In the context of the global transition toward renewable energy, the integration of wind and solar power introduces significant uncertainty and variability into power systems. Battery energy storage systems have emerged as a critical enabler to mitigate these challenges due to their fast response and regulation capability. However, as the penetration of energy storage batteries increases, their own failure characteristics—such as thermal runaway and performance degradation—begin to exert a growing influence on the overall reliability of power systems. In this paper, I present a comprehensive framework for operational reliability assessment that explicitly incorporates the failure behavior of energy storage batteries. The proposed approach combines a multi-dimensional degradation model with thermal runaway warning probabilities to construct an available output power model for battery energy storage systems. Then, a load curtailment optimization model considering these failure characteristics is formulated, and a Monte Carlo simulation-based reliability evaluation method is developed. Case studies on the IEEE RTS-79 system demonstrate that neglecting battery storage failures may lead to overly optimistic reliability estimates, and that the capacity, power rating, and operating temperature of energy storage batteries significantly affect system reliability.
The remainder of this article is organized as follows. Section 1 introduces the failure model for energy storage batteries, including thermal runaway and multi-dimensional performance degradation. Section 2 develops the available output power model. Section 3 presents the load curtailment optimization model. Section 4 describes the reliability assessment methodology. Section 5 reports the case study results, and Section 6 concludes the paper.
| Symbol | Description |
|---|---|
| $$R_{Tr}$$ | Thermal runaway failure coefficient (0 or 1) |
| $$P_{thermal}$$ | Thermal runaway warning probability |
| $$u_Q(z)$$ | Universal generating function for capacity degradation |
| $$u_d(z)$$ | Universal generating function for voltage degradation |
| $$R_Q$$ | Capacity degradation coefficient |
| $$R_d$$ | Voltage degradation coefficient |
| $$R’_S$$ | Comprehensive reliability coefficient of BESS |
| $$P_{d,t}$$ | Discharge power at time t |
| $$P_{c,t}$$ | Charge power at time t |
| $$E_{B,t}$$ | Stored energy at time t |
1. Failure Model of Energy Storage Battery
Energy storage battery failures can be categorized into two main types: thermal runaway failure and performance degradation failure. Thermal runaway is an exothermic chain reaction that leads to a rapid temperature increase, potentially causing fire or explosion. This type of failure directly eliminates the output capability of the battery. In practice, thermal runaway is difficult to detect in its early stages; therefore, a data-driven early warning model based on reconstruction error is adopted to estimate the probability of thermal runaway.
Using the battery management system (BMS) real-time measurements of voltage, current, state of charge (SOC), and temperature, a neural network is trained under normal operating conditions to reconstruct the input features with near-zero error. When abnormal patterns occur, the reconstruction error increases significantly. By applying an ensemble of such networks, the thermal runaway probability $$P_{thermal}$$ is calculated. Then, a binary coefficient $$R_{Tr}$$ is defined based on a threshold $$\delta$$:
$$R_{Tr} = \begin{cases} 0, & P_{thermal} > \delta \\ 1, & P_{thermal} \leq \delta \end{cases}$$
For multi-dimensional performance degradation, we consider both capacity fade and voltage depression. The measured values are discretized into different performance state levels. For the capacity performance, a universal generating function is constructed as:
$$u_Q(z) = \sum_{e_Q=1}^{L_Q} p_{Q,e_Q} z^{e_Q}$$
Similarly, for the voltage characteristic, the universal generating function is:
$$u_d(z) = \sum_{e_d=1}^{L_v} p_{d,e_d} z^{e_d}$$
where $$p_{Q,e_Q}$$ and $$p_{d,e_d}$$ are the probabilities associated with each performance state level. The degradation coefficients are defined as the probabilities that the state level falls below the required minimum levels $$\gamma_Q$$ and $$\gamma_d$$:
$$R_Q = \Pr(e_Q \leq \gamma_Q) = \sum_{e_Q \leq \gamma_Q} p_{Q,e_Q}$$
$$R_d = \Pr(e_d \leq \gamma_d) = \sum_{e_d \leq \gamma_d} p_{d,e_d}$$
A typical energy storage battery system is illustrated below:
2. Available Output Power Model Considering BESS Failures
Under normal operation, a battery energy storage system is subject to charging/discharging power limits and energy capacity limits. However, when accounting for failure characteristics, these limits are scaled by the comprehensive reliability coefficient. The comprehensive reliability of the energy storage battery is defined as:
$$R’_S = R_{Tr} \cdot R_Q \cdot R_d$$
Then, the actual available charging and discharging power limits become:
$$0 \leq P_{d,t} \leq R’_S \cdot P_{d,\max}$$
$$0 \leq P_{c,t} \leq R’_S \cdot P_{c,\max}$$
Similarly, the available energy storage capacity is bounded by:
$$E_{B,\min} \leq E_{B,t} \leq R’_S \cdot E_{B,\max}$$
The state transition of the stored energy is governed by:
$$E_{B,t} = E_{B,t-1} + \left( \eta_c P_{c,t} – \frac{P_{d,t}}{\eta_d} \right) \Delta t$$
where $$\eta_c$$ and $$\eta_d$$ are the charging and discharging efficiencies, respectively. Additionally, the simultaneous charge and discharge prohibition is enforced by:
$$P_{d,t} \cdot P_{c,t} = 0$$
These constraints are integrated into the subsequent load curtailment optimization model, enabling a realistic representation of the energy storage battery capability under failure conditions.
3. Load Curtailment Optimization Model
The proposed load curtailment optimization model aims to minimize the total load shedding, wind curtailment, and solar curtailment while respecting operational constraints. The objective function is formulated as:
$$\min F = \sum_{i=1}^{N_{ld}} \sum_{t=1}^{T} \lambda_{ld,i} C_{e,i,t} \Delta t + \sum_{k=1}^{N_w} \sum_{t=1}^{T} \lambda_{w,k} \Delta P_{W,k,t} \Delta t + \sum_{r=1}^{N_s} \sum_{t=1}^{T} \lambda_{s,r} \Delta P_{S,r,t} \Delta t$$
where $$C_{e,i,t}$$ is the load curtailment at bus i at time t, $$\Delta P_{W,k,t}$$ is the wind power curtailment, $$\Delta P_{S,r,t}$$ is the solar power curtailment, and the $$\lambda$$ values are penalty weights.
The constraints include the power balance equation:
$$\sum_{m=1}^{N_g} P_{F,m,t} + \sum_{k=1}^{N_w} P_{W,\max,k,t} + \sum_{r=1}^{N_s} P_{S,\max,r,t} + \sum_{j=1}^{N_b} P_{d,j,t} + \sum_{i=1}^{N_{ld}} C_{e,i,t} = \sum_{i=1}^{N_{ld}} P_{load,i,t} + \sum_{j=1}^{N_b} P_{c,j,t} + \sum_{k=1}^{N_w} \Delta P_{W,k,t} + \sum_{r=1}^{N_s} \Delta P_{S,r,t}$$
Line flow constraints are given by:
$$P_{l,\min} \leq P_{l,t} \leq P_{l,\max}$$
Ramp rate limits for conventional generators are:
$$r_{m,\min} \leq P_{F,m,t} – P_{F,m,t-1} \leq r_{m,\max}$$
Load curtailment limits ensure that curtailment cannot exceed the local demand:
$$0 \leq C_{e,i,t} \leq P_{load,i,t}$$
Similarly, wind and solar curtailment are bounded by their maximum available outputs:
$$0 \leq \Delta P_{W,k,t} \leq P_{W,\max,k,t}$$
$$0 \leq \Delta P_{S,r,t} \leq P_{S,\max,r,t}$$
The actual wind and solar power injections are expressed as the maximum available power minus the curtailment:
$$P_{W,k,t} = P_{W,\max,k,t} – \Delta P_{W,k,t}$$
$$P_{S,r,t} = P_{S,\max,r,t} – \Delta P_{S,r,t}$$
Finally, the battery energy storage constraints are enforced as described in Section 2 for each storage unit j:
$$0 \leq P_{d,j,t} \leq R’_{S,j} P_{d,\max,j}$$
$$0 \leq P_{c,j,t} \leq R’_{S,j} P_{c,\max,j}$$
$$P_{c,j,t} P_{d,j,t} = 0$$
$$E_{B,j,t} = E_{B,j,t-1} + \left( \eta_{c,j} P_{c,j,t} – \frac{P_{d,j,t}}{\eta_{d,j}} \right) \Delta t$$
$$E_{B,j,\min} \leq E_{B,j,t} \leq R’_{S,j} E_{B,j,\max}$$
This optimization model is solved within each system state sampled by the Monte Carlo procedure to determine the minimum load curtailment and renewable curtailment for that state.
4. Reliability Assessment Methodology
The operational reliability of the power system is evaluated using sequential Monte Carlo simulation. The procedure is outlined below:
- Data input: Read the system topology, component reliability data, time series of load, wind, solar, and battery parameters.
- Build the BESS available output power model: Compute the comprehensive reliability coefficient $$R’_S$$ for each energy storage battery based on its current degradation and thermal runaway probability.
- State sampling: Sample the state of each component (generators, lines, transformers) and the stochastic variables (load, wind power, solar power) using Monte Carlo simulation.
- Network analysis and power flow: Perform connectivity checks and linearized DC power flow to identify any overloaded lines or islanding.
- Optimization and reliability index calculation: For states with overload or load curtailment, solve the load curtailment optimization model. Compute the reliability indices:
The loss of load probability (LOLP) is defined as:
$$R_{LOLP} = \sum_{x \in G} P(x)$$
where $$G$$ is the set of states with load curtailment and $$P(x)$$ is the probability of state x. The expected demand not supplied (EDNS) is:
$$R_{EDNS} = \sum_{x \in G} P(x) C_e(x)$$
The simulation terminates when the coefficient of variation of the indices is below a threshold (e.g., 0.01) or the maximum number of samples is reached.
5. Case Study and Results
5.1 System Description
The modified IEEE RTS-79 system is used for the case study. The original system is augmented with wind farms at buses 2, 5, 9, and 15, each with an installed capacity of 100 MW, and solar farms at buses 1, 3, 7, and 19, each with 100 MW. The load profile is taken from a typical internal city. Initially, the system is evaluated without any battery storage. Then, nine battery storage systems are installed at buses 1, 2, 3, 5, 7, 9, 15, 18, and 19. The nominal capacity of each energy storage battery is 100 MWh, and the maximum charging/discharging power is 50 MW unless otherwise specified. The charging and discharging efficiencies are both 0.9.
5.2 Impact of BESS Failure on System Reliability
Three scenarios are compared: (1) no battery storage; (2) battery storage with ideal operation (failure ignored); (3) battery storage with failure characteristics considered. The storage temperature is 25°C and the C-rate is 2C for the third scenario. The reliability indices are summarized in Table 2.
| Scenario | REDNS (MW) | RLOLP (%) |
|---|---|---|
| No BESS | 15.1903 | 0.0866 |
| BESS without failure | 13.7812 | 0.0804 |
| BESS with failure | 14.5468 | 0.0839 |
From Table 2, the integration of ideal battery storage reduces REDNS by 1.4091 MW and RLOLP by 0.0062%. However, when the failure characteristics are considered, the improvements drop to only 0.6435 MW and 0.0027%. This clearly demonstrates that ignoring battery storage failures would lead to an overly optimistic assessment of system reliability.
5.3 Influence of Battery Capacity
To investigate the effect of battery capacity on system reliability, the capacity of each energy storage battery is varied while the charging/discharging power is fixed at 50 MW and the temperature at 25°C. The REDNS values for capacities ranging from 0 to 1500 MWh are shown in Figure 1 (not displayed). The results indicate that for capacities above 800 MWh, the REDNS changes very little, implying that the energy storage battery capacity is sufficiently large to cover fluctuations. However, when the capacity is between 0 and 700 MWh, the REDNS increases by 0.6665 MW as the capacity decreases, meaning that the failure-induced capacity degradation has a more pronounced effect when the original capacity is small.
5.4 Influence of Charging/Discharging Power
With the battery capacity fixed at 200 MWh, the maximum charging/discharging power is varied from 10 MW to 100 MW. As shown in Figure 2 (not displayed), the REDNS changes substantially when the power rating is below 70 MW. For example, reducing the power rating from 70 MW to 10 MW leads to a significant increase in load curtailment. In contrast, when the power rating exceeds 70 MW, the available power is sufficient for system support, and the impact of power degradation becomes less severe. Therefore, the failure-induced reduction in charging/discharging power can be critical, especially for systems with undersized storage power ratings.
5.5 Influence of Operating Temperature on BESS Failure and System Reliability
The operating temperature is a crucial factor that affects both thermal runaway probability and aging degradation. We evaluate the system reliability under three temperature levels: 15°C, 25°C, and 35°C, while maintaining the same capacity (100 MWh) and power rating (50 MW). The results are summarized in Table 3.
| Temperature (°C) | REDNS (MW) | RLOLP (%) |
|---|---|---|
| 15 | 14.1831 | 0.0816 |
| 25 | 14.5468 | 0.0839 |
| 35 | 15.2717 | 0.0897 |
Table 3 shows that as the temperature increases from 15°C to 35°C, the REDNS grows by 1.0886 MW and RLOLP increases by 0.0081. This indicates that higher operating temperatures accelerate the failure and degradation processes of energy storage batteries, thereby reducing the reliability of the host power system. Consequently, effective thermal management is essential to maintain high system reliability.
5.6 Summary of Sensitivity Analysis
The sensitivity analysis reveals that the influence of battery storage failure on power system reliability is highly dependent on the storage system’s capacity and power rating. When the storage resources are abundant, the degradation and failure have minimal impact; however, when the storage is relatively weak or undersized, the failure characteristics become a dominant factor. Furthermore, operating conditions such as temperature strongly affect the failure probability and degradation speed of the energy storage battery, which in turn affects the overall system performance.
6. Conclusion
In this paper, I have presented a power system operational reliability assessment methodology that explicitly accounts for the failure characteristics of energy storage batteries. The key contributions are as follows:
- An integrated model for energy storage battery failures is developed, combining thermal runaway warning probabilities with multi-dimensional performance degradation (capacity and voltage) using universal generating functions.
- The available output power model of battery storage is modified by incorporating a comprehensive reliability coefficient, which scales both power limits and energy capacity limits.
- A load curtailment optimization model is formulated that includes the failure-aware battery constraints, and a Monte Carlo simulation procedure is used to derive the reliability indices.
- Case studies on the IEEE RTS-79 system demonstrate that ignoring energy storage battery failures leads to optimistic reliability estimates. The impact of failure is particularly significant when the storage capacity or power rating is insufficient relative to system needs.
- Operating temperature is shown to substantially affect system reliability through its influence on battery failure and degradation, highlighting the importance of thermal management in battery storage deployment.
The proposed framework provides a more realistic assessment of power systems with high penetration of battery storage and can support operators in planning and dispatching decisions. Future work may extend this approach to dynamic thermal models and consider more detailed battery degradation mechanisms.