As the penetration of renewable energy sources such as wind and photovoltaic power increases in modern power systems, the challenges of accommodating renewable generation while maintaining grid frequency and voltage stability become more pronounced. The battery energy storage system (BESS) offers fast and flexible four-quadrant regulation capabilities, which can not only enhance the absorption of renewable energy but also provide rapid frequency and voltage support during emergency conditions. However, standalone applications often fail to recover the investment costs of BESSs. Therefore, a comprehensive planning methodology that jointly considers multiple functions—renewable energy consumption, frequency regulation, and voltage support—is critically needed. This paper presents a novel optimization framework for the location and sizing of both centralized BESSs in transmission networks and distributed BESSs in distribution networks, aiming at maximizing the utilization efficiency of BESS while minimizing the total system cost.
1. Overall Framework
The proposed methodology is structured in three stages. First, a BESS planning model for renewable energy consumption is built, which determines the preliminary location and sizing of centralized and distributed BESSs. Second, a planning method specifically for frequency and voltage support is developed, optimizing the site, reactive power capacity, active power capacity, and energy capacity of BESSs based on transient voltage stability and frequency security constraints. Finally, the two models are integrated into a unified optimization that simultaneously addresses renewable energy consumption and frequency-voltage support. The hierarchical structure couples transmission and distribution networks through boundary node power exchanges, as shown in the following table.
| Symbol | Description |
|---|---|
| \(P_{\text{Trans}}^1,\dots,P_{\text{Trans}}^n\) | Active power exchange at boundary nodes from transmission side |
| \(Q_{\text{Trans}}^1,\dots,Q_{\text{Trans}}^n\) | Reactive power exchange at boundary nodes from transmission side |
| \(P_{\text{Dis}}^1,\dots,P_{\text{Dis}}^n\) | Active power exchange at boundary nodes from distribution side |
| \(Q_{\text{Dis}}^1,\dots,Q_{\text{Dis}}^n\) | Reactive power exchange at boundary nodes from distribution side |
| \(n\) | Number of distribution networks |
2. BESS Planning Model for Renewable Energy Consumption
The first stage establishes a hierarchical optimization model that minimizes the sum of investment costs of BESSs and operational costs of the system across transmission and distribution networks. The uncertainty of renewable generation and load is represented by typical daily scenarios. The transmission-level centralized BESS optimization and distribution-level distributed BESS optimization are both formulated as mixed-integer second-order cone programming (MISOCP) problems, solved by an improved analytical target cascading method that relaxes integer constraints. The objective function is:
$$
\min \; C_{\text{Inv}} + \sum_{s \in \Omega_S} D_s \left( \sum_{k} C_{k,s}^{\text{OM}} + C_s^{\text{G}} + C_s^{\text{Aban}} – C_s^{\text{Sell}} + C_s^{\text{Ess\_ope}} + C_s^{\text{Punish}} \right)
$$
where \(C_{\text{Inv}}\) is the annualized investment cost of BESSs, \(\Omega_S\) is the set of typical day scenarios, \(D_s\) is the number of days per year for scenario \(s\), and the operational costs include O&M, generation, renewable curtailment penalty, electricity sales to distribution networks, battery degradation, and power exchange deviation penalties.
3. BESS Planning Model for Frequency and Voltage Support
3.1 Siting Based on Transient Voltage Stability
The siting problem identifies the most critical buses for voltage support. Using time-domain simulation, the transient voltage recovery time (duration when voltage stays below 0.75 p.u. after fault clearance) is computed for each bus under multiple fault scenarios. The objective is to maximize the total recovery time weighted by electrical distance to select \(N_{\text{Ess}}\) optimal locations. The model is:
$$
\max \; \sum_{b=1}^{N_{\text{Fault}}} \left( \sum_{i=1}^{N_{\text{Node}}} t_{i,b}^{\text{Re}} x_i + \sum_{i,j=1}^{N_{\text{Node}}} t_{i,j,b}^{\text{Diff}} x_i x_j \right)
$$
$$
\sum_{i=1}^{N_{\text{Node}}} x_i = N_{\text{Ess}}, \quad x_i \in \{0,1\}
$$
where \(t_{i,b}^{\text{Re}}\) is the transient voltage recovery time at bus \(i\) under fault \(b\), \(t_{i,j,b}^{\text{Diff}}\) is the difference in recovery time between buses \(i\) and \(j\) (indicating similarity), and \(x_i\) is the binary decision variable for BESS installation. After clustering based on electrical distance, the optimal number of BESSs is set, and the selected buses for the test system (IEEE 39-bus) are BUS-22, BUS-29, and BUS-31.
3.2 Reactive Power Capacity Optimization using Voltage Trajectory Sensitivity
The reactive power capacity of each BESS is determined by minimizing the total installed reactive power subject to transient voltage constraints. The voltage trajectory sensitivity \(\frac{\partial u}{\partial Q}\) is computed from time-domain simulations and used to linearize the critical voltage and maximum voltage constraints:
$$
\sum_{m=1}^{N_{\text{Ess}}} \left( \frac{\partial u_{i,b}}{\partial Q_m} \bigg|_{t=t_{\text{Cut}}+t_{\text{Lim}}} \Delta Q_m \right) + u_{i,b}(t_{\text{Cut}}+t_{\text{Lim}}) \ge u_{\text{Lim}}
$$
$$
\sum_{m=1}^{N_{\text{Ess}}} \left( \frac{\partial u_{i,b}}{\partial Q_m} \bigg|_{t=t_{\text{Max}}} \Delta Q_m \right) + u_{i,b}(t_{\text{Max}}) \le u_{\text{Max}}
$$
An iterative procedure adjusts the reactive power capacity until all buses satisfy the constraints. For the test system, the final reactive capacities are: \(Q_1 = 52.66\) Mvar, \(Q_2 = 60.26\) Mvar, \(Q_3 = 10\) Mvar.
3.3 Active Power Capacity Optimization with Frequency Security
The active power capacity is optimized to satisfy frequency nadir constraints after a generator outage. The system frequency response model yields the maximum frequency deviation \(\Delta f_{\max}\) as a nonlinear function of the total BESS active power capacity \(P_{\text{Sum}}\). This function is linearized piecewise to enable efficient optimization. The optimization model is:
$$
\min \; \sum_{i=1}^{N_{\text{Ess}}} G^{\text{Inv}} \left( C_1^i + C_2^i E_i^{\text{Ess}} + C_3^i S_i^{\text{Ess}} \right)
$$
subject to power flow constraints, generation limits, renewable utilization constraints, and frequency security constraints:
$$
a_z P_{\text{Sum}} – b_z = 0 \quad \text{for linearized segment } z
$$
The resulting active power capacities for the three selected buses are: \(P_1 = 56.94\) MW, \(P_2 = 101.09\) MW, \(P_3 = 10.81\) MW.
3.4 Apparent Power and Energy Capacity
Given the active and reactive capacities, the apparent power capacity is determined by the four-quadrant operation:
$$
\left(P_i^{\text{Ess}}\right)^2 + \left(Q_i^{\text{Ess}}\right)^2 = \left(S_i^{\text{Ess}}\right)^2
$$
Assuming the BESS must provide primary frequency support for 1 minute, the energy capacities are:
$$E_1 = 0.949\ \text{MWh},\quad E_2 = 1.685\ \text{MWh},\quad E_3 = 0.180\ \text{MWh}$$
$$S_1 = 77.56\ \text{MVA},\quad S_2 = 117.69\ \text{MVA},\quad S_3 = 14.73\ \text{MVA}$$
4. Integrated Planning for Combined Functions
4.1 Methodology
The integrated model merges the consumption-oriented and support-oriented planning by:
- Adding revenue from frequency and voltage regulation to the objective function.
- Taking the union of candidate nodes from both previous stages as the set of possible installation sites.
- Introducing reserve constraints for frequency/voltage support: the BESS must always reserve a minimum amount of charging/discharging energy capacity and discharging power capacity.
- Constraining the installed capacities at each node to not exceed the capacities derived from the individual single-function optimizations.
- Including the frequency security constraint (piecewise linearized) in the final model.
The revised transmission-level BESS planning model remains an MISOCP problem and is solved together with the distribution-level model using the analytical target cascading method.
4.2 Key Constraints
The reserve constraints are:
$$
\sum_{k \in \Lambda_{\text{FreV}}} (S_{\max}^{\text{SOC}} – S_{s,k,t}^{\text{SOC}}) E_k \ge \sum_{k \in \Lambda_{\text{FreV}}} E_k^{\text{FreV}}
$$
$$
\sum_{k \in \Lambda_{\text{FreV}}} (S_{s,k,t}^{\text{SOC}} – S_{\min}^{\text{SOC}}) E_k \ge \sum_{k \in \Lambda_{\text{FreV}}} E_k^{\text{FreV}}
$$
$$
\sum_{k \in \Lambda_{\text{FreV}}} (P_k – P_{s,k,t}^{\text{dis}}) \ge \sum_{k \in \Lambda_{\text{FreV}}} P_k^{\text{FreV}}
$$
where \(\Lambda_{\text{FreV}}\) is the set of nodes selected for frequency/voltage support, \(E_k^{\text{FreV}}\) and \(P_k^{\text{FreV}}\) are the reserved energy and power capacities. Additionally, the maximum capacities at each node are bounded by the results from the single-function planning:
$$
0 \le E_k \le E_k^{\text{Con}}, \; 0 \le P_k \le P_k^{\text{Con}} \quad \forall k \in \Lambda_{\text{Con}}
$$
$$
0 \le E_k \le E_k^{\text{FreV}}, \; 0 \le P_k \le P_k^{\text{FreV}} \quad \forall k \in \Lambda_{\text{FreV}}
$$
where \(\Lambda_{\text{Con}}\) is the set of nodes selected for renewable energy consumption.
5. Case Study and Results
5.1 Test System and Scenarios
The test system consists of an IEEE 39-bus transmission network and two IEEE 33-bus distribution networks. Typical daily scenarios for different seasons are generated. The demand for frequency and voltage support is evaluated using six fault scenarios (three-phase short-circuit faults at selected transmission lines with 0.5 s duration).
5.2 Results of Single-Function Planning
The planning results for renewable energy consumption (from a previous work) and for frequency/voltage support are summarized below.
| Function | Selected Nodes | Total Power (MW) | Total Energy (MWh) |
|---|---|---|---|
| Renewable consumption | 25 (115.86 MW), 28 (0), 18 (0) | 115.86 | 554.09 |
| Frequency/voltage support | 22, 29, 31 | 209.55 | 2.81 |
| Combined (union of nodes) | 18, 25, 28, 22, 29, 31 | 325.41 | 556.90 |
| Function | Selected Nodes | Total Power (MW) | Total Energy (MWh) |
|---|---|---|---|
| Renewable consumption | 2, 3, 13, 15, 22, 25 | 8.68 | 43.49 |
| Frequency/voltage support | N/A (only transmission) | – | – |
5.3 Integrated Planning Results
With the integrated model, the algorithm converges after five iterations. The final planning results are shown in the tables below. Note that the integrated planning reduces the total BESS power and energy compared to simply adding the two single-function results, demonstrating the benefit of multi-function reuse.
| Function | Selected Nodes | Total Power (MW) | Total Energy (MWh) |
|---|---|---|---|
| Integrated | 25 (299.40 MW), 29 (5.04 MW), 31 (0.54 MW) | 304.98 | 531.69 |
| Function | Selected Nodes | Total Power (MW) | Total Energy (MWh) |
|---|---|---|---|
| Integrated | 2, 3, 13, 15, 22, 25 | 8.66 | 43.33 |
5.4 Economic and Technical Analysis
The total system cost for the integrated planning is 16.65 billion RMB (annualized). Compared to the sum of costs of separate single-function plannings (which would be higher due to duplicated investment), the integrated approach saves approximately 572.74 million RMB annually. The reserved discharge power and energy capacities throughout a typical summer day are shown in the table below, confirming that the BESS always meets the minimum reserve requirement of 209.55 MW and 2.81 MWh.
| Time (h) | Reserved Discharge Power (MW) | Reserved Charging Energy (MWh) | Reserved Discharging Energy (MWh) |
|---|---|---|---|
| 1–2 | 209.55 | >2.81 | >2.81 |
| 10–15 | >209.55 | min ≈ 2.81 | >2.81 |
| 5–9, 22 | >209.55 | >2.81 | min ≈ 2.81 |
When all installed BESSs (304.98 MW active power) are fully available for frequency support, the frequency nadir after the worst generator outage is significantly improved, as shown by the simulation results. Similarly, with full reactive power capability, the transient voltage recovery is enhanced, keeping all bus voltages within 0.96–1.08 p.u. after faults.
6. Conclusions
This paper has proposed a comprehensive optimization planning method for battery energy storage systems that simultaneously addresses renewable energy consumption, frequency support, and voltage support. The key findings are:
- By integrating multiple functions, the total installed BESS power and energy capacities are reduced compared to separate single-function planning, leading to a significant cost saving of approximately 572.74 million RMB per year for the test system.
- The integrated model ensures that the BESS satisfies both normal operation (renewable energy absorption) and emergency requirements (frequency and voltage support) at all times, with sufficient reserve margins.
- The reserve capacities are fully maintained during the daily operation; in most hours, the actual reserve exceeds the minimum requirement, providing additional safety margins.
- The proposed analytical target cascading algorithm efficiently solves the hierarchical MISOCP problem, converging within a few iterations.
Future work can extend this framework to consider site selection of hybrid energy storage systems, grid-forming BESS configurations, and combined optimization with renewable power plants.