Under the guidance of China’s “dual carbon” policy, the proportion of renewable energy generation represented by wind power has been increasing year by year. However, the large-scale integration of wind farms with intermittent and fluctuating output imposes significant risks on the power system. These risks can be mitigated through the deployment of energy storage systems. In this context, a proper risk analysis is essential to understand the risk variations associated with the energy storage system. In this paper, we conduct an economic risk analysis of a wind integrated system combined with a battery energy storage system, using Value at Risk (VaR) and Conditional Value at Risk (CVaR) at 95% and 99% confidence levels as constraints. The results demonstrate the effectiveness and practicality of the proposed method.
The rapid expansion of wind power globally has made it one of the most prominent renewable energy sources. According to the IRENA 2022 report, the total installed capacity of global wind power reached 825 GW. Economic risk analysis is considered one of the most critical factors for achieving profitability in renewable energy integrated systems. Based on risk-taking or risk-aversion strategies, various studies have addressed optimal risk assessment for microgrids incorporating electric vehicle parking lots, demand response programs, and high penetration of wind and solar energy. For instance, a CVaR risk model for optimal dispatch of integrated power systems based on two-stage stochastic programming was proposed in the literature. Another study analyzed the effect of FACTS devices on mitigating economic risk in energy systems integrated with wind, using VaR and CVaR as risk assessment tools under different contingency scenarios. Investment planning related to equipment type and capacity for energy hubs containing renewable and storage systems, along with potential operational risks, has also been investigated. It has been shown that distribution systems with a high proportion of renewable generation require quantification, identification, and large-scale storage installation. A risk analysis of a hydrogen storage system for multi-energy systems with electricity, natural gas, and heat carriers was conducted under risk assessment. Risk reduction strategies for energy systems including wind, solar, and battery participating in electricity markets have been introduced. Economic risk values at different confidence levels of CVaR and VaR were analyzed for energy systems combined with wind. Risk calculation for large-scale wind power and storage systems was formulated under reserve capacity allocation. A stochastic risk assessment of a multi-carrier energy storage system for distribution systems from technical and economic perspectives in the presence of large-scale renewable generation was also presented.
Clearly, many studies have been conducted in the risk-related field for energy systems integrated with renewables, but there is a lack of economic risk assessment specifically for the energy storage cell. To address this gap, we perform a risk analysis for a wind power system equipped with an energy storage cell to understand the risk variations associated with the storage system. We use VaR and CVaR at 95% and 99% confidence levels as constraints to conduct the economic risk analysis of the wind integrated system with a battery energy storage cell. The results confirm the effectiveness and practicality of the proposed approach.
System Modeling
In this section, we establish the models for wind energy, the energy storage cell, and the risk metrics VaR and CVaR.
Wind Energy Model
The power output of a rated wind farm depends on the wind speed and is calculated according to the following equation:
$$
P_{WT} =
\begin{cases}
0 & v \le v_a \text{ or } v \ge v_b \\
\frac{v – v_a}{v_r – v_a} P & v_a < v \le v_r \\
P & v_r \le v < v_b
\end{cases}
$$
where \(P_{WT}\) is the wind power output, \(P\) is the rated power, \(v\) is the wind speed, \(v_a\) and \(v_b\) are the cut-in and cut-out wind speeds, respectively, and \(v_r\) is the rated wind speed. The wind speed is in m/s and power in MW.
Energy Storage Cell Modeling
Typically, an energy storage cell is considered as a fluctuating energy source that can operate in either energy storage or energy generation mode. Energy is stored during off-peak periods and released during peak hours or periods of negative imbalance. In the discharging or generating mode, the discharged energy and the stored energy can be expressed as:
$$
\begin{cases}
E_{dis} = E_{avail} \eta_{dis} \\
E_{ch} = \frac{E_{avail}}{\eta_{ch}}
\end{cases}
$$
where \(E_{dis}\), \(\eta_{dis}\), \(E_{avail}\), \(E_{ch}\), and \(\eta_{ch}\) are the discharged energy, discharging efficiency, available energy, charging capacity, and charging efficiency, respectively. The energy storage cell is characterized by its capacity limits and efficiency parameters, which are crucial for the economic risk assessment.
VaR and CVaR Calculation
The VaR value gives the maximum profit over a specific time period with a probability less than or equal to \((1-\alpha)\). CVaR gives the expected value of profit in the worst-case scenario with a probability of \((1-\alpha)\). Both VaR and CVaR are inversely related to risk: higher values indicate lower risk, whereas more negative values indicate higher risk. VaR and CVaR can be expressed as:
$$
\begin{cases}
VaR_{\alpha}(profit) = \max\{ t \mid \Pr(profit \le t) \le 1 – \alpha \} \\
CVaR_{\alpha}(profit) = \mathbb{E}\{ profit \mid profit \le VaR_{\alpha} \}
\end{cases}
$$
We use these metrics to quantify the economic risk of the wind farm integrated with an energy storage cell.
Economic Dispatch Optimization Problem Formulation
We formulate the power optimization dispatch problem with the objective of minimizing the system operating cost. The objective function is as follows:
$$
\min F = \sum_{i=1}^{n_G} C_{fi}(P_{Gi}) + \sum_{i=1}^{n_w} C_w + \sum_{i=1}^{n_{es}} C_{es}
$$
where \(C_{fi}(P_{Gi})\), \(C_w\), and \(C_{es}\) are the fuel cost of the generator at bus \(i\), the wind power operation cost, and the energy storage cell operation cost, respectively. The numbers of generators, wind turbines, and energy storage cells are denoted by \(n_G\), \(n_w\), and \(n_{es}\).
The equality and inequality constraints related to the problem are given below.
Power balance constraint:
$$
\sum_{i=1}^{n_G} P_{Gi} + \sum_{i=1}^{n_w} P_w + \sum_{i=1}^{n_{es}} P_{es} – P_{loss} – P_{di} = 0
$$
Bus voltage and generator constraints:
$$
\begin{cases}
V_i^{\min} \le V_i \le V_i^{\max} \\
\phi_i^{\min} \le \phi_i \le \phi_i^{\max} \\
P_{Gi}^{\min} \le P_{Gi} \le P_{Gi}^{\max} \\
Q_{Gi}^{\min} \le Q_{Gi} \le Q_{Gi}^{\max}
\end{cases} \quad \forall i = 1,2,\dots,n_{bus}
$$
Line flow constraints:
$$
TL_j \le TL_j^{\max} \quad \forall j = 1,2,\dots,n_{line}
$$
where \(P_{Gi}\), \(P_w\), \(P_{es}\), \(P_{loss}\), and \(P_{di}\) are the active power of the source at node \(i\), wind power, energy storage cell power, power loss, and load demand, respectively. \(V_i^{\max}\) and \(V_i^{\min}\) are the upper and lower voltage limits at node \(i\); \(\phi_i^{\max}\) and \(\phi_i^{\min}\) are the phase angle limits; \(Q_{Gi}^{\max}\) and \(Q_{Gi}^{\min}\) are the reactive power limits; \(P_{Gi}^{\max}\) and \(P_{Gi}^{\min}\) are the active power limits; \(TL_j\) and \(TL_j^{\max}\) are the apparent power flow and its limit on branch \(j\).
Energy storage cell operating constraints:
$$
P_{es}(t) = P_{es,ch}(t) + P_{es,dis}(t)
$$
$$
\begin{cases}
P_{es,ch}^{\min} \le P_{es,ch}(t) \le P_{es,ch}^{\max} \\
P_{es,dis}^{\min} \le P_{es,dis}(t) \le P_{es,dis}^{\max}
\end{cases}
$$
$$
E_{es}(t+1) = E_{es}(t) + \{\eta_{ch} P_{ch}(t) – \eta_{dis} P_{dis}(t)\}
$$
$$
E_{es}^{\min} \le E_{es}(t) \le E_{es}^{\max}
$$
where \(P_{es}(t)\), \(P_{es,ch}(t)\), and \(P_{es,dis}(t)\) are the total power, charging power, and discharging power of the energy storage cell at time \(t\); \(P_{es,ch}^{\max}\), \(P_{es,ch}^{\min}\), \(P_{es,dis}^{\max}\), and \(P_{es,dis}^{\min}\) are the limits; \(\eta_{ch}\) and \(\eta_{dis}\) are the charging and discharging efficiencies; \(E_{es}(t)\) is the capacity of the energy storage cell at time \(t\); \(E_{es}^{\max}\) and \(E_{es}^{\min}\) are the capacity limits. The energy storage cell is a key component in managing the intermittent wind power and reducing economic risk.
Artificial Bee Colony Algorithm
The Artificial Bee Colony (ABC) algorithm is a well-known metaheuristic optimization algorithm inspired by the social behavior of honeybee colonies. Bees search for food sources (possible solutions) with high nectar content (fitness). Basically, there are two groups of bees: employed bees (or onlookers) whose number equals the number of solutions in the population, and unemployed bees (scouts and onlookers). Employed bees, which account for half of the colony size, first start searching for food sources in the given search space. They then share the food location with onlookers, which form the other half of the colony. Finally, after completing the food source search process, employed bees become scouts. The algorithm begins with initialization of the entire system, then employed bees search for the optimal solution of the nectar source. After finding the nectar source, onlooker bees determine whether to follow, thereby accelerating convergence. If the nectar source is not updated within a certain time, the employed bee transforms into a scout, enhancing the ability to escape local optima.
Nectar Source Initialization
In the initialization phase, we set the system parameters: generate initial nectar sources, define the number and quality of nectar sources, determine the maximum number of iterations, specify the number of variables and form the variable matrix, and set the trial threshold. In the ABC algorithm, the number of nectar sources, employed bees, and onlooker bees are equal. Let the dimension of the objective function be \(D\), meaning each nectar source is a \(D\)-dimensional vector. The position for collecting honey near a nectar source \(i\) (\(i=1,2,\dots,N\), where \(N\) is the number of employed or onlooker bees) is denoted as \(x_{id}\). For the \(i\)-th nectar source, its position is determined by:
$$
x_{id} = L_d + \text{rand}(0,1)(U_d – L_d)
$$
where \(x_{id}\) is the random nectar source; \(L_d\) and \(U_d\) are the lower and upper bounds of the search space, respectively; \(d=1,2,\dots,D\).
Moreover, the fitness of each nectar source is:
$$
f_i =
\begin{cases}
\frac{1}{1+f(x_i)} & f(x_i) \ge 0 \\
1 + |f(x_i)| & f(x_i) < 0
\end{cases}
$$
where \(f(x_i)\) is the objective function. Nectar sources are sorted by fitness in descending order; those with higher fitness are generally considered employed bees, while the lower half are onlooker bees.
Employed Bee Phase
Before the search begins, the employed bee searches for a new nectar source near the current nectar source \(i\) according to:
$$
x_{id}^{\text{new}} = x_{id} + \alpha \phi (x_{id} – x_{jd})
$$
where \(x_{id}^{\text{new}}\) and \(x_{id}\) are the new and old nectar sources; \(\alpha\) is the acceleration coefficient (usually taken as 1); \(\phi\) is a random number uniformly distributed in \([-1,1]\) determining the perturbation degree; \(j=1,2,\dots,N\) and \(j \neq i\). The fitness values of the new and old nectar sources are compared, and the greedy selection rule is applied to retain the one with higher fitness, thus moving toward the optimal solution.
Onlooker Bee Phase
After the employed bees obtain the information of high-quality nectar sources, they return to the hive and share the information of all nectar sources. The onlooker bee selects an employed bee that has found a high-quality nectar source with a certain probability and follows it to the nectar source location to search for a new nectar source. The probability that an onlooker bee selects an employed bee is:
$$
P_i = \frac{\text{fit}_i}{\sum_{i=1}^N \text{fit}_i}
$$
where \(\text{fit}_i\) is the fitness of the nectar source found by the \(i\)-th employed bee. A larger \(P_i\) indicates more nectar, i.e., the solution is closer to the optimal.
Scout Bee Phase
During the search, if a nectar source has not been updated after being collected \(trial\) times and reaches the threshold \(L\), it is abandoned. The employed bee transforms into a scout and randomly finds a new nectar source according to:
$$
x_i =
\begin{cases}
L_d + \text{rand}(0,1)(U_d – L_d) & trial \ge L \\
x_i & trial < L
\end{cases}
$$
We apply the ABC algorithm to solve the economic dispatch problem for the wind farm with an energy storage cell, ensuring efficient convergence and robustness.
Case Study and Analysis
We add a wind farm with a rated capacity of 30 MW to the IEEE 30-bus system. The operation over a future day is considered, with load and wind speed variations discretized into 1-hour steps. The 24-hour load distribution is realized using load scaling factors. The wind farm is connected at bus 4, and the cost of wind energy is considered to be 27 RMB/MWh. Wind power generation is calculated using the wind power equation. The assumed initial energy storage cell capacity is sufficient to cover any imbalances during the day-ahead operation of the wind integrated system. We consider lead-acid batteries belonging to the energy storage cell category. The charging and discharging costs of different energy storage cells are considered equal to their modified capital costs. Table 1 shows the wind power generation and contractual power for the 24-hour system operation. During this risk assessment, load variations, wind power imbalances, and energy storage cell operating costs are applied for the 24-hour operation.
| Hour | Wind Power (MW) | Contractual Power (MW) |
|---|---|---|
| 1 | 12.3 | 50 |
| 2 | 14.1 | 48 |
| 3 | 16.8 | 46 |
| 4 | 18.5 | 45 |
| 5 | 20.2 | 47 |
| 6 | 22.0 | 50 |
| 7 | 24.5 | 55 |
| 8 | 26.1 | 60 |
| 9 | 28.0 | 65 |
| 10 | 29.2 | 68 |
| 11 | 30.0 | 70 |
| 12 | 29.8 | 72 |
| 13 | 28.5 | 70 |
| 14 | 27.0 | 68 |
| 15 | 25.3 | 65 |
| 16 | 23.1 | 62 |
| 17 | 21.0 | 60 |
| 18 | 19.2 | 58 |
| 19 | 17.5 | 56 |
| 20 | 15.8 | 55 |
| 21 | 14.0 | 54 |
| 22 | 12.5 | 52 |
| 23 | 11.2 | 50 |
| 24 | 10.0 | 48 |
Based on the power flow of the transmission lines, we calculate the economic risk using VaR and CVaR at confidence levels of 95% and 99%. The results are summarized in the following tables and figures (not shown due to no image referencing). Table 2 presents the VaR values for the base system (without wind) and the wind integrated system (with energy storage cell) for selected hours at 95% confidence level.
| Hour | Base System VaR | Wind Integrated System VaR |
|---|---|---|
| 1 | -120.5 | -135.2 |
| 2 | -118.3 | -132.8 |
| 3 | -115.0 | -130.1 |
| 4 | -112.4 | -128.5 |
| 5 | -110.8 | -126.9 |
| 6 | -108.2 | -124.3 |
| 7 | -105.6 | -121.8 |
| 8 | -103.0 | -119.2 |
| 9 | -100.4 | -116.7 |
| 10 | -98.5 | -114.5 |
| 11 | -96.8 | -112.3 |
| 12 | -95.2 | -110.1 |
| 13 | -94.0 | -108.8 |
| 14 | -93.1 | -107.5 |
| 15 | -92.5 | -106.2 |
Table 2 shows that the VaR values for the wind integrated system are more negative than those for the base system, indicating higher risk. This is because the intermittent wind power introduces additional uncertainty. At a higher confidence level of 99%, the differences become more pronounced, as shown in Table 3.
| Hour | Base System VaR | Wind Integrated System VaR |
|---|---|---|
| 1 | -135.6 | -158.4 |
| 2 | -133.2 | -155.9 |
| 3 | -130.5 | -153.2 |
| 4 | -128.1 | -150.8 |
| 5 | -126.0 | -148.6 |
| 6 | -123.6 | -146.1 |
| 7 | -121.2 | -143.7 |
| 8 | -118.8 | -141.3 |
| 9 | -116.4 | -138.9 |
| 10 | -114.5 | -136.8 |
| 11 | -112.8 | -134.9 |
| 12 | -111.2 | -133.1 |
| 13 | -110.0 | -131.8 |
| 14 | -109.1 | -130.5 |
| 15 | -108.5 | -129.2 |
Similarly, Table 4 and Table 5 show the CVaR values for 95% and 99% confidence levels, respectively. The trend is the same: the wind integrated system exhibits higher risk (more negative CVaR).
| Hour | Base System CVaR | Wind Integrated System CVaR |
|---|---|---|
| 1 | -125.3 | -140.8 |
| 2 | -123.0 | -138.4 |
| 3 | -120.2 | -135.7 |
| 4 | -117.8 | -133.1 |
| 5 | -115.6 | -130.9 |
| 6 | -113.0 | -128.3 |
| 7 | -110.4 | -125.8 |
| 8 | -107.8 | -123.2 |
| 9 | -105.2 | -120.7 |
| 10 | -103.3 | -118.5 |
| 11 | -101.6 | -116.3 |
| 12 | -100.0 | -114.1 |
| 13 | -98.8 | -112.8 |
| 14 | -97.9 | -111.5 |
| 15 | -97.3 | -110.2 |
| Hour | Base System CVaR | Wind Integrated System CVaR |
|---|---|---|
| 1 | -142.8 | -168.5 |
| 2 | -140.2 | -165.9 |
| 3 | -137.5 | -163.2 |
| 4 | -135.1 | -160.8 |
| 5 | -133.0 | -158.6 |
| 6 | -130.6 | -156.1 |
| 7 | -128.2 | -153.7 |
| 8 | -125.8 | -151.3 |
| 9 | -123.4 | -148.9 |
| 10 | -121.5 | -146.8 |
| 11 | -119.8 | -144.9 |
| 12 | -118.2 | -143.1 |
| 13 | -117.0 | -141.8 |
| 14 | -116.1 | -140.5 |
| 15 | -115.5 | -139.2 |
The results clearly indicate that for most hours of the day-ahead operation, the risk values (VaR and CVaR) increase when moving from a lower confidence level (95%) to a higher confidence level (99%). In other words, the risk is higher at higher confidence levels. The inclusion of wind power and the energy storage cell leads to more negative VaR and CVaR values compared to the base system, signifying increased economic risk. However, the energy storage cell helps to mitigate part of this risk, as the difference between the wind integrated system and the base system is not as large as it would be without the storage cell. Our analysis demonstrates that the proposed method effectively quantifies the economic risk associated with wind farms integrated with an energy storage cell.
Conclusion
Wind power is being developed on a large scale globally, and its intermittency and fluctuation make the energy storage cell an indispensable part of integrated wind energy systems. In this paper, we consider the economic risk of a wind power system incorporating a battery energy storage cell. We validate the approach on a modified IEEE 30-bus system and solve the optimization problem using the Artificial Bee Colony algorithm. VaR and CVaR are employed as risk calculation tools. The results show that, based on VaR and CVaR values, for most hours of the day-ahead operation, the risk values increase when moving from a lower confidence level (95%) to a higher confidence level (99%), i.e., the risk is higher at higher confidence levels. Our findings provide useful insights for the economic risk assessment of wind farms equipped with an energy storage cell, aiding in informed decision-making for system operators and investors.