In recent years, the global shift toward renewable energy sources has accelerated, driven by policies aimed at reducing carbon emissions. Wind energy, in particular, has emerged as a cost-effective and scalable solution for large-scale power generation. However, the inherent intermittency and volatility of wind power introduce significant operational risks when integrated into electrical grids. These risks can be mitigated through the deployment of energy storage systems, such as energy storage cells, which provide balancing capabilities by storing excess energy during low-demand periods and releasing it during peak demand. This paper focuses on evaluating the economic risks associated with wind farms combined with battery-based energy storage cells, using Value at Risk (VaR) and Conditional Value at Risk (CVaR) as key risk metrics at confidence levels of 95% and 99%. The analysis employs an optimized economic dispatch model to minimize operational costs while accounting for uncertainties in wind power generation and storage operation. By applying this framework to a modified IEEE 30-bus system, we demonstrate the effectiveness of the proposed approach in quantifying and managing economic risks in renewable energy integration.
The integration of wind power into existing power systems presents both opportunities and challenges. On one hand, wind energy offers a low-cost alternative to fossil fuels; on the other, its unpredictable nature can lead to grid instability and financial losses. Energy storage cells play a crucial role in addressing these issues by smoothing out power fluctuations and enhancing grid reliability. In this study, we develop a comprehensive model that incorporates wind power generation, energy storage cell dynamics, and risk assessment tools to evaluate the economic performance of such integrated systems. The primary objective is to minimize total operational costs, including fuel costs for conventional generators, wind power operation costs, and storage-related expenses, while adhering to technical constraints such as power balance, voltage limits, and transmission line capacities. The Artificial Bee Colony (ABC) algorithm is utilized to solve the optimization problem, providing efficient and robust solutions. Results indicate that higher confidence levels in VaR and CVaR calculations correspond to increased economic risks, highlighting the importance of risk-aware decision-making in wind-storage systems.
System Modeling
To assess the economic risks of wind farms with energy storage cells, we first establish mathematical models for wind power generation, storage systems, and risk metrics. These models form the foundation for the optimization framework.
Wind Power Model
The power output of a wind turbine depends on wind speed, which can be described using a piecewise function. For a rated wind farm, the generated power \( P_{\text{WT}} \) is calculated as follows:
$$ P_{\text{WT}} =
\begin{cases}
0 & v \leq v_a \text{ or } v \geq v_b \\
\frac{v – v_a}{v_r – v_a} P & v_a < v \leq v_r \\
P & v_r \leq v < v_b
\end{cases} $$
where \( P_{\text{WT}} \) is the wind power output in MW, \( P \) is the rated power in MW, \( v \) is the wind speed in m/s, \( v_a \) and \( v_b \) are the cut-in and cut-out wind speeds in m/s, respectively, and \( v_r \) is the rated wind speed in m/s. This model captures the nonlinear relationship between wind speed and power generation, which is essential for accurate risk assessment.
Energy Storage Cell Model
Energy storage cells, such as battery-based systems, operate in either charging or discharging modes to balance supply and demand. The energy dynamics during discharge and charge cycles are expressed as:
$$ E_{\text{dis}} = E_{\text{avail}} \eta_{\text{dis}} $$
$$ E_{\text{ch}} = E_{\text{avail}} \eta_{\text{ch}} $$
Here, \( E_{\text{dis}} \) and \( E_{\text{ch}} \) represent the discharged and charged energy in MWh, respectively, \( E_{\text{avail}} \) is the available energy in the storage system in MWh, and \( \eta_{\text{dis}} \) and \( \eta_{\text{ch}} \) are the discharge and charge efficiencies, typically ranging from 0.9 to 0.95 for modern energy storage cells. The state of charge (SOC) of the storage system is updated hourly based on the net energy flow, subject to minimum and maximum capacity limits.
Risk Metrics: VaR and CVaR
Value at Risk (VaR) and Conditional Value at Risk (CVaR) are widely used in financial and energy sectors to quantify economic risks. VaR measures the maximum potential loss at a given confidence level over a specified time horizon, while CVaR represents the expected loss beyond the VaR threshold. For a profit distribution, these metrics are defined as:
$$ \text{VaR}_{\alpha}(\text{profit}) = \max\{ t \mid \Pr(\text{profit} \leq t) \leq 1 – \alpha \} $$
$$ \text{CVaR}_{\alpha}(\text{profit}) = \mathbb{E}[\text{profit} \mid \text{profit} \leq \text{VaR}_{\alpha}] $$
where \( \alpha \) is the confidence level (e.g., 0.95 or 0.99). In this context, higher negative values of VaR and CVaR indicate greater economic risk, emphasizing the need for robust risk management strategies in systems with energy storage cells.
Economic Dispatch Optimization Model
The economic dispatch problem aims to minimize the total operational cost of the integrated wind-storage system while satisfying physical and operational constraints. The objective function is formulated as:
$$ \min F = \sum_{i=1}^{n_G} C_{fi}(P_{Gi}) + \sum_{i=1}^{n_w} C_{w} + \sum_{i=1}^{n_{\text{es}}} C_{\text{es}} $$
where \( C_{fi}(P_{Gi}) \) is the fuel cost of generator \( i \) in $/h, \( C_{w} \) is the wind power operation cost in $/MWh, and \( C_{\text{es}} \) is the operational cost of energy storage cells in $/MWh. The variables \( n_G \), \( n_w \), and \( n_{\text{es}} \) denote the number of conventional generators, wind turbines, and energy storage units, respectively.
The optimization is subject to the following constraints:
- Power Balance Constraint: The total generation must meet the load demand and losses:
$$ \sum_{i=1}^{n_G} P_{Gi} + \sum_{i=1}^{n_w} P_{w} + \sum_{i=1}^{n_{\text{es}}} P_{\text{es}} – P_{\text{loss}} – P_{d} = 0 $$
- Voltage and Phase Angle Limits: Bus voltages and angles must remain within specified bounds:
$$ V_i^{\min} \leq V_i \leq V_i^{\max}, \quad \phi_i^{\min} \leq \phi_i \leq \phi_i^{\max} \quad \forall i = 1, 2, \ldots, n_{\text{bus}} $$
- Generator Limits: Active and reactive power outputs are constrained by:
$$ P_{Gi}^{\min} \leq P_{Gi} \leq P_{Gi}^{\max}, \quad Q_{Gi}^{\min} \leq Q_{Gi} \leq Q_{Gi}^{\max} $$
- Transmission Line Limits: The power flow on each line must not exceed its thermal capacity:
$$ T_{Lj} \leq T_{Lj}^{\max} \quad \forall j = 1, 2, \ldots, n_{\text{line}} $$
- Energy Storage Cell Constraints: The operation of energy storage cells is governed by:
$$ P_{\text{es}}(t) = P_{\text{es,ch}}(t) + P_{\text{es,dis}}(t) $$
$$ P_{\text{es,ch}}^{\min} \leq P_{\text{es,ch}}(t) \leq P_{\text{es,ch}}^{\max}, \quad P_{\text{es,dis}}^{\min} \leq P_{\text{es,dis}}(t) \leq P_{\text{es,dis}}^{\max} $$
$$ E_{\text{es}}(t+1) = E_{\text{es}}(t) + \left\{ \eta_{\text{ch}} P_{\text{ch}}(t) – \eta_{\text{dis}} P_{\text{dis}}(t) \right\} $$
$$ E_{\text{es}}^{\min} \leq E_{\text{es}}(t) \leq E_{\text{es}}^{\max} $$
These constraints ensure the safe and efficient operation of the grid and energy storage cells, which are critical for maintaining system stability and minimizing costs.
Artificial Bee Colony Algorithm
The Artificial Bee Colony (ABC) algorithm is a metaheuristic optimization technique inspired by the foraging behavior of honey bees. It is particularly effective for solving complex, non-linear problems like economic dispatch in power systems. The algorithm consists of three phases: employed bees, onlooker bees, and scout bees, each contributing to the search for optimal solutions.
Initialization Phase
In this phase, initial food sources (solutions) are generated randomly within the search space. For a problem with \( D \) dimensions, the position of each food source \( i \) is given by:
$$ x_{id} = L_d + \text{rand}(0,1) \times (U_d – L_d) $$
where \( x_{id} \) is the \( d \)-th component of the \( i \)-th solution, and \( L_d \) and \( U_d \) are the lower and upper bounds of the \( d \)-th dimension, respectively. The fitness of each solution is evaluated using:
$$ f_i =
\begin{cases}
\frac{1}{1 + f(x_i)} & f(x_i) \geq 0 \\
1 + |f(x_i)| & f(x_i) < 0
\end{cases} $$
Solutions are sorted based on fitness, with the top half designated as employed bees and the bottom half as onlooker bees.
Employed Bee Phase
Employed bees explore new solutions in the vicinity of their current positions. A new solution \( x_{\text{new}} \) is generated as:
$$ x_{\text{new}, id} = x_{id} + \alpha \phi (x_{id} – x_{jd}) $$
where \( \alpha \) is an acceleration coefficient (typically set to 1), \( \phi \) is a random number in \([-1, 1]\), and \( j \) is a randomly selected solution different from \( i \). The new solution is accepted if it has higher fitness, following a greedy selection process.
Onlooker Bee Phase
Onlooker bees select employed bees based on the probability proportional to their fitness:
$$ P_i = \frac{\text{fit}_i}{\sum_{i=1}^N \text{fit}_i} $$
where \( \text{fit}_i \) is the fitness of the \( i \)-th employed bee. This phase enhances exploitation by focusing on promising regions of the search space.
Scout Bee Phase
If a solution does not improve after a predetermined number of trials (threshold \( L \)), the employed bee becomes a scout bee and generates a new random solution:
$$ x_i =
\begin{cases}
L_d + \text{rand}(0,1) \times (U_d – L_d) & \text{trial} \geq L \\
x_i & \text{trial} < L
\end{cases} $$
This mechanism helps avoid local optima and maintains diversity in the population. The ABC algorithm is applied to solve the economic dispatch problem, ensuring efficient computation of optimal schedules for generators, wind turbines, and energy storage cells.
Case Study and Results
To validate the proposed framework, we conducted a case study using a modified IEEE 30-bus system integrated with a 30 MW wind farm and battery-based energy storage cells. The system was simulated over a 24-hour period with hourly time steps, considering variations in load demand and wind speed. The wind power cost was set at $27/MWh, and the storage parameters included charge/discharge efficiencies of 0.95 and capacity limits of 20-100 MWh. The ABC algorithm was implemented to minimize operational costs while calculating VaR and CVaR at 95% and 99% confidence levels.
The following table summarizes the hourly wind power generation and contracted power for the 24-hour period:
| Hour | Wind Power (MW) | Contract Power (MW) | Load Demand (MW) |
|---|---|---|---|
| 1 | 12.5 | 10.0 | 85.2 |
| 2 | 15.3 | 12.0 | 82.1 |
| 3 | 18.7 | 15.0 | 78.9 |
| 4 | 22.1 | 18.0 | 76.3 |
| 5 | 25.4 | 20.0 | 74.5 |
| 6 | 28.9 | 22.0 | 72.8 |
| 7 | 26.3 | 21.0 | 75.1 |
| 8 | 23.8 | 19.0 | 77.4 |
| 9 | 21.2 | 17.0 | 80.2 |
| 10 | 19.6 | 16.0 | 83.7 |
| 11 | 17.9 | 14.0 | 86.5 |
| 12 | 16.4 | 13.0 | 88.9 |
| 13 | 14.8 | 12.0 | 90.3 |
| 14 | 13.2 | 11.0 | 91.7 |
| 15 | 11.7 | 10.0 | 92.4 |
| 16 | 10.1 | 9.0 | 93.1 |
| 17 | 9.5 | 8.0 | 94.2 |
| 18 | 8.9 | 7.0 | 95.8 |
| 19 | 8.3 | 6.0 | 96.5 |
| 20 | 7.7 | 5.0 | 97.3 |
| 21 | 7.1 | 4.0 | 98.1 |
| 22 | 6.5 | 3.0 | 98.9 |
| 23 | 5.9 | 2.0 | 99.7 |
| 24 | 5.3 | 1.0 | 100.0 |
The economic risk analysis was performed by computing VaR and CVaR values for each hour, considering the uncertainties in wind power and storage operation. The results are illustrated in the following sections.
VaR at 95% Confidence Level
At the 95% confidence level, the VaR values for the base system (without wind) and the wind-integrated system were compared. The wind-integrated system exhibited higher negative VaR values during most hours, indicating increased economic risk due to wind power variability. For instance, during peak wind generation hours (e.g., hours 5-7), the VaR values were more negative, reflecting greater potential losses. This underscores the need for energy storage cells to mitigate risks by providing backup power and balancing services.
VaR at 99% Confidence Level
When the confidence level was increased to 99%, the VaR values became more negative for both systems, but the wind-integrated system showed a more pronounced increase in risk. This trend highlights that higher confidence levels amplify the perceived economic risks, especially in systems with intermittent renewables. The integration of energy storage cells helped reduce these risks by smoothing power output and enhancing grid stability, as evidenced by less negative VaR values in scenarios with optimized storage dispatch.
CVaR at 95% and 99% Confidence Levels
Similar to VaR, CVaR values at 95% and 99% confidence levels were analyzed. The wind-integrated system consistently demonstrated higher CVaR magnitudes, implying greater expected losses beyond the VaR threshold. For example, at the 99% confidence level, the CVaR for the wind-integrated system was approximately 15-20% more negative than that of the base system during high-wind hours. This emphasizes the importance of using CVaR as a complementary risk metric to capture tail risks effectively. The deployment of energy storage cells significantly improved CVaR outcomes by reducing the frequency and severity of extreme loss events.
The following table provides a comparative summary of average VaR and CVaR values (in $) for the base and wind-integrated systems over 24 hours:
| System Type | VaR (95%) | VaR (99%) | CVaR (95%) | CVaR (99%) |
|---|---|---|---|---|
| Base System | -1250 | -1850 | -1450 | -2100 |
| Wind-Integrated System | -1550 | -2250 | -1750 | -2550 |
| Wind-Integrated with Storage | -1350 | -1950 | -1550 | -2200 |
These results clearly show that the inclusion of energy storage cells reduces economic risks, as reflected in the less negative VaR and CVaR values. The optimization model successfully minimizes costs while managing risks, demonstrating the practicality of the proposed approach.
Conclusion
In this paper, we have presented a comprehensive framework for assessing the economic risks of wind farms integrated with energy storage cells. By combining wind power modeling, storage dynamics, and risk metrics like VaR and CVaR, we developed an optimization model that minimizes operational costs while accounting for uncertainties. The Artificial Bee Colony algorithm proved effective in solving this complex problem, providing robust solutions for economic dispatch. Our case study on the modified IEEE 30-bus system revealed that higher confidence levels in risk assessment lead to increased perceived economic risks, but the integration of energy storage cells mitigates these risks by enhancing grid flexibility and reliability. The repeated emphasis on energy storage cells throughout the analysis underscores their critical role in future renewable energy systems. This work provides valuable insights for policymakers and system operators in designing risk-aware strategies for wind-storage integration, contributing to the sustainable development of power systems.