Accurate assessment of the State of Charge (SoC) is a cornerstone for advanced Battery Management Systems (BMS) and is integral to the energy and power management strategies of modern microgrids. In systems incorporating pulsed or highly variable loads, the load power changes intermittently, placing dynamic stress on the energy storage battery. To ensure sustainability and reliability, the microgrid’s control systems must manage charging during load intervals and discharge during pulse events, all of which fundamentally rely on precise, real-time knowledge of the battery’s SoC for optimal capacity sizing, remaining energy estimation, and power capability assessment.
Traditional SoC estimation methods, such as the Coulomb counting (Ampere-hour integration) and Open-Circuit Voltage (OCV) methods, often struggle with dynamic conditions. Coulomb counting, defined as:
$$SoC(t) = SoC(t_0) – \frac{1}{C_I} \int_{t_0}^{t} I(\tau) d\tau$$
where $C_I$ is the nominal capacity at a constant current $I$, accumulates errors over time and fails to account for the rate-capacity effect. This effect causes the available capacity $C_I$ to vary with the discharge current, leading to inaccuracies. For instance, a battery discharged at a high current to its cutoff voltage may still deliver energy if the current is reduced, a scenario where simple Coulomb counting would erroneously suggest a negative SoC.
To address these limitations, particularly for energy storage battery systems in dynamic applications, this article adopts a framework that distinguishes between different SoC definitions and proposes a calculation method based on energy integration. The SoC is categorized into Absolute SoC (SoCa), Static SoC (SoCs), and Dynamic SoC (SoCd). While SoCa relates to physical material states, SoCs and SoCd are defined from an energetic perspective, which is more practical for system control.
The Static SoC (SoCs) represents the total remaining energy relative to the maximum storable energy, calculated via integration of power:
$$SoC_s(t) = SoC_s(t_0) – \frac{1}{W_{\text{max}}} \int_{t_0}^{t} P(\tau) d\tau$$
Here, $W_{\text{max}}$ is the maximum energy the energy storage battery can absorb or deliver under ideal, low-rate conditions, and $P(\tau)$ is the instantaneous power (positive for discharge, negative for charge). This method inherently incorporates terminal voltage variations ($P = V \times I$), making it more accurate than Ampere-hour integration when voltage fluctuates significantly under pulsed loads.
The Dynamic SoC (SoCd) is a more operational metric. It indicates the battery’s capability to sustain the *current* power demand until depletion. It is defined relative to the energy that can be delivered *at the present instantaneous current* $i(t)$:
$$SoC_d(t) = SoC_s(t_0) – \frac{1}{W_{i(t)}} \int_{t_0}^{t} P(\tau) d\tau$$
where $W_{i(t)}$ is the total energy the battery can deliver when discharged at the constant current $i(t)$ from a fully charged state to its cutoff voltage. A more practical, derived relationship between SoCd and SoCs is:
$$SoC_d(t) = \frac{W_{i(t)} \cdot (1 – SoC_s(t))}{W_{i(t)}}$$
This formula allows for the direct calculation of the critical SoCd from the estimated SoCs and the pre-characterized energy-capacity $W_{i}$ for different currents. When SoCd reaches zero, it signals that the energy storage battery can no longer support the present load power, even though its SoCs may be greater than zero, indicating remaining energy at a lower power level.
The accurate implementation of this energy-integration-based model requires detailed characterization of the energy storage battery. Experimental tests were conducted on three types widely used in microgrids. A programmable battery test system was employed to perform charge-discharge cycles under various constant currents, recording voltage, current, and time data. The key parameters extracted are the total charge energy ($E_c$), total discharge energy ($E_d$), and the maximum charge/discharge energies ($E_{c\_max}$, $E_{d\_max}$) at a defined low reference current.
The following tables summarize the energy characteristics of the tested batteries under different currents. Table 1 and Table 2 detail the charge and discharge energies for a Lithium Iron Phosphate (LFP) energy storage battery and a Lead-Acid energy storage battery, respectively. Table 3 presents data for a Vanadium Redox Flow energy storage battery.
| Current (A) | Charge Energy, E_c (Wh) | Discharge Energy, E_d (Wh) |
|---|---|---|
| 7.5 | 92.02 | 88.43 |
| 12.5 | 92.03 | 88.91 |
| 25.0 | 92.23 | 87.57 |
| 50.0 | 92.79 | 85.82 |
| 75.0 | 92.99 | 84.68 |
| 100.0 | 93.35 | 83.53 |
| 125.0 | 93.56 | 82.28 |
| Current (A) | Charge Energy, E_c (Wh) | Discharge Energy, E_d (Wh) |
|---|---|---|
| 20 | 382.17 | 344.57 |
| 40 | 347.00 | 300.24 |
| 60 | 322.30 | 276.04 |
| 80 | 300.82 | 251.85 |
| 100 | 283.70 | 234.30 |
| Current (A) | Charge Energy, E_c (Wh) | Discharge Energy, E_d (Wh) |
|---|---|---|
| 30 | 4987.1 | 4745.8 |
| 50 | 3962.8 | 3728.4 |
| 70 | 3117.2 | 3032.1 |
| 80 | 2825.8 | 2703.6 |
The experimental data clearly shows the rate-capacity effect: for each energy storage battery, the deliverable energy $E_d$ decreases as the discharge current increases. These $E_d$ values correspond directly to the parameter $W_{i}$ used in the SoCd calculation. Initial SoC (SoC_s(t_0)) was determined either by charging the battery to its voltage/current cutoff point (SoC=1) or by mapping a measured open-circuit voltage to a pre-established EMF-SoC curve after a sufficient rest period.
Applying the energy integration formula, the evolution of SoCs during charge and discharge cycles at various currents was computed. The results demonstrate that SoCs declines more rapidly at higher discharge currents due to the lower total energy $W_i$ available at that rate, even though the integrated power is the same in the initial phase. The critical advantage of the proposed method is illuminated by calculating SoCd. Using the data for the Lead-Acid energy storage battery as an example, with $W_{max}$ = 346 Wh, $W_{20A}$ = 344.57 Wh, and $W_{100A}$ = 234.30 Wh, the relationship between SoCs and SoCd during a constant-current discharge is derived.
The analysis reveals a significant finding: at the end of a high-current discharge (e.g., 100A), the SoCd reaches zero, correctly indicating that the battery cannot maintain that specific high-power demand any longer. However, the corresponding SoCs at that moment is not zero but a positive value (e.g., ~0.32). This remaining SoCs represents the energy still stored in the energy storage battery, which could be accessed if the load power (current) is reduced. Conversely, at a lower discharge current (e.g., 20A), SoCd reaches zero much closer to the point where SoCs also approaches zero. This quantitative distinction is vital for proactive energy management. For instance, a BMS can use a low SoCd threshold to initiate load-shedding or source-switching actions before the energy storage battery is completely depleted, thereby preventing sudden system failure and allowing for a controlled transition to a lower power state or a charging cycle.
In conclusion, for microgrids with dynamic or pulsed loads where terminal voltage varies significantly, the traditional Ampere-hour integration method for SoC estimation is insufficient. The energy-integration-based framework, differentiating between Static SoC (SoCs) and Dynamic SoC (SoCd), provides a more accurate and operationally meaningful assessment. SoCs gives the total relative energy remaining, while SoCd explicitly quantifies the remaining capability to support the *instantaneous* load power. The method requires comprehensive characterization of the energy storage battery‘s energy-capacity versus current, as demonstrated for LFP, Lead-Acid, and Vanadium Flow batteries. Implementing this approach enables more sophisticated BMS algorithms, allowing for optimal power dispatch, prevention of over-discharge under high-rate conditions, and ultimately enhancing the reliability and longevity of the energy storage battery system within a microgrid.