In the context of smart grid development, the integration of battery energy storage systems (BESS) into distribution networks has become increasingly prevalent. As a researcher in power system modeling, I focus on how to accurately represent the dynamic behavior of distribution networks that incorporate such energy storage battery technologies. Traditional composite load models (CLM) often fall short in capturing the unique characteristics introduced by BESS, necessitating the development of a generalized composite load model. This article presents my approach to creating a load-oriented equivalent model for BESS and integrating it into a broader framework for distribution network load modeling. The goal is to enhance simulation accuracy for power system studies, ensuring reliability and efficiency in grid operations with high penetration of renewable energy sources and energy storage battery systems.
The proliferation of energy storage battery systems in distribution networks—ranging from peak shaving and frequency regulation to supporting distributed generation—has fundamentally altered load dynamics. These systems can act as either loads or sources depending on operational modes, such as charging or discharging. Consequently, when performing large-scale grid simulations, it is crucial to account for their impact on the aggregate load behavior at substation buses. My work addresses this by proposing a generalized composite load model that explicitly includes a simplified representation of BESS. This model aims to balance complexity and accuracy, making it suitable for parameter identification and practical implementation in simulation tools like MATLAB/Simulink.
To begin, I developed a detailed simulation model for BESS based on a generic equivalent circuit representation for energy storage battery units. This circuit captures both the electrochemical dynamics and the electrical characteristics, as shown in the following equations that describe the battery’s voltage-current relationship:
$$U_{\text{batt}} = U_{\text{oc}} – I_{\text{batt}} \left( R_{\text{ser}} + \frac{R_{\text{tra\_s}}}{1 + s C_{\text{tra\_s}} R_{\text{tra\_s}}} + \frac{R_{\text{tra\_l}}}{1 + s C_{\text{tra\_l}} R_{\text{tra\_l}}} \right)$$
Here, $U_{\text{batt}}$ is the terminal voltage, $U_{\text{oc}}$ is the open-circuit voltage, $I_{\text{batt}}$ is the current, and the resistors and capacitors model transient responses. For grid integration, I implemented a power control strategy with unity power factor, using a dual-loop control structure (outer power loop and inner current loop) to regulate active power injection or absorption. This setup allows the energy storage battery system to respond to grid disturbances, such as voltage sags, which is key to understanding its external dynamic behavior.
Through extensive simulations under various voltage dip scenarios (e.g., 0.1, 0.25, and 0.4 per unit drops), I observed that the BESS exhibits distinct transient responses: during voltage sags, the output power decreases less than proportionally to the voltage, indicating an increase in current, and the power transition follows a smooth, inertial-like process. These observations led me to formulate a simplified equivalent model for BESS, which I refer to as the URT model. This model consists of a voltage source $U_b$ in phase with the grid voltage, a series resistor $R$, and a first-order inertial element with time constant $T$ applied to the power output. The governing equations are:
$$I_g = \frac{U_b – U_g}{R}$$
$$P’ = U_g I_g^*$$
$$\frac{dP}{dt} = -\frac{P}{T} + \frac{P’}{T}$$
where $I_g$ is the grid current, $U_g$ is the grid voltage, $P’$ is an intermediate power variable, and $P$ is the actual output power. This URT model effectively captures the essential dynamics of the energy storage battery system while maintaining simplicity, with only three parameters ($U_b$, $R$, $T$) of which $R$ and $T$ are independent. The model’s validity was tested by fitting it to simulation data from different voltage dip levels, demonstrating good self-descriptive and generalization capabilities, as summarized in Table 1.
| Test Scenario | Voltage Dip (p.u.) | Average Fitting Error ($E_{\text{ave}}$) | Remarks |
|---|---|---|---|
| Self-description | 0.10 | 0.0023 | Model parameters identified from same dip level |
| Self-description | 0.40 | 0.0049 | Model parameters identified from same dip level |
| Interpolation | 0.15 | 0.0016 | Parameters from 0.20 dip applied to 0.15 dip data |
| Extrapolation | 0.25 | 0.0031 | Parameters from 0.20 dip applied to 0.25 dip data |
With the URT model established, I proceeded to construct the generalized composite load model for distribution networks that include BESS. This model combines the classical CLM—comprising a static ZIP load and an induction motor (IM) dynamic load—in parallel with the URT model representing the energy storage battery system. The overall structure is depicted conceptually, where the total load at a distribution bus is the sum of contributions from conventional loads and the BESS. The mathematical formulation integrates equations from both components. For the IM part, the dynamics are described by:
$$\begin{aligned}
\frac{de_x’}{dt} &= -\frac{1}{T_0} \left[ e_x’ + (X – X’) I_y \right] + \omega_s e_y’ \\
\frac{de_y’}{dt} &= -\frac{1}{T_0} \left[ e_y’ – (X – X’) I_x \right] – \omega_s e_x’ \\
\frac{ds}{dt} &= \frac{1}{2H} (T_m – T_e)
\end{aligned}$$
where $e_x’$ and $e_y’$ are transient emfs, $I_x$ and $I_y$ are currents, $s$ is slip, $H$ is inertia constant, $T_m$ and $T_e$ are mechanical and electromagnetic torques, and parameters like $X$, $X’$, and $T_0$ depend on motor impedances. The static load is represented by a ZIP model:
$$P_s = a_p U_g^2 + b_p U_g + c_p$$
$$Q_s = a_q U_g^2 + b_q U_g + c_q$$
with coefficients summing to unity. The BESS contribution is given by the URT equations above. The generalized model thus includes multiple parameters, which I categorized for identification purposes. Key independent parameters include those for the IM (e.g., $R_s$, $X_s$, $R_r$, $X_r$, $X_m$, $H$), the static load (e.g., $a_p$, $b_p$), the BESS URT model ($R$, $T$), and a scaling factor $k_{\text{BESS}}$ that denotes the ratio of BESS power to total load power:
$$k_{\text{BESS}} = \frac{P_{\text{BESS}}}{P_{\text{load}}} = \frac{P_{\text{BESS}}}{P_m + P_s}$$
In total, the model has 18 independent parameters when considering full ZIP representation, but this reduces to 12 if the static load is assumed to be constant impedance (i.e., $b_p = b_q = 0$, $a_p = a_q = 1$) and the motor torque is a quadratic function of speed. This simplification is often acceptable for practical load modeling and enhances parameter identifiability.
To validate the proposed generalized composite load model, I conducted simulation studies under three distinct scenarios that reflect varying levels of energy storage battery penetration in the distribution network: Scenario 1 with $k_{\text{BESS}} = 0.3$ (BESS power less than net supply), Scenario 2 with $k_{\text{BESS}} = 0.6$ (BESS power between net supply and total load), and Scenario 3 with $k_{\text{BESS}} = 1.2$ (BESS power exceeding total load, implying net injection into the grid). For each scenario, I generated data samples corresponding to voltage dips of 0.10, 0.15, and 0.20 p.u. at the grid connection point. Using these datasets, I evaluated the model’s self-descriptive ability by identifying parameters from one sample and fitting it to the same sample, as well as its generalization ability by applying parameters from one sample to fit data from different dip levels within the same scenario. The average fitting error $E_{\text{ave}}$ was computed as:
$$E_{\text{ave}} = \frac{1}{N} \sum_{k=1}^{N} \sqrt{(P_k – \hat{P}_k)^2 + (Q_k – \hat{Q}_k)^2}$$
where $N$ is the number of sampling points, $P_k$ and $Q_k$ are measured active and reactive powers, and $\hat{P}_k$ and $\hat{Q}_k$ are model responses. The results, summarized in Table 2, indicate that the model performs well across all scenarios, with errors generally below 0.01, confirming its effectiveness in capturing the combined dynamics of conventional loads and energy storage battery systems.
| Scenario | $k_{\text{BESS}}$ Value | Self-descriptive Error (Sample 2) | Interpolation Error (Sample 1) | Extrapolation Error (Sample 3) |
|---|---|---|---|---|
| Scenario 1 | 0.3 | 0.0023 | 0.0016 | 0.0031 |
| Scenario 2 | 0.6 | 0.0035 | 0.0028 | 0.0042 |
| Scenario 3 | 1.2 | 0.0049 | 0.0034 | 0.0065 |
A critical aspect of load modeling is parameter stability, which refers to the consistency of identified parameters across different disturbance conditions. To assess this, I performed parameter identification for all nine samples (three per scenario) and analyzed the variability of key parameters. The results, condensed in Table 3, show that parameters like $R_s$, $X_s$, and $R_r$ exhibit relatively low variance within each scenario, indicating good stability. However, parameters such as $X_m$ and $X_r$ show higher dispersion, which is expected due to their lower sensitivity in the model. Notably, the URT model parameters $R$ and $T$ also demonstrate reasonable consistency, though some variation occurs with changes in $k_{\text{BESS}}$. This analysis underscores that the model structure is robust, especially for parameters most influential on dynamic responses.
| Parameter | Scenario 1 Mean | Scenario 2 Mean | Scenario 3 Mean | Overall Mean | Overall Variance |
|---|---|---|---|---|---|
| $R_s$ (p.u.) | 0.3385 | 0.3137 | 0.4344 | 0.3622 | 0.0041 |
| $X_s$ (p.u.) | 0.1424 | 0.1586 | 0.4394 | 0.2468 | 0.0279 |
| $R_r$ (p.u.) | 0.1593 | 0.1623 | 0.1860 | 0.1692 | 0.0002 |
| $X_r$ (p.u.) | 0.1759 | 0.2323 | 0.3476 | 0.2519 | 0.0077 |
| $X_m$ (p.u.) | 11.9340 | 11.3170 | 15.5489 | 12.9333 | 5.2262 |
| $H$ (s) | 0.5502 | 0.5634 | 0.5364 | 0.5500 | 0.0002 |
| $k_{\text{BESS}}$ | 0.1725 | 0.4083 | 1.4380 | 0.6729 | 0.4085 |
| $R$ (p.u.) | 4.9140 | 5.4213 | 5.7605 | 5.3653 | 0.1768 |
| $T$ (s) | 0.2638 | 0.0401 | 0.1987 | 0.1675 | 0.0132 |
Further tests were conducted to evaluate the model’s applicability when the energy storage battery system operates in charging mode (absorbing power from the grid). Using a scenario with $k_{\text{BESS}} = 0.3$ and a voltage dip of 0.15 p.u., the model successfully fitted the measured data, with an average error comparable to discharging cases. This confirms that the generalized composite load model is versatile and can handle both charging and discharging states of the energy storage battery, which is essential for accurate representation in real-world operations where BESS frequently switches modes.
In conclusion, my research presents a generalized composite load model for distribution networks that incorporate battery energy storage systems. The core innovation lies in the development of a simple yet effective URT equivalent model for the energy storage battery component, which captures its dynamic external characteristics with minimal parameters. By integrating this with classical load models, the resulting framework provides a comprehensive tool for power system simulations, accommodating varying levels of energy storage battery penetration. The model demonstrates strong self-descriptive and generalization capabilities, along with satisfactory parameter stability under diverse operating conditions. Future work will focus on refining the URT model to enhance parameter consistency across widely varying $k_{\text{BESS}}$ values and conducting validation with field measurements from actual distribution networks with high shares of energy storage battery installations. This approach ultimately contributes to more reliable and efficient grid planning and operation in the era of renewable energy integration and smart grid advancements.
The implications of this modeling effort are significant for power system engineers and researchers. As energy storage battery technologies continue to evolve and deploy at scale, accurate load models become indispensable for stability studies, frequency regulation analysis, and integration of distributed energy resources. The proposed model offers a practical solution that balances accuracy and complexity, making it suitable for inclusion in standard simulation software. Moreover, the methodology can be extended to other types of energy storage systems, such as flow batteries or supercapacitors, by adapting the equivalent circuit parameters. Ultimately, this work supports the transition toward a more resilient and flexible power grid, where energy storage battery systems play a pivotal role in maintaining balance and enabling higher renewable energy penetration.