An isolated hybrid power system generates the required power to satisfy the required load from various remote and renewable sources as the system is not connected to the primary grid. Renewable sources (RES), such as PV, wind, biomass etc., provides the power essential for IHPS, backed by energy storage sources (ESS), depending on their availability and shortage. Frequency and voltage deviations will be regular in these types of systems due to the volatile nature of the environment and load. These oscillations are primarily addressed by the inertia of the rotating machines available at the source end, which are low in portion in IHPS, as shown in Figure 1A. Recently, the shortage of inertia has been addressed by virtual inertia provided by ESS. The effective utilization of available ESS for IHPS can address frequency and voltage oscillations. The inertia control alone couldn’t suppress these oscillations, which requires appropriate secondary control mechanism, as shown in Figure 1B.

This led to a resourceful research contribution towards secondary controllers aiding virtual inertia control to support stability of the IHPS. The following section provides such glimpses of authors contribution towards stability issues of modern power systems.

Reports (Denholm et al., 2020) at NREL state that integrating renewable sources into the traditional grid and remote areas is progressing rapidly. These integration RES reduces system inertia, which leads to contingencies, as shown in Figure 1B. International practices of inertia estimation and offline estimation methods in India are assessed by authors in Report on Assessment of Inertia in Indian Power System (2022), and a detailed analysis of the inertia-generating units in India implies load-side inertia contribution, estimated to be 20% of total system inertia. Khan et al. (2023) address frequency stability challenges in hybrid power systems, exploring load frequency control methodologies and power system flexibility and highlighting the need for fine-tuned controllers and virtual inertia backup. A virtual gas inertia model (Miao et al., 2023a) that represents the gas storage’s capability to mitigate power impact and explores the joint use of gas inertia with other energy forms, focusing on fully utilizing multi-energy inertia resources like thermal and natural gas energy inertia to power support optimization. The potential of gas-thermal inertia-based frequency response strategy in Integrated Energy Systems (IESs) (Miao et al., 2023b), leveraging the slow-dynamic characteristics of gas-thermal systems, addresses power grid inertia challenges. The limitations of single control methods are overcome by proposing an integrated control method that combines virtual inertia control, virtual negative inertia control, and virtual droop control, thereby improving comprehensive control performance for PFR (Zhu et al., 2021). This integrated approach enhances the frequency regulation effect but also helps in reducing the ESS capacity requirements, making the system more efficient and cost-effective for frequency regulation applications. Thus, the combined multi energy inertia support is an emerging research area for addressing stability enhancement of hybrid power systems.

Ranjan et al. (2021) discuss voltage and frequency control in a 3-area interconnected hybrid power system with solar and wind power, incorporating FACTS devices and a demand response scheme. Latif et al. (2023) developed a frequency-voltage response model for a photon exchange membrane fuel cell (PEMFC) for the first time. They assessed the dynamic responses using an integer order proportional-integral-derivative (IOPID) controller. A novel approach is introduced in Kumar Barik et al. (2019) focusing on optimal load-frequency regulation of 4-interconnected unequal hybrid microgrids with demand response support. The paper utilizes particle swarm optimization (PSO) tuning classical PID controllers for load-frequency control of bio-renewable cogeneration-based interconnected hybrid microgrids with demand response support, ensuring efficient power management in different climatic scenarios. The efficacy of the cascaded PI-TID controller tuned using chaotic butterfly optimization algorithm (CBOA) (Bhuyan et al., 2023) through sensitivity analysis under significant changes in source and load conditions, highlighting its robustness and adaptability. Analysis of dynamic performance of the hybrid generation system using time-domain simulations under various operating conditions and disturbances, presenting optimal gain settings for classical and PSO-based PI controllers (Das et al., 2011). Most of the single and multi-area power systems are addressed by the authors for load side control along with sources side control. The authors contribution towards research on load side control like DSM for virtual inertia supported IHPS is very few.

A robust load-frequency controller for the dynamic stability of interconnected power systems was proposed in Yang and Lu (1999), Vrdoljak et al. (2009). Mi et al. (2013), Xinxin et al. (2020), and Kumar et al. (2021) proposed decentralised sliding mode (SM) LFC designed for multi-area interconnected power systems with robust stability. The proposed method outperforms other reported methods in frequency deviation improvement. PI switching surface is considered in the above works, and Lyapunov stability theory proof is studied for controller stability studies. FOSMC enhance system stability and outperforms PID, FOPID, and SMC (Guha et al., 2021). FOSMC effectively dampens power-frequency oscillations in low-inertia systems. Pavan Kumar et al. (2024) introduced the TISMC technique with proven stability and improved AVOA for optimising controller parameters for mitigating frequency fluctuations. A comparative analysis of cascaded SMC and FOSMC for ball trajectory control (Das and Roy, 2016; Roy et al., 2018) shows that the fractional order SMC (FOSMC) outperforms SMC in speed and tracking accuracy. Contribution towards design of controllers for frequency enhance of micro grid performance utilizing fuzzy logic (Chandra Sahu et al., 2023; Kumar Mohapatra et al., 2024) and in cascaded fuzzy logic connection (Kumar Mohapatra et al., 2024). Considering the advantages from literatures behind cascading controllers to enhance their stability and to improve their performance is a futuristic work. Cascading nonlinear controllers like SMC have been identified as less focused area in terms of addressing stability issues related to modern power systems.

The paper introduces the following novel contributions from the detailed literature survey.

• Developed a novel multi-energy inertia-based power support approach (gas inertia – hydrogen storage, thermal inertia – solar thermal storage, hydro inertia – gravity hydro storage, chemical inertia – battery energy storage) for simultaneous voltage and frequency regulation.

Biodiesel extracted from the transesterification of waste edible oils/suitable energy crops has properties analogous to diesel (Denholm et al., 2020). The linearized model of BDEG is expressed as in Equation 2, considering the actions of the inlet valve and engine. T F B D E G = K b e 1 + s T b e K b a 1 + s T b a (2)

Inertia support is highly necessary for the power system to enhance stability. It’s a regular practice for synchronous generators to take part in inertia support. In the RES integrated power system, the lack of rotating machines results in less inertia support (Tamrakar, 2017). Hence, virtual inertia is introduced with multiple storage devices to enhance the stability of the system. In Miao et al. (2023a), detailed virtual inertia support for the stability of the power system is discussed. Multi-energy inertia support for the power system is a new concept detailed in Miao et al. (2023b). From this idea, in the present work, we proposed a concurrent multi-energy inertia system for voltage and frequency support of IHPS. Concurrent virtual damping, virtual droop, virtual inertia and virtual negative inertia techniques are proposed in the present work, as discussed below.

In IHPS, virtual damping control plays a vital role in time-based control of oscillation caused by a mismatch in frequency/voltage. The damping signal is generated by the proportional gain of the error signal as given in Equation 3. Δ P D = K D × Δ f (3)

The virtual droop control regulates the active power output of an Energy Storage System (ESS) based on the system’s droop characteristic and frequency deviation. By utilizing virtual droop control, the steady-state frequency deviation of the system can be minimized. The virtual droop control mechanism determines the active power output of ESS as given in Equation 4. Δ P D P = ―   K D × Δ f (4)

Under virtual inertia control, the Energy Storage System (ESS) replicates the inertia properties typically seen in a synchronous machine. The charging or discharging capability of the ESS is directly influenced by the rate of change in frequency, serving to alleviate fluctuations in system frequency and bolster overall system stability. The functionalities of the ESS can be delineated as follows as given in Equation 5: Δ P I 1 = ―   K I   × d Δ f   d t (5)

Virtual inertia control is effective in reducing system frequency deviations, but it may impede frequency recovery. Therefore, virtual negative inertia control can be implemented during the recovery phase to accelerate the process. The performance of Energy Storage Systems (ESS) under virtual negative inertia control is presented below in Equation 6 as follows: Δ P I 2 = K I   ′ × d Δ f   d t (6)

This paper presents a comprehensive control approach that utilises frequency deviation and rate of change of frequency deviation. The integrated control strategy incorporates virtual damping control, virtual droop control, virtual inertia control, and virtual negative control to improve the frequency regulation effect. The frequency regulation processes can be divided into two phases: frequency deterioration and frequency recovery, as shown in Figure 1B. During the frequency deterioration phase, the system frequency moves away from the nominal frequency, with the criteria defined as (Δf * df/dt > 0). In the frequency recovery phase, the system frequency moves back towards the nominal frequency, with the criteria defined as (Δf * df/dt < 0). The proposed integrated control strategy integrates virtual damping, virtual droop control and virtual inertia control during the frequency deterioration phase to lessen frequency deviation and prevent frequency deterioration. In the frequency recovery phase, virtual damping, virtual droop control and virtual negative inertia control are combined to reduce frequency deviation and hasten frequency recovery. The ESS output power in the frequency regulation phase can be expressed as: Δ P P F R = Δ P D + Δ P D P + Δ P I 1 , i f   Δ f × d f / d t > 0 Δ P D + Δ P D P + Δ P I 2 , i f   Δ f × d f / d t < 0 (7)

An aqua electrolyser-powered fuel cell with hydrogen storage is considered to provide gas inertia support to the IHPS. Gas inertia is modelled to mitigate power fluctuations in isolated power systems. Gas network constraints are analysed for the system’s strategy, economy, and power outputs (Zhou et al., 2024a; Zhou et al., 2024b).

The proposed concurrent virtual inertia strategy of the hydrogen gas storage system is presented in Figure 3.

Solar-powered parabolic trough collector system is the main source of power generation in IHPS. Solar power generating system are backed with thermal storage to provide power without required insolation. Thermal storage provides the concurrent virtual inertia strategy, as shown in Figure 4.

Hydro storage is a vital option for high-rated storage capacity. The working principle of GHPS is explained in Berrada et al. (2027), Yaghoubi et al. (2024), and detailed modelling for solar-powered energy systems is provided. In the present work, a concurrent virtual inertia model of GHPS is proposed and implemented for simultaneous frequency and voltage control of IHPS, as shown in Figure 5.

BESS is a highly used ESS option because of their longer life and cost (Meng et al., 2024a; Meng et al., 2024b). In the present work, a concurrent virtual inertia model of a BESS is proposed and implemented for simultaneous frequency and voltage control of IHPS, as shown in Figure 6.

HEV is a controllable load considered in the present work. Load side control provides a lesser impact on the system than the source side control (Kumar Barik et al., 2019). ∆ P H E V = − ∆ f ∆ f m ⁢ ∆ P D S M ; i f − ∆ f m ≤ ∆ f ≤ ∆ f m − ∆ f ∆ f ⁢ ∆ P D S M ; o t h e r w i s e T F H E V = K H E V 1 + s T H E V ; ∆ P D S M = ∆ P S O C * T F H E V

The main objective in the present work is to minimise voltage and frequency oscillation by properly tuning controllers using optimisation techniques. The objective function is formed by the algebraic relation of error signals in the system, and optimization techniques are implemented to minimize the function, as shown in Figure 2. In the present work, integral square error (J_ISE) is considered an objective function as presented in Equation 7. J I S E = ∫ 0 T ∆ f 2 + ∆ v 2 d t

In contemporary times, the sliding mode controller (SMC) has gained recognition as a reliable, robust controller that can be applied to linear and non-linear systems. Given the dynamic fluctuations in solar insolation and load over time, this controller is particularly well-suited for the current issue. Introducing the cascaded PI- TISMC, with a tilt integral order sliding surface, represents an innovative approach, offering the controller additional flexibility to minimise frequency and voltage deviations promptly as shown in Figure 7.

In the present paper five optimization techniques, that works on five different principles are considered as follows:

1. Genetic algorithm (evolutionary principle based) Das et al., 2012,

These different optimization techniques are implemented for frequency and voltage oscillations individually. But comparison of these class of techniques for concurrent voltage and frequency control is a notable novel attempt (Zhang J. et al., 2023; Ma et al., 2019; Shirkhani et al., 2023).

In the initial phase an efficient optimization technique has been chosen for controller parameter tuning. The results have been analysed for step increment in disturbance of load and solar insolation of microgrid system. Optimization techniques were used to tune PID controller parameters for the system. Five different classes of optimization techniques have been considered for the work, genetic algorithm (GA- evolutionary based), particle swarm optimization (PSO-swarm based), gravitational search algorithm (GSA-physics based), human behaviour-based optimization (HBBO- human behaviour based), Tasmanian devil optimization (TDO-bio inspired). The performance comparison of optimization techniques is presented below (Ju et al., 2022; Wang et al., 2023; Liu et al., 2024).

Convergence curves of multiple optimization techniques considered in the work are shown in Figure 8 and compared in Table 1. The results of frequency and voltage deviation for multiple optimization techniques are presented in Figure 9.

It is evident from the results that TDO (bio-inspired) algorithm exhibits minimum deviations and fastest settling time for disturbances, supporting its better performance compared to other classes of techniques. So, for the rest of analysis TDO is considered for tuning controller parameter.

The proposed concurrent virtual inertia techniques are compared with each individual combination to opt the best technique from it. The results have been analysed for step increment in disturbance of load and solar insolation of microgrid system and presented in Figure 10.

It is evident from the above presented results, the proposed concurrent virtual inertia control outcomes better results than other combination of techniques. The presented control scheme performance is also evaluated with PID controller for frequency and voltage control of IHPS and presented in Figure 11.

As stated previously DSM is more precisely implementing technique for frequency and voltage disturbance reduction. In the present work an HEV is considered and its performance in IHPS has been compared as presented in Figure 12.

It is evident from the above results, that providing load side control for concurrent voltage and frequency control by proper DSM technique enhances its stability.

The proposed cascaded PI-TISMC is compared with PID, cascaded PI-PID, and PISMC controllers for step disturbance for load and solar insolation as provided in Figures 13, 14.

From results Figures 15, 16 and Table 2 it is clear that the proposed controllers performs better than other controllers for step disturbance. Figure 17 depicts the active power variations of sources in IHPS, due to system disturbances.

From the above results it identified that TDO optimized cascaded PI-TISMC provides better control of IHPS against frequency and voltage deviations. Now it’s been tested for variable load and solar insolation as shown in Figure 18, 19, for the best combination obtained.

From the results provided in Figures 20, 21, proposed technique is effective even for variable disturbances in IHPS and are in permissible range. The superiority among the controllers for variable load disturbance is also supported by Table 3. Figure 22 depicts the active power variations of sources in IHPS, due to variable system disturbances.