Two-area System Research Articles

Towards non-virtual inertia control of renewable energy for frequency regulation: Modeling, analysis and new control scheme

Currently, when renewable generation participates in frequency regulation, the traditional control method is to emulate synchronous generators through virtual inertia control. However, virtual inertia has a time delay, so essentially, it is a fast power response. Meanwhile, virtual inertia control is likely to be affected by frequency fluctuation since it responds to the derivative of frequency. Hence, it’s worth exploring non-virtual inertia control for renewable energy when participating in frequency regulation. For this reason, a novel two-segment droop control scheme for renewable energy frequency regulation is proposed in this research. Firstly, the extended system frequency regulation (SFR) model, which contains virtual inertia with time delay, is built and analytically solved by order decrement based on the Routh approximation method. Afterwards, according to the analytical solution, time delay affects the frequency response of renewable energy. It can also be analytically proved that the non-virtual inertia control, e.g., sole droop control, could replace virtual inertia under the same frequency deviation. Still, more energy may be needed for frequency regulation. Furthermore, a novel two-segment droop control is presented, and to analytically prove its ability to replace virtual inertia, the impulse function balancing principle and the integration by parts algorithm were adopted to address the initial conditions of the differential equation. Based on the analytical expression, it can be analytically proved that a lower frequency deviation can be obtained under the same frequency regulation energy. Accordingly, a parameter-setting method for two-segment droop control was proposed. Finally, the effectiveness of the proposed method is verified by using a two-area system frequency response model, and the results reveal that it can be used to replace virtual inertia and has better performance.

Takagi-Sugeno fuzzy gain controller for Vehicle-to-Grid (V2G) load frequency control

Load Frequency Control (LFC) has gained more importance with the introduction of deregulated Renewable Energy Sources (RES) connectivity with the grid. Electrical Vehicles (EVs) can feed electricity back into the grid in Vehicle-to-Grid (V2G) mode to maintain stability. However, the increasing number of EVs penetrating the grid causes frequency instability in the power system. If required, EVs may utilize bi-directional chargers to transfer power back to the grid in the V2G mode while they are charging or in a grid-connected state, restoring the frequency instability of the grid. The frequency restoration response time is important to reset the grid frequency fluctuations in the shortest time possible to avoid shutting down the power system. This paper presents a Takagi-Sugeno (T-S) fuzzy linear output controller for LFC in two-area systems with tie-line control. This work models EV batteries as a single lump of large-capacity battery energy storage systems. The EV's battery system provides ancillary power to the two-area power system to reset it to a steady state after a load disturbance. The T-S fuzzy controller's linear output dependency on its inputs enables it to respond efficiently to load variations in the nonlinear two-area power systems. The proposed controller parameters are evaluated from stability analyses and its robustness is tested with sensitivity analysis. It is compared with other fuzzy controllers, and it demonstrates a fast-settling time and reduced frequency deviation response.

Spider Wasp Optimizer-Optimized Cascaded Fractional-Order Controller for Load Frequency Control in a Photovoltaic-Integrated Two-Area System

The integration of photovoltaic (PV) systems into traditional power grids introduces significant challenges in maintaining system stability, particularly in multi-area power systems. This study proposes a novel approach to load frequency control (LFC) in a two-area power system, where one area is powered by a PV grid and the other by a thermal generator. To enhance system performance, a cascaded control strategy combining a fractional-order proportional–integral (FOPI) controller and a proportional–derivative with filter (PDN) controller, FOPI(1+PDN), is introduced. The controller parameters are optimized using the spider wasp optimizer (SWO). Extensive simulations are conducted to validate the effectiveness of the SWO-tuned FOPI(1+PDN) controller. The proposed method demonstrates superior performance in reducing frequency deviations and tie-line power fluctuations under various disturbances. The results are compared against other advanced optimization algorithms, each applied to the FOPI(1+PDN) controller. Additionally, this study benchmarks the SWO-tuned controller against recently reported control strategies that were optimized using different algorithms. The SWO-tuned FOPI(1+PDN) controller demonstrates superior performance in terms of faster response, reduced overshoot and undershoot, and better error minimization.

Impact of the Exciter and Governor Parameters on Forced Oscillations

In recent years, the frequency of forced oscillation events due to control system malfunctions or improper parameter settings has increased. Tuning the parameters of exciters and governor models is crucial for maintaining power system stability. Traditional simulation studies typically involve small transient disturbances or step changes to find optimal parameter sets, but existing optimization algorithms often fall short in fine-tuning for forced oscillations. Identifying the sensitive parameters within these control models is essential for ensuring stability during large, sustained disturbances. This study focuses on identifying these critical exciter and governor model parameters by analyzing their influence on sustained forced oscillations. Using Kundur’s two-area system, we analyze common exciter models such as SCRX, ESST1A, and AC7B, along with governor models like GAST, HYGOV, and GGOV1, utilizing PSS®E software version 34. Sustained forced oscillations are injected at generator-1 of area-1, with individual parameter changes dynamically simulated. By considering a local oscillation frequency of 1.4 Hz and an inter-area oscillation mode of 0.25 Hz, we analyze the impact of each parameter change on the magnitude and frequency of forced oscillations as well as on active and reactive power outputs. This novel approach highlights the most influential parameters of each tested model—such as exciter, governor, and turbine gains, as well as time constant parameters—on the impact of forced oscillations. Based on our findings, the sensitive parameters of each tested model are ranked. These would provide valuable insights for industry operators to fine-tune control settings during oscillation events, ultimately enhancing system stability.

Development of an equivalent system frequency response model based on aggregation of distributed energy storage systems

Energy storage systems (ESSs) installed in distribution networks have been widely adopted for frequency regulation services due to their rapid response and flexibility. Unlike existing ESS design methods which focus on control strategies, this paper proposes a new method based on an ESS equivalent aggregated model (EAM) for calculating the capacity and the droop of an ESS to maintain the system frequency nadir and quasi-steady state frequency using low-order functions. The proposed method 1) uses first-order functions to describe the frequency response (FR) of synchronous generators (SGs); 2) ignores the control strategies of SGs, making the method systematic and allowing it to avoid analyzing complex high-order functions; and 3) is suitable for low inertia systems. The applicability and accuracy of the method is demonstrated using a modified four-generator two-area (4G2A) system.

Application of Robust Super Twisting to Load Frequency Control of a Two-Area System Comprising Renewable Energy Resources

The main concern of the present article is to design a robust load frequency control for a two-area power system (TAPS) comprising renewable energy resources. Three different controllers are suggested. The first is based on a robust super twisting (ST) technique, which is an enhanced approach of the sliding mode control and is considered to be one of the most excellent control techniques. The second and the third are based on two recent metaheuristic techniques, namely the one-to-one based optimizer (OOBO) and hippopotamus optimizer (HO). The studied TAPS contains different energy resources, such as solar thermal, photovoltaic, wind energy, hydropower and energy storage in addition to other conventional sources. The OOBO and HO are used to determine the parameters of PI controllers, and the objective function is to minimize the integral square error of frequency and tie line power. The obtained results verify the high performance of the suggested three controllers with superiority to ST because of its intrinsic capability to cope with parameter changes.

Capacitor virtual inertia control and equivalent inertia analysis for a grid-forming wind generation system

A grid-forming wind generation system exhibits exceptional grid frequency support abilities. The DC capacitor of the grid-forming wind generation system, which is characterized by rapid response and high sensitivity to minor disturbances, can provide short-term inertia support for the power system. This paper proposes the capacitor virtual inertia control for the grid-forming wind generation system, coupling the DC capacitor voltage with the power system frequency, which enables the DC capacitor to participate in the system frequency response process and reduces the rate of change of the system frequency during the disturbance. To analyze the inertia of the wind power generation system, this paper establishes an equivalent Philips–Heffron model for the grid-forming wind generation system and uses the equivalent inertia constant to quantify the inertia of the wind power generation system. The effectiveness of the proposed control strategy and the reasonableness of the inertia assessment method are verified through simulations in the single-turbine system and the IEEE four-machine two-area system.

Synchronous and non synchronous delay-dependent robust wide-area controllers for power system

Wide-area control is highly efficacious for maintaining sufficient damping of the low-frequency oscillations in the power system. The Wide-Area Measurement System (WAMS) provides wide-area signals to the control site through a communication channel. Even though the wide-area signal improved the dynamic behavior of the power system, a time delay usually exists during the transmission, which is unavoidable. The damping performance of the power system is degraded due to the time delay. In this paper, synchronized and non-synchronized feedback configurations are considered, and the time delay margin is calculated. The Lyapunov theory is adopted for investigating the synchronous and non-synchronous delay-dependent stability criteria for the power system. A lead–lag and a robust H∞ wide-area damping controller (WADC) are proposed to measure the delay margin for synchronized and non-synchronized delay feedback. The relationship between the damping performance and the delay margin is established. It is observed that a non-synchronous feedback-based controller can endure a larger time delay variation than a synchronous feedback-based controller. The nonlinear simulation is carried out to verify the effectiveness of the proposed controllers in Kundur’s two-area system and the IEEE-39 bus test system.

Improving The Dynamic Performance of Two-area System Based Integration of RES

Improving The Dynamic Performance of Two-area System Based Integration of RES

A Proportional-Integral-One Plus Double Derivative Controller-Based Fractional-Order Kepler Optimizer for Frequency Stability in Multi-Area Power Systems with Wind Integration

This study proposes an enhanced Kepler Optimization (EKO) algorithm, incorporating fractional-order components to develop a Proportional-Integral-First-Order Double Derivative (PI–(1+DD)) controller for frequency stability control in multi-area power systems with wind power integration. The fractional-order element facilitates efficient information and past experience sharing among participants, hence increasing the search efficiency of the EKO algorithm. Furthermore, a local escaping approach is included to improve the search process for avoiding local optimization. Applications were performed through comparisons with the 2020 IEEE Congress on Evolutionary Computation (CEC 2020) benchmark tests and applications in a two-area system, including thermal and wind power. In this regard, comparisons were implemented considering three different controllers of PI, PID, and PI–(1+DD) designs. The simulations show that the EKO algorithm demonstrates superior performance in optimizing load frequency control (LFC), significantly improving the stability of power systems with renewable energy systems (RES) integration.

A Comparative Study of Load Frequency Regulation for Multi-Area Interconnected Grids Using Integral Controller

The present paper provides an optimal design for load frequency control (LFC) in the interconnected power system. To obtain an adequate LFC response alongside shortening implementation time and minimizing costs, an integral (I) controller is used. A deep analysis of the I controller-based LFC is presented. At first, a two-area interconnected power system is used, and to enhance the LFC response, the I controller and frequency bias parameters are optimized using three novel optimization algorithms, which are the incomprehensible but intelligible-in-time logic algorithm (ILA), the coati optimization algorithm (COA), and the brown-bear optimization algorithm (BOA). Also, five well-known techniques, namely, particle swarm optimization (PSO), genetic algorithm (GA), simulated annealing (SA), pattern search (PS), and nonlinear programming (NP), are used. A new objective function utilizing the integral of squared error (ISE), settling time, settling-max, and settling-min of the dynamic response is used to increase the efficacy of estimating the parameters. The presented results in this paper showed that the optimized I controller outperforms the classic I controller. After considering a load change in one area by 18.75%, the optimized I controller achieved the lowest ISE values. ISE values were: 0.00582, 0.00179, 0.00176, 0.00178, 0.00321, 0.00304, 0.00179, 0.00185, and 0.00181, for classic I, PSO-I, GA-I, SA-I, PS-I, NP-I, ILA-I, COA-I, and BOA-I. Then, the proposed method is applied to a nonlinear two-area system, demonstrating that the proposed strategies can deal with nonlinearity. As the purpose of the hybrid power system is to create a robust energy infrastructure that adheres to sustainability standards, the proposed algorithms are analyzed in a three-area multi-source power system comprising renewable energy sources (RESs) such as photovoltaic (PV) and wind turbine (WT), a battery energy storage system (BESS), and an electric vehicle (EV).

Damping Characteristics Improvement of Wind-PV Hybrid System by Coordinated Optimization of SVC-POD Controller Parameters

Background: With the increasing penetration of new energy resources such as wind farms and photovoltaic power plants, there is concern about the stability of power systems. Methods: Aiming at the low-frequency oscillation issue of the wind-PV hybrid system, a coordinated optimal design strategy based on Static Var Compensator (SVC) and Power Oscillation Damping (POD) control is proposed. Modal analysis is used to locate the controller, then the Whale Optimization Algorithm (WOA) is introduced to optimize the SVC-POD controller parameters. To solve the wind-PV hybrid energy system's low frequency oscillation issues, the damping ratio and angular velocity of the generator rotor are considered in the objective function. Results: Taking IEEE four-machine two-area system as an example, several working conditions are designed, including changing the power of the contact line. The eigenvalue analysis and simulation findings verify that the suggested proposed method can successfully raise the damping ratio of the system, keep the generator speed stable, and restrain the occurrence of low-frequency oscillation. Conclusion: Simulation results demonstrate that this method efficiently suppresses the lowfrequency oscillation and increases the robustness of the system.

Multi-segment droop control and optimal parameter setting strategy of wind turbine for frequency regulation

Traditionally, virtual inertia is used as the control strategy for wind turbines when participating in frequency regulation. However, it has inherent defects in measurement error amplification due to the frequency differential. Also, when control delay of wind turbines is taken into consideration, virtual inertia is essentially a fast power response, just the same as droop control. Hence, considering the adaptability of droop control, it is valuable to explore a novel droop control method without virtual inertia, as the frequency response model of wind turbines. For this reason, a multi-segment droop control strategy is proposed to provide a reliable frequency regulation model for wind turbines that can be broadly applied to other inverter-based power sources. Firstly, based on the extended system frequency response model, a differential equation including piecewise time-varying coefficients is established, and the analytical expression of the frequency response is obtained using the impulse function balancing principle and the integration by parts algorithm. Subsequently, based on analytical expression, the performance of the presented strategy is theoretically analyzed via comparison with virtual inertia control, and the conclusion that the presented multi-segment droop control has better frequency regulation performance can be got. Furthermore, to achieve optimal frequency regulation performance, a Lagrangian function is established to determine the optimal parameters of the proposed control strategy. Finally, the performance of the proposed strategy was verified in a two-area system model constructed on MATLAB/Simulink. Results show that the proposed multi-segment droop control has better frequency regulation performance.

A hybrid optimization algorithm for improving load frequency control in interconnected power systems

The objective of this study is to develop an algorithm named Modified Artificial Bee Colony and Particle Swarm Optimization (MHABC-PSO) to address load frequency control (LFC) challenges in a two-area interconnected power system. The proposed MHABC-PSO algorithm is designed with two key modifications to enhance global exploration capability and improve convergence speed. Hence, a decision block is introduced in the employed bee (EB) phase incorporating a control parameter “limit” to allow each candidate solution (CS) to explore itself up to the “limit” value and boost local exploration. In addition, an introduction of a novel selection mechanism utilizing heuristic information (η) in EBs phase guides the onlooker bee (OB) phase to select better solutions based on success and failure history, thus promoting exploitation and reducing biased exploration. To address the efficacy of the proposed algorithm at the system level, three different two-area power systems are studied, incorporating various complexities, linearity, and non-linearity such as thermal-hydro, reheat thermal, and thermal-hydro-gas turbine configurations with HVDC link, SSSC, and CES. The algorithm is applied to optimize four objective functions (i.e. ITAE, IAE, ISAE, and ITE). The fitness function maximizes controller gains by utilizing the integral time multiplied absolute error (ITAE). Other objective functions like IAE, ISAE, and ITE are employed for a comprehensive analysis. Evaluation of MHABC-PSO effectiveness is conducted through ITAE values, peak deviations, and settling times of frequency and power deviations in different two-area systems. Results demonstrate that MHABC-PSO settles the system more quickly with zero steady-state error under step load perturbations (SLPs) of 1% and 2%. Comparative analysis with ABC, PSO, SFLA-TLBO, and OHABC-PSO using ITAE index and controller settling times shows the superiority of MHABC-PSO for LFC analysis. In conclusion, the proposed MHABC-PSO algorithm proves to be an efficient and effective solution for LFC, outperforming other algorithms in terms of the specified objective functions and exhibiting rapid convergence and optimal gains for controllers, effectively addressing LFC issues by combining exploration and exploitation techniques.

Frequency Security Control Technology for Simulated Wind Storage Integrated Power Grid

Electronic control strategies are pivotal in the evolution of power systems, which have higher requirements for power leveling and optimization, frequency safety, and frequency stability. In contrast, the core objectives of existing energy storage services are mostly limited to one function, which cannot fully meet the operational requirements of power systems. This paper presents research on a frequency security controller based on digital twin technology and aimed to enhance the safety of the system. The proposed controller can simultaneously smooth out active wind power fluctuations and optimize reactive power, participate in system frequency regulation, and improve system damping to damp low-frequency oscillations based on simulating the actual operating environment. Simulations also verify the effectiveness of the proposed controller in DIgSILENT/PowerFactory based on a two-area system. This active/reactive power-based system support service will bring new economic benefits to wind energy storage systems.

A multi-purpose battery energy storage system using digital twin technology

This paper presents a concept of multi-purpose Battery Energy Storage System (BESS) which is integrated into a large wind farm (WF). The BESS aims to suppress the fluctuation of the output of active power and reactive power of the wind farm WF, participate in frequency regulation and damp low-frequency oscillations. Firstly, the concept and structure of the multi-purpose of BESS is presented. After that, the digital twin technology is applied to configure the capacity of the BESS. The performance of the multi-purpose BESS is demonstrated in the two-area system model constructed using DIgSILENT PowerFactory. The simulation results show that the multi-purpose BESS significantly improves the stability of the system in terms of suppressing the fluctuation of the out of WF, frequency regulation and damping low-frequency oscillations, which is the essential step to the practical implementation of the multi-purpose BESS.

Performance comparison of dynamically controlled particle swarm optimization and grey wolf optimizer for dynamic power reserve scheduling in multi areas problems

The primary goal of Multi-Area Economic Dispatch (MAED) is to effectively meet the dynamic power demands of multiple interconnected regions while optimizing the economical generation dispatch strategy. This paper introduces a comprehensive investigation into the application of two advanced optimization techniques, namely Dynamically Controlled Particle Swarm Optimization (DCPSO) and thereafter Grey Wolf Optimizer (GWO), and their variant adaptations to address the complex challenges posed by MAED issue. The performance and efficacy of these strategies are rigorously assessed in three distinct scenarios: (a) Single-Area Power System with Three Generation Units: This scenario represents a fundamental single-area power network comprising three generation units. (b) Two-Area System with Four Generating Units: In this case, a two-area system with four generating units is analyzed. (c) Four-Area System with Forty Generation Units and Six Tie Lines. In the most intricate scenario, a four-area interconnected power system is scrutinized, featuring a total of forty generation units. GWO technique produces the cost saving of $ 0.1 for single area, 2 area cost saving is $ 0.11 likewise for 4 area the cost saving is $ 474.10 over the PSO. The execution time taken by GWO is 12.7 sec. less compared to DPSO.

Discrete-Time Port-Hamiltonian Systems for Power and Energy Applications

The Port-Hamiltonian formalism has demonstrated to be useful in different applications, allowing to explore structural properties to obtain stable controls. A common approach is to design controls in a continuous domain although, in practice, they are implemented in discrete time. However, the study of discrete-time port-Hamiltonian systems is challenging since the system may lose structural properties such as passivity after discretization. This paper shows that passivity is conserved for the backward Euler discretization method when the Hamiltonian is convex, and its gradient is Lipschitz. This result is relevant for power systems applications such as the control of two-area systems, high-voltage direct-current transmission, and microgrids. Although our method is simple and preserves passivity, it does not preserve the symplectic structure of the hamiltonian.

Frequency and voltage stability of multi microgrid system using 2-DOF TIDF FUZZY controller

ABSTRACT Two parameters, voltage and frequency, are required for smooth delivery of quality power to consumer. Therefore, in this paper enhancement of frequency and voltage stability of multi microgrid system with a proposed hybrid fuzzy logic controller with two-degree of freedom tilt-integral derivative with filter (2DOFTIDFFUZZY) are analyzed. A novel algorithm known as artificial electric field algorithm (AEFA) technique is employed to obtain optimal controller parameters. Firstly, a two-area system widely used in literature is considered for proper comparison. Efficacy of 2DOFTIDFFUZZY controller is confirmed by comparing it with different controllers for the same system. Further, a multi microgrid system is considered for unified voltage-frequency control. Automatic Voltage Regulator (AVR) effect states a substantial improvement in system dynamics with the proposed controller. Under different unfavorable conditions like source and load variation, dynamic system performances are studied to enlighten robustness of proposed controller. Simulation results elucidate that proposed 2DOFTIDFFUZZY controller optimized with AEFA technique can achieve better system stability in case of any vulnerability.

Unlocking inter-regional flexibility for the HVDC-connected two-area system with a multistage model

In recent years, the deployment of high-voltage direct current (HVDC) tie-lines in power grids has become a prevalent solution in some countries to transmit renewable energy from remote locations to load centers. However, the variability and uncertainty associated with renewable energy generation pose challenges to effectively utilizing this technology. This work proposes a novel multistage planning-operation model, aiming to unlock the potential flexibility in the HVDC transmission system and increase the renewable penetration. By incorporating flexibility, which is essential for accommodating the uncertainty in renewable generation, our model optimally shares the inter-regional flexibility between the sending- and receiving-end grids. One of the key features of our proposed model is its robustness and non-anticipativity, meaning it can account for different levels of uncertainty and make decisions that are suitable for multiple scenarios. This work develops two solution approaches to solve this challenging multistage model with variable uncertainty sets. We validate the proposed approach through a case study conducted on a real-world inter-regional grid. The numerical results demonstrate that our approach effectively unlocks more inter-regional flexibility and assists in increasing the renewable hosting capacity.