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

- 71 Downloads

## Abstract

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.

## Keywords

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

*n*th area- \(x_{m} (t)\)
Neighbouring state vector of \(x_{n} (t)\)

- \(T_{{G_{n} }}\)
*n*th governor time constant- \(T_{{T_{n} }}\)
*n*th turbine time constant- \(T_{{P_{n} }}\)
*n*th subsystem model time constant- \(K_{{P_{n} }}\)
*n*th subsystem gain- \(K_{{E_{n} }}\)
*n*th subsystem integral control gain- \(K_{{B_{n} }}\)
*n*th subsystem frequency biasing factor- \(R_{n}\)
*n*th speed regulation coefficient- \(K_{snm}\)
Interconnection gain between area

*n*and*m*- \(\Delta P_{{d_{n} }} (t)\)
Load disturbance for the

*n*th system- \(u_{n} (t)\)
Input control signal

- \(\left\| . \right\|\)
Matrix norm

- NCS
Network control system

- VSC
Variable structure control

- LFC
Load frequency control

- SMC
Sliding mode control

- DTSMC
Discrete-time siding mode control

- QSMC
Quasi sliding mode control

- ET
Event triggering

- ISMC
Integral sliding mode control

- IHOSMC
Integral higher-order sliding mode control

- AIHOSMC
Adaptive integral higher-order sliding mode control

- GRC
Generation rate constraints

## References

- Aditya SK, Das D (2003) Design of load frequency controllers using genetic algorithm for two areas inter connected hydropower system. Electr Power Compon Syst 31(1):81–94Google Scholar
- Bandyopadhyay B, Fulwani D, Kim KS (2009) Sliding mode control using novel sliding surfaces. Lecture notes in control and information science. Springer, BerlinGoogle Scholar
- Bartoszewicz A (1998) Discrete-time quasi-sliding mode control strategies. IEEE Trans Ind Electron 45(4):637–663Google Scholar
- Behera AK, Bandyopadhyay B (2015) Event based sliding mode control with quantized measurement. In: International workshop on recent advances in sliding modes (RASM)Google Scholar
- Behera AK, Bandyopadhyay B (2016) Event-triggered sliding mode control for a class of nonlinear systems. Int J Control 89(9):1916–1931MathSciNetzbMATHGoogle Scholar
- Bevrani H, Daneshfar F, Daneshmand R (2010) Intelligent power system frequency regulation concerning the integration of wind power units. In: Wang L et al (eds) Wind power system. Springer, Berlin, pp 407–437Google Scholar
- Chaturvedi DK, Satsangi PS, Kalra PK (1999) Load frequency control, a generalized neural network approach. Electr Power Energy Syst 21(6):405–415Google Scholar
- Concordia C, Kirchmayer LK (1953) Tie line power and frequency control of electric power systems. Am Inst Electr Eng Trans 72(2):562–572Google Scholar
- Cucuzzella M, Incremona GP, Ferrara A (2016) Event-triggered sliding mode control algorithms for a class of uncertain nonlinear systems: experimental assessment. In: American control conference (ACC)Google Scholar
- Fosha CE, Elgerd OI (1970) The megawatt frequency control problem: a new approach via optimal control theory. IEEE Trans Power Appar Syst 89(4):556–563Google Scholar
- Ghoshal SP (2003) Multi area frequency and tie line power flow control with fuzzy logic based integral gain scheduling. J Inst Eng 84(3):135–141Google Scholar
- Gracia JPF, Ribeiro JMS, Silva JJF, Martins ES (2005) Continuous-time and discrete-time sliding mode control accomplished using a computer. IEE Proc Control Theory Appl 152(2):220–228Google Scholar
- Hasan AY, Kalfan AL-K, Mohammed HA, Hosseinzadeh N (2014) Load frequency control of a multi-area power system: an adaptive fuzzy logic approach. IEEE Trans Power Syst 29(4):1822–1830Google Scholar
- Indulkar CS, Raj B (1995) Application of fuzzy controller to automatic generation control. Electr Mach Power Syst 23(2):209–220Google Scholar
- Juang CF, Lu CF (2006) Load–frequency control by hybrid evolutionary fuzzy PI controller. IEE Proc Gener Transm Distrib 153(2):196–204Google Scholar
- Khodabakhshian A, Edrisi M (2008) A new robust PID load frequency controller. Control Eng Pract 16(9):1069–1080Google Scholar
- Kumari K, Bandyopadhyay B, Behera AK, Reger J (2016) Event-triggered sliding mode control for delta operator systems. In: IECON 42nd annual conference of the IEEE industrial electronics societyGoogle Scholar
- Kuo G, Markham P, Hadley S, King T, Liu Y (2015) Impact of governor deadband on frequency response of the U.S. eastern interconnection. IEEE Trans Smart Grid 07(3):1368–1377Google Scholar
- Lee DJ, Li W (2008) Small signal stability analysis of an autonomous hybrid renewable energy power generation/energy storage system part I: time domain simulation. IEEE Trans Energy Convers 23(1):311–320Google Scholar
- Lee KA, Yee H, Teo CY (1991) Self-tuning algorithm for automatic generation control in an interconnected power system. Electr Power Syst Res 20(2):157–165Google Scholar
- Lim KY, Wang Y, Zhou R (1996) Robust decentralized load-frequency Control of multi-area power systems. Proc Inst Electr Eng Gener Transm Distrib 143(5):377–386Google Scholar
- Mi Y, Fu Y, Wang C (2013) Decentralized sliding mode load frequency control for multi-area power systems. IEEE Trans Power Syst 28(4):4301–4309Google Scholar
- Milan C (1972) Linear regulator design for a load and frequency control. IEEE Trans Power Appar Syst 91(6):271–2285Google Scholar
- Mondal S, Mahanta C (2011) Nonlinear sliding surface based second order sliding mode controller for uncertain linear systems. Commun Nonlinear Sci Numer Simul 16(9):3760–3769MathSciNetzbMATHGoogle Scholar
- Mondal S, Mahanta C (2012) Adaptive second-order sliding mode controller for a twin rotor multi-input–multi-output system. IET Control Theory Appl 6(14):2157–2167MathSciNetGoogle Scholar
- Mondal S, Mahanta C (2013) Adaptive integral higher order sliding mode controller for uncertain systems. J Control Theory Appl 11(1):61–68MathSciNetzbMATHGoogle Scholar
- Pan CT, Liaw CM (1989) An adaptive controller for power system and load frequency control. IEEE Trans Power Syst 4(1):122–128Google Scholar
- Prasad S, Purwar S, Kishor N (2017) Non-Linear sliding mode load frequency control in multi area power systems. Control Eng Pract 61:81–92Google Scholar
- Qu S, Xia X, Zhang J (2014) Dynamics of discrete-time sliding-mode-control of uncertain systems with a disturbance compensator. IEEE Trans Ind Electron 61(7):3502–3510Google Scholar
- Ray G, Dey S, Bhattacharyya TK (2004) Multi-area load frequency control of power systems: a decentralized variable structure approach. Electr Power Compon Syst 33(3):315–331Google Scholar
- Sheirah MA, Abid-Ei-Fattah MM (1983) Improved load frequency self-tuning regulator. Int J Control 39(1):143–158zbMATHGoogle Scholar
- Su X, Liu X, Song YD (2017) Event-triggered sliding mode control for multi-area power systems. IEEE Trans Ind Electron 64(8):6741–7632Google Scholar
- Tavakoli MR, Khodabakhshian A, Hooshmand R (2012) A robust PI based LFC design using BF-NM algorithm. In: Proceedings of CCECE Conference, CanadaGoogle Scholar
- Van Ness JE (1963) Root loci of load frequency control systems. IEEE Trans Power Appar Syst 82(5):712–726Google Scholar
- Vrdoljak K, Petrovic I, Peric N (2009) Discrete-time sliding mode control of load frequency in power systems with input delay. In: 12th international power electronics and motion control conferenceGoogle Scholar
- Wen S, Yu X, Zeng Z, Wang J (2015) Event-triggering load frequency control for multi-area power system with communication delays. IEEE Trans Ind Electron 63(2):1308–1317Google Scholar