Event-Triggered Adaptive Integral Higher-Order Sliding Mode Control for Load Frequency Problems in Multi-area Power Systems

  • Ark Dev
  • Mrinal Kanti SarkarEmail author
  • Pankhuri Asthana
  • Daijiry Narzary
Research Paper


The study proposes a method to design continuous-time event-triggered adaptive integral higher-order sliding mode control for load frequency problems in multi-area power system under load disturbances and parameter uncertainties. Event-triggered strategy reduces the communication burden and lowers the control updating frequency while ensuring high-performance system stability. Event-triggered integral higher-order sliding mode control is used to attain need-based chattering-free control signal compared to event-triggered integral sliding mode control which assures its easy practical implementation. Adaptive estimation of switching gain is used with higher-order integral sliding mode control that eliminates the need of prior knowledge about the system uncertainties. Nonlinear uncertainties in power system like generation rate constraints (GRC) and governor deadband lead to load disturbance that results in deviation of frequency from its nominal value. Robustness of the controller is tested for plant considered with such nonlinearities. System performance without GRC is better; however, proposed controller still ensures finite time convergence of change in frequency under GRC and governor deadband. Proposed controller also guarantees finite time convergence of change in frequency under random varying load disturbances. We have also integrated renewable energy resources in the system and tried to handle relevant output power uncertainty in load frequency problem.


Load frequency control Sliding mode control Higher-order sliding mode control Robust control Event-triggered sliding mode control Multi-area power system 

List of symbols

\(\Delta f_{n} (t)\)

Incremental frequency deviation

\(\Delta P_{{g_{n} }} (t)\)

Incremental change in power output

\(\Delta X_{{g_{n} }} (t)\)

Incremental change in governor valve position

\(\Delta E_{n} (t)\)

Incremental change in integral control

\(\Delta \delta_{n} (t)\)

Incremental change in rotor angle deviation

\(x_{n} (t)\)

State vector of nth area

\(x_{m} (t)\)

Neighbouring state vector of \(x_{n} (t)\)

\(T_{{G_{n} }}\)

nth governor time constant

\(T_{{T_{n} }}\)

nth turbine time constant

\(T_{{P_{n} }}\)

nth subsystem model time constant

\(K_{{P_{n} }}\)

nth subsystem gain

\(K_{{E_{n} }}\)

nth subsystem integral control gain

\(K_{{B_{n} }}\)

nth subsystem frequency biasing factor


nth speed regulation coefficient


Interconnection gain between area n and m

\(\Delta P_{{d_{n} }} (t)\)

Load disturbance for the nth system

\(u_{n} (t)\)

Input control signal

\(\left\| . \right\|\)

Matrix norm


Network control system


Variable structure control


Load frequency control


Sliding mode control


Discrete-time siding mode control


Quasi sliding mode control


Event triggering


Integral sliding mode control


Integral higher-order sliding mode control


Adaptive integral higher-order sliding mode control


Generation rate constraints


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  • Ark Dev
    • 1
  • Mrinal Kanti Sarkar
    • 1
    Email author
  • Pankhuri Asthana
    • 1
  • Daijiry Narzary
    • 1
  1. 1.Department of Electrical EngineeringNational Institute of Technology ManipurImphalIndia

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