies of 118-bus system.

Outage	Island Node	pj	ENS [MW]
183	116	0.000280	51.916
184	117	0.000695	14.43
183,184	116, 117	0.00000317	66.38
183,121	78, 79	0.00000317	53.83
184,125	79	0.000000793	16.31

presents an analysis of the most representative contingencies of this case study for the peak demand period. For a single power output, the isolated nodes have 51.9 and 14.43 [MW] of ENS due to the integration of the RES. For an N-2 element outage, the contingency with the highest ENS is the one obtained in lines 183–184, with 66.38 [MW].

The EENS of the system, once the energy storage systems are integrated, is 142.86 [GW/year]. The final EENS obtained has as a counterpart in the sizing of the BESS and its optimal location, which was not considered in this work, even though grid conditions could be improved due to its capacity.

6. Conclusions

This paper introduces the implementation of strategies integrating a BESS to increase the reliability of nodes isolated in the PS due to contingencies up to the order of N-2.

It is concluded that the BESS presents an increase in the complexity of reliability studies in power systems, due to consideration of the restrictions of the temporality of the BESS as well as the correct sizing, location, and integration with renewable energies.

The results obtained make it possible to identify the island nodes due to the contingencies presented in the PS generated from the reliability assessment.

These strategies allow a reliability analysis to be carried out, as well as a planning analysis to identify security problems in the system.

The strategy was initially evaluated with the six-node RBTS, and the main isolated nodes identified, with the ENS by node, before the implementation of the BESS strategies. The evaluation without strategies presented less control in energy management and higher reliability indices. The results show that contingencies, when considering strategies as part of the analysis of isolated nodes, allow for better energy management with a direct impact on the reduction of the ENS.

The holistic contingency analysis model focused on the BESS and reliability of RES. It was adapted to the 118-bus system, and had direct impacts on the reduction in the EENS at the system level and the nodal level, mainly having an impact on isolated nodes.

As future work, the integration of generator ramps into the DCOPF, system operating reserves for thermal generation, and renewable generation are being pursued. The high intermittency of renewable generators would allow the model to be adapted in a stochastic context to analyse the effects of EENS.