In recent years, the global energy landscape has shifted significantly towards renewable sources, driven by policies aimed at reducing carbon emissions. Wind energy, in particular, has emerged as a cost-effective and scalable solution, with installed capacity reaching unprecedented levels. However, the inherent intermittency and volatility of wind power generation introduce substantial risks when integrated into power systems. These challenges can be mitigated through the deployment of a battery energy storage system (BESS), which enhances grid stability and economic viability. Despite extensive research on renewable integration, there remains a gap in comprehensive economic risk evaluations specifically for wind farms coupled with a BESS. This paper addresses this gap by conducting an economic risk analysis using Value at Risk (VaR) and Conditional Value at Risk (CVaR) at 95% and 99% confidence levels as constraints. We develop models for wind power, the BESS, and risk metrics, and apply an artificial bee colony algorithm to optimize system dispatch. Our findings demonstrate the effectiveness of this approach in quantifying and managing risks, providing practical insights for operators.
The integration of wind energy into power systems has been widely studied, but the economic implications of adding a BESS are less explored. A BESS can store excess energy during low-demand periods and discharge it during peaks, reducing imbalances and associated costs. However, this introduces complexities in risk assessment, as the BESS operation affects revenue streams and exposure to market fluctuations. Traditional methods often overlook the dynamic interactions between wind generation and the BESS, leading to suboptimal decisions. In this work, we focus on the economic risks, employing VaR and CVaR to capture tail risks under uncertainty. VaR measures the maximum loss over a specified period at a given confidence level, while CVaR estimates the expected loss beyond the VaR threshold, offering a more conservative risk perspective. By incorporating these into an optimization framework, we aim to provide a robust tool for evaluating the economic performance of wind farms with a BESS.
To model the system, we first define the wind power output based on wind speed. The power generated by a wind turbine, \( P_{WT} \), is calculated as follows:
$$ P_{WT} = \begin{cases} 0 & v \leq v_a \text{ or } v \geq v_b \\ \frac{v – v_a}{v_r – v_a} P & v_a < v \leq v_r \\ P & v_r \leq v < v_b \end{cases} $$
where \( v \) is the wind speed in m/s, \( v_a \) and \( v_b \) are the cut-in and cut-out speeds, \( v_r \) is the rated speed, and \( P \) is the rated power in MW. This piecewise function accounts for the nonlinear relationship between wind speed and power output, which is critical for accurate risk modeling.
For the battery energy storage system, we consider its charging and discharging modes. The energy dynamics are described by:
$$ E_{dis} = E_{avail} \eta_{dis} $$
$$ E_{ch} = E_{avail} \eta_{ch} $$
Here, \( E_{dis} \) and \( E_{ch} \) represent the discharged and charged energy, respectively, \( E_{avail} \) is the available energy, and \( \eta_{dis} \) and \( \eta_{ch} \) are the discharge and charge efficiencies, typically ranging from 0.8 to 0.95 for a BESS. The state of charge (SOC) of the BESS is updated hourly to reflect real-time operations, ensuring that storage constraints are adhered to during optimization.
Risk assessment is performed using VaR and CVaR, defined as:
$$ \text{VaR}_{\alpha}(\text{profit}) = \max\{ t | \Pr(\text{profit} \leq t) \leq 1 – \alpha \} $$
$$ \text{CVaR}_{\alpha}(\text{profit}) = \mathbb{E}\{ \text{profit} | \text{profit} \leq \text{VaR}_{\alpha} \} $$
where \( \alpha \) is the confidence level (e.g., 0.95 or 0.99). These metrics help quantify the economic risk by focusing on the worst-case scenarios, which is essential for decision-making under uncertainty. A higher VaR or CVaR value indicates lower risk, as it represents a less negative profit threshold.
The economic dispatch optimization problem aims to minimize the total operating cost, formulated as:
$$ \min F = \sum_{i=1}^{n_G} C_{fi}(P_{Gi}) + \sum_{i=1}^{n_w} C_w + \sum_{i=1}^{n_{es}} C_{es} $$
where \( C_{fi}(P_{Gi}) \) is the fuel cost of generator \( i \), \( C_w \) is the wind operation cost, and \( C_{es} \) is the BESS operation cost. The variables \( n_G \), \( n_w \), and \( n_{es} \) denote the number of generators, wind turbines, and BESS units, respectively. The cost functions are typically quadratic for generators and linear for wind and the BESS, reflecting their operational characteristics.
The optimization is subject to several constraints. The power balance equation ensures that generation meets demand plus losses:
$$ \sum_{i=1}^{n_G} P_{Gi} + \sum_{i=1}^{n_w} P_w + \sum_{i=1}^{n_{es}} P_{es} – P_{loss} – P_{di} = 0 $$
where \( P_{Gi} \), \( P_w \), \( P_{es} \), \( P_{loss} \), and \( P_{di} \) are the generator power, wind power, BESS power, power loss, and load demand at node \( i \), respectively. Additional constraints include voltage limits, phase angle limits, and generator capacity bounds:
$$ V_i^{\min} \leq V_i \leq V_i^{\max} $$
$$ \phi_i^{\min} \leq \phi_i \leq \phi_i^{\max} $$
$$ P_{Gi}^{\min} \leq P_{Gi} \leq P_{Gi}^{\max} $$
$$ Q_{Gi}^{\min} \leq Q_{Gi} \leq Q_{Gi}^{\max} $$
for all buses \( i = 1, 2, \dots, n_{bus} \). Transmission line limits are enforced to prevent overloads:
$$ TL_j \leq TL_j^{\max} \quad \forall j = 1, 2, \dots, n_{line} $$
For the BESS, operational constraints include:
$$ P_{es}(t) = P_{es,ch}(t) + P_{es,dis}(t) $$
$$ P_{es,ch}^{\min} \leq P_{es,ch}(t) \leq P_{es,ch}^{\max} $$
$$ P_{es,dis}^{\min} \leq P_{es,dis}(t) \leq P_{es,dis}^{\max} $$
$$ E_{es}(t+1) = E_{es}(t) + \left\{ \eta_{ch} P_{ch}(t) – \eta_{dis} P_{dis}(t) \right\} $$
$$ E_{es}^{\min} \leq E_{es}(t) \leq E_{es}^{\max} $$
These ensure that the BESS operates within its power and energy capacities, maintaining reliability and longevity. The SOC is updated recursively, with efficiency factors accounting for energy losses during charging and discharging.
To solve this complex optimization problem, we employ the artificial bee colony (ABC) algorithm, a metaheuristic inspired by honeybee behavior. The ABC algorithm is efficient for handling non-convex constraints and stochastic elements, such as wind variability and BESS dynamics. The process begins with initialization, where solution vectors (food sources) are generated randomly within bounds:
$$ x_{id} = L_d + \text{rand}(0,1) (U_d – L_d) $$
for each dimension \( d = 1, 2, \dots, D \), where \( L_d \) and \( U_d \) are the lower and upper bounds. The fitness of each solution is evaluated using:
$$ f_i = \begin{cases} \frac{1}{1 + f(x_i)} & f(x_i) \geq 0 \\ 1 + |f(x_i)| & f(x_i) < 0 \end{cases} $$
which prioritizes solutions with lower costs. The algorithm proceeds through employed bee, onlooker bee, and scout bee phases. In the employed bee phase, new solutions are explored around existing ones:
$$ x_{id}^{\text{new}} = x_{id} + \alpha \phi (x_{id} – x_{jd}) $$
where \( \alpha \) is an acceleration coefficient (set to 1), and \( \phi \) is a random number in \([-1,1]\). Greedy selection retains the better solution based on fitness. Onlooker bees choose solutions probabilistically:
$$ P_i = \frac{\text{fit}_i}{\sum_{i=1}^N \text{fit}_i} $$
emphasizing higher-fitness sources. If a solution does not improve after a threshold number of trials, scout bees replace it with a random search:
$$ x_i = \begin{cases} L_d + \text{rand}(0,1) (U_d – L_d) & \text{trial} \geq L \\ x_i & \text{trial} < L \end{cases} $$
This mechanism avoids local optima and enhances global convergence. The ABC algorithm is iterated until maximum iterations are reached, providing a near-optimal dispatch schedule that minimizes costs while respecting risk constraints.
For case analysis, we modify the IEEE 30-bus system by integrating a 30 MW wind farm at bus 4. The BESS is modeled as a lead-acid battery system with typical efficiency parameters. We simulate a 24-hour operation with hourly time steps, incorporating load and wind variations. Wind power generation is derived from historical data, and the BESS is initialized with sufficient capacity to handle imbalances. The wind operation cost is set at 27 currency units per MW, and BESS costs include capital and operational components. The table below summarizes key parameters for the wind and BESS integration:
| Hour | Wind Power (MW) | Contract Power (MW) | BESS Charging (MW) | BESS Discharging (MW) |
|---|---|---|---|---|
| 1 | 15.2 | 12.0 | 5.0 | 0.0 |
| 2 | 18.5 | 14.0 | 3.5 | 0.0 |
| 3 | 22.1 | 16.0 | 2.0 | 1.0 |
| 4 | 25.8 | 18.0 | 0.0 | 2.5 |
| 5 | 28.3 | 20.0 | 0.0 | 4.0 |
| 6 | 30.0 | 22.0 | 0.0 | 5.5 |
| 7 | 27.6 | 24.0 | 1.0 | 3.0 |
| 8 | 24.2 | 26.0 | 3.0 | 1.0 |
| 9 | 20.7 | 28.0 | 4.5 | 0.0 |
| 10 | 17.4 | 30.0 | 6.0 | 0.0 |
| 11 | 14.8 | 28.0 | 5.5 | 0.0 |
| 12 | 12.5 | 26.0 | 4.0 | 0.0 |
| 13 | 10.9 | 24.0 | 3.0 | 1.0 |
| 14 | 9.3 | 22.0 | 2.0 | 2.0 |
| 15 | 8.1 | 20.0 | 1.5 | 3.0 |
| 16 | 7.2 | 18.0 | 1.0 | 4.0 |
| 17 | 6.8 | 16.0 | 0.5 | 5.0 |
| 18 | 7.5 | 14.0 | 0.0 | 6.0 |
| 19 | 9.0 | 12.0 | 0.0 | 5.5 |
| 20 | 11.2 | 10.0 | 0.0 | 4.0 |
| 21 | 13.8 | 12.0 | 1.0 | 2.0 |
| 22 | 16.5 | 14.0 | 2.5 | 0.0 |
| 23 | 19.1 | 16.0 | 4.0 | 0.0 |
| 24 | 21.7 | 18.0 | 5.5 | 0.0 |
The optimization results are analyzed using VaR and CVaR at 95% and 99% confidence levels. The following figure illustrates the system configuration, including the wind farm and BESS integration, which is essential for visualizing the setup.
At the 95% confidence level, the VaR values for the base system (without wind) and the wind-integrated system with a BESS are compared. The wind-integrated system shows higher negative VaR values during most hours, indicating increased economic risk due to wind variability. For instance, during peak wind hours, the VaR decreases, reflecting greater exposure to losses. Similarly, the CVaR at 95% confidence reveals that the wind-BESS system has higher expected losses in worst-case scenarios. This trend intensifies at the 99% confidence level, where both VaR and CVaR become more negative, emphasizing the heightened risk under extreme conditions. The BESS helps mitigate some risk by shifting energy, but its effect is limited during high-variability periods.
To quantify the risk reduction, we compute the average VaR and CVaR across the 24-hour period. For the base system, the average VaR at 95% confidence is -120 currency units, while the wind-BESS system averages -150 units. At 99% confidence, these values drop to -180 and -210 units, respectively. The CVaR follows a similar pattern, with base system averages of -140 (95%) and -200 (99%), compared to -170 and -240 for the wind-BESS system. These results underscore the importance of risk-aware dispatch when integrating a BESS with wind farms.
Further analysis involves sensitivity studies on BESS parameters. For example, increasing the BESS capacity from 30 MWh to 50 MWh reduces the average VaR by 10% at 95% confidence, demonstrating the risk-mitigating potential of larger storage. However, this comes at higher capital costs, which must be balanced in economic evaluations. The table below summarizes the risk metrics for different BESS configurations:
| BESS Capacity (MWh) | Average VaR (95%) | Average CVaR (95%) | Average VaR (99%) | Average CVaR (99%) |
|---|---|---|---|---|
| 30 | -150 | -170 | -210 | -240 |
| 40 | -140 | -160 | -190 | -220 |
| 50 | -135 | -155 | -180 | -210 |
The artificial bee colony algorithm proves effective in solving this optimization, converging within 500 iterations for most scenarios. The algorithm’s ability to handle non-linear constraints and stochastic elements makes it suitable for real-world applications. Compared to traditional methods like linear programming, the ABC approach reduces computation time by 20% while improving solution quality by 15%, as measured by cost savings and risk metric adherence.
In conclusion, this paper presents a comprehensive framework for economic risk assessment of wind farms integrated with a battery energy storage system. By leveraging VaR and CVaR at high confidence levels, we capture the tail risks associated with wind intermittency and BESS operations. The models and optimization approach demonstrate that while a BESS can alleviate some risks, the overall economic exposure increases with higher confidence levels, necessitating careful planning. Future work could explore hybrid storage systems or multi-market participation to further enhance risk management. This research provides valuable insights for policymakers and operators seeking to optimize renewable energy investments in a risk-aware manner.