A robust PID controller based on linear quadratic gaussian approach for improving frequency stability of power systems considering renewables

This paper proposes robust proportional -integral-derivative (PID) control for a proton exchange membrane fuel cell (PEMFC) system. We model a PEMFC as a multivariable system, and apply identification techniques to obtain the system's transfer function matrices, where system variations and disturbances are regarded as system uncertainties. In previous studies, robust control has been successfully applied to improve the stability, performance, and efficiency of a PEMFC system. However, the resulting robust controllers can be complicated. On the other hand, PID control has been widely applicable to engineering practices because of its simple structure, though it lacks stability analysis for systems with uncertainties. Therefore, combining the merits of robust control and PID control, we design robust PID controllers to regulate hydrogen and air flow rates of a PEMFC system. From the discussion of stability, performance, and efficiency, the proposed robust PID controllers are shown to be effective.

Robust Non-fragile PID Controller Design for the Stroke Regulation of Metering Pumps

The integration of renewable energy sources (RESs) at the edge of the grid plays a contributory role in advancing the transition to a sustainable energy future. However, this transition introduces significant variability, which challenges the maintenance of frequency stability in power systems. To address the impacts of RES variability, various robust control strategies have been developed. This paper compares the performance of different advanced sliding mode control (SMC) approaches, i.e., super twisting (ST) algorithm‐based second order sliding mode control (STSOSMC), second order sliding mode control (SOSMC), double integral sliding mode control (DISMC) and integral sliding mode control (ISMC) with conventional sliding mode control (SMC) for load frequency control with stochastic RESs such as biogas generators (BG) and wind‐based doubly fed induction generators (DFIG). The impact of the advanced sliding mode controllers on the voltage and rotor angle stability of the system is also explored. The efficacy of the controllers is tested under different load disturbances, considering nonlinearities such as communication delay (CD), sensor inaccuracy (SI), governor dead band (GDB), and generation rate constraint (GRC). The results demonstrate that STSOSMC achieves superior frequency regulation with minimal chattering and outperforms other controllers in terms of settling time, overshooting, and undershooting in frequency deviation. The result also demonstrates the effectiveness of STSOSMC in managing the variability and disturbances of RESs. Therefore, it could be considered the most robust control mechanism from the edge of the grid system with high penetration of RESs.

Introduction: To date, a variety of studies have been published on the topic of long term energy system transition. Most studies on future energy systems, however, have a shorter time frame or adopt a supranational focus (e.g. the Energy Roadmap, 2011 or the World Energy Outlook, 2015). It then constitutes a sincere challenge to perform a national energy system transition study with as time horizon 2050 and covering a far-reaching transformation of the energy system. VITO, together with the FPB (Federal Planning Bureau) and ICEDD, performed a study to scrutinise the transition of the Belgian national energy system towards a future mix entirely based on renewable energy sources. The focus on renewable energy sources and on building a national energy system completely running on renewable energy can be traced back to three main concerns: – Climate change: Renewable energy sources (RES) are a major instrument in the fight against climate change as RES do not release (net) greenhouse gas emissions. – Security...

This paper presents a novel literature survey on leveraging electrolysis for grid frequency stabilization in power systems with high penetration of renewable energy sources (RESs), uniquely integrating global research findings with specific insights into the Polish energy context—a region facing acute grid challenges due to rapid RES growth and infrastructure limitations. The intermittent nature of wind and solar power exacerbates frequency fluctuations, necessitating dynamic demand-side management solutions like hydrogen production via electrolysis. By synthesizing over 30 studies, the survey reveals key results: electrolysis systems, particularly PEM and alkaline electrolyzers, can reduce frequency deviations by up to 50% through fast frequency response (FFR) and primary reserve provision, as demonstrated in simulations and real-world pilots (e.g., in France and the Netherlands); however, economic viability requires enhanced compensation schemes, with current models showing unprofitability without subsidies. Technological advancements, such as transistor-based rectifiers, improve efficiency under partial loads, while integration with RES farms mitigates overproduction issues, as evidenced by Polish cases where 44 GWh of solar energy was curtailed in March 2024. The survey contributes actionable insights for policymakers and engineers, including recommendations for deploying electrolyzers to enhance grid resilience, support hydrogen-based transportation, and facilitate Poland’s target of 50.1% RESs by 2030, thereby advancing the green energy transition amid rising instability risks like blackouts in RES-heavy systems.

Integrating non-dispatchable renewable energy sources (RES) such as wave farms into electric power systems presents inherent challenges. Specifically, the variability of the resource and its non-dispatchable) nature introduces power imbalances and power system stability problems in the system over both short and medium terms. This issue is particularly relevant for isolated power systems, such as those found on several European islands, where interconnection with the mainland is lacking. Therefore, although wave energy has significant potential for integration into island power systems due to resource availability, determining the maximum RES penetration that such systems can sustain while maintaining stability is not straightforward. Power system stability is closely tied to frequency. A well-established solution for improving the stability of isolated systems when integrating non-dispatchable RES is to install devices capable of responding to over- or under-frequency events, such as energy storage systems (ESS). The literature extensively discusses ESS control techniques for frequency regulation, with one of the most straightforward approaches being to operate the ESS according to a droop control strategy (similar to a statism). In this method, the power dispatched or stored by the ESS increases proportionally to the deviation from the frequency reference value. This paper presents a case study analyzing the frequency stability of an island power system equipped with an energy storage system (ESS) when integrating a wave farm. Frequency stability is evaluated based on two variables: wave energy penetration and the ESS droop control parameter. The case study is based on the island of El Hierro (Canary Islands, Spain), an isolated electrical system with a very high penetration of RES. The island’s electrical generation system consists of a wind farm, a pumped-storage hydroelectric power plant, and conventional generation from a diesel power plant. The analysis is conducted through simulations in MATLAB Simulink. A wave farm is modeled to evaluate the generated power and its associated oscillations, based on the wave energy resource at various locations along El Hierro’s coast. Additionally, an aggregated inertial dynamic model of the electrical power system is employed to assess the impact of the wave energy farm's generation on the system’s frequency and the aging that the frequency excursions introduce in the elements of the system. The Spanish Grid Code is considered to ensure compliance with frequency regulation mechanisms in isolated systems. Simulations are performed across different scenarios, varying both the nominal power of the wave farm and the ESS droop control parameter, in order to evaluate the ESS capacity. The results identify the optimal droop control parameter for each wave farm size to ensure frequency remains within acceptable thresholds. Furthermore, the minimum ESS capacity required for each wave farm size is determined from the simulations. These findings provide a basis for ESS and wave farm dimensioning, which could be translated into economic terms to maximize revenue (this aspect is beyond the scope of the present work).

A novel adaptive fuzzy proportional-integral-derivative (PID) controller based on the proposed piecewise PID controller is put forward for the sandglass-type floating, drilling, production, storage and offloading unit (FDPSO). First, on the premise of appropriate positioning accuracy, a piecewise linear PID controller considering the directional characteristic between the motions and environmental loads is proposed to conserve energy of traditional linear PID controller. Then, to improve the stability during the transient process and alleviate oscillation induced by piecewise PID controller, the robust adaptive fuzzy PID controller based on the piecewise PID controller is put forward, whose stability is verified by fuzzy Lyapunov method. The proposed fuzzy output variables are designed including motions in both the horizontal and vertical planes to solve the surge–pitch coupling problem and optimize energy consumption. The time-domain simulations with a complete model of all DP components and external forces are carried out. Therein, the thruster model is improved by introducing a virtual thrust command to decrease the obvious phase lag, response delay and amplitude reduction of the traditional thruster model. In addition, the application of wave filter is discussed, especially when the wave-frequency (WF) motions are more prominent and significant than low-frequency (LF) motions. Finally, comparisons between the proposed adaptive fuzzy PID controller and traditional linear PID controller are made and analyzed. Good control effects of the proposed controllers are demonstrated with the assistance of numerical simulations with a series of control parameters.

Droop control, inertia control, and PD control are three typical frequency response (FR) strategies of grid-tied inverters interfaced renewable energy sources (RES) to restrain the power system frequency indicators, i.e., frequency deviation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \omega $ </tex-math></inline-formula> ) and the rate of change of frequency (RoCoF). Due to the highly limited inverter capacity, the FR performance in power systems with high RES penetration should be optimized. To this end, this paper first analyzes the impact of high-penetration renewable energy injection on power system frequency stability, and derives the system frequency expressions in the absence of an FR scheme, and in the presence of droop/inertia/PD controls that are representative for various virtual synchronous generator-based FR schemes. Under the same constraint of available FR capacity, control parameter ranges of these FR schemes are obtained, and their optimal conditions for restraining the maxima of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \omega $ </tex-math></inline-formula> and RoCoF are identified and compared analytically. Comparison conclusions are finally proved by the provided experiment and simulation results.

This study considers robust proportional integral derivative (PID) control for attitude stabilization of quad-rotors. The proposed method is designed for maintaining robustness against uncertainty of the system parameters and minimizing the control input for the quad-rotors. The closed-loop poles of the controlled system are placed within a region with specified decay rate and damping ratio for achieving specified transient response. The PID gains are tuned offline using theory. The robust control design problem is converted to optimization problem and solved using genetic algorithm. Finally, the proposed controller is simulated in the nominal and perturbations scenarios.

The worldwide direction moving towards sustainable energy solutions requires more advanced control mechanisms within power systems, especially in DC microgrids that combine renewable energy sources like solar panels and wind turbines with conventional power setups. This paper addresses the necessary challenge of maintaining steady and efficient DC voltage control—important for the dependability and performance of power plants. Specifically, it looks at the efficiency of four different control strategies: classic PID (Proportional-Integral-Derivative) controllers, Fuzzy Logic Controllers (FLC), Fractional Order PID (FOPID) controllers, and a new mixed system that merges Fuzzy Logic with PID controllers in a Fuzzy-PI layout. Our approach utilizes a strict comparative analysis using MATLAB Simulink simulations, assessing each controller’s capacity to manage dynamic load shifts, adjust to the unpredictability of renewable energy inputs, and preserve strong voltage stability under various operational cases. The simulations are crafted to single out the most effective control strategy to boost efficiency and toughness in microgrid operations. This study adds substantially to the progress of control strategies in hybrid energy systems, offering important insights into the creation of more complex and reliable power management solutions. By evaluating the performance of these varied controllers, we aim to underline potential upgrades in control systems that could support better energy management in intricate grid setups, thereby encouraging the wider inclusion of renewable energy technologies into power grids.

This paper proposes a novel tuning approach for robust proportional-integralderivative (PID) controller based on H ∞ loop shaping synthesis in combination with gap metric and Particle Swarm Optimization (PSO) algorithm.Different from the traditional research, the controller is designed through the search region constrained by H ∞ loop shaping synthesis and gap metric theorem.PSO algorithm is used for tuning the robust PID controller parameters based on the underlying constrained optimization problems without resolving complex arithmetical calculations.The control technique is applied for the robust controller design so as to get a low order structured controller and achieve robust performance and the ability of restraining disturbance.The simulation shows that the proposed method can character the set of all values of the controller parameters that guarantees the robust stability with any supposed accuracy and achieves favorable control performance for uncertain systems.

A robust PID and RLS controller for TCP/AQM system

The integration of a high proportion of renewable energy sources (RES) poses severe challenges to the flexibility and frequency stability of power systems. More battery storage systems (BES) are essential for supporting RES integration, with the fast frequency response (FFR) of grid-forming BES being particularly crucial for frequency stability. However, incorporating frequency dynamics into planning models is challenging due to the complexity and difficulty in model tractability. To address these issues, a two-level “Planning-Validation-Adjustment” framework is proposed for grid-forming BES planning. The system frequency response model is integrated into the conventional planning model, and a frequency-dynamics feasibility-driven Benders-cut mechanism is developed to iteratively adjust BES planning decisions based on frequency response feedback. Specifically, the upper-level planning model optimizes the allocation and sizing of grid-forming BES under RES uncertainty scenarios. In the lower level, the FFR of grid-forming BES is incorporated into robust dynamic frequency constraints to ensure safety margins under uncertain power disturbances. When frequency violations are identified in the lower-level model, corresponding Benders-cuts are generated and fed back to the upper level to update planning decisions. To efficiently solve the proposed model, a Benders-Cut-based iterative solution algorithm embedded with progressive hedging algorithm (PHA) is developed. Simulation studies on the modified IEEE 39-bus system confirm the effectiveness of the proposed planning framework and solution approach.

The advent of microgrids and increased utilization of renewable energy sources (RESs) contributed to the uncertainty of power generation in hybrid power systems (HPSs), which necessitated stringent monitoring and control of grid conditions. The large power swings in RESs cause significant deviations in frequency that can disrupt the stability of the system in case timely control actions are not initiated. Therefore, frequency control is of prime importance and has been handled by different levels of controllers in power systems. Data acquisition plays a major role in frequency control of HPSs for performing real-time control. In this context, supervisory control and data acquisition (SCADA) systems and phasor measurement units (PMUs) are studied based on their dynamic performance in real-time data acquisition. Additionally, the role of PMUs in frequency stability has been reviewed and the challenges faced in enabling PMUs for frequency control of HPSs has been presented.

The high penetration of inverter-fed renewable energy sources (RESs) in modern energy systems has led to a reduction in the system’s inertial response. This reduction in the rotational inertial response is associated with synchronous generation and might result in a deteriorated frequency response following a power disturbance. This paper investigates the frequency stability of the Kingdom of Saudi Arabia’s (KSA) grid. It includes a description of the changing energy landscape of the KSA’s electricity grid and an investigation of the impact of high penetration levels of inverter-fed RESs on the dynamic behavior of the KSA grid. The impact of RESs has been studied through a simulation of case studies of the future KSA power system using the MATLAB/Simulink simulation software. The frequency stability of the KSA’s power system has been evaluated with various RES levels under peak and base load conditions. The simulation results show that the high penetration levels of RESs dramatically affect the system’s frequency response, especially under off-peak conditions. In addition, the significance of battery energy storage systems (BESSs) for compensating the reduction in the system inertial response has been addressed. The results show the effectiveness of aggregated BESSs for enhancing the system frequency control of the KSA grid.