In my research, I focus on the modeling of an all‑vanadium redox flow battery (VRB) energy storage system considering energy limitations. This system is critical for maintaining grid stability, and the energy storage battery plays a key role in providing both active and reactive power support. I developed a comprehensive electromechanical transient model using the Power System Analysis Software Package (PSASP) and incorporated energy limit modules to ensure safe and efficient operation. The model accounts for the capacity of the converter, the state of charge (SOC) of the energy storage battery, and dynamic constraints on reactive power output. Through simulation studies, I validated the model’s engineering applicability under different control strategies and battery sizes.
The energy storage battery model I used is based on an improved loss equivalent circuit, as shown in the following equations. The battery stack voltage Ustack is a controlled voltage source representing the open‑circuit voltage, while Ub is the terminal voltage. The internal losses are divided into reaction loss RReac (60%) and resistance loss RRes (40%), with additional pump and parasitic losses represented by Rfix. The electrode capacitance is Celec, and UCelec is the voltage across it.
$$
\begin{aligned}
U_b &= \left( C_{\text{elec}} \frac{dU_{C\text{elec}}}{dt} + I \right) R_{\text{Res}} + U_{C\text{elec}} \\
U_{C\text{elec}} &= U_{\text{stack}} + I R_{\text{Reac}} \\
C_{\text{elec}} \frac{dU_{C\text{elec}}}{dt} &= I_b – I – \frac{U_b}{R_{\text{fix}}}
\end{aligned}
$$
The open‑circuit voltage of a single VRB cell is derived from the Nernst equation. At 298 K, the standard electrode potential E0 is 1.259 V.
$$
U_{\text{cell}} = E_0 – \frac{RT}{nF} \ln \frac{[\text{V}^{3+}][\text{V}^{4+}]}{[\text{V}^{2+}][\text{V}^{5+}][\text{H}^+]}
$$
For a stack consisting of Ncell cells in series, the stack open‑circuit voltage is:
$$
U_{\text{stack}} = N_{\text{cell}} U_{\text{cell}}
$$
The state of charge (SOC) of the energy storage battery is defined as the ratio of remaining capacity Estack to rated capacity Ec. In the VRB system, SOC can also be expressed in terms of vanadium ion concentrations.
$$
\text{SOC} = \frac{E_{\text{stack}}}{E_c}
$$
When the positive and negative electrolytes are in equilibrium, SOC is the same on both sides. At 298 K, the single‑cell voltage becomes a function of SOC:
$$
U_{\text{cell}} = E_0 – \frac{RT}{nF} \ln \left( \frac{1 – \text{SOC}}{\text{SOC} [\text{H}^+]} \right)^2
$$
During charging or discharging, the SOC update is:
$$
\text{SOC}_{t+1} = \text{SOC}_t + \Delta\text{SOC}, \quad \Delta\text{SOC} = \frac{P_s \Delta t}{E_c} = \frac{I U_{\text{stack}} \Delta t}{E_c}
$$
Table 1 summarizes the key parameters of the energy storage battery model used in my simulations.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Standard electrode potential | E0 | 1.259 | V |
| Gas constant | R | 8.314 | J/(mol·K) |
| Temperature | T | 298 | K |
| Faraday constant | F | 96485 | C/mol |
| Number of electrons transferred | n | 1 | – |
| Reaction loss resistance | RReac | 60% of total internal loss | Ω |
| Resistance loss resistance | RRes | 40% of total internal loss | Ω |
| Rated capacity | Ec | Configured per scenario | MWh |
The grid‑connected converter (PCS) employs a dual‑loop control strategy: an outer power loop (frequency/active power control and voltage/reactive power control) and an inner current loop. I designed the SOC limiting module to protect the energy storage battery from overcharging and overdischarging. The module monitors SOC in real time and forces the active power reference to zero when SOC exceeds [SOCmin, SOCmax]. The flow of the SOC limit is illustrated conceptually, though I implement it using PSASP’s UD (User‑Defined) components. The charging and discharging efficiencies are considered as:
$$
P_s = P \eta_{\text{charge}} \quad \text{(charging)}, \quad P = P_s \eta_{\text{discharge}} \quad \text{(discharging)}
$$
The reactive power limit is critical for the energy storage battery because the converter’s apparent power capacity S is finite. Typically, S is set 0%–10% higher than the maximum active power output Pmax. The constraints are:
$$
– P_{\text{max}} \le P \le P_{\text{max}}, \quad – Q_{\text{max}} \le Q \le Q_{\text{max}}, \quad Q_{\text{max}} = \sqrt{S^2 – P^2}
$$
I developed a reactive power limiting module that adjusts Qmax dynamically based on the actual active power output. This allows the energy storage battery to provide maximum reactive support when active power is low, and to be automatically curtailed when active power approaches the limit.
Figure 1 shows a conceptual diagram of the reactive power limiting logic. The module first takes the absolute value of the reactive power reference, applies a limiter based on S and P, and then restores the sign. The mathematical representation is:
$$
Q_{\text{limit}} = \text{sgn}(Q_{\text{ref}}) \cdot \min\left( |Q_{\text{ref}}|, \, S \sqrt{1 – \frac{P^2}{S^2}} \right)
$$
In the PSASP environment, I used the User‑Defined (UD) function to implement the entire energy storage battery controller. The model outputs nodal injection currents IR and II, which are derived from the active and reactive power references and the bus voltage U = UR + jUI. The conversion formulas are:
$$
I_R = \frac{U_R P + U_I Q}{U_R^2 + U_I^2}, \quad I_I = \frac{U_I P – U_R Q}{U_R^2 + U_I^2}
$$
Table 2 lists the signals used in the UD model and their physical meanings.
| Signal | Physical Quantity |
|---|---|
| TM1 | Active power output (inner loop) |
| TM2 | Reactive power output (inner loop) |
| TM3 | Reactive power reference (outer loop) |
| TM4 | State of charge (SOC) |
| TM5 | Active power reference (outer loop) |
| TM6 | SOC control signal |
I validated the model using the CEPRI‑7 standard grid (a 7‑bus system). The base capacity was 100 MVA. A single‑line‑to‑ground fault was applied at the line between buses B3 and B4 at t = 0.02 s, cleared at 0.15 s, and the line reclosed at 0.70 s. The energy storage battery was connected at bus B1. I compared two reactive power limiting strategies: one with a fixed maximum reactive power (Qmax = 0.69 pu when P = 1.5 pu and S = 1.65 pu) and my dynamic limiting method. Results showed that my dynamic method allowed the energy storage battery to deliver higher reactive power during the initial voltage dip because active power was not at its maximum, leading to better voltage support and reduced oscillation. Table 3 summarizes the simulation parameters for this comparison.
| Parameter | Fixed Limit | Dynamic Limit |
|---|---|---|
| Converter capacity S | 1.65 pu | 1.65 pu |
| Max active power Pmax | 1.5 pu | 1.5 pu |
| Reactive power limit | 0.69 pu (constant) | √(S²−P²) (variable) |
| Initial SOC | 0.5 | 0.5 |
| Dead band | 0.01 | 0.01 |
To test the scalability of my energy storage battery model, I performed simulations with different battery sizes: maximum active powers of 0.1 pu, 0.5 pu, and 1.5 pu, each with corresponding converter capacities of 0.11 pu, 0.55 pu, and 1.65 pu. The initial SOC was set to 0.5. The results indicated that larger energy storage battery installations provided greater damping to the system oscillations after the fault. The active power output ramped up quickly to compensate for the power deficit, and the SOC changed accordingly. In all cases, the energy storage battery operated within safe SOC limits due to the implemented SOC limiter. Table 4 presents the observed performance metrics.
| Max Active Power (pu) | Converter Capacity (pu) | Max Reactive Support (pu) | SOC Range During Fault | Oscillation Damping Improvement |
|---|---|---|---|---|
| 0.1 | 0.11 | 0.046 | 0.48–0.51 | Moderate |
| 0.5 | 0.55 | 0.229 | 0.46–0.54 | Significant |
| 1.5 | 1.65 | 0.687 | 0.38–0.62 | Very high |
A key advantage of my dynamic reactive power limiting approach is that it fully utilizes the converter capacity of the energy storage battery at all times. When the system requires reactive power, the energy storage battery can inject it as long as the active power is below the converter limit. In contrast, a fixed reactive limit can be overly conservative, reducing the support capability. The simulation results confirmed that my model provides a more flexible and effective voltage regulation while maintaining the safety limits of the energy storage battery.
Furthermore, I examined the SOC changing process during a fault scenario. For the largest energy storage battery (1.5 pu), the SOC dropped from 0.5 to about 0.38 during the discharging phase, and then recovered as the system stabilized. The SOC limiter prevented further discharge when SOC reached the lower threshold (set to 0.2 in this study). The charging efficiency and internal losses were properly accounted for, making the model suitable for long‑term dynamic studies.
In conclusion, I have developed a comprehensive model of an all‑vanadium redox flow battery energy storage system that incorporates both SOC and converter capacity limits. The energy storage battery model includes realistic internal losses and an accurate SOC calculation. The control strategy dynamically adjusts the reactive power limit based on the instantaneous active power output, ensuring that the converter is not overloaded while maximizing the voltage support capability. Simulations on the CEPRI‑7 test system demonstrate the effectiveness and scalability of the proposed approach. My work provides a reliable tool for analyzing the impact of energy storage battery on power system transient stability and can be used for planning and operation studies.