Abstract
The technological revolution has significantly advanced global industrialization, resulting in a surging demand for electricity. Relying solely on fossil fuels to meet this demand has led to energy crises and environmental pollution. Renewable Energy Sources (RES), such as wind and solar, have emerged as promising alternatives. However, the intermittent and volatile nature of RES poses challenges to grid stability. Battery Energy Storage System (BESS) serve as bidirectional energy regulators, mitigating RES integration issues and ensuring grid reliability. Given the high cost of storage batteries, strategic planning for their placement and capacity is crucial. This paper aims to optimize battery energy storage system (BESS) capacity allocation in distribution networks with wind and solar sources to minimize daily average network losses. The main contributions are:
- Systematic Overview: Introducing battery energy storage system (BESS) components, functions, and application scenarios, analyzing their impact on network losses upon grid connection.
- Model Development: Establishing a mathematical model for battery energy storage system (BESS) capacity allocation optimization, considering RES output characteristics and their impact on grid loads.
- Algorithm Innovation: Proposing an Improved Simulated Annealing Genetic Algorithm (ISAGA) to solve the capacity allocation problem, addressing genetic algorithm limitations.
- Empirical Validation: Demonstrating ISAGA’s effectiveness through simulations in the IEEE-33 node test system.
1. Introduction
1.1 Background and Significance
The growing global electricity demand, fueled by industrialization and improved living standards, has intensified the reliance on fossil fuels. However, these are finite resources, leading to environmental degradation and resource depletion concerns. Renewable energy sources (RES) like wind and solar are clean, abundant, and sustainable alternatives. While they significantly contribute to energy diversity and environmental protection, their intermittent nature poses challenges to grid stability and reliability.
Battery Energy Storage System (BESS) play a pivotal role in addressing these challenges by offering bidirectional power flow capabilities, rapid response times, and compatibility with energy management systems. battery energy storage system (BESS) effectively balance power supply and demand, mitigating the impact of RES fluctuations on the grid.
1.2 Research Objectives
This paper focuses on optimizing battery energy storage system (BESS) capacity allocation in distribution networks integrated with wind and solar power sources. The objectives are:
- Introducing battery energy storage system (BESS) components, functions, and application scenarios.
- Analyzing the impact of battery energy storage system (BESS) integration on network losses.
- Developing battery energy storage system (BESS) capacity allocation optimization model aimed at minimizing daily average network losses.
- Proposing an Improved Simulated Annealing Genetic Algorithm (ISAGA) to solve the capacity allocation problem.
- Validating the proposed approach through simulations in the IEEE-33 node test system.
2. Battery Energy Storage System Components and Applications
2.1 System Composition and Functions
Battery energy storage system (BESS) primarily consists of the Supervisory Control And Data Acquisition (SCADA) system, Battery System (BS), Battery Management System (BMS), and Power Conversion System (PCS).
- SCADA System: Monitors and controls the entire battery energy storage system (BESS), ensuring efficient and reliable operation.
- Battery System (BS): Stores and releases electrical energy, determined by battery cells arranged in series and parallel configurations.
- Battery Management System (BMS): Monitors battery states, protects against overcharge/discharge, and balances cell voltages.
- Power Conversion System (PCS): Controls energy exchange between the battery and the grid, enabling AC/DC conversion.
2.2 Main Application Scenarios
Battery energy storage system (BESS) finds extensive applications in various parts of the power system, including:
- User Side: Demand response, peak shaving, and integrated energy systems.
- Grid Side: Power supply reliability, peak shaving, and voltage support.
- Generation Side: Renewable energy smoothing, energy storage, and frequency regulation.
2.3 Impact on Network Losses
Battery energy storage system (BESS) integration significantly impacts distribution network losses by:
- Active Power Charging and Discharging: Balancing grid loads, reducing peak demands, and mitigating losses.
- Reactive Power Support: Improving voltage profiles and reducing reactive power flows, further decreasing losses.
3. Mathematical Modeling for Battery Energy Storage System Capacity Allocation
3.1 RES Output Models
3.1.1 Wind Power Generation Model
Wind power output (P_w) is determined by the turbine’s rated power (P_rated), rated wind speed (v_rated), cut-in (v_ci), and cut-out (v_co) wind speeds, following the Weibull distribution for wind speeds (v):
f(v)=(sk)(sv)k−1e−(sv)k
The wind power output model is:
P_w = begin{cases} 0 & \text{if } v < v_{ci} \text{ or } v > v_{co} \\ P_{rated} \left( \frac{v – v_{ci}}{v_{rated} – v_{ci}} \right)^3 & \text{if } v_{ci} \leq v \leq v_{rated} \\ P_{rated} & \text{if } v > v_{rated} end{cases}
3.1.2 Photovoltaic Output Model
Photovoltaic (PV) output (P_pv) depends on solar irradiance (R) and panel efficiency (δ):
Ppv=δ⋅S⋅R
where S is the panel area.
3.2 BESS Output Model
The battery energy storage system (BESS) output (P_bess) depends on its state of charge (SOC), rated capacity (C), charging/discharging efficiency (η_c, η_d), and power limits (P_{max,c}, P_{max,d}):
P_{bess}(t) = begin{cases} frac{C \cdot (\text{SOC}_{\text{max}} – \text{SOC}(t)) \cdot \eta_c}{\Delta t} & \text{(Charging)} \\ frac{C \cdot (\text{SOC}(t) – \text{SOC}_{\text{min}}) \cdot \eta_d}{\Delta t} & \text{(Discharging)} end{cases}
with SOC constraints:
textSOCmin≤SOC(t)≤SOCmax
3.3 Network Loss Minimization Model
The objective is to minimize daily average network losses (L_avg) by strategically allocating battery energy storage system (BESS) capacity:
textMinimizeLavg=T1t=1∑Ta=1∑AAIa2(t)⋅Za
subject to:
- Node Voltage Constraints:UiH≥Ui(t)≥UiL
- Branch Current and Phase Angle Constraints:Ia(t)≤IaH,θaL≤θa(t)≤θaH
- Power Flow Constraints:PiD(t)−PiC(t)−g=1∑GDg(t)+k=1∑KBk(t)=j=1∑nYij⋅∣Ui(t)∣⋅∣Uj(t)∣⋅(cos(θi(t)−θj(t))⋅Gij+sin(θi(t)−θj(t))⋅Bij)
- BESS Power and SOC Constraints:PB,min≤Pbess(t)≤PB,max,SOCmin≤SOC(t)≤SOCmax
- System Power Balance:suma=1APa(t)=i=1∑NPDi(t)+g=1∑GDg(t)−k=1∑KBk(t)
where Ia(t) and Za are branch current and impedance, Ui(t) and θi(t) are node voltage magnitude and phase angle, Yij, Gij, and Bij are admittance matrix elements, PDi(t) and Dg(t) are node load and RES output, and Bk(t) is battery energy storage system (BESS) output at node k.
4. Improved Simulated Annealing Genetic Algorithm (ISAGA)
4.1 Genetic Algorithm (GA) Basics
GA mimics natural selection processes to solve optimization problems. It involves:
- Selection: Individuals with higher fitness are more likely to survive and reproduce.
- Crossover: Offspring are created by combining genetic material from two parents.
- Mutation: Random changes in genetic material introduce diversity.
4.2 Simulated Annealing Algorithm (SA)
SA simulates the physical process of annealing, where material properties improve as temperature gradually decreases. SA accepts worse solutions with a probability determined by the Metropolis criterion, aiding in escaping local optima.
4.3 ISAGA Proposal
To address GA’s limitations (fixed crossover and mutation probabilities, uncontrollable convergence speed), ISAGA introduces:
- Iterative Temperature Control Module: Replaces GA’s fixed iteration scheme with a variable step size controlled by an exponential cooling function, adapting to population fitness.T(e)=T0⋅e−q⋅FΔ⋅eT/Qwhere T(e) is the current temperature, T0 is the initial temperature, FΔ is the fitness difference, eT is the current iteration, Q and q are constants.
- Adaptive Crossover and Mutation Modules: Crossover and mutation probabilities adapt based on population fitness, expanding the search space and avoiding local optima.Pc=max(Pc1−Fmax−FavgF−Favg⋅(Pc1−Pc2),Pc2)Pm=max(Pm1−Fmax−FavgFmax−F⋅(Pm1−Pm2),Pm2)
- Simulated Annealing Mutation Module: Combines SA’s Metropolis criterion with adaptive mutation probability for dual-threshold control.
5. Simulation and Case Studies
5.1 Simulation Setup
Simulations were conducted on the IEEE-33 node test system with wind (400 kW) and PV (300 kW) sources integrated at nodes 10 and 18, respectively. battery energy storage system (BESS) capacities were optimized using ISAGA to minimize daily average network losses.
5.2 Results and Analysis
5.2.1 BESS Capacity Allocation
Table 1 summarizes the optimal battery energy storage system (BESS) capacity allocation schemes for different numbers of battery energy storage system (BESS) units using ISAGA and traditional GA.
Table 1: Optimal BESS Capacity Allocation
| Number of BESS | ISAGA Allocation (Node, Capacity [kWh]) | GA Allocation (Node, Capacity [kWh]) | Daily Avg. Loss [kW] (ISAGA) | Daily Avg. Loss [kW] (GA) |
|---|---|---|---|---|
| 1 | (29, 161.61) | (11, 112.26) | 171.10 | 173.72 |
| 2 | (2, 40.97), (11, 117.74) | (3, 73.87), (17, 189) | 170.77 | 173.17 |
| 3 | (8, 167.1), (12, 200), (17, 178.06) | (16, 161.61), (13, 73.87), (29, 183.55) | 169.90 | 172.86 |
| 4 | (4, 73.87), (7, 73.87), (10, 101.29), (31, 172.59) | (4, 73.87), (8, 167.1), (11, 117.74), (29, 161.61) | 170.05 | 173.32 |
ISAGA consistently outperforms GA, achieving lower daily average network losses.
5.2.2 Convergence Performance
The convergence performances of ISAGA and GA for different numbers of battery energy storage system (BESS) units.
ISAGA converges faster and to lower loss values, indicating its superior performance.
5.2.3 BESS Output and SOC Profiles
Typical battery energy storage system (BESS) output and SOC profiles for different numbers of battery energy storage system (BESS) units optimized by ISAGA.
The profiles align with expected charging and discharging patterns during peak and off-peak hours, effectively balancing grid loads and minimizing losses.
5.3 Comparison with Simulated Annealing
Table 2 compares the optimal battery energy storage system (BESS) allocations and resulting daily average losses obtained using ISAGA and SA.
Table 2: Comparison of ISAGA and SA Results
| Number of BESS | ISAGA Allocation (Node, Capacity [kWh]) | SA Allocation (Node, Capacity [kWh]) | Daily Avg. Loss [kW] (ISAGA) | Daily Avg. Loss [kW] (SA) |
|---|---|---|---|---|
| 1 | (29, 161.61) | (29, 120.26) | 171.10 | 173.55 |
| 2 | (2, 40.97), (11, 117.74) | (29, 120.49), (11, 74.33) | 170.77 | 173.41 |
| 3 | (8, 167.1), (12, 200), (17, 178.06) | (29, 106.27), (15, 77.5), (29, 173.52) | 169.90 | 173.30 |
| 4 | (4, 73.87), (7, 73.87), (10, 101.29), (31, 172.59) | (30, 112.75), (12, 73.42), (27, 163.1), (17, 109.29) | 170.05 | 173.66 |
ISAGA consistently achieves lower daily average network losses compared to SA, demonstrating its superiority.
6. Conclusion and Future Work
6.1 Conclusion
This paper investigated battery energy storage system (BESS) capacity allocation optimization in distribution networks integrated with wind and solar power sources. Key findings include:
- Battery energy storage system (BESS) integration significantly reduces daily average network losses.
- ISAGA, an improved version of GA, outperforms traditional GA and SA in terms of optimization performance and convergence speed.
- Optimal battery energy storage system (BESS) allocations identified through simulations effectively balance grid loads, minimizing network losses.
6.2 Future Work
Several avenues for future research include:
- Incorporating battery degradation models to account for long-term operational impacts.
- Developing detailed battery energy storage system (BESS) operation strategies based on optimal power flow algorithms.
- Expanding the optimization model to include economic considerations, such as battery energy storage system (BESS) investment costs and operational benefits over its lifetime.
These enhancements will further improve the practical applicability and economic viability of battery energy storage system (BESS) in modern power systems.