Abstract
Energy storage battery, with their rapid response and bidirectional regulation capabilities, are pivotal in modern power systems for frequency modulation. However, their lifespan remains a critical constraint. This study proposes an adaptive frequency modulation strategy that integrates virtual inertial control and virtual droop control, dynamically adjusting their contribution ratios through a fuzzy controller and state-of-charge (SOC) feedback. Simulations using real-world data demonstrate that the proposed strategy extends the energy storage battery lifespan by 25.53% compared to conventional methods, while maintaining grid stability.
Introduction
The integration of renewable energy sources has heightened the demand for rapid frequency regulation in power systems. Energy storage battery, particularly lithium iron phosphate (LiFePO₄) systems, are widely adopted due to their high efficiency and scalability. However, frequent charge-discharge cycles and deep discharging accelerate battery degradation, necessitating strategies that balance performance with longevity.
Traditional methods, such as fixed or variable proportional coefficient (KK) strategies, often fail to adapt to real-time grid conditions or optimize SOC management. This paper addresses these limitations by introducing an adaptive factor (μμ) that harmonizes virtual inertial and droop control outputs while incorporating SOC feedback to mitigate overcharging/discharging.
Methodology
1. Frequency Modulation Control Model
The grid frequency deviation (ΔfΔf) is calculated as:Δf=ΔPb+ΔPe−ΔPagcHs+DΔf=Hs+DΔPb+ΔPe−ΔPagc
where:
- ΔPbΔPb: Power output variation of the energy storage battery
- ΔPeΔPe: Power output variation of thermal units (assumed constant)
- ΔPagcΔPagc: AGC dispatch instruction variation
- HsHs: System inertia constant
- DD: Damping coefficient
The total power output of the energy storage battery (ΔPbΔPb) comprises contributions from virtual inertial control (ΔPb,IΔPb,I) and virtual droop control (ΔPb,DΔPb,D):ΔPb=ΔPb,I+ΔPb,DΔPb=ΔPb,I+ΔPb,DΔPb,I=μ1⋅Mb⋅dΔfdt⋅Gbess(s)ΔPb,I=μ1⋅Mb⋅dtdΔf⋅Gbess(s)ΔPb,D=μ2⋅Kb⋅Δf⋅Gbess(s)ΔPb,D=μ2⋅Kb⋅Δf⋅Gbess(s)
where Gbess(s)=1Tb⋅s+1Gbess(s)=Tb⋅s+11 is the transfer function of the energy storage battery, and TbTb is its time constant.
2. Adaptive Factor (μμ) Design
The adaptive factor μμ is determined by input coefficients (αα) from a fuzzy controller and feedback coefficients (ββ) derived from SOC:μ1=α1⋅β1,μ2=α2⋅β2μ1=α1⋅β1,μ2=α2⋅β2
with α1+α2=1α1+α2=1.
2.1 Fuzzy Controller for Input Coefficients
The fuzzy controller maps frequency deviation (ΔfΔf) and its rate of change (dΔf/dtdΔf/dt) to α1α1 (virtual inertial control weight). Input and output membership functions are defined as:
| ΔfΔf Range | dΔf/dtdΔf/dt Range | α1α1 Range |
|---|---|---|
| [-0.5, 0.5] Hz | [-1, 1] Hz/s | [0, 1] |
Control rules prioritize virtual inertial control during high dΔf/dtdΔf/dt and virtual droop control during large ΔfΔf (Table 1).
Table 1: Fuzzy Control Rules
| dΔf/dtdΔf/dt | ΔfΔf | α1α1 |
|---|---|---|
| NB | NB | VB |
| NM | NM | B |
| … | … | … |
NB: Negative Big, NM: Negative Medium, VB: Very Big, B: Big
2.2 SOC Feedback for ββ Coefficients
SOC feedback prevents overcharging (SOC>0.8SOC>0.8) and overdischarging (SOC<0.23SOC<0.23). Logistic functions adjust charging (KcKc) and discharging (KdKd) coefficients:Kc=P0⋅Kmax⋅ev0(0.8−SSOC)(0.8−0.23)/2Kmax+P0⋅ev0(0.8−SSOC)(0.8−0.23)/2−1Kc=Kmax+P0⋅e(0.8−0.23)/2v0(0.8−SSOC)−1P0⋅Kmax⋅e(0.8−0.23)/2v0(0.8−SSOC)Kd=P0⋅Kmax⋅ev0(SSOC−0.23)(0.8−0.23)/2Kmax+P0⋅ev0(SSOC−0.23)(0.8−0.23)/2−1Kd=Kmax+P0⋅e(0.8−0.23)/2v0(SSOC−0.23)−1P0⋅Kmax⋅e(0.8−0.23)/2v0(SSOC−0.23)
where P0=0.01P0=0.01, v0=15v0=15, and Kmax=1Kmax=1.
The feedback coefficients β1β1 and β2β2 are:β1={λ⋅Kc,dΔfdt>0λ⋅Kd,dΔfdt<0,β2={Kc,Δf>0Kd,Δf<0β1={λ⋅Kc,λ⋅Kd,dtdΔf>0dtdΔf<0,β2={Kc,Kd,Δf>0Δf<0
where λ=1/3λ=1/3 balances control contributions.
Simulation and Results
1. Case Setup
A 330 MW thermal plant with a 10 MW/5 MWh energy storage battery was simulated using Matlab/Simulink. Three strategies were compared:
- Fixed KK: Constant droop control weight.
- Variable KK: KK adjusted based on SOC.
- Adaptive Strategy: Combines fuzzy control and SOC feedback.
2. Performance Metrics
- SOC Maintenance: Evaluated using:
QSOC=1n∑i=1n(Qi−0.55)2QSOC=n1i=1∑n(Qi−0.55)2
- Lifespan Prediction: Rain-flow counting method quantified cycle counts under varying discharge depths (DODDOD).
3. Key Findings
Table 2: SOC Maintenance Comparison
| Strategy | QSOCQSOC | SOC Range |
|---|---|---|
| Fixed KK | 0.142 | [0.199, 0.701] |
| Variable KK | 0.098 | [0.301, 0.752] |
| Adaptive Strategy | 0.086 | [0.402, 0.781] |
Table 3: Lifespan Improvement
| Strategy | Average Lifespan (Years) | Improvement vs. Fixed KK |
|---|---|---|
| Fixed KK | 8.93 | – |
| Variable KK | 10.08 | +12.88% |
| Adaptive Strategy | 12.34 | +38.19% |
The adaptive strategy reduced SOC fluctuations by 5.91–7.78% compared to variable KK, minimizing deep discharge cycles. Rain-flow counting confirmed 8,783 cycles under adaptive control versus 5,556 (variable KK) and 6,422 (fixed KK), with the latter invalid due to SOC violations.
Conclusion
- The adaptive strategy synergizes virtual inertial and droop control through real-time adjustments of αα and ββ, enhancing grid stability while prolonging energy storage battery life.
- SOC feedback mechanisms effectively limit charge/discharge depths, reducing degradation.
- Field data simulations validated a 25.53% lifespan extension over current methods, underscoring the strategy’s economic and operational benefits.
Future work will explore integration with machine learning for predictive SOC management and multi-objective optimization under diverse grid conditions.