Under the carbon peaking and carbon neutrality goals, the integration of renewable energy into power systems has significantly increased, necessitating coordinated capacity planning between thermal generation and multi-type energy storage systems. This paper proposes a novel method for evaluating and optimizing the capacity requirements of thermal power and energy storage systems (ESS) using spectrum splitting techniques. The approach leverages discrete Fourier transform (DFT) and spectral distribution coefficients to achieve efficient resource allocation, overcoming the limitations of traditional cutoff frequency methods.
1. Methodology
1.1 Spectral Analysis and Clustering
The net load time series \( L_t \) is decomposed using DFT:
$$ X(k) = \sum_{n=0}^{N-1} x(n)e^{-j\frac{2\pi}{N}nk} $$
where \( N = 8760 \) for annual hourly data. Spectral components are clustered into 27 groups based on frequency characteristics (Table 1), enabling efficient computation.
| Group | Frequency Range | Typical Period |
|---|---|---|
| 1 | DC component | – |
| 2-6 | Seasonal variations | Year to week |
| 7-14 | Diurnal cycles | 24h-6h |
| 15-27 | Intra-day fluctuations | <4h |
1.2 Spectral Distribution Coefficients
Continuous distribution coefficients \( c_g \), \( c_h \), and \( c_b \) allocate spectral components to thermal generation, pumped hydro storage, and battery storage:
$$ Z_g(n) = c_g(n)Z(n) $$
$$ Z_h(n) = c_h(n)Z(n) $$
$$ Z_b(n) = c_b(n)Z(n) $$
subject to:
$$ c_g(n) + c_h(n) + c_b(n) = 1 \quad \forall n $$
1.3 Optimization Model
The linear programming formulation minimizes total system costs:
$$ \text{min } C_{\text{total}} = C_{Eh} + C_{Eb} + C_g $$
where:
$$ C_{Eh} = \lambda_{Eh}ES_h + \lambda_{Ph}PS_h + C_{\text{OPh}} $$
$$ C_{Eb} = \lambda_{Eb}ES_b + \lambda_{Pb}PS_b + C_{\text{OPb}} $$
$$ C_g = \lambda_g \sum_{t=1}^T G_t + \lambda_a \sum_{t=1}^T (H_t^a + B_t^a) $$
2. Case Study: Northwest China Power Grid
2.1 System Configuration
| Parameter | Pumped Hydro | Battery |
|---|---|---|
| Cycle Efficiency | 75% | 90% |
| Lifetime (years) | 50 | 10 |
| Power Cost ($/kW) | 42 | 210 |
2.2 Key Results
The proposed method reduces ESS requirements compared to cutoff frequency approaches:
| Method | Thermal (GW) | Pumped Hydro (GW/GWh) | Battery (GW/GWh) |
|---|---|---|---|
| Cutoff Frequency | 111.98 | 73.95/1350.2 | 18.49/44.32 |
| Spectral Coefficients | 103.62 | 22.98/324.97 | 3.70/10.14 |
2.3 Renewable Penetration Analysis
Figure 1 shows the impact of renewable penetration ratio \( \omega \) on system configuration. Optimal ESS sizing occurs at \( \omega = 1.05 \), where:
$$ \frac{dES_h}{d\omega} = 0 \quad \text{and} \quad \frac{dES_b}{d\omega} = 0 $$
3. Conclusion
The spectral distribution coefficient method demonstrates superior performance in coordinating thermal generation and energy storage systems:
- Enables continuous spectral allocation, reducing ESS capacity by 58-76% compared to traditional methods
- Maintains thermal power ramping utilization at 40% vs. 6.2% with cutoff frequency approach
- Optimal renewable penetration occurs at \( \omega = 1.05 \) with 2:1 wind-PV ratio
This methodology provides a robust framework for planning hybrid energy storage systems in high-renewable power grids, effectively balancing operational flexibility and economic constraints.