Lyapunov–Krasovskii based FPID controller for LFC in a time-delayed micro-grid system with fuel cell power units

Purpose In this paper, a novel Lyapunov–Krasovskii stable fuzzy proportional-integral-derivative (PID) (FPID) controller is introduced for load frequency control of a time-delayed micro-grid (MG) system that benefits from a fuel cell unit, wind turbine generator and plug-in electric vehicles. Design/methodology/approach Using the Lyapunov–Krasovskii theorem, the adaptation laws for the consequent parameters and output scaling factors of the FPID controller are developed in such a way that an upper limit (the maximum permissible value) for time delay is introduced for the stability of the closed-loop MG system. In this way, there is a stable FPID controller, the adaptive parameters of which are bounded. In the obtained adaptation laws and the way of stability analyses, there is no need to approximate the nonlinear model of the controlled system, which makes the implementation process of the proposed adaptive FPID controller much simpler. Findings It has been shown that for a different amount of time delay and intermittent resources/loads, the proposed adaptive FPID controller is able to enforce the frequency deviations to zero with better performance and a less amount of energy. In the proposed FPID controller, the increase in the amount of time delay leads to a small increase in the amount of overshoot/undershoot and settling time values, which indicate that the proposed controller is robust to the time delay changes. Originality/value Although the designed FPID controllers in the literature are very efficient in being applied to the uncertain and nonlinear systems, they suffer from stability problems. In this paper, the stability of the FPID controller has been examined in applying to the frequency control of a nonlinear input-delayed MG system. Based on the Lyapunov–Krasovskii theorem and using rigorous mathematical analyses, the stability conditions and the adaptation laws for the parameters of the FPID controller have been obtained in the presence of input delay and nonlinearities of the MG system.

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Robust LFC Strategy for Wind Integrated Time-Delay Power System Using EID Compensation

Energies ◽

10.3390/en12173223 ◽

2019 ◽

Vol 12 (17) ◽

pp. 3223 ◽

Cited By ~ 4

Author(s):

Liu ◽

Zhang ◽

Zou

Keyword(s):

Time Delay ◽

Power System ◽

Closed Loop ◽

Frequency Control ◽

Loop System ◽

Load Frequency Control ◽

System Stability ◽

Linear Matrix ◽

Closed Loop System ◽

The Stability

This paper presents an active disturbance rejection control (ADRC) technique for load frequency control of a wind integrated power system when communication delays are considered. To improve the stability of frequency control, equivalent input disturbances (EID) compensation is used to eliminate the influence of the load variation. In wind integrated power systems, two area controllers are designed to guarantee the stability of the overall closed-loop system. First, a simplified frequency response model of the wind integrated time-delay power system was established. Then the state-space model of the closed-loop system was built by employing state observers. The system stability conditions and controller parameters can be solved by some linear matrix inequalities (LMIs) forms. Finally, the case studies were tested using MATLAB/SIMULINK software and the simulation results show its robustness and effectiveness to maintain power-system stability.

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A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systems

Energies ◽

10.3390/en11123460 ◽

2018 ◽

Vol 11 (12) ◽

pp. 3460 ◽

Cited By ~ 8

Author(s):

Ashraf Khalil ◽

Ang Swee Peng

Keyword(s):

Time Delay ◽

Power Systems ◽

Control Systems ◽

Frequency Control ◽

Pi Controller ◽

Load Frequency Control ◽

New Method ◽

Load Frequency ◽

The Stability ◽

Delay Margin

Open communication is an exigent need for future power systems, where time delay is unavoidable. In order to secure the stability of the grid, the frequency must remain within its limited range which is achieved through the load frequency control. Load frequency control signals are transmitted through communication networks which induce time delays that could destabilize power systems. So, in order to guarantee stability, the delay margin should be computed. In this paper, we present a new method for calculating the delay margin in load frequency control systems. The transcendental time delay characteristics equation is transformed into a frequency dependent equation. The spectral radius was used to find the frequencies at which the root crosses the imaginary axis. The crossing frequencies were determined through the sweeping test and the binary iteration algorithm. A one-area load frequency control system was chosen as a case study. The effectiveness of the proposed method was proven through comparison with the most recent published methods. The method shows its merit with less conservativeness and less computations. The impact of the proportional integral (PI) controller gains on the delay margin was investigated. It was found that increasing the PI controller gains reduces the delay margin.

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The effects on stability region of the fractional-order PI controller for one-area time-delayed load–frequency control systems

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331216642839 ◽

2016 ◽

Vol 39 (10) ◽

pp. 1509-1521 ◽

Cited By ~ 16

Author(s):

Vedat Çelik ◽

Mahmut Temel Özdemir ◽

Gökay Bayrak

Keyword(s):

Time Delay ◽

Control Systems ◽

Fractional Order ◽

Stability Region ◽

Fractional Integral ◽

Frequency Control ◽

Pi Controller ◽

Load Frequency Control ◽

Fractional Order Pi Controller ◽

The Stability

One of the controllers used in load–frequency control systems is the PI controller, taking account of time delay originating from measurement and communication. In control systems, along with the use of the fractional-order controller, computing parameter space exhibited stable behaviour on the controller parameters and analysing its efficiency have become a significant issue. This study focuses on computing the effects of the fractional integral order ( α) on the stable parameter space for the control of a one-area delayed load–frequency control system in the case of a fractional-order PI controller. The effect of time delay on the stable parameter space is also investigated at different fractional integral orders ( α) in the time-delayed system with fractional-order PI controller. For this purpose, a characteristic equation of the delayed system with the fractional-order PI controller is obtained, and the stable parameter spaces of the controller are computed according to the fractional integral order ( α) and time delay ( τ) values using the stability boundary locus method, which is graphics based. Moreover, the generalized modified Mikhailov criterion is used for testing the stability region on the Kp − Ki plane. The obtained results verified that the stability region on the Kp − Ki plane change depending on the α and τ.

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A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systems

10.20944/preprints201810.0146.v1 ◽

2018 ◽

Author(s):

Ashraf Khalil ◽

Ang Swee Ping

Keyword(s):

Time Delay ◽

Control Systems ◽

Frequency Control ◽

Pi Controller ◽

Load Frequency Control ◽

New Method ◽

Open Communication ◽

Load Frequency ◽

The Stability ◽

Delay Margin

The open communication is an exigent need for future power system where the time delay is unavoidable. In order to secure the stability of the grid, the frequency must remain within its limited range which is achieved through the load frequency control. The load frequency control signals are transmitted through communication networks which induces time delay that could destabilize the power systems. So, in order to guarantee the stability the delay margin should be computed. In this paper, we present a new method for calculating the delay margin in load frequency control systems. The transcendental time delay characteristics equation is transformed to frequency dependant equation. The spectral radius is used to find the frequencies at which the roots crosses the imaginary axis. The crossing frequencies are determined through the sweeping test and the binary iteration algorithm. A one-area load frequency control system is chosen as case study. The effectiveness of the proposed method has been proved through comparing with the most recent published methods. The method shows its merit with less conservativeness and less computations. The PI controller gains are preferable to be chosen large to reduce the damping, however, the delay margin decreases with increasing the PI controller gains.

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MVO optimized hybrid FOFPID-LQG controller for load frequency control of an AC micro-grid system

World Journal of Engineering ◽

10.1108/wje-05-2019-0142 ◽

2020 ◽

Vol 17 (5) ◽

pp. 675-686

Author(s):

Sonalika Mishra ◽

Suchismita Patel ◽

Ramesh Chandra Prusty ◽

Sidhartha Panda

Keyword(s):

Energy Storage ◽

Frequency Control ◽

Renewable Energy Sources ◽

Storage System ◽

Energy Storage System ◽

Load Frequency Control ◽

Fuzzy Pid ◽

Content Type ◽

Load Frequency ◽

Micro Grid

Purpose This paper aims to implement a maiden methodology for load frequency control of an AC multi micro-grid (MG) by using hybrid fractional order fuzzy PID (FOFPID) controller and linear quadratic Gaussian (LQG). Design/methodology/approach The multi MG system considered is consisting of photovoltaic, wind turbine and a synchronous generator. Different energy storage devices i.e. battery energy storage system and flywheel energy storage system are also integrated to the system. The renewable energy sources suffer from uncertainty and fluctuation from their nominal values, which results in fluctuation of system frequency. Inspired by this difficulty in MG control, this research paper proposes a hybridized FOFPID and LQG controller under random and stochastic environments. Again to confer viability of proposed controller its performances are compared with PID, fuzzy PID and fuzzy PID-LQG controllers. A comparative study among all implemented techniques i.e. proposed multi-verse optimization (MVO) algorithm, particle swarm optimization and genetic algorithm has been done to justify the supremacy of MVO algorithm. To check the robustness of the controller sensitivity analysis is done. Findings The merged concept of fractional calculus and state feedback theory is found to be efficient. The designed controller is found to be capable of rejecting the effect of disturbances present in the system. Originality/value From the study, the authors observed that the proposed hybrid FOPID and LQG controller is robust hence, there is no need to reset the controller parameters with a large change in network parameters.

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