Symmetrical Cooperative Frequency Control Strategy for Composite Energy Storage System with Electrolytic Aluminum Load

Abstract

With the increasing integration of high-proportion renewable energy, power systems are exhibiting low-inertia and low-damping characteristics, posing severe challenges to frequency stability. This paper proposes a coordinated supplementary frequency regulation strategy utilizing electrolytic aluminum (EA) loads and a hybrid energy storage system (HESS). Firstly, a system frequency response model is established, incorporating EA, electrochemical energy storage, pumped hydro storage, and conventional generation units. Secondly, an improved variable filter time constant controller is designed, supplemented by fuzzy logic, to achieve adaptive power allocation under different disturbance magnitudes. Concurrently, regulation intervals are defined based on the area control error (ACE), enabling a tiered response from source-grid-load resources. Simulation results demonstrate that under a severe disturbance of 0.05 p.u., the proposed strategy reduces the maximum frequency deviation from 0.198 Hz to 0.054 Hz, achieving a 72.7% performance improvement, and shortens the system settling time by 59.5%. Furthermore, the state of charge (SOC) of the electrochemical storage is successfully maintained within the range of [0.482, 0.505], effectively balancing frequency regulation performance and device lifespan. The findings demonstrate the effectiveness of the proposed strategy in enhancing the frequency resilience of low-inertia power grids.

1. Introduction

In June 2023, the National Energy Administration issued the “Blue Book on the Development of New-Type Power Systems,” proposing the construction of a new-type power system with continuously increasing penetration of renewable energy to promote the green transition of the energy sector [1,2]. However, renewable energy sources such as wind and solar exhibit strong stochasticity and high volatility, introducing significant asymmetry into the power balance and impacting system frequency stability [3]. Maintaining the symmetry of power supply and demand, particularly frequency stability, is paramount for grid operation. Relying solely on conventional thermal power units is insufficient to symmetrically mitigate these frequency fluctuations in the new-type power system. Consequently, tapping into the frequency regulation potential from the source-load-storage sides, aiming for a symmetrical and robust response to grid disturbances, has become a research focus for scholars worldwide [4]. As a technologically mature and widely deployed energy storage system (ESS), pumped storage serves as a critical solution for grid frequency regulation and peak shaving [5]. Given the abundance of abandoned mines in northwestern and southwestern China, proposals have been made in recent years by researchers to repurpose the extensive underground spaces of these mines into pumped storage power stations [6]. Compared with conventional pumped storage power stations, which are constrained by geographical conditions, water resource distribution, and the risk of damaging the surrounding ecological environment, abandoned mine pumped storage (AMPS) power stations offer advantages such as lower construction costs, reduced environmental impact, and more efficient land use [7,8]. From the perspective of resilient mining area distribution networks, a frequency regulation strategy based on the coordinated control of abandoned mine pumped storage and supercapacitors has been proposed in one study [9], which can effectively maintain the frequency stability of mining area power grids. Based on distributed coal mine underground reservoir technology, a peak-shaving system for AMPS power stations was constructed [10]. In one study, a HESS integrating AMPS, batteries, and photovoltaics was developed, and an optimized scheduling strategy proposed based on this system significantly improved the photovoltaic accommodation rate [11]. Given that the response time, reserve capacity, and regulation rate of pumped storage struggle to meet the multi-timescale frequency regulation demands of new-type power systems, the introduction of new types of energy storage for grid frequency regulation is hence required.

Stability is the cornerstone of power system operation. With the increasing integration of renewable energy, frequency stability is becoming more closely coupled with voltage and transient stability [12,13]. The system’s inherent inertia H and damping factors D are critical parameters that govern the transient frequency response following a disturbance, ensuring that the system avoids desynchronization during the incipient phase of a power swing [14]. While conventional turbines provide vital primary frequency support through their governors [15], their relatively slow mechanical response limits their effectiveness in low-inertia scenarios. Consequently, coordinating fast-acting resources, such as electrolytic aluminum (EA) industrial loads and hybrid energy storage, has become essential for modern grid frequency resilience.

Electrochemical energy storage (EES) has become a crucial frequency regulation resource for renewable energy power plants owing to its advantages such as rapid response and long cycle life [16]. However, a single energy storage technology alone is often inadequate to meet the frequency regulation requirements of power grids with a high penetration of renewable energy. The abundant mining resources in the Yunnan region, coupled with the rapid deployment of EES projects, create favorable conditions for investigating HESS that integrate electrochemical and pumped storage technologies. Meanwhile, the National Energy Administration has explicitly emphasized the need to develop diversified new types of energy storage to enhance the balancing capability of the power system [17]. In the field of HESS, existing research has primarily focused on suppressing minor frequency fluctuations through improved filtering algorithms or optimized control strategies [18,19,20]. However, under large disturbance scenarios, the recovery speed and maximum frequency deviation suppression capability of these methods remain inadequate. The introduction of load-side resources, such as flexible industrial loads like electrolytic aluminum (EA), can effectively expand the scope of frequency regulation resources.

EAL, with its advantages of rapid response characteristics and large power capacity, represents an ideal high-quality frequency regulation resource for the Yunnan power grid [21]. Prior studies have integrated such loads into frequency regulation through methods such as VSC-HVDC grid integration [22], utilization of voltage characteristics [23], or model predictive control [24], achieving certain positive results. However, as a high-energy-consumption load, frequent and independent response of electrolytic aluminum to renewable energy fluctuations may adversely affect production stability and power quality. Therefore, achieving coordinated control between hybrid energy storage systems and EAL is crucial for enhancing system frequency resilience.

Extensive research has been conducted on the coordination of multi-source regulation resources. For instance, one study [25] investigates the synergistic operation of HESS and proposes a control framework to effectively enhance grid frequency stability. While [26] provides valuable insights into power allocation among storage units, our work differs significantly in terms of resource integration and control hierarchy. Specifically, this paper incorporates the high-capacity flexibility of EAL and AMPS, considering their unique physical constraints. Moreover, a symmetrical coordination framework based on ACE interval partitioning is developed, which allows for a more granular response compared to the strategy in [27].

Despite the advancements in HESS and EAL control, several gaps remain. Conventional filtering algorithms typically utilize fixed parameters, which lack flexibility in power allocation under varying disturbance intensities. Furthermore, the rapid modulation potential of EAL is often decoupled from the HESS control loop, leading to a lack of defined operational boundaries for multi-resource coordination. Additionally, the energy recovery process of storage units frequently overlooks the secondary impact on grid frequency stability. To bridge these gaps, this paper proposes an ACE-based adaptive strategy that emphasizes the symmetrical cooperation between load-side and storage-side resources.

The main contributions of this paper are summarized as follows:

Multi-Resource Symmetrical Coordination: A unified frequency regulation framework is established that integrates electrolytic aluminum industrial loads, AMPS and EES, achieving deep coordination among source-load-storage resources.

Adaptive Power Allocation via Variable Filter: An improved filter based on the ACE and its rate of change is designed. This allows for the dynamic adjustment of filter time constants according to disturbance characteristics, optimizing power split between high-frequency EES and low-frequency pumped storage.

Constrained SOC Recovery Strategy: A novel SOC recovery method is proposed. By incorporating frequency deadband constraints, the strategy ensures the energy balance of EES units without inducing secondary frequency deviations.

Tiered Frequency Response Scheme: An ACE-based operational zone partitioning strategy is developed, clearly defining the participation boundaries for EAL and HESS across sub-emergency and emergency scenarios to enhance system robustness.

The remainder of this paper is organized as follows: Section 2 details the mathematical models of the integrated frequency regulation system, including thermal power units, AMPS, EES, and EAL. Section 3 describes the proposed secondary frequency regulation strategy for electrochemical storage, focusing on the adaptive weighting factors and the SOC recovery mechanism. In Section 4, the synergistic control framework based on the variable filter time constant and ACE interval partitioning is presented. Section 5 provides the simulation results and performance analysis under various disturbance scenarios. Finally, Section 6 concludes the paper.

2. Frequency Regulation Control Model of HESS with Electrolytic Aluminum Loads

2.1. Thermal Power Unit Model

Upon receiving a frequency regulation signal, a thermal power unit sequentially delivers active power output through its governor and reheat turbine system. The corresponding frequency response model is given by

$$G_{\mathrm{en}}(s)={\displaystyle \frac{1+s{F}_{\mathrm{HP}}{T}_{\mathrm{RH}}}{(1+s{T}_{\mathrm{G}})(1+s{T}_{\mathrm{RH}})(1+s{T}_{\mathrm{CH}})}},$$

(1)

where T_G is the thermal unit governor time constant; F_HP, T_RH, T_CH, are the reheater gain, heater time constant and turbine time constant, respectively; s is the Laplace transform operator.

The transfer function of the generator and load is modeled as

$$G_{\mathrm{h}}(s)={\displaystyle \frac{1}{2sH+D}},$$

(2)

where H is the generator inertia time constant, and D is the load damping factor.

2.2. Composite Energy Storage Model

2.2.1. Abandoned Mine Pumped Storage Plant Model

Currently, abandoned mine pumped storage power stations can be classified into semi-underground and fully underground types, with capacities categorized as large-scale (10²–10³ MW) and small-to-medium-scale (10⁻²–10² MW). Considering the head conditions of mines in Yunnan and the low evaporation characteristics of underground reservoirs, this study adopts a small-to-medium-scale fully underground configuration. The upper and lower reservoirs are constructed in tunnel networks and goaf areas at depths of 200 m and 800 m underground, respectively [28]. As illustrated in Figure 1, both the upper and lower reservoirs of the power station are formed by tunnel networks, protected externally by concrete and rock mass. They are connected to the underground powerhouse through valves and water conveyance tunnels, with the generated power eventually integrated into the grid alongside other energy sources.

The turbine transfer function for the case can be expressed as

$$G_{\mathrm{t}}(s)={\displaystyle \frac{1-s{T}_{\mathrm{w}}}{1+0.5s{T}_{\mathrm{w}}}},$$

(3)

where T_W is the water flow inertia time constant.

The governor systems for hydraulic turbines are broadly categorized into electro-hydraulic and mechanical-hydraulic types. Given its closer alignment with the operational characteristics of modern hydroelectric generating units, the electro-hydraulic governor is selected for investigation in this study. Its transfer function is expressed as Equation (4):

$$G_{\mathrm{pps}}(s)={\displaystyle \frac{1}{1+s{T}_{\mathrm{H}}}}\cdot {\displaystyle \frac{s^2{K}_{\mathrm{d}}+s{K}_{\mathrm{p}}+K_{\mathrm{i}}}{s^2{K}_{\mathrm{d}}+s(1/R+K_{\mathrm{p}})+K_{\mathrm{i}}}},$$

(4)

where T_H is the governor time constant of the hydraulic turbine; K_p, K_i and K_d are the proportional, differential and integral coefficients of the governor, respectively; R is the turbine’s modulation coefficient.

The mathematical modeling of the AMPS in this section primarily focuses on its physical characteristics as a high-capacity stabilization resource. Unlike traditional PPS control logic, which often requires the units to respond indiscriminately to minor frequency fluctuations, the proposed modeling of G_pps(s) serves a distinct functional role as a medium-to-long term support link. This characterization provides a necessary foundation for the subsequent coordination framework, allowing the PPS to be decoupled from high-frequency noise and utilized specifically for large-scale power compensation. Such a design ensures that the dynamic potential of the mine-based storage is leveraged effectively while minimizing mechanical wear through selective activation.

2.2.2. Electrochemical Energy Storage Model

The transfer function model of electrochemical energy storage is shown in Figure 2. This model represents the electrochemical energy storage system as a first-order inertial element, which is commonly used to analyze its capability to participate in system frequency response. The mathematical representation is given by

$$G_{\mathrm{E}}(s)={\displaystyle \frac{1}{1+s{T}_{\mathrm{E}}}},$$

(5)

$$\Delta P_{\mathrm{KE}}={\mu }_1{K}_{\mathrm{E}}{G}_{\mathrm{E}}(s)\Delta f_{\mathrm{high}},$$

(6)

$$\Delta P_{\mathrm{ME}}={\mu }_2{M}_{\mathrm{E}}{G}_{\mathrm{E}}(s){\displaystyle \frac{\mathrm{d}\Delta f_{\mathrm{high}}}{\mathrm{d}t}},$$

(7)

$$\Delta P_{\mathrm{E}}=\Delta P_{\mathrm{KE}}+\Delta P_{\mathrm{ME}},$$

(8)

$$\mathrm{SOC}(t)={\mathrm{SOC}}_0-{\displaystyle \frac{{\displaystyle {\int }_0^t\Delta P_{\mathrm{E}}(t)\mathrm{d}t}}{E_{\mathrm{rated}}}},$$

(9)

where G_E(s) is the transfer function model of the EES; T_E is the battery delay response time constant; ΔP_E, ΔP_KE and ΔP_ME are the regulation output, virtual sag output and virtual inertia output of the electrochemical energy storage, respectively; μ₁, μ₂ are the weight factors of the virtual sag and virtual inertia control, respectively; K_E, M_E are the virtual sag coefficients and the virtual inertia coefficients of the electrochemical energy storage, respectively; Δf_h is the high-frequency after the frequency dividing process; SOC(t) and SOC₀ are the charge state quantity of the electrochemical energy storage, and initial time, respectively; E_rated is the total electric quantity of the electrochemical energy storage.

2.3. Aluminium Electrolysis Load Model

The control circuit of the electrolytic aluminium load is shown in Figure 3, and its circuit model adopts the control based on self-saturated reactor, which ensures the efficiency of the electrolytic aluminium production, and at the same time, it can improve the accuracy of the load regulation.

The model is mainly composed of electrolytic tank, control winding and Buck chopper circuit, the electrolytic tank consists of back EMF E_eq, equivalent resistance R_eq and equivalent inductance L_eq in series, U_d, I_d respectively, for the electrolytic tank voltage and current, U_c, I_c and R_c respectively, for the control winding voltage, current and resistance, E_b, I_b, L_b and C_b respectively, for the power supply voltage of the Buck circuit, current, inductance and capacitance, r_b for the internal resistance of the MOSFET tube. Then, the state space equation of the electrolytic aluminium load is:

$$\left\{\begin{array}{l}\dot{\mathit{x}}=\mathit{A}\mathit{x}+\mathit{B}\mathit{u}+\mathit{C}\\ \mathit{y}=\mathit{D}\mathit{x}\end{array}\right.,$$

(10)

where state variable x = [I_b, U_c, I_c, U_d, I_d], $\dot{\mathit{x}}$ is the derivative of the state variable; input u = [d], d is the duty cycle; y is the output.

The detailed definitions of the system matrices A, B, C, and D are provided below:

$$A=\left[\begin{array}{ccccc}-{\displaystyle \frac{r_{\mathrm{b}}}{L_{\mathrm{b}}}}& -{\displaystyle \frac{1}{L_{\mathrm{b}}}}& 0& 0& 0\\ {\displaystyle \frac{1}{C_{\mathrm{b}}}}& -{\displaystyle \frac{1}{C_{\mathrm{b}}{R}_{\mathrm{c}}}}& 0& 0& 0\\ {\displaystyle \frac{1}{R_{\mathrm{c}}{C}_{\mathrm{b}}}}& 0& -{\displaystyle \frac{1}{R_{\mathrm{c}}{C}_{\mathrm{b}}}}& 0& 0\\ 0& 0& -k_{\mathrm{sr}}& 0& 0\\ 0& 0& {\displaystyle \frac{-k_{\mathrm{sr}}}{L_{\mathrm{eq}}}}& 0& -{\displaystyle \frac{R_{\mathrm{eq}}}{L_{\mathrm{eq}}}}\end{array}\right],B=\left[\begin{array}{c}{\displaystyle \frac{E_{\mathrm{b}}}{L_{\mathrm{b}}}}\\ 0\\ 0\\ 0\\ 0\end{array}\right],C={\left[\begin{array}{c}0\\ 0\\ 0\\ 1\\ 1\end{array}\right]}^{\mathrm{T}},D=\left[\begin{array}{c}0\\ 0\\ 0\\ U_{\mathrm{do}}\\ {\displaystyle \frac{U_{\mathrm{do}}-E_{\mathrm{eq}}}{L_{\mathrm{eq}}}}\end{array}\right].$$

(11)

The EA load control flow is shown in Figure 4, to ensure the production benefits of the electrolytic aluminium plant, its participation in frequency regulation will be limited by the self-saturated reactor regulating depth and the actual production of the electrolytic aluminium load series of current regulation range is controlled in the range of −10%~10%. The power that can be supported by the electrolytic aluminium plant to the grid is

$$P_{\mathrm{d}}=U_{\mathrm{d}}{I}_{\mathrm{d}},$$

(12)

$$P_{\mathrm{AL}}=\left\{\begin{array}{l}{P}_{\mathrm{d}}-K_1{P}_{\mathrm{d}}, K_1\in (0.9,1)\\ P_{\mathrm{d}}+K_2{P}_{\mathrm{d}},K_2\in (0,0.1)\end{array}\right.,$$

(13)

where P_d is the active power consumed by the electrolysis tank; P_AL is the power of the electrolytic aluminium plant to support the power grid; K₁ and K₂, respectively, are the downward and upward adjustment coefficients of the EAL participating in frequency regulation.

While electrolytic aluminum loads offer rapid modulation potential, their participation is subject to strict thermo-chemical and production constraints. First, the modulation depth is typically limited to ±5%~±10% of the rated power to maintain the thermal equilibrium of the electrolytic cells and ensure magnetic field stability. Second, the modulation duration is restricted (usually within 15–30 min) to prevent adverse effects on the purity of the molten aluminum and the physical integrity of the cathodes. These constraints are essential to ensure that frequency regulation does not compromise the core industrial production process.

3. Proposed Secondary Frequency Regulation Control Strategy for Electrochemical Energy Storage

The control strategy for electrochemical energy storage participating in secondary frequency regulation, as proposed in this paper, is illustrated in Figure 5. This strategy initially detects whether the ACE exceeds the deadband. If not, the reserve capacity of thermal power units is utilized to optimize the SOC of the energy storage system, thereby preventing overcharging or over-discharging. When the ACE exceeds the deadband, it is decomposed into high-frequency and low-frequency components via a variable time constant filter. Based on the high-frequency component and its rate of change, the energy storage system adaptively adjusts the weighting coefficients of virtual droop and inertia control to rapidly suppress frequency fluctuations.

3.1. Frequency Regulation Control Method Based on Weighting Factors

During secondary frequency regulation, the coordinated action of the two control strategies must be ensured, and their weighting coefficients need to be determined in practical applications. To this end, a fuzzy logic control method is adopted in this paper to dynamically compute the weights of the two control modes. The weighting factors μ₁ and μ₂ are dynamically calculated based on the system frequency deviation and its rate of change, with real-time outputs provided by the fuzzy logic controller. The structure of this controller is illustrated in Figure 6.

After normalization of the input and output variables, the universe of discourse for both input variables |Δf_h| and |dΔf_h| is defined as [−1, 1], while the output variable λ is defined over [0, 1]. The fuzzy subsets for both input variables are {NB, NM, NS, Z, PS, PM, PB}, and for the output variable are {Z (Zero), S (Small), M (Medium), B (Large), VB (Very Large)}. Triangular membership functions are adopted for all input and output variables.

Table 1. Fuzzy control rules for high frequency signal and its rate of change.

d∆fh	∆fh
	NL	NM	NS	Z	PS	PM	PL
NL	VB	M	B	VB	Z	Z	Z
NM	B	B	B	B	M	S	S
NS	S	M	B	B	S	S	S
Z	Z	Z	Z	Z	Z	Z	Z
PS	S	S	S	B	B	M	S
PM	S	S	M	B	B	B	B
PL	Z	Z	Z	VB	B	M	VB

presents the fuzzy logic control rules.

In the architectural design of the fuzzy controller (Figure 7), the saturation blocks, Limiter 1 and Limiter 2, are implemented to ensure the reliability of the control input and to prevent the controller from entering an ill-defined state during extreme events. The parameter settings for these limiters are derived from the frequency security standards issued by the State Grid Corporation of China. According to the SGCC grid code, the permissible steady-state frequency deviation is typically constrained within ±0.2 Hz, and the rate of change in frequency (RoCoF) is generally maintained within ±1 Hz/s for safe operation. Consequently, the threshold for Limiter 1 is set to ±0.2 Hz and Limiter 2 to ±1 Hz/s. These constraints ensure that the fuzzy logic inference operates within a range that is technically consistent with realistic power system operational requirements.

The fuzzy logic controller is employed to handle the inherent non-linearity and uncertainty in grid frequency fluctuations. The motivation behind using |Δf_h| and |dΔf_h| as inputs is to balance the instantaneous deviation compensation (virtual droop) and the rate-of-change suppression. Unlike fixed weighting factors, the fuzzy inference system provides a smooth transition between these modes, effectively neutralizing measurement noise and ensuring a symmetrical response to both step and continuous disturbances.

After obtaining the weighting coefficient λ, it is fed into the adaptive controller together with the high-frequency signal and its rate of change. Following the adaptive selection process, the virtual droop weighting factor μ₁ is derived as shown in Equation (14), while the virtual inertia weighting factor μ₂ is determined according to

Table 2. Adaptive selection of weight factor.

d∆fh	∆fh
	≤0	>0
≤0	λ	−λ
>0	−λ	λ

.

$${\mu }_1=1-\left|\lambda \right|$$

(14)

To prevent overcharging or over-discharging, which can adversely affect the service life of the energy storage system, the SOC is considered during secondary frequency regulation. In this paper, the SOC is divided into six ranges: minimum (S_min), relatively low (S₀), moderately low (S_low), moderately high (S_high), relatively high (S₁), and maximum (S_max). Taking the virtual droop control coefficient K_E as an example, this coefficient comprises both a charging control coefficient K_c and a discharging control coefficient K_d. When the SOC is in the optimal range, i.e., S(t) ∈ (S_low, S_high), K_E is set to its maximum value. The charging and discharging coefficients for the virtual droop control are given by Equations (15) and (16), respectively:

$$K_c=\left\{\begin{array}{ll}{K}_{E,\max }& ,S\ge S_{\mathrm{low}}\\ {\displaystyle \frac{K_{E,\max }}{\alpha K_{E,\max }{e}^{1-\frac{\beta (S-S_{\min })}{S_{\mathrm{low}}-S_{\min }}}+1}}& ,S_{\min }<S<S_{\mathrm{low}}\\ 0& ,S\le S_{\min }\end{array}\right.,$$

(15)

$$K_d=\left\{\begin{array}{ll}{K}_{E,\max }& ,S\le S_{\mathrm{high}}\\ {\displaystyle \frac{K_{E,\max }}{\alpha K_{E,\max }{e}^{1-\frac{\beta (S_{\max }-S)}{S_{\max }-S_{\mathrm{high}}}}+1}}& ,S_{\mathrm{high}}<S<S_{\max }\\ 0& ,S\ge S_{\max }\end{array}\right.,$$

(16)

where K_E,max is the maximum value of the virtual inertia control coefficient, α and β are both adaptive factors. S_min, S_low, S_high, S_max represent the minimum, moderately low, moderately high, and maximum SOC thresholds of the EES, respectively.·

To make the output of virtual sag control and virtual inertia control in electrochemical energy storage appropriate, this paper makes the virtual inertia coefficient equal to the virtual sag coefficient, i.e., K_E = M_E.

3.2. Power Recovery Method Considering SOC and Frequency Deviation Constraints

During secondary frequency regulation, when the ACE frequency deviation signal Δf_ACE remains within the deadband and the SOC is in an undesirable condition, a recovery coefficient must be calculated based on the SOC. This coefficient directs the energy storage SOC toward an optimal range while preventing Δf_ACE from exceeding the normal regulation zone during the recovery process.

(1) SOC constraints

From the perspective of the energy storage system’s intrinsic recovery needs, and to facilitate the analysis of its recovery demand coefficient under different SOC levels, the recovery output depth is determined based on the current SOC. The charging and discharging recovery demand coefficients, R_c1 and R_d1, calculated according to the SOC, are given by Equations (17) and (18), respectively:

$$R_{\text{c1}}=\left\{\begin{array}{ll}{K}_{E,\max }& ,S<S_{\min }\\ {\displaystyle \frac{K_{E,\max }}{1+e^{-\beta (1-\frac{S-S_{\min }}{S_0-S_{\min }})}}}& ,S_{\min }\le S<S_0\\ {\displaystyle \frac{K_{E,\max }}{1+e^{\beta (1+\frac{S-S_{\mathrm{low}}}{S_{\mathrm{low}}-S_0})}}}& ,S_0\le S<S_{\mathrm{low}}\\ 0& ,S\ge S_{\mathrm{low}}\end{array}\right.,$$

(17)

$$R_{\text{d1}}=\left\{\begin{array}{ll}0& ,S\le S_{\mathrm{high}}\\ {\displaystyle \frac{K_{E,\max }}{1+e^{\beta (1-\frac{S-S_{\mathrm{high}}}{S_1-S_{\mathrm{high}}})}}}& ,S_{\mathrm{high}}<S\le S_1\\ {\displaystyle \frac{K_{E,\max }}{1+e^{-\beta (1+\frac{S-S_{\max }}{S_{\max }-S_1})}}}& ,S_1<S\le S_{\max }\\ K_{E,\max }& ,S>S_{\max }\end{array}\right.$$

(18)

(2) Frequency deviation constraint

Since the SOC has to avoid the system frequency exceeding the frequency regulation dead zone when recovering, from the recovery constraint of the system, in order to facilitate the analysis of the memory recovery constraint coefficients under different ACE frequency deviation signals, the h is partitioned, i.e., $-\Delta f_{\mathrm{ACE}}^{\mathrm{db}}$, $\Delta f_{\mathrm{ACE}}^{\min }$, $\Delta f_{\mathrm{ACE}}^0$, $\Delta f_{\mathrm{ACE}}^{\mathrm{low}}$, $\Delta f_{\mathrm{ACE}}^{\mathrm{high}}$, $\Delta f_{\mathrm{ACE}}^1$, $\Delta f_{\mathrm{ACE}}^{\max }$, $\Delta f_{\mathrm{ACE}}^{\mathrm{db}}$ correspond to the lower dead band limit, the minimum value, the smaller value, the smaller value, the larger value, the larger value and the maximum value of the ACE frequency deviation signals, respectively, the upper dead band limit, different ACE frequency deviation signal intervals correspond to different recovery constraint coefficients0, and the charging and discharging recovery constraint coefficients calculated based on the ACE frequency deviation signals are shown in (19) and (20), respectively:

$$R_{\text{c2}}=\left\{\begin{array}{ll}0& ,\Delta f_{\mathrm{ACE}}<\Delta f_{\mathrm{ACE}}^{\min }\\ {\displaystyle \frac{K_{E,\max }}{1+e^{\beta (1+\frac{\Delta f_{\mathrm{ACE}}-\Delta f_{\mathrm{ACE}}^{\min }}{\Delta f_{\mathrm{ACE}}^{\min }-\Delta f_{\mathrm{ACE}}^0})}}}& ,\Delta f_{\mathrm{ACE}}^{\min }\le \Delta f_{\mathrm{ACE}}<\Delta f_{\mathrm{ACE}}^0\\ {\displaystyle \frac{K_{E,\max }}{1+e^{-\beta (1+\frac{\Delta f_{\mathrm{ACE}}-\Delta f_{\mathrm{ACE}}^{\mathrm{low}}}{\Delta f_{\mathrm{ACE}}^{\mathrm{low}}-\Delta f_{\mathrm{ACE}}^0})}}}& ,\Delta f_{\mathrm{ACE}}^0\le \Delta f_{\mathrm{ACE}}<\Delta f_{\mathrm{ACE}}^{\mathrm{low}}\\ K_{E,\max }& ,\Delta f_{\mathrm{ACE}}\ge \Delta f_{\mathrm{ACE}}^{\mathrm{low}}\end{array}\right.,$$

(19)

$$R_{\text{d2}}=\left\{\begin{array}{ll}{K}_{E,\max }& ,\Delta f_{\mathrm{ACE}}\le \Delta f_{\mathrm{ACE}}^{\mathrm{high}}\\ {\displaystyle \frac{K_{E,\max }}{1+e^{-\beta (1+\frac{\Delta f_{\mathrm{ACE}}-\Delta f_{\mathrm{ACE}}^{\mathrm{high}}}{\Delta f_{\mathrm{ACE}}^{\mathrm{high}}-\Delta f_{\mathrm{ACE}}^1})}}}& ,\Delta f_{\mathrm{ACE}}^{\mathrm{high}}<\Delta f_{\mathrm{ACE}}\le \Delta f_{\mathrm{ACE}}^1\\ {\displaystyle \frac{K_{E,\max }}{1+e^{\beta (1+\frac{\Delta f_{\mathrm{ACE}}-\Delta f_{\max }}{\Delta f_{\mathrm{ACE}}^{\max }-\Delta f_{\mathrm{ACE}}^1})}}}& ,\Delta f_{\mathrm{ACE}}^1<\Delta f_{\mathrm{ACE}}\le \Delta f_{\mathrm{ACE}}^{\max }\\ 0& ,\Delta f_{\mathrm{ACE}}>\Delta f_{\mathrm{ACE}}^{\max }\end{array}\right.,$$

(20)

where $-\Delta f_{\mathrm{ACE}}^{\mathrm{db}}$, $\Delta f_{\mathrm{ACE}}^{\min }$, $\Delta f_{\mathrm{ACE}}^0$, $\Delta f_{\mathrm{ACE}}^{\mathrm{low}}$, $\Delta f_{\mathrm{ACE}}^{\mathrm{high}}$, $\Delta f_{\mathrm{ACE}}^1$, $\Delta f_{\mathrm{ACE}}^{\max }$, $\Delta f_{\mathrm{ACE}}^{\mathrm{db}}$ correspond to the lower dead band limit, the minimum value, the smaller value, the smaller value, the larger value, the larger value and the maximum value of the ACE frequency deviation signals, respectively.

To ensure grid frequency remains within permissible limits during the recovery of the energy storage system’s output power, an integrated consideration of both the battery’s SOC recovery requirements and the power system’s load-bearing limit is required. The corresponding SOC recovery coefficient is specified in Equation (21):

$$K_{\mathrm{R}}=\left\{\begin{array}{ll}\min (R_{\mathrm{c}1},R_{\mathrm{c}2}),& S\le S_{\mathrm{low}}, \Delta f_{\mathrm{ACE}}<0\\ R_{\mathrm{c}1}, & S\le S_{\mathrm{low}}, \Delta f_{\mathrm{ACE}}\ge 0 \\ 0,& S_{\mathrm{low}}<S<S_{\mathrm{high}}\\ -R_{\mathrm{d}1}, & S\ge S_{\mathrm{high}}, \Delta f_{\mathrm{ACE}}<0\\ -\min (R_{\mathrm{d}1},R_{\mathrm{d}2}),& S\ge S_{\mathrm{high}}, \Delta f_{\mathrm{ACE}}\ge 0\end{array}\right..$$

(21)

(3) SOC recovery factor

Once the SOC recovery coefficient is determined, the recovery output power of the energy storage system can be calculated to restore the SOC of the electrochemical energy storage to its optimal range. The recovery output power for the electrochemical energy storage SOC is expressed as Equation (22):

$$\Delta P_{\mathrm{R}}=-K_{\mathrm{R}}\left|\Delta f_{\mathrm{ACE}}\right|.$$

(22)

4. Cooperative Frequency Regulation Strategies for Composite Energy Storage Systems Considering Aluminum Loads

4.1. Control Strategy for Composite Energy Storage System Based on Variable Filter Time Constant

To address the issues of SOC limit violations in electrochemical energy storage and frequent start-stop operations of pumped storage units in hybrid energy storage systems, this paper proposes an adaptive frequency allocation strategy based on the rate of change in ACE. This strategy decomposes the frequency deviation signal through an adaptive filter and allocates the components to pumped storage (low-frequency) and electrochemical energy storage (high-frequency), respectively, enabling coordinated frequency regulation. The filter expression is given by Equation (23):

$$W(s)={\displaystyle \frac{1}{1+s(T_{\mathrm{N}0}+\Delta T_{\mathrm{N}})}},$$

(23)

where T_N0 is the initial value of the filter time constant; ΔT_N is the variation in the filter time constant.

The relationship curve between the variation in filtering time constant and the rate of change of ACE frequency deviation is shown in Figure 8. The selection of the variable filter time constant mapping is motivated by the distinct response dynamics of the HESS components. During the incipient phase of a disturbance where dΔf_ACE is high, a reduced T_N is prioritized to facilitate rapid power injection from the electrochemical storage, thereby minimizing the primary frequency dip. As the system stabilizes, T_N is increased to smoothly transfer the regulation burden to the high-capacity abandoned mine pumped storage units. This adaptive mechanism prevents premature EES exhaustion while alleviating mechanical wear on the hydraulic units.

Based on the relationship curve between the filter time constant and the rate of change in the ACE frequency deviation, their corresponding relationship is expressed by Equation (15). To facilitate subsequent simulation data processing, the rate of change in the ACE frequency deviation is normalized in this study, with dΔf_ACE,α/dt and dΔf_ACE,β/dt set to 0.1 and 0.9, respectively.

$$\Delta T_{\mathrm{N}}=\left\{\begin{array}{ll}-0.5T_{\mathrm{N}0};& -0.1\le {\displaystyle \frac{\mathrm{d}\Delta f_{\mathrm{ACE}}}{\mathrm{d}t}}\le 0.1\\ -1.25T_{\mathrm{N}0}\cdot ({\displaystyle \frac{\mathrm{d}\Delta f_{\mathrm{ACE}}}{\mathrm{d}t}}+1.4);& -0.9\le {\displaystyle \frac{\mathrm{d}\Delta f_{\mathrm{ACE}}}{\mathrm{d}t}}\le -0.1\\ 1.25T_{\mathrm{N}0}\cdot ({\displaystyle \frac{\mathrm{d}\Delta f_{\mathrm{ACE}}}{\mathrm{d}t}}-1.4);& 0.1\le {\displaystyle \frac{\mathrm{d}\Delta f_{\mathrm{ACE}}}{\mathrm{d}t}}\le 0.9\\ 0.5T_{\mathrm{N}0};& {\displaystyle \frac{\mathrm{d}\Delta f_{\mathrm{ACE}}}{\mathrm{d}t}}\le -0.9 \mathrm{or}{\displaystyle \frac{\mathrm{d}\Delta f_{\mathrm{ACE}}}{\mathrm{d}t}}\ge 0.9\end{array}\right.$$

(24)

4.2. Partitioning Rules for Frequency Regulation Intervals

When load fluctuations in the power grid result in power deficit or surplus, different frequency regulation resources respond to the commands of the coordinated control strategy by adjusting their active power to achieve power balance of the electrical power system. The ACE interval partitioning strategy is illustrated in Figure 9.

(1) When |Δf| ≤ Δf_db, the grid operates within the regulation deadband. In this scenario, only the electrochemical energy storage performs SOC recovery, while other frequency regulation resources remain inactive. This maintains the energy storage SOC within the optimal range, thereby preventing overcharging or over-discharging.

(2) When Δf_db < |Δf| ≤ Δf_CES, the grid enters the normal regulation zone. During this condition, only conventional thermal power units participate in frequency regulation.

(3) When Δf_CES < |Δf| ≤ Δf_AL, the grid operates in the sub-emergency regulation zone. Under such circumstances, the hybrid energy storage system assists conventional thermal power units in grid frequency regulation. A variable-filter time constant controller decomposes the ACE frequency deviation signal into high-frequency and low-frequency components, with the low-frequency component handled by abandoned mine pumped storage plants and the high-frequency component managed by electrochemical energy storage.

(4) When Δf_AL < |Δf| ≤ Δf_OVER, the grid enters the emergency regulation zone. Here, restoring grid frequency takes the highest priority, with conventional thermal power units, the hybrid energy storage system, and electrolytic aluminum loads jointly participating in frequency regulation.

(5) When |Δf| > Δf_OVER, the grid reaches the super-emergency regulation zone. In this state, neither the hybrid energy storage system nor conventional thermal power units can suppress grid frequency fluctuations, and all frequency regulation resources fail to respond. Ultimately, system frequency can only be gradually restored to a safe range through forced load-shedding operations.

$$\Delta P=\left\{\begin{array}{ll}\Delta P_{\mathrm{R}}, & \left|\Delta f\right|\le \Delta f_{\mathrm{db}}\\ \Delta P_{\mathrm{G}}, & \Delta f_{\mathrm{db}}<\left|\Delta f\right|\le \Delta f_{\mathrm{CES}} \\ \Delta P_{\mathrm{G}}+\Delta P_{\mathrm{PPS}}+\Delta P_{\mathrm{E}}, & \Delta f_{\mathrm{CES}}<\left|\Delta f\right|\le \Delta f_{\mathrm{AL}}\\ \Delta P_{\mathrm{G}}+\Delta P_{\mathrm{PPS}}+\Delta P_{\mathrm{E}}+P_{\mathrm{AL}}, & \Delta f_{\mathrm{AL}}<\left|\Delta f\right|\le \Delta f_{\mathrm{OVER}}\\ 0,& \left|\Delta f\right|>\Delta f_{\mathrm{OVER}}\end{array}\right.,$$

(25)

where ΔP is the frequency regulation output of the load, ΔP_G is the frequency regulation output of the thermal power units, and ΔP_PPS is the frequency regulation output of the mine waste pumped storage power plants.

To bridge the gap between theoretical control and industrial production safety, the physical limitations of the aluminum electrolysis load are integrated into the logic of Section 4.2 via a ‘Condition-Triggered + Output-Clamped’ mechanism.

First, to respect the duration constraint and maintain production stability, the aluminum load is not employed for continuous regulation. As illustrated in the ACE interval partitioning (Figure 10), it is designated as a high-tier contingency resource. The load modulation is only triggered when the system frequency deviation enters the ‘Emergency’ zone (|Δf| > Δf_AL), indicating that the primary and secondary regulation capacities of thermal and hybrid storage units are exhausted. This threshold-based initiation minimizes the frequency of interventions and preserves the thermal balance of the electrolysis cells.

Second, the modulation depth constraint is expressed by mapping the calculated frequency regulation requirement to a physical power limit. In Equation (25), the control command ΔP_AL,cmd is subjected to a saturation operator before execution.

5. Simulation Analysis

This paper models the frequency regulation process of a two-area system incorporating electrolytic aluminum loads and a HESS using the MATLAB/Simulink simulation platform. The architecture of this model is shown in Figure 10. The installed capacity of conventional thermal power units in the system is set to 500 MW. Area 1 is equipped with EAL and the HESS, where the EAL has an installed capacity of 306 MW, and the remaining load in the system has an installed capacity of 194 MW.

5.1. Robustness Evaluation and Optimal Parameter Determination Under Varying H and D

Before evaluating the cooperative strategy under specific disturbance scenarios, it is essential to establish the controller’s robustness against variations in system physical parameters, namely the inertia constant (H) and damping factor (D), which represent varying grid strengths. A comprehensive sensitivity analysis was conducted by varying H from 3.0 to 5.0 s (representing a transition from a low-inertia to a standard grid) and D from 0.8 to 1.2 p.u. Simultaneously, the control parameter T_N0 was tested at 5 s,10 s, and 15 s to identify the optimal configuration. The system simulation parameters are shown in

Table 3. Simulation Parameters and Settings.

Parameter	Symbol	Value	Unit
Thermal unit rated capacity	Pgen	500	MW
Equivalent inertia constant	H	5.0	s
Load damping factor	D	1.0	p.u./Hz
Reheater time constant	TRH	10.0	s
Governor time constant	TG	0.08	s
EES rated energy capacity	Erated	0.5	MWh
EES response time constant	TE	0.1	s
Pumped storage water inertia	TW	1.0	s
Pumped storage governor PID	Kp, Ki, Kd	1.2, 0.05, 0	-
SOC operational boundaries	Smin, Smax	0.1, 0.9	-
SOC optimal range	Slow, Shigh	0.4, 0.6	-
SOC sensitivity factors	α,β	2.0, 3.0	-
Frequency deadband	Δfdb	0.03	Hz
Normal regulation boundary	ΔfCES	0.05	Hz
Sub-emergency boundary	ΔfAL	0.10	Hz
Emergency limit	ΔfOVER	0.20	Hz
Initial filter time constant	TN0	10.0	s
Fuzzy input/output universe	U	[−1, 1]/[0, 1]	-

.

The results, summarized in

Table 4. Results of Parameter Sensitivity Analysis.

H (s)	D (p.u.)	TN0 (s)	Max Δf (Hz)	ITAE Index	Stability
3.0	1.0	10	0.048	2.54	Robust performance
5.0	0.8	10	0.032	1.95	Stable recovery
5.0	1.0	10	0.024	1.82	Optimal Setting
5.0	1.0	5	0.026	2.15	High-freq chattering
5.0	1.0	15	0.035	2.88	Sluggish response

, indicate that while a decrease in H or D naturally leads to larger frequency deviations, the proposed controller with T_N0 = 10 s consistently yields the lowest ITAE indices and maintains the frequency nadir within a safe margin (<0.1 Hz even in low-inertia cases). In contrast, a smaller T_N0 (5 s) causes excessive EES power chattering in low-damping scenarios, whereas a larger T_N0 (15 s) results in sluggish recovery. Consequently, the combination of H = 5.0, D = 1.0, and T_N0 = 10 s is adopted as the baseline for subsequent case studies in Section 5.2 and Section 5.3 to demonstrate more complex multi-resource coordination.

5.2. Analyzing the Frequency Regulation Performance of the Variable Filter Time Constant Controller

A 5 min continuous load fluctuation data segment from an actual power grid was applied as the analysis sample and introduced into the control area. In the simulation, the sampling period was set to 0.1 s, and the corresponding load disturbance profile is shown in Figure 11. To validate the effectiveness of the proposed controller, simulations were conducted under identical grid load fluctuations for three scenarios: without a filter, with a first-order low-pass filter, and with the proposed variable time constant filter. The simulation results are presented in Figure 12.

It is about 0.032 Hz smaller than the case without filter, and the oscillation is reduced, but the regulation time is not significantly shortened. When the system adopts the variable filter time constant controller designed in this paper, the system oscillation is smaller, the control time is also shortened, and the maximum frequency difference is reduced to 0.024 Hz, which verifies that the variable filter time constant controller has better dynamic continuous performance.

5.3. Simulation Analysis of Electrochemical Energy Storage Strategies

To verify the effectiveness of the electrochemical energy storage strategy proposed in this paper, the configured capacity of the electrochemical energy storage is set to 0.5 MWh and the initial SOC value is 0.5. After a sudden load increase of 0.04 p.u. at 6 s, the system enters the sub-emergency frequency regulation zone, at this time, it is necessary for the conventional unit, abandoned mine pumped storage and electrochemical storage to jointly participate in frequency regulation, and the proposed electrochemical storage frequency regulation strategy is compared with the fixed-K adaptive control and no storage, and the frequency deviation, electrochemical storage system output and its SOC change curves in the three scenarios are shown in Figure 13.

A step disturbance of 0.04 p.u. (20 MW) is applied at t = 6 s to evaluate the performance of the proposed EES strategy. This magnitude is specifically chosen to drive the system frequency into the ‘Sub-emergency’ regulation zone (Δf_CES < |Δf| ≤ Δf_AL) as defined in Section 4.2. In this zone, the coordination between EES and abandoned mine pumped storage (PPS) is prioritized to stabilize the grid. The disturbance occurs at t = 6 s to ensure that the simulation has reached a complete initial steady state, thereby eliminating any start-up numerical transients and allowing for an accurate assessment of the EES output and SOC recovery behavior following the ‘sudden’ power deficit.

As can be seen from Figure 13, the load surges by 0.04 p.u. at 6 s. The frequency fluctuation deviation of the system is large when relying solely on the conventional frequency regulation unit, and the maximum frequency difference reaches 0.135 Hz. When the electrochemical energy storage added to the composite energy storage system is controlled by fixed-K adaptive control, the maximum frequency deviation of the system is reduced to 0.063 Hz, whereas the system frequency deviation is limited to 0.05 Hz when the electrochemical energy storage strategy proposed in this paper is used. Meanwhile, the storage power under the proposed electrochemical energy storage strategy is reduced by 17% compared to the fixed K adaptive control, and its SOC is improved by 9.8% compared to the fixed K adaptive control, which avoids overcharging and over discharging of the electrochemical energy storage, and results in better maintenance of the SOC of the electrochemical energy storage system.

5.4. Cooperative Control Strategy Participation in Grid Frequency Control Performance Analysis

Assuming that the grid is initially under normal operation, the load increases suddenly by 0.05 p.u. at 6 s. At this time, the system is in the emergency regulation zone due to excessive load increment, which requires the joint participation of conventional thermal power units, abandoned mine pumped storage power stations, electrochemical energy storage and electrolytic aluminium loads in frequency regulation, and the simulation results are shown in Figure 14.

As shown in Figure 14, the maximum frequency difference is 0.195 Hz when relying on the conventional frequency regulation unit alone in emergency situations. Under the two scenarios of relying only on waste mine pumped storage for frequency regulation and using composite energy storage for frequency regulation, the maximum frequency difference is reduced to 0.155 Hz and 0.112 Hz, respectively, which significantly improves the frequency regulation performance compared with that when only the conventional unit is used for frequency regulation, and the value of the maximum frequency difference is further reduced to 0.054 Hz after adopting the method proposed in this paper. At the same time, the method proposed in this paper can reduce the depth of action of the waste mine pumped storage and electrochemical energy storage compared to conventional methods and relying on a single frequency regulation source. In the strategy proposed in this paper, the power of the aluminium electrolytic load is reduced from 306 MW to 297 MW, releasing 9 MW of active power, and under the action of the aluminium electrolytic load, the tailings pumped storage plant and the electrochemical storage have a faster response and a smaller depth of action, which reduces mechanical wear of the tailings pumped storage plant, avoids overcharging or over discharging of the electrochemical storage, and extends their life.

To evaluate the performance more comprehensively, standard control indices are reported, including settling time (t_s, defined as the time to enter and remain within ±0.02 Hz), overshoot (M_p), the Integral of Time-weighted Absolute Error (ITAE), SOC operational range, and the peak power action of the abandoned mine pumped storage (PPS) unit.

Table 5. Comparison of Performance Indices Under Step Disturbance.

Control Scheme	Δf	ts (s)	Mp (Hz)	ITAE	SOC Range	MaxΔPPPS (p.u.)
Conventional Units Only	0.195	45.2	0.195	14.52	N/A	N/A
PPS-Only Participation	0.155	32.8	0.155	9.92	N/A	0.045
HESS (Fixed-K Adaptive)	0.112	26.5	0.112	6.85	[0.465, 0.500]	0.040
Proposed Symmetrical Strategy	0.054	18.2	0.054	3.42	[0.482, 0.500]	0.031

summarizes the comparative indices for four scenarios under a 0.05 p.u. step disturbance. The proposed strategy achieves the lowest ITAE (3.42), which is 65.5% lower than the PPS-only case, indicating superior cumulative error suppression. Furthermore, by coordinating with the aluminum load, the peak power demand on PPS is reduced by 31.1% (from 0.045 p.u. to 0.031 p.u.), effectively alleviating mechanical fatigue. The EES unit also maintains a healthy SOC within a narrow range of [0.482, 0.500], ensuring device longevity while achieving rapid frequency restoration within 18.2 s.

6. Conclusions

In this paper, a symmetrical cooperative frequency control strategy integrating electrolytic aluminum loads and a HESS is proposed and validated. The main quantitative findings are as follows:

(1) Under a severe 0.05 p.u. step disturbance, the proposed strategy reduces the maximum frequency deviation from 0.198 Hz to 0.054 Hz, achieving a 72.7% improvement in frequency nadir suppression compared to conventional thermal-only regulation.

(2) The settling time of the grid frequency is shortened by approximately 59.5%, and the frequency recovery slope is significantly enhanced, mitigating the risks of large-scale renewable energy disconnection triggered by high RoCoF.

(3) The collaborative logic maintains the State of Charge (SOC) of the electrochemical storage within a narrow and safe range of [0.482, 0.505], effectively preventing over-discharge and extending device longevity while ensuring sufficient reserve capacity.

(4) The ACE-based zoning approach ensures a tiered response where EA loads and pumped storage are activated only during high-stress contingencies, optimizing the utilization of flexible resources.

It should be clarified that the simulation model developed in this study is based on System Frequency Response (SFR) transfer functions. While this lumped-parameter modeling approach is highly efficient and widely accepted for evaluating secondary frequency regulation and mid-to-long term dynamics, it presents certain limitations:

The SFR model assumes a uniform frequency across the entire power grid, thereby neglecting the spatial frequency distribution and inter-area oscillations found in large-scale multi-area interconnected systems.

The use of transfer functions simplifies the high-order nonlinear switching characteristics of power electronic interfaces and the complex electromagnetic transient processes within synchronous generators. Future work will aim to validate the proposed cooperative strategy within a more detailed electromagnetic transient (EMT) framework and multi-node network topologies to account for these localized variations.

With the new power system and “carbon peaking and carbon neutrality” goals of continuous promotion, the grid frequency stability problem is becoming more and more prominent, this paper only from the theoretical level to consider the electrolytic aluminium load, abandoned mine pumping station and electrochemical energy storage and other resources to participate in the grid secondary frequency regulation, in order to ensure that the composite energy storage and electrolytic aluminium loads to participate in the frequency regulation auxiliary services market, the composite energy storage optimal capacity allocation, relevant government policies and operation mechanisms still need to be further studied [29,30].