A Coordinated Neuro-Fuzzy Control System for Hybrid Energy Storage Integration: Virtual Inertia and Frequency Support in Low-Inertia Power Systems

Abstract

Energy policies and economies of scale have promoted the expansion of renewable energy sources, leading to the displacement of conventional generation units and a consequent reduction in system inertia. Low inertia amplifies frequency deviations in response to generation–load imbalances, increasing the risk of load shedding and service interruptions. To address this issue, this paper proposes a coordinated control strategy based on neuro-fuzzy networks, applied to a hybrid energy storage system (HESS) composed of batteries and supercapacitors. The controller is designed to simultaneously emulate virtual inertia and implement virtual droop control, thereby improving frequency stability and reducing reliance on spinning reserve. Additionally, a state-of-charge (SOC) management layer is integrated to prevent battery operation in critical zones, mitigating degradation and extending battery lifespan. The neuro-fuzzy controller dynamically coordinates the power exchange both among the energy storage technologies (batteries and supercapacitors) and between the HESS and the conventional generation unit, enabling a smooth and efficient transition in response to power imbalances. The proposed strategy was validated through simulations in MATLAB R2022b using a two-area power system model with parameters sourced from the literature and validated references. System performance was evaluated using standard frequency response metrics, including performance indicators (ITSE, ISE, ITAE and IAE) and the frequency nadir, demonstrating the effectiveness of the approach in enhancing frequency regulation and ensuring the operational safety of the energy storage system.

1. Introduction

Energy policies aimed at decarbonizing electricity production to reduce greenhouse gas emissions have accelerated the integration of renewable energy sources into modern power systems. As a consequence, conventional synchronous generators, which inherently provide rotational inertia, are being replaced by non-conventional generation units equipped with power electronic inverters [1]. This transition significantly reduces the total system inertia, impairing the grid’s ability to resist sudden frequency deviations caused by generation–load imbalances. Low-inertia systems are characterized by higher rates of change of frequency (ROCOFs) and deeper frequency nadirs, which may exceed operational thresholds and lead to under-frequency load shedding or even cascading outages [2]. These challenges are particularly pronounced in weak or isolated grids with high levels of renewable penetration. Recent studies have highlighted the urgent need for fast frequency support services and inertia emulation mechanisms to ensure system stability under these conditions [3,4,5]. Recent developments in virtual inertia control and virtual droop control applied to energy storage systems have demonstrated strong potential to enhance frequency stability in modern power grids. These strategies rely on advanced control architectures and dynamic responses that consider operational constraints such as the state of charge, enabling faster and more reliable support during power imbalances [6,7,8].

While the need for fast frequency response and virtual inertia support has become increasingly evident in low-inertia systems, renewable energy sources such as wind and solar still face important limitations that hinder their direct contribution to frequency regulation. Their power output is inherently variable and non-dispatchable, and their connection through power electronic inverters decouples them from the mechanical inertia traditionally provided by synchronous machines. In many emerging economies, regulatory frameworks prioritize investment in renewable technologies but often exclude these units from participating in frequency control services. In contrast, international standards and guidelines such as IEEE 1547 [9], ENTSO-E operational requirements [10], and NERC standards [11] emphasize the importance of integrating fast frequency response and active power support capabilities, particularly in low-inertia systems. These frameworks highlight the growing role of energy storage systems in maintaining grid stability under high-renewable-penetration scenarios. As a result, the burden of maintaining frequency stability falls on conventional power plants, which are responsible for providing both primary and secondary frequency regulation via spinning reserves. This issue has been widely discussed in recent review studies, which emphasize the need for flexible grid support strategies involving energy storage systems to compensate for the lack of inertial response in systems predominantly supplied by renewable energy sources [12]. To address this challenge, recent research has investigated control strategies that enable renewable energy plants to contribute more actively to system stability. For example, deloading techniques in wind farms reserve a portion of the available mechanical power to provide active power support during frequency deviations [13,14]. Similarly, battery energy storage systems (BESSs) have been deployed in solar and wind power plants to emulate virtual inertia and contribute to frequency regulation. These systems can be integrated at various points in the plant, such as within the back-to-back converter of a wind turbine [15,16] or through dedicated inverters connected to the point of common coupling [17].

Several authors have proposed the use of BESSs for both inertial and primary frequency response. In [18,19], virtual inertia control strategies for BESSs were introduced, while [2,20] examined their role in primary frequency regulation. Hybrid energy storage systems (HESSs), which combine batteries and supercapacitors, have also been investigated for this purpose. Studies such as [15,21,22] suggest that supercapacitors are well-suited for fast inertial response, whereas batteries are more appropriate for sustained primary frequency support. The benefits of coordinated action between both technologies to improve the frequency nadir and the rate of change of frequency (ROCOF) are highlighted in [23].

Regarding control methods for primary frequency regulation, one of the most commonly used strategies is virtual droop control, as proposed in [24,25,26]. However, this type of controller does not take into account the state of charge (SOC) of the energy storage system (ESS). Operating at a low SOC poses a risk, as reaching the lower limit can trigger a sudden shutdown of the BESS, potentially returning the power system to a state of generation–load imbalance. To address this issue, strategies have been proposed in [20,23,27] that reduce the output power as the SOC decreases. Nevertheless, these strategies often overlook the actual power level being supplied when defining the power reduction functions. A two-stage fuzzy logic controller for determining the reference power of distributed BESS units during primary frequency regulation was proposed in [28]. Moreover, recent reviews have highlighted the increasing importance of control strategies that are aware of the state of charge and capable of adapting in real time, particularly in hybrid configurations where the power flow between storage layers must be dynamically optimized to prevent over-discharge and ensure long-term system resilience [29].

Based on the reviewed literature, it is evident that most publications focus on enhancing specific aspects of the dynamic frequency response, such as inertial support or primary regulation, rather than proposing comprehensive and integrated solutions. Furthermore, most approaches consider the energy storage system (ESS) as an independent generation unit within the power system, rather than as a subsystem integrated into the conventional generation plant. This gap has also been acknowledged in recent review articles, which emphasize the lack of fully integrated control architectures that combine virtual inertia, state-of-charge management, and coordination with synchronous generation units [29]. This perspective overlooks the potential of using a HESS not only to meet the operational requirements established by local regulations, but also to generate economic benefits for conventional power plants. Such integration could motivate investment in HESS technologies without the need for regulatory mandates.

This paper proposes a coordinated control strategy based on neuro-fuzzy networks applied to a hybrid energy storage system (HESS) composed of batteries and supercapacitors. The controller is designed to emulate virtual inertia and implement primary frequency regulation while actively managing the SOC to prevent battery degradation. The proposed coordinated approach independently adjusts the reference power outputs of the supercapacitors and batteries within the HESS, depending on the specific stage of frequency regulation (inertial or primary) and the real-time state of charge of each storage element. This ensures proper allocation of fast-response power from supercapacitors and sustained power support from batteries, while coordinating with the conventional generation unit (CGU) to maintain system stability and efficiency.

The main contributions of this paper are as follows:

-

The design of a neuro-fuzzy controller applied to the HESS for providing virtual inertia and virtual droop control, considering the state of charge of the supercapacitors.

-

A control strategy for power transition based on SOC, which coordinates energy exchange between the HESS and the conventional generation unit (CGU), ensuring reliable and efficient energy dispatch.

The rest of the paper is organized as follows: Section 2 presents the modeling of the two-area power system and the energy storage components. Section 3 introduces the control architecture and strategies employed in each stage of frequency regulation. Section 4 discusses the simulation results and performance evaluation. Finally, Section 5 summarizes the main conclusions of the study.

2. System Modeling

The two-area model has been widely used in numerous investigations to analyze the performance of control strategies in frequency regulation. This model consists of analyzing two generation units interconnected by a tie line, as shown in Figure 1. It considers the linear models of thermal power plants without overheating. Based on this, the dynamics of governors and turbines are represented in Equations (1) and (2), respectively. The swing equations of the frequency depend on the inertia of the system in each area, as defined in Equation (3), while the transfer power depends on the difference of the frequency between both areas, see Equation (4) [30].

$$G_{g,i}\left(s\right)={\displaystyle \frac{∆P_{v,i}\left(s\right)}{∆P_{Lref,i}\left(s\right)}}={\displaystyle \frac{1}{{\tau }_{g,i}s+1}}$$

(1)

$$G_{t,i}\left(s\right)={\displaystyle \frac{∆P_{m,i}\left(s\right)}{∆P_{v,i}\left(s\right)}}={\displaystyle \frac{1}{{\tau }_{t,i}s+1}}$$

(2)

$$2H_i∆\dot{{\omega }_i}=-D∆\omega +∆P_{m_i}+∆P_{RER}+∆P_H-∆P_{12}-∆P_{L,i}$$

(3)

$$∆\dot{P_{12}}=T({\omega }_1-{\omega }_2)$$

(4)

In the proposed model, the reference power for primary regulation is obtained through droop control, and the reference power for secondary regulation is defined with a PID controller, as indicated in Equations (5) and (6), respectively.

$$∆P_{L_{pr},i}=-{\displaystyle \frac{1}{R_i}}∆{\omega }_i$$

(5)

$$∆P_{L_{sr},i}=K_{P,i}AC{E}_i+K_{I,i}\int AC{E}_{i}dt+K_D{\displaystyle \frac{dAC{E}_1}{dt}}$$

(6)

The HESS block diagram is shown in Figure 2. These are two systems that can be controlled independently, but with the restriction that the sum of the power from batteries and supercapacitors must not exceed the maximum power of the inverter. The transfer function of the power generated by the battery system taking into account a reference power is defined in Equation (7). In this expression, it can be seen that it is a first-order transfer function, in which the settling time will depend only on the time constant ${\tau }_b$ [31].

$$G_B\left(s\right)={\displaystyle \frac{∆P_B\left(s\right)}{∆P_{B,ref}\left(s\right)}}={\displaystyle \frac{1}{{\tau }_{b}s+1}}$$

(7)

The state of charge of the battery (SOC) represents the level of stored energy expressed in per-unit values. An SOC of 50% is considered the ideal operating condition, since it allows the storage element to both absorb and deliver energy during a frequency regulation event. Accordingly, the deviation of the SOC ($∆SOC$) is measured with respect to this 50% condition, as defined in Equations (8) and (9) [23].

$$∆So{C}_B\left(s\right)=-{\displaystyle \frac{K_{E,B}}{s}}∆P_B{\displaystyle (}s{\displaystyle )}$$

(8)

$$K_{e,B}={\displaystyle \frac{1}{3600}}{\displaystyle \frac{S_B}{E_B}}$$

(9)

Similarly, the transfer function of the power generated by the supercapacitors and the state of charge are defined in Equations (10)–(12) [23,31].

$$G_{SC}\left(s\right)={\displaystyle \frac{\Delta P_{SC}\left(s\right)}{\Delta P_{SC,ref}\left(s\right)}}={\displaystyle \frac{1}{{\tau }_{sc}s+1}}$$

(10)

$$\Delta SO{C}_{SC}\left(s\right)=-{\displaystyle \frac{K_{e,SC}}{s}}\Delta P_{SC}\left(s\right)$$

(11)

$$K_{e,SC}={\displaystyle \frac{1}{3600}}{\displaystyle \frac{S_{SC}}{E_{SC}}}$$

(12)

Based on what was mentioned above, the equation of the states of the two-area system that includes a HESS in Area 1 is defined in Equation (13), where the state variables and inputs are presented in Equation (14) and the parameters of matrices A and B are shown with detail in Appendix A.

$$x=Ax+Bu+Ew$$

(13)

$$\begin{gathered} x={\left[\begin{array}{ccccccccccccc}\Delta {\omega }_1& \Delta {\omega }_2& \Delta P_{v,1}& \Delta P_{m,1}& \Delta P_{v,2}& \Delta P_{m,2}& \Delta P_{12}& \Delta P_{L_{sr},1}& \Delta P_{L_{sr},2}& \Delta P_B& \Delta P_{SC}& \Delta SO{C}_B& \Delta SO{C}_{SC}\end{array}\right]}^T \\ u={\left[\begin{array}{cccc}\Delta P_{L_{pr},1}& \Delta P_{L_{pr},2}& \Delta P_{B,ref}& \Delta P_{SC,ref}\end{array}\right]}^T \\ w={\left[\begin{array}{cccc}\Delta P_{L,1}& \Delta P_{L,2}& \Delta P_{RER,1}& \Delta P_{RER,2}\end{array}\right]}^T \end{gathered}$$

(14)

3. Control Strategies

In this section, the control strategies applied to BESSs and HESSs, which have been proposed in recent research to provide inertial response and frequency regulation, are detailed, and the proposed control strategy is introduced. In the first subsection, the control strategies applied to virtual inertial and primary regulation are presented. In the second section, control strategies for secondary regulation are detailed. Finally, in the third section the proposed strategy is introduced, which includes inertial response and primary and secondary regulation.

3.1. Inertial Response and Primary Regulation

3.1.1. Strategy 1: Inertial Response and Primary Regulation with BESS

The inertial response in batteries has been widely used in scientific publications, a control system that enables a BESS to deliver energy for inertial response and primary regulation was proposed in [32]. The power required to provide virtual inertia is defined in Equation (15), where the value of $K_{vi}$ is determined according to Equation (16). It can be noted in Equation (17) that $K_{vi}$ depends on the penetration rate of renewable energy; a higher rate implies a greater number of conventional plants displaced, and therefore, a higher value of $K_{vi}$ will be required in order to mitigate the effects of a low inertia value in the electrical power system.

It is worth mentioning that the virtual inertia only becomes effective until the frequency reaches the nadir, that is, until $t=t_{ndr}$, considering $t=0$ at the moment in which the load–generation power imbalance event is detected.

$$P_{B,vi}=\left\{\begin{array}{c}{K}_{vi}{\displaystyle \frac{d\Delta {\omega }_1}{dt}}, t\le t_{ndr}\\ 0 , t>t_{ndr}\end{array}\right.$$

(15)

$$K_{vi}={\displaystyle \frac{2S_{ESS}{H}_{ESS}}{f_o}}$$

(16)

$$H_{ref}={\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^m\left(S_{CG,i}{H}_i+S_{ESS,i}{H}_{ESS,i}\right)}{P_L}}$$

(17)

The power that the battery must deliver during primary regulation is defined in Equation (18) using the virtual droop method. In this way, the total power that the battery must deliver is defined in Equation (19).

$$P_{B,pr}=-{\displaystyle \frac{\Delta {\omega }_1}{R_1}}$$

(18)

$$P_{B,ref}=\left\{\begin{array}{c}-K_{vi}{\displaystyle \frac{d\Delta {\omega }_1}{dt}}-{\displaystyle \frac{\Delta {\omega }_1}{R_1}}, t\le t_{ndr}\\ -{\displaystyle \frac{K_{pr}}{R_1}}\Delta {\omega }_1 , t>t_{ndr}\end{array}\right.$$

(19)

3.1.2. Strategy 2: Inertial Response with Supercapacitors and Primary Regulation with Batteries (HESS)

This method was proposed in [15]. Although this method is used in the article for a wind turbine and not a conventional plant as in this case, it presents results that are comparable to those of the proposed method. This strategy consists of virtual inertial power being delivered by supercapacitors, given their high-power density and the requirement for a very fast response. On the other hand, due to the longer duration of primary regulation compared to inertial regulation, the use of batteries is proposed, given that these have a high energy density. Thus, the reference powers of the batteries and supercapacitors are defined in Equations (20) and (21), respectively.

$$P_{C,ref}=\left\{\begin{array}{c}{K}_{vi}{\displaystyle \frac{d\Delta {\omega }_1}{dt}}, t\le t_{ndr}\\ 0 , t>t_{ndr}\end{array}\right.$$

(20)

$$P_{B,ref}=-{\displaystyle \frac{\Delta {\omega }_1}{R_1}}$$

(21)

3.2. SOC Control

3.2.1. Strategy 1: Sigmoid Function

This method consists of defining the participation factor of the batteries as a function that depends only on their state of charge [33], one of the most commonly used functions is the sigmoid, see Equation (22).

$${\beta }_t=\left\{\begin{array}{c}{\displaystyle \frac{1}{1+e^{-\frac{\left(\Delta SO{C}_B+c\right)}{a}}}}, \Delta SO{C}_B<0\\ {\displaystyle \frac{1}{1+e^{\frac{\left(\Delta SO{C}_B-c\right)}{a}}}}, \Delta SO{C}_B\ge 0\end{array}\right.$$

(22)

3.2.2. Strategy 1: Fuzzy-Logic Controller

This method, proposed in [34,35], employs fuzzy logic to establish the battery reference power value ($P_{B,ref}$) as a function of the demand power input variables to the batteries ($P_{B,d}$) and the state of charge ($\Delta SO{C}_B$). The operation is that, if the state-of-charge level of the batteries is within the operating level, then the reference power will be equal to the demand power. On the other hand, if the state of charge is low or high then the reference power must be set to minimum values. Figure 3 shows the membership functions of the inputs and outputs of the controller, and the rule base for this controller is defined in

Table 1. The rule base of the fuzzy-logic controller of state of charge of the batteries.

		${\overline{\mathit{P}}}_{\mathit{d},\mathit{B}}$
		NB	NM2	NM1	NS	ZE	PS	PM1	PM2	PB
$\Delta SO{C}_B$	PB	NB	NM2	NM1	NS	ZE	ZE	ZE	ZE	ZE
	PM	NB	NM2	NM1	NS	ZE	PS	PM1	PM2	PB
	PS	NB	NM2	NM1	NS	ZE	PS	PM1	PM2	PB
	ZE	NB	NM2	NM1	NS	ZE	PS	PM1	PM2	PB
	NS	NB	NM2	NM1	NS	ZE	PS	PM1	PM2	PB
	NM	NB	NM2	NM1	NS	ZE	PS	PM1	PM2	PB
	NB	ZE	ZE	ZE	ZE	ZE	PS	PM1	PM2	PB

.

3.3. Proposed Strategy

Frequency regulation goes through different stages, and in each stage it is necessary to meet different requirements regarding values of the active power reference, frequency reference, and period of time over which the regulation will be carried out, among others. However, the problem is not only in the control of frequency and active power, but also in the transition from supercapacitors to batteries during their use in power supply. In the case of batteries, care must be taken that the supplied power begins to decrease as the state of charge (SOC) decreases and that the conventional plant takes over, ensuring that the transition does not generate alterations in the frequency response during regulation. Controlling the SOC value in batteries is significant, since if it reaches a very low level, it can cause a decrease in their lifetime.

For this reason, a coordinated control system based on neuro-fuzzy networks is proposed, the objective of which is to improve the performance of the frequency response based on an optimal transition between energy storage technologies and conventional power plants. As shown in Figure 4, the control system has as its input signals the frequency of Area 1 ($\Delta {\omega }_1$), the output powers ($P_B$ and $P_{SC}$), and states of charge ($\Delta SO{C}_B$ and $\Delta SO{C}_{SC}$) of the batteries and supercapacitors, respectively, and as its outputs it has the reference signals of the batteries and supercapacitors ($P_{B,ref}$ and $P_{SC,ref}$) and the power reference for primary regulation ($\Delta P_{L_{pr},1}$), which is the power that the conventional plant must assume when the state of charge of the batteries is located in the transition zone.

The internal structure of the neuro-fuzzy controller is illustrated in Figure 5; it follows the general framework introduced in [36], consisting of five processing layers: an input layer that receives the signals, a fuzzification layer where each input is mapped into membership degrees, a rule evaluation layer where fuzzy conditions are combined, a normalization layer that weights the activation strength of each rule, and finally an output layer where defuzzification using a weighted average yields a crisp output.

Unlike traditional Adaptive Neuro-Fuzzy Inference System (ANFIS) implementations, this study adopts a fixed-parameter neuro-fuzzy controller with zero-order Takagi–Sugeno consequents and no adaptive training. This choice prioritizes predictability during fast frequency events, simplifies verification and embedded implementation, and avoids sensitivity to measurement noise and dataset specific bias [37]. A fixed-parameter design is employed instead of adaptive training for the following reasons:

-

Inertial response and the initial stage of primary regulation unfold over short time windows (hundreds of milliseconds to a few seconds). Introducing online adaptation during these transients may yield time-varying closed loop dynamics and nonmonotonic actions, which can jeopardize frequency recovery [38]. A fixed parameter zero-order Takagi–Sugeno design guarantees deterministic behavior and repeatability [37].

-

Grid support controllers often face stringent requirements for verification, validation, and fail-safe operation according to IEEE 1547-2018 [9] and IEEE 1547.1-2020 [39]. In practice, product certification, such as UL-1741 Supplement SB [40], follows prescribed test procedures with specified parameter ranges and response times. Controllers with deterministic, bounded settings therefore align naturally with these test matrices and facilitate verification and repeatability, whereas online adaptation can complicate repeatable testing under fixed test conditions.

-

Online adaptation can be sensitive to measurement noise (frequency estimation, ROCOF, SOC observers). Prior reviews have noted that measurement noise and modeling uncertainties can undermine the robustness of online or adaptive SOC estimators, particularly for Kalman filter-based and observer-based approaches [41].

-

Recent reviews indicate that machine-learning models in power systems face risks of overfitting and limited generalization under nonstationary and heterogeneous data, which motivates scenario-based design with explicit rule structures rather than purely data-driven tuning [42].

In the proposed control strategy, the inputs are the required power (normalized by the inverter rating) and the state-of-charge deviation of the corresponding storage element. Gaussian membership functions are used in the central region and sigmoidal functions at the boundaries to ensure continuity and saturation. The rule bases define the participation factors of the supercapacitor and battery branches according to SOC and power demand, enabling a smooth transfer of the required power. Tuning scenarios span negative and positive frequency deviations and low, medium, and high required power levels, consistent with the cases reported in Section 4. The tuning criteria and the complete rule bases and membership function parameters are provided in the following subsections.

3.3.1. Supercapacitor Control System

The hybrid energy storage system is composed of supercapacitor groups and a battery bank. In this paper, it is proposed that during a generation–load power imbalance event, only one of the supercapacitor groups will supply active power, so that the other groups will remain in reserve for the following power imbalance events.

The selection of the supercapacitor group participating in frequency regulation is determined by its state-of-charge deviation ($\Delta SO{C}_{SC,k}$) and cumulative charge throughput ($Q_k$), as indicated in Equation (23). As described in [43,44], the selected group is the one whose operating conditions minimize the cost function ${\mathcal{L}}_{\left(k\right)}$, which is designed to ensure active and balanced management of the supercapacitor bank.

$${\mathcal{L}}_{\left(k\right)}={\mathrm{\gamma }\mathrm{\phi }}_{\left(k\right)}+\mathsf{\lambda }\left({\displaystyle \frac{Q_k-\overline{Q}}{\overline{Q}}}\right)$$

(23)

The function ${\mathrm{\phi }}_{\left(k\right)}$ depends on the type of frequency deviation. For a positive deviation, the selection favors groups with lower state-of-charge deviation values, while for a negative deviation, it favors groups with higher values, as defined in Equation (24). In addition, the accumulated charge of each group is compared with the average throughput across all groups ($\overline{Q}$). Consequently, groups with higher accumulated usage incur a greater cost and are less likely to be selected, whereas groups with lower accumulated usage are prioritized.

$${\mathrm{\phi }}_{\left(k\right)}=\left\{\begin{array}{c}\Delta SO{C}_{SC,k}, \Delta \omega >0\\ -\Delta SO{C}_{SC,k}, \Delta \omega <0\end{array}\right.$$

(24)

Group selection can be computed in advance while the HESS is in standby mode, anticipating a frequency regulation event. This allows the groups with the lowest cost to be pre-identified for both positive and negative frequency deviations, thereby alleviating computational overhead at the onset of a regulation event.

The parameters $\mathrm{\gamma }$ and $\mathsf{\lambda }$ are weighting factors assigned to each term of the cost function. Their values are manually adjusted according to the relative cumulative throughput of the groups. Thus, if certain supercapacitors exhibit faster degradation, the weight $\mathsf{\lambda }$ is increased relative to $\mathrm{\gamma }$, ensuring that aging effects are properly accounted for in the selection process.

The design of the supercapacitor controller consists in the supercapacitors being used for inertial response and primary regulation, in the latter, fully or partially, depending on their state of charge and the required power. Equations (25) and (26) define the power to provide virtual inertial and primary regulation, respectively; the value of the required power must be within the operating range of the inverter, as indicated in Equation (27). Therefore, the reference power of the supercapacitors ($P_{SC,ref}$) is introduced into Equation (28), where ${\alpha }_t$ is the participation factor of the supercapacitors, that is, the proportion of power provided by the supercapacitors during the inertial response and primary regulation, which has a value between 0 and 1.

$$P_{vi}=\left\{\begin{array}{c}{K}_{vi}{\displaystyle \frac{d\Delta {\omega }_1}{dt}}, t<t_{ndr}\\ 0 , t\ge t_{ndr}\end{array}\right.$$

(25)

$$P_{pr}=-{\displaystyle \frac{1}{R_1}}\Delta {\omega }_1$$

(26)

$$P_{SC,d}=\left\{\begin{array}{c}-P_{H,máx}, P_{vi}+P_{pr}<-P_{H,máx} \\ P_{vi}+P_{pr},-P_{H,máx}\le P_{vi}+P_{pr}\le P_{H,máx}\\ P_{H,máx}, P_{vi}+P_{pr}>P_{H,máx}\end{array}\right.$$

(27)

$$P_{SC,ref}={\alpha }_t{P}_{SC,d}$$

(28)

The participation factor is calculated by means of a neuro-fuzzy controller ($N{F}_{SC}$) which has as inputs the required power and the state of charge of the supercapacitors. The power that enters as input to the neuro-fuzzy controller is expressed based on the maximum power of the inverter ($P_{H,máx}$), as shown in Figure 6.

The tuning criterion is to ensure a smooth transition of the required power from the supercapacitors to the batteries. In this scheme, the supercapacitors supply energy during the inertial response and the initial part of primary regulation, after which the batteries take over, thereby avoiding a sudden increase in battery power.

The parameters of the membership functions (see Figure 7) and the rule base were defined through multiple simulations under different levels of generation and load power imbalance and the percentage of renewable energy penetration (PRER), for negative frequency deviations and with the initial deviation of the supercapacitor state of charge equal to zero. For high required power, the transition between storage technologies proceeds gradually as the deviation of the supercapacitor state of charge decreases. For medium required power, the transition begins at a deviation of the supercapacitor state of charge of approximately −0.25, which increases the participation of the supercapacitors in primary regulation. For low required power, the transition begins only at a deviation close to −0.375. Thus, the supercapacitors contribute more than the batteries during the time window in which only primary regulation occurs. Symmetrical thresholds are used when the frequency deviation is positive.

The rule base is defined in

Table 2. The rule base of the neuro-fuzzy controller $N{F}_{SC}$.

		${\overline{\mathit{P}}}_{\mathit{v}\mathit{i},\mathit{t}}$
		NB	NM2	NM1	NS	ZE	PS	PM1	PM2	PB
$\Delta SO{C}_{SC}$	PB	0	0	0	0	0	1.00	1.00	1.00	1.00
	PM2	0.25	0.33	0.50	1.00	1.00	1.00	1.00	1.00	1.00
	PM1	0.50	0.67	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	PS	0.75	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	ZE	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	NS	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.75
	NM1	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.67	0.50
	NM2	1.00	1.00	1.00	1.00	1.00	1.00	0.50	0.33	0.25
	NB	1.00	1.00	1.00	1.00	0	0	0	0	0

. This table shows that each input variable has nine linguistic values, being “NB”, large negative; “NM2”, medium negative 2; “NM1”, medium negative 1; “NS”, small negative; “ZE”, zero; “PS”, small positive; “PM1”, medium positive 1; “PM2”, medium positive 2; and “PB”, large positive.

3.3.2. Battery Control System

Unlike supercapacitors, batteries have a high energy density, which is why they are used for longer periods. In this work, it is proposed that the batteries complement the operation of the supercapacitors during the inertial response and primary regulation when the charge level of the supercapacitors is low, as indicated in Equation (29).

Unlike the other methods described in Section 3.2, the proposed controller explicitly considers the required power as an additional input, see Figure 8. In the alternative methods, the absence of this input leads to a reduction in battery participation when entering the transition zone, even if the required power demand is minimal. As a result, these approaches do not allow the minimum power to be continuously supplied until the state of charge (SOC) reaches a prudent level at which battery participation can be safely reduced. In contrast, the proposed method enables more effective utilization of the batteries, preventing the SOC from entering the prohibited zone and thereby preserving battery health.

$$P_{B,d}=\left(1-{\alpha }_t\right)P_{SC,d}$$

(29)

The required power that enters as input to the neuro-fuzzy controller is saturated according to inverter limits, as expressed in Equation (30). The reference power is defined in Equation (31), where ${\beta }_t$ is the participation factor of the batteries, that is, the proportion of power provided by the batteries during frequency regulation, which is a value between 0 and 1.

$$P_{B,d}=\left\{\begin{array}{c}-P_{H,máx}-P_{SC}, P_{SC}+P_{B,vi+rp}<-P_{H,máx} \\ P_{B,vi+rp}, -P_{H,máx}\le P_{SC}+P_{B,vi+rp}\le P_{H,máx}\\ P_{H,máx}-P_{SC}, P_{SC}+P_{B,vi+rp}>P_{H,máx}\end{array}\right.$$

(30)

$$P_{B,ref}={\beta }_t{P}_{B,d}$$

(31)

The participation factor ${\beta }_t$ is calculated by means of the neuro-fuzzy controller $N{F}_{B,s}$, which has as inputs the normalized required power (${\overline{P}}_{B,d}$) and the SOC deviation of the batteries ($\Delta SO{C}_B$).

The tuning criterion is used to achieve a smooth transition of the required power from the batteries to the conventional generating unit (CGU) when spinning reserve is available. It also aims to maximize battery capacity utilization when spinning reserve is not available by preventing the state of charge from falling below −0.4, since operating in this prohibited zone is detrimental to the battery [33,45].

The membership function parameters (see Figure 9) and the rule base were defined through multiple simulations under different levels of generation and load power imbalance and the percentage of renewable energy penetration (PRER) offsets, for cases with negative frequency deviation and zero initial deviation of the battery state of charge. For high required power, battery participation begins to decrease gradually once the deviation of the battery state of charge reaches approximately −0.25, thereby avoiding abrupt reductions in battery power that could cause unwanted transients in the frequency response. At medium required power, the transition is initiated at about −0.30, a value that approaches the prohibited zone. For low required power, the transition is triggered only near −0.35, and this threshold is chosen to avoid entering the prohibited zone. In this way, the remaining energy in the batteries is used to attenuate the frequency deviation. Symmetrical thresholds are used when the frequency deviation is positive.

The rule base is defined in

Table 3. The rule base of the neuro-fuzzy controller $N{F}_B$.

		${\overline{\mathit{P}}}_{\mathit{B},\mathit{d}}$
		NB	NM2	NM1	NS	ZE	PS	PM1	PM2	PB
$\Delta SO{C}_B$	PB	0	0	0	0	0	1.00	1.00	1.00	1.00
	PM3	0.25	0.33	0.50	1.00	1.00	1.00	1.00	1.00	1.00
	PM2	0.50	0.67	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	PM1	0.75	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	PS	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	ZE	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	NS	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
	NM1	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.75
	NM2	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.67	0.50
	NM3	1.00	1.00	1.00	1.00	1.00	1.00	0.50	0.33	0.25
	NB	1.00	1.00	1.00	1.00	0	0	0	0	0

. This table shows that the input variable ${\overline{P}}_{B,d}$ has nine linguistic values, being “NB”, large negative; “NM2”, medium negative 2; “NM1”, medium negative 1; “NS”, small negative; “ZE”, zero; “PS”, small positive; “PM1”, medium positive 1; “PM2”, medium positive 2; and “PB”, large positive. The other input variable $\Delta SO{C}_{SC}$ has eleven linguistic values, being: “NB”, large negative; “NM3”, medium negative 3; “NM2”, medium negative 2; “NM1”, medium negative 1; “NS”, small negative; “ZE”, zero; “PS”, small positive; “PM1”, medium positive 1; “PM2”, medium positive 2; “PM3”, medium positive 3; and “PB”, large positive.

3.3.3. Conventional Generation Unit

The signal that the controller sends to the conventional generation unit ($\Delta P_{L_{pr},1}$) is introduced in Equation (32). This quantity, here referred to as the compensated power, represented the reduction in the battery reference power when the state of charge enters the transition zone. To avoid creating a new generation–load power imbalance, this reduction must be assumed by the conventional plant.

$$\Delta P_{L_{pr},1}=\left(1-{\beta }_t\right)P_{B,ref}$$

(32)

3.4. Implementation Considerations for Real-World Deployment

The proposed controller acts as a supervisory layer that issues reference powers to the storage subsystems while respecting device limits and the timing of inner converter loops. Although the study is simulation-based, the structure and tuning were chosen to support practical deployment with predictable behavior, modest computational demand, and clear interfaces for sensing and actuation. The following items summarize practical considerations for implementing the proposed controller in real-world deployment and should guide its realization from simulation to field prototypes and commercial systems.

Sensing and estimation: Frequency, ROCOF, and SOC signals must be filtered to balance noise rejection and delay. Practical implementations should include input validation and simple plausibility checks to avoid nonmonotonic actions during fast transients [46,47].

Actuation bandwidth and device limits: Reference updates must respect inverter current and power limits, DC-bus constraints, and safe operating areas of batteries and supercapacitors. The controller enforces hard limits on total HESS power and applies rate limiting to prevent step-like commands that could excite inner current or voltage loops [48].

Real-time computation budget: The neuro-fuzzy supervisor uses a zero-order Takagi–Sugeno structure with fixed parameters. Per-cycle cost grows linearly with the number of rules; in the configuration used here (two inputs, Gaussian and sigmoidal membership functions, zero-order consequents), the supervisor performs on the order of 102 rule evaluations per cycle. At supervisory rates of 50–200 Hz, the computational load is modest for typical embedded targets such as digital signal processors (DSPs) or field-programmable gate arrays (FPGAs), with additional headroom on modern devices, while inner converter loops continue to operate at kHz rates. No online training is executed at run time, so the computational profile is fixed and deterministic [36,37].

Timing, delays, and communications: To reduce sensitivity to delay and jitter, the supervisory logic should execute locally at the HESS controller. If remote signals are required, include watchdogs, timestamps, and safe fallback modes, and limit the rate of change in setpoints to maintain stable closed-loop behavior [49].

SOC estimation and device protection: Participation factors are scheduled with SOC-dependent thresholds to ensure a smooth handover from supercapacitors to batteries and to avoid entry into prohibited SOC regions. Periodic recalibration of SOC estimators and logging of depth of discharge and temperature are recommended for condition-based maintenance [41].

Verification, validation, and compliance: Grid-support functions are verified against defined settings and response criteria as specified in IEEE 1547 [9] and IEEE 1547.1 [40]. Product certification commonly follows UL 1741 Supplement SB [40], which references test procedures aligned with IEEE 1547.1. A fixed-parameter design with bounded outputs simplifies controller-in-the-loop and hardware-in-the-loop testing and facilitates repeatable compliance assessment.

Integration with plant controls: Define interfaces for reference powers, status flags, fault handling, and curtailment requests from the plant controller. Ensure that supervisory decisions do not conflict with protections and that limits from the plant controller take precedence when required [9,39].

Decentralized deployment and scalability: Each HESS executes the fixed-parameter neuro-fuzzy supervisor locally using only local signals (frequency, required power, and SOC). There is no centralized optimization or online training. As a result, the approach scales by replication across sites and is largely independent of the total number of generators or the renewable penetration level in the wider system. Optional plant-level coordination exchanges setpoints and status flags but does not change the per-site computational cost.

A summary of thresholds, membership functions, and rule bases is provided in the preceding subsections. The scenario-based results in Section 4 illustrate the expected behavior under a range of operating conditions.

4. Results

This section presents the simulation results obtained using a hybrid energy storage system (HESS) for frequency regulation in a two-area power system. The first subsection presents the results for the inertial response and primary frequency regulation, while the second subsection shows the simulation results for battery state-of-charge control.

The data used in the simulations are provided in

Table 4. Parameters of the conventional generation units and the hybrid energy storage system. Per-unit values are defined on a power base of 20 MW and an energy base of 20 MWh.

Parameter	Value (p.u.)	Parameter	Value (p.u.)
${\tau }_{g,1}$	0.5	${\tau }_{g,2}$	0.3
${\tau }_{t,1}$	0.2	${\tau }_{t,2}$	0.6
$D_1$	0.6	$D_2$	0.9
$H_1$	5.0	$H_2$	4.0
$R_1$	0.05	$R_2$	0.0625
$B_1$	20.6	$B_2$	16.9
$k_{i,1}$	0.1	$k_{i,2}$	0.3
${\tau }_b$	0.5	${\tau }_{sc}$	0.05
$\Delta P_{m,nom}$	5.0	$P_s$	2.0
$P_{H,max}$	0.15	$E_H$	0.496
$E_B$	0.04	$E_{SC}$	12 × 0.0008

. The parameters related to conventional generation units correspond to typical values extracted from [30], the classical reference by Prabha Kundur, which has been widely employed in high-impact studies on frequency regulation. The supercapacitor and battery data were taken from [50,51], respectively, both published in high-impact journals. In this study, per-unit values are defined on a power base of 20 MW and an energy base of 20 MWh; the HESS is assumed to have an energy storage capacity of 0.04 p.u. for the battery and 0.0008 p.u. for each of the 12 supercapacitor groups, resulting in a combined energy storage capacity of 0.496 p.u., corresponding to realistic scales that have been deployed in functional projects using supercapacitors and batteries, such as Longyuan Power’s HESS project located in Zhaoyuan City, Shandong Province, China. Furthermore, the inverter rating was defined considering a 3% spinning reserve for primary frequency regulation, which is consistent with mandatory requirements in countries such as Peru [52], Colombia [53], and Spain [54].

4.1. Inertial Response and Primary Frequency Regulation

Nine scenarios are proposed to analyze the performance of the proposed control strategy in comparison with the other three strategies described in the previous chapter. These cases are detailed in

Table 5. Simulation scenarios for inertial response and primary regulation.

Scenario	$\mathbf{\Delta }{\mathit{P}}_{\mathit{L},1}$ (p.u.)	PRER (%)
1	0.5	10
2	0.5	20
3	0.5	40
4	1.0	10
5	1.0	20
6	1.0	40
7	1.5	10
8	1.5	20
9	1.5	40

, which shows that the variables that change are the load power variation ($\Delta P_{L,1}$) and the percentage of renewable energy penetration (PRER). In all scenarios, non-conventional generation is assumed to have replaced conventional generation in Area 1, resulting in a direct reduction in the inertia constant in that area. Additionally, non-conventional generation is not considered in Area 2. These simulation scenarios are used to evaluate both the inertial response and primary frequency regulation.

As shown in

Table 6. Summary of the simulation results of inertial response and primary regulation.

Scenario	Strategy	ITSE	ISE	ITAE	IAE	Nadir
1	Without ESS	0.00054	0.00006	0.35336	0.03206	−0.00374
	Only BESS	0.00053	0.00005	0.35419	0.03186	−0.00299
	SC-VI/BESS-PR	0.00053	0.00005	0.35422	0.03186	−0.00299
	Proposed method	0.00054	0.00005	0.35595	0.03157	−0.00219
2	Without ESS	0.00054	0.00006	0.35314	0.03209	−0.00396
	Only BESS	0.00053	0.00005	0.35403	0.03183	−0.00298
	SC-VI/BESS-PR	0.00053	0.00005	0.35408	0.03183	−0.00298
	Proposed method	0.00054	0.00005	0.35578	0.03155	−0.00219
3	Without ESS	0.00055	0.00006	0.35269	0.03217	−0.00456
	Only BESS	0.00053	0.00005	0.35371	0.03177	−0.00296
	SC-VI/BESS-PR	0.00053	0.00005	0.35381	0.03177	−0.00296
	Proposed method	0.00053	0.00005	0.35546	0.03153	−0.00219
4	Without ESS	0.00216	0.00023	0.70673	0.06412	−0.00748
	Only BESS	0.00214	0.00021	0.70842	0.06369	−0.00594
	SC-VI/BESS-PR	0.00214	0.00021	0.70849	0.06369	−0.00595
	Proposed method	0.00218	0.00021	0.71759	0.06347	−0.00439
5	Without ESS	0.00217	0.00023	0.70628	0.06419	−0.00792
	Only BESS	0.00213	0.00021	0.70809	0.06362	−0.00590
	SC-VI/BESS-PR	0.00213	0.00021	0.70822	0.06362	−0.00593
	Proposed method	0.00218	0.00021	0.71725	0.06343	−0.00438
6	Without ESS	0.00221	0.00024	0.70538	0.06433	−0.00913
	Only BESS	0.00212	0.00021	0.70748	0.06348	−0.00581
	SC-VI/BESS-PR	0.00213	0.00021	0.70771	0.06347	−0.00587
	Proposed method	0.00217	0.00021	0.71658	0.06337	−0.00437
7	Without ESS	0.00486	0.00051	1.06009	0.09618	−0.01122
	Only BESS	0.0049	0.00052	1.06381	0.09774	−0.00977
	SC-VI/BESS-PR	0.00492	0.00053	1.06416	0.09788	−0.00986
	Proposed method	0.0049	0.00047	1.07488	0.09542	−0.00658
8	Without ESS	0.00488	0.00052	1.05941	0.09628	−0.01187
	Only BESS	0.0049	0.00052	1.06309	0.09775	−0.00993
	SC-VI/BESS-PR	0.00493	0.00053	1.06383	0.09804	−0.01011
	Proposed method	0.00489	0.00047	1.07441	0.09537	−0.00657
9	Without ESS	0.00497	0.00055	1.05807	0.0965	−0.01369
	Only BESS	0.00491	0.00054	1.06168	0.09835	−0.01085
	SC-VI/BESS-PR	0.00497	0.00055	1.06333	0.09873	−0.01100
	Proposed method	0.00488	0.00047	1.07348	0.09526	−0.00656

, the performance indicators ITSE, ISE, ITAE, and IAE, together with the frequency nadir, are reported for all scenarios, and the proposed method achieves the best values, especially in the most challenging cases with higher generation and load imbalance and higher renewable penetration. These indicators, along with the frequency nadir and ROCOF, have been widely used in prior studies [55,56,57] to demonstrate the benefits of control strategies under diverse system conditions, and in our study, they evidence robustness by confirming superior performance across scenarios with varying power imbalance and PRER.

The time-domain results for Scenario 9 are shown in the following figures. In this scenario, $\Delta P_{L,1}=0.15 \mathrm{p}.\mathrm{u}.$ and $PRER=40\%.$ Figure 10 displays the time-domain frequency response of Area 1, where it can be seen and corroborated by the performance indicators in Table 6 that the proposed method significantly outperforms the others. It achieves a better nadir and rate of change of frequency (ROCOF), with a faster frequency recovery, as shown in Figure 11.

The time-domain frequency response without the energy storage system (ESS) exhibits the worst performance, clearly highlighting the need for virtual inertia provided by an ESS to counteract the reduced system inertia resulting from increased non-conventional generation. The time-domain frequency response of Area 2 using the proposed method exhibits fewer oscillations compared to the other strategies, as shown in Figure 12.

Figure 13 shows that the inverter power response under the proposed method reaches the lowest peak value compared to the other methods, indicating a greater capacity margin to support larger generation–load imbalances. Additionally, it is observed that the participation factor ${\alpha }_t$ decreases to approximately 0.265, see Figure 14, suggesting that 73.5% of the power initially supplied by the supercapacitors is instead delivered by the batteries at the end of the regulation period. This redistribution reduces the impact on the frequency time response in Area 1, ensures a smooth transition between supercapacitors and batteries, and prevents sudden increases in the high rates of change in battery power (see Figure 15).

The time-domain frequency response of Area 1 during primary and secondary regulation is shown in Figure 16. It is assumed that secondary frequency regulation lasts for 5 min, and that the conventional generation unit (CGU) has sufficient spinning reserve to restore the frequency. As observed in this figure, all control strategies exhibit similar performance during the secondary regulation period.

Additional results include the energy supplied by the ESSs and the CGU to the power system in order to mitigate the generation–load imbalance. These results are shown in

Table 7. Energy delivered by the ESS and CGU during inertial response and primary and secondary frequency regulation.

Scenario	Strategy	Only Primary Regulation						Primary and Secondary Regulation
		${\mathit{E}}_{\mathit{B}}$	${\mathit{E}}_{\mathit{S}\mathit{C}}$	${\mathit{E}}_{\mathit{H}}$	${\mathit{E}}_{\mathit{M}}$	${\mathit{P}}_{\mathit{H},\mathit{m}\mathit{a}\mathit{x}}$	${\mathit{P}}_{\mathit{M},\mathit{m}\mathit{a}\mathit{x}}$	${\mathit{E}}_{\mathit{B}}$	${\mathit{E}}_{\mathit{S}\mathit{C}}$	${\mathit{E}}_{\mathit{M}}$
1	Without ESS	0	0	0	0.000173	0	0.061509	0	0	0.003699
	Only BESS	0.000174	0	0.000174	0	0.052071	0	0.000856	0	0.002844
	SC-VI/BESS-PR	0.000173	0.000001	0.000174	0	0.051917	0	0.000856	0.000001	0.002844
	Proposed method	0	0.000175	0.000175	0	0.043893	0	0.000484	0.000371	0.002847
2	Without ESS	0	0	0	0.000173	0	0.063515	0	0	0.003699
	Only BESS	0.000174	0	0.000174	0	0.05184	0	0.000857	0	0.002844
	SC-VI/BESS-PR	0.000173	0.000001	0.000174	0	0.051524	0	0.000855	0.000001	0.002844
	Proposed method	0	0.000176	0.000176	0	0.043882	0	0.000484	0.000371	0.002847
3	Without ESS	0	0	0	0.000173	0	0.068575	0	0	0.003699
	Only BESS	0.000175	0	0.000175	0	0.051343	0	0.000858	0	0.002843
	SC-VI/BESS-PR	0.000173	0.000003	0.000175	0	0.050657	0	0.000855	0.000003	0.002843
	Proposed method	0	0.000177	0.000177	0	0.043976	0	0.000485	0.000371	0.002847
4	Without ESS	0	0	0	0.000346	0	0.123019	0	0	0.007400
	Only BESS	0.000348	0	0.000348	0	0.103678	0	0.001712	0	0.005689
	SC-VI/BESS-PR	0.000346	0.000002	0.000348	0	0.103521	0	0.001711	0.000002	0.005689
	Proposed method	0.000041	0.000309	0.00035	0	0.087752	0	0.001327	0.000383	0.005692
5	Without ESS	0	0	0	0.000346	0	0.127031	0	0	0.007399
	Only BESS	0.000349	0	0.000349	0	0.103039	0	0.001713	0	0.005689
	SC-VI/BESS-PR	0.000346	0.000003	0.000349	0	0.102715	0	0.001710	0.000003	0.005689
	Proposed method	0.000041	0.000309	0.000351	0	0.087718	0	0.001328	0.000383	0.005692
6	Without ESS	0	0	0	0.000347	0	0.137151	0	0	0.007399
	Only BESS	0.000351	0	0.000351	0	0.101672	0	0.001715	0	0.005688
	SC-VI/BESS-PR	0.000345	0.000006	0.000351	0	0.100955	0	0.001709	0.000006	0.005688
	Proposed method	0.000042	0.000310	0.000353	0	0.087883	0	0.001329	0.000384	0.005691
7	Without ESS	0	0	0	0.000519	0	0.184528	0	0	0.011100
	Only BESS	0.000511	0	0.000511	0	0.139059	0	0.002558	0	0.008534
	SC-VI/BESS-PR	0.000508	0.000003	0.000511	0	0.13895	0	0.002554	0.000003	0.008534
	Proposed method	0.000188	0.000335	0.000523	0	0.131609	0	0.002082	0.000387	0.008720
8	Without ESS	0	0	0	0.000519	0	0.190546	0	0	0.011099
	Only BESS	0.000513	0	0.000513	0	0.138983	0	0.002558	0	0.008534
	SC-VI/BESS-PR	0.000506	0.000005	0.000511	0	0.138724	0	0.002552	0.000005	0.008534
	Proposed method	0.000189	0.000336	0.000525	0	0.131554	0	0.002083	0.000387	0.008719
9	Without ESS	0	0	0	0.000520	0	0.205726	0	0	0.011099
	Only BESS	0.000512	0	0.000512	0	0.138829	0	0.002558	0	0.008532
	SC-VI/BESS-PR	0.000499	0.000012	0.00051	0	0.138038	0	0.002544	0.000012	0.008532
	Proposed method	0.000191	0.000336	0.000527	0	0.131798	0	0.002085	0.000387	0.008718

. As observed, the energy provided by the CGU without ESS is approximately the same as that of the other alternatives; however, the impact of the disturbance is greater in the frequency time response of Area 1.

As shown in Table 7, under the proposed method, the energy delivered by the supercapacitor is greater than that delivered by the battery in all scenarios during primary frequency regulation. Even in scenarios with low generation–load power imbalance, the supercapacitor supplies all the energy. However, when both primary and secondary regulation are considered, the energy delivered by the battery exceeds that delivered by the supercapacitor. The battery-to-supercapacitor energy ratio is approximately 1.3:1 in low-imbalance scenarios and increases to 5.38:1 in high-imbalance scenarios.

This implies that, under average conditions, the supercapacitor could replace a significant portion of the battery’s energy storage capacity and contribute to improved system performance. Moreover, since supercapacitors are less expensive than batteries and offer a significantly higher number of life cycles [58], the installation cost of the ESS can be reduced, and a HESS may achieve a longer lifetime compared to a BESS.

The “SC-VI/BESS-PR” method also employs a HESS; however, unlike the proposed method, it uses the supercapacitor exclusively for inertial response and the battery for primary regulation. As shown in Table 7, this strategy does not contribute to reducing the battery’s energy storage requirements. In all scenarios, the amount of energy delivered by the battery is nearly the same when comparing the “Only BESS” and “SC-VI/BESS-PR” strategies.

Furthermore, when comparing the “Only BESS” and “SC-VI/BESS-PR” strategies, the energy delivered by the supercapacitor is not significant relative to the energy delivered by the batteries. Considering the similarities in the time-domain frequency response and performance indicators in Area 1, the contribution of the supercapacitor in providing virtual inertia is mainly noticeable in the ROCOF improvement, as shown in Figure 11.

To evaluate the impact of the proposed method on battery lifespan, degradation metrics were computed from the onset of the generation–load imbalance until full frequency restoration (see

Table 8. Degradation metrics during inertial response and primary and secondary frequency regulation.

Scenario	Strategy	${\mathit{C}}_{\mathit{a}\mathit{v}\mathit{g}}$	${\mathit{C}}_{\mathit{r}\mathit{m}\mathit{s}}$	${\mathit{C}}_{\mathit{p}\mathit{e}\mathit{a}\mathit{k}}$	$\mathit{D}\mathit{o}\mathit{D}$	$\mathit{E}\mathit{F}\mathit{C}$	${\frac{\mathit{d}\mathbf{\Delta }{\mathit{P}}_{\mathit{B}}}{\mathit{d}\mathit{t}}}_{\mathit{p}\mathit{e}\mathit{a}\mathit{k}}$	${\mathit{D}}_{\mathit{M}}$ ($\mathbf{\times }{10}^{-3}\mathbf{\%}$)
1	Only BESS	0.191484	0.259649	1.041423	0.017127	0.008564	0.057213	0.046195
	SC-VI/BESS-PR	0.191329	0.259329	1.038347	0.017113	0.008557	0.053859	0.046142
	Proposed method	0.108202	0.138577	0.283576	0.009678	0.004839	0.001291	0.020387
2	Only BESS	0.19158	0.259738	1.036807	0.017136	0.008568	0.06238	0.046229
	SC-VI/BESS-PR	0.191272	0.259093	1.030478	0.017108	0.008554	0.053817	0.046122
	Proposed method	0.108272	0.138653	0.283712	0.009684	0.004842	0.001292	0.020406
3	Only BESS	0.191769	0.259948	1.026863	0.017153	0.008576	0.087328	0.046294
	SC-VI/BESS-PR	0.191158	0.258631	1.013137	0.017098	0.008549	0.053703	0.046083
	Proposed method	0.108414	0.138805	0.28398	0.009697	0.004849	0.001292	0.020445
4	Only BESS	0.382859	0.519121	2.073568	0.034245	0.017122	0.110901	0.12468
	SC-VI/BESS-PR	0.382521	0.518463	2.070418	0.034214	0.017107	0.105567	0.124522
	Proposed method	0.296698	0.376365	0.790042	0.026538	0.013269	0.004989	0.086522
5	Only BESS	0.383076	0.519319	2.060772	0.034264	0.017132	0.119098	0.124781
	SC-VI/BESS-PR	0.382404	0.517985	2.054305	0.034204	0.017102	0.105306	0.124468
	Proposed method	0.296873	0.376546	0.790402	0.026554	0.013277	0.00499	0.086596
6	Only BESS	0.383502	0.519791	2.033438	0.034302	0.017151	0.160126	0.12498
	SC-VI/BESS-PR	0.382174	0.517052	2.019091	0.034183	0.017092	0.104729	0.124361
	Proposed method	0.297223	0.376906	0.79112	0.026585	0.013293	0.004984	0.086742
7	Only BESS	0.57188	0.772081	2.781172	0.051152	0.025576	0.16507	0.221575
	SC-VI/BESS-PR	0.571154	0.770576	2.778993	0.051087	0.025543	0.156337	0.221172
	Proposed method	0.465532	0.599735	1.338839	0.041639	0.02082	0.014209	0.164996
8	Only BESS	0.572081	0.772095	2.77966	0.05117	0.025585	0.176244	0.221686
	SC-VI/BESS-PR	0.570581	0.76893	2.774477	0.051035	0.025518	0.151769	0.220854
	Proposed method	0.465789	0.600016	1.33894	0.041662	0.020831	0.014254	0.165127
9	Only BESS	0.571862	0.770748	2.776583	0.05115	0.025575	0.233615	0.221565
	SC-VI/BESS-PR	0.568863	0.764276	2.76076	0.050882	0.025441	0.131557	0.219901
	Proposed method	0.466309	0.600586	1.339854	0.041709	0.020854	0.014341	0.165391

). These indicators cover both primary and secondary regulation stages and include the following: average C-rate ($C_{avg}$), RMS C-rate ($C_{rms}$), peak C-rate ($C_{peak}$), depth of discharge ($DoD$), equivalent full cycles ($EFC$), peak rate of change in battery power, and the Miner’s damage fraction ($D_M$). Such metrics are widely adopted in the scientific literature to assess battery degradation [59,60,61].

The results indicate that the proposed method achieves the most favorable values across all metrics, with a notable reduction in the Miner’s damage fraction, thereby mitigating battery degradation. This effect is further illustrated in Figure 14, which depict the rate of change in battery power in Scenario 9.

To analyze the controller’s sensitivity to variations in load power and PRER, normalized sensitivity calculations were performed for Scenario 5, as the selected load and PRER values lie in the middle of the studied ranges. The results are summarized in the following tables.

The load power results presented in

Table 9. Summary of the sensitivity values for load power changes.

Scenario	Strategy	${\mathcal{S}}_{\mathit{I}\mathit{T}\mathit{S}\mathit{E}}$	${\mathcal{S}}_{\mathit{I}\mathit{S}\mathit{E}}$	${\mathcal{S}}_{\mathit{I}\mathit{T}\mathit{A}\mathit{E}}$	${\mathcal{S}}_{\mathit{I}\mathit{A}\mathit{E}}$	${\mathcal{S}}_{\mathit{n}\mathit{a}\mathit{d}\mathit{i}\mathit{r}}$
2	Without ESS	1.5023	1.4783	1.0000	1.0002	1.0000
	Only BESS	1.5023	1.5238	1.0000	0.9994	0.9898
	SC-VI/BESS-PR	1.5023	1.5238	1.0001	0.9994	0.9949
	Proposed method	1.5046	1.5238	1.0079	1.0052	1.0000
8	Without ESS	2.4977	2.5217	1.0000	0.9998	0.9975
	Only BESS	2.6009	2.9524	1.0027	1.0729	1.3661
	SC-VI/BESS-PR	2.6291	3.0476	1.0042	1.0820	1.4098
	Proposed method	2.4862	2.4762	0.9959	1.0071	1.0000

show that when the load decreases, no significant differences are observed. However, when the load increases, the proposed method exhibits lower sensitivity than the other controllers in terms of the ITSE and ITAE performance indicators.

Regarding PRER sensitivity, the proposed method was found to be slightly less sensitive in the integral performance indicators, but it showed a notably lower sensitivity in the frequency nadir compared to the other strategies, see

Table 10. Summary of the sensitivity values for changes in PRER.

Scenario	Strategy	${\mathcal{S}}_{\mathit{I}\mathit{T}\mathit{S}\mathit{E}}$	${\mathcal{S}}_{\mathit{I}\mathit{S}\mathit{E}}$	${\mathcal{S}}_{\mathit{I}\mathit{T}\mathit{A}\mathit{E}}$	${\mathcal{S}}_{\mathit{I}\mathit{A}\mathit{E}}$	${\mathcal{S}}_{\mathit{n}\mathit{a}\mathit{d}\mathit{i}\mathit{r}}$
4	Without ESS	0.0092	0.0000	−0.0013	0.0022	0.1111
	Only BESS	−0.0094	0.0000	−0.0009	−0.0022	−0.0136
	SC-VI/BESS-PR	−0.0094	0.0000	−0.0008	−0.0022	−0.0067
	Proposed method	0.0000	0.0000	−0.0009	−0.0013	−0.0046
6	Without ESS	0.0369	0.0870	−0.0025	0.0044	0.3056
	Only BESS	−0.0094	0.0000	−0.0017	−0.0044	−0.0305
	SC-VI/BESS-PR	0.0000	0.0000	−0.0014	−0.0047	−0.0202
	Proposed method	−0.0092	0.0000	−0.0019	−0.0019	−0.0046

.

It should be noted that in the “Only BESS” strategy, supercapacitors are not included, and in the “SC-VI/BESS-PR” strategy, supercapacitors are employed only for the inertial response. Consequently, these strategies are not affected by changes in the capacities of the supercapacitors and batteries, and therefore a sensitivity analysis is not applicable for a direct comparison with the proposed method. Similarly, in the battery controller, variations in battery capacity would only affect runtime rather than sensitivity, and thus would not provide a meaningful comparison with other control strategies.

4.2. SOC Control

In this section, four scenarios are simulated to compare three battery state-of-charge (SOC) control strategies. These scenarios are detailed in

Table 11. Simulation scenarios for SOC control.

Scenario	$\mathbf{\Delta }{\mathit{P}}_{\mathit{L}1}$ (p.u.)	$\mathbf{\Delta }\mathit{S}\mathit{O}{\mathit{C}}_{\left(0\right)}$	Spinning Reserve for Primary Regulation
10	0.10	−0.275	Yes
11	0.10	−0.275	No
12	0.15	−0.325	Yes
13	0.15	−0.325	No

and show that the variables that differ are the load power variation $\left(\Delta P_{L,1}\right)$, the initial SOC condition ($\Delta SO{C}_{\left(0\right)}$), and whether spinning reserve is considered in addition to the HESS.

Scenarios 10 and 11 consider the same $\Delta P_{L,1}$ value of 0.10 and an initial $\Delta SO{C}_{\left(0\right)}$ of −0.275; however, only Scenario 10 includes additional spinning reserve for primary regulation. These two scenarios are designed to compare the control strategies when the power requirement is low and the SOC is at the beginning of the transition zone.

Similarly, Scenarios 12 and 13 have the same $\Delta P_{L,1}$ value of 0.15 and $\Delta SO{C}_{\left(0\right)}$ of −0.325, but only in Scenario 12 is additional spinning reserve considered for primary regulation. These scenarios are intended to compare the strategies under higher power demand, with the SOC positioned in the middle of the transition zone.

Table 12. A summary of the simulation results of SOC control.

Scenario	SOC Control Strategy	ITSE	ISE	ITAE	IAE	$\mathbf{\Delta }\mathit{S}\mathit{O}{\mathit{C}}_{\left(\mathit{e}\mathit{n}\mathit{d}\right)}$
10	Sigmoid Function	0.0022	0.0002	0.7167	0.0634	−0.27539
	Fuzzy Logic	0.0022	0.0002	0.7163	0.0633	−0.27538
	Neuro-Fuzzy	0.0022	0.0002	0.7166	0.0634	−0.27540
11	Sigmoid Function	0.0022	0.0002	0.7204	0.0636	−0.27540
	Fuzzy Logic	0.0022	0.0002	0.7184	0.0636	−0.27538
	Neuro-Fuzzy	0.0022	0.0002	0.7166	0.0634	−0.27540
12	Sigmoid Function	0.0049	0.0005	1.0752	0.0954	−0.3259
	Fuzzy Logic	0.0049	0.0005	1.0755	0.0954	−0.32555
	Neuro-Fuzzy	0.0049	0.0005	1.0745	0.0954	−0.32636
13	Sigmoid Function	0.0075	0.0006	1.3369	0.1125	−0.32625
	Fuzzy Logic	0.0096	0.0008	1.5138	0.1238	−0.3259
	Neuro-Fuzzy	0.0059	0.0005	1.1883	0.1027	−0.32658

shows the results of performance indicators (IAE, ISE, ITAE, and ITSE) and also presents the values at the end of the simulation of the state of charge of the batteries and the time at which the decrease in the delivered power starts to avoid operating in the forbidden zone and damaging the lifetime of the batteries.

The time-domain frequency response in Scenarios 10 and 11 is shown in Figure 17 and Figure 18, respectively. As observed in these figures and the corresponding performance indicators, the results are similar across the three strategies, and the battery’s SOC also reaches the same value in all methods.

The most notable difference among the control strategies is found in the power response of the CGU, see Figure 19, when additional spinning reserve is considered for primary regulation. In this case, the power required by the proposed method is significantly lower, practically zero, compared to the other methods.

On the other hand, in Scenarios 12 and 13, the power required from the batteries is greater than in the previous scenarios, and SOC of the batteries is located in the middle of the transition zone. The results of Scenario 12 show a more pronounced difference in the power delivered by the CGU when additional spinning reserve is available for primary regulation (see Figure 20), with the proposed method being the least demanding on the CGU while achieving comparable performance indicator values (see Table 12 and Figure 21).

In Scenario 13, when no additional reserve is considered, the time-domain frequency response of Area 1 shows a noticeably better performance under the proposed method (see Figure 22). This method achieves the best performance indicators, but also requires the highest amount of battery energy. Consequently, it results in the lowest SOC value, a behavior clearly depicted in Figure 23. However, in neither case does the SOC enter the prohibited zone.

Based on the information presented regarding conventional generation plants in some countries, it would not be necessary to maintain a spinning reserve in plants equipped with a HESS, since the stored energy effectively fulfills that role. Consequently, the 3% originally allocated as spinning reserve can instead be traded in the daily scheduling market. As a simple illustrative exercise, considering the parameters outlined in Section 4.1 and assuming an energy price of 130 USD/MWh, the sale of 3 MW continuously over one year would yield approximately 1.14 MUSD.

According to [62], the average investment costs are 132 USD/kWh for batteries and 2628 USD/kWh for supercapacitors.

Table 13. A summary of the storage technology costs for each strategy.

Strategy	${\mathit{E}}_{\mathit{B}}$ (MWh)	${\mathit{E}}_{\mathit{S}\mathit{C}}$ (MWh)	${\mathit{C}}_{\mathit{B}}$ (kUSD)	${\mathit{C}}_{\mathit{S}\mathit{C}}$ (kUSD)	${\mathit{C}}_{\mathit{H}}$ (kUSD)
Only BESS	0.992	0	130.944	0	130.944
SC-VI/BESS-PR	0.988	0.04	130.416	105.12	235.536
Proposed method	0.8	0.192	105.6	504.576	610.176

summarizes the storage technology costs (in kUSD) for each of the proposed alternatives, where it can be observed that the proposed HESS configuration exhibits the highest capital requirement among the hybrid options. It should also be noted that the cost of the conversion system is higher in HESS implementations, as they require an additional DC–DC converter for the supercapacitor branch.

Nevertheless, the performance results obtained in this study, including frequency regulation metrics and degradation indicators, demonstrate that despite the higher investment, the proposed method provides superior benefits in terms of frequency stability under high renewable penetration and in extending battery lifetime.

5. Conclusions

This work presented a coordinated control strategy based on neuro-fuzzy networks applied to a hybrid energy storage system composed of batteries and supercapacitors. The proposed controller was designed to emulate virtual inertia and provide primary frequency regulation, leveraging the high-power density and fast dynamic response of supercapacitors to support the initial phase of frequency regulation. By dynamically adjusting the participation factor, and thus the power references of the supercapacitors and batteries, according to the real-time state of charge of supercapacitors and the level of power demand, the control system enabled a smooth transition of regulatory responsibility from supercapacitors to batteries. This approach prevents the rapid onset of high discharge rates in the battery subsystem, enabling a more gradual and controlled activation of the batteries. Consequently, the system achieved a better primary frequency regulation performance, reflected in improved dynamic metrics such as the frequency nadir, ISE, and ITAE.

In addition, the proposed controller for state-of-charge management in the battery subsystem was tested under scenarios with different initial conditions and levels of spinning reserve. Notably, in the absence of spinning reserve, the controller showed significant improvements in performance. The performance indices IAE, ITAE, ISE, and ITSE all demonstrated that the proposed method outperformed conventional control approaches, achieving better primary regulation while preserving the integrity of the energy storage system.

Finally, the coordinated interaction with the conventional generation unit, when spinning reserve is considered, ensured reliable frequency support during transitions, avoiding disturbances when storage limits were reached. In conclusion, the proposed strategy effectively addresses frequency regulation challenges in low-inertia systems.

As future work, we intend to integrate the control strategy into a model of a real power grid and evaluate it under realistic conditions using historical renewable profiles, sensor noise, bounded communication delays, and diverse operating scenarios, with an emphasis on overall performance, scalability on larger multi-area systems, and the impact of smoother power transfers on battery lifespan in long-term simulations. In parallel, we plan to develop a HESS sizing methodology that accounts for grid conditions, PRER, inverter ratings, and SOC constraints, and we expect to design a supercapacitor-group selection and rotation policy to minimize differential aging and promote homogeneous wear. Finally, we aim to conduct controller-in-the-loop and hardware-in-the-loop validation to assess real-time execution, latency margins, and numerical stability, including runtime profiling of the fixed-parameter neuro-fuzzy supervisor on embedded DSP/FPGA targets to report per-cycle computational cost and achievable supervisory rates.