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(1 + PD)-PID cascade controller design for performance betterment of load frequency control in diverse electric power systems

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Abstract

In our world of today developing incredibly fast, load frequency control (LFC) is an indispensable and vital element in increasing the standard of living of a country by providing a good quality of electric power. To this end, rapid and notable development has been recorded in LFC area. However, researchers worldwide need for the existence of not only effective but also computationally inexpensive control algorithm considering the limitations and difficulties in practice. Hence, this paper deals with the introduction of (1 + PD)-PID cascade controller to the relevant field. The controller is simple to implement and it connects the output of 1 + PD controller with the input of PID controller where the frequency and tie-line power deviation are applied to the latter controller as feedback signals also, which is the first attempt made in the literature. To discover the most optimistic results, controller gains are tuned concurrently by dragonfly search algorithm (DSA). For the certification purpose of the advocated approach, two-area thermal system with/without governor dead band nonlinearity is considered as test systems initially. Then single/multi-area multi-source power systems with/without a HVDC link are employed for the enriched validation purpose. The results of our proposal are analyzed in comparison with those of other prevalent works, which unveil that despite its simplicity, DSA optimized (1 + PD)-PID cascade strategy delivers better performance than others in terms of smaller values of the chosen objective function and settling time/undershoot/overshoot of the frequency and tie-line power deviations following a step load perturbation.

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Abbreviations

\(S\) :

Speed governor regulation parameter

\({T}_{rs}\) :

Hydro turbine speed governor reset time constant

\(B\) :

Frequency bias constant

\({T}_{rh}\) :

Hydro turbine speed governor transient droop time constant

\({T}_{g}\) :

Speed governor time constant

\({T}_{w}\) :

Nominal starting time of water in penstock

\({T}_{t}\) :

Steam turbine time constant

\({c}_{g}\)0:

Gas turbine valve positioner

\({K}_{ps}\) :

Power system gain constant

\({b}_{g}\) :

Gas turbine constant of valve positioner

\({T}_{ps}\) :

Power system time constant

\({X}_{c}\) :

Lead time constant of gas turbine speed governor

\({T}_{12}\) :

Tie line power coefficient

\({Y}_{c}\) :

Lag time constant of gas turbine speed governor

\(\Delta {P}_{ref}\) :

Incremental change in controller output

\({T}_{cr}\) :

Gas turbine combustion reaction time delay

\(\Delta {P}_{g}\) :

Incremental change in governor valve position

\({T}_{f}\) :

Gas turbine fuel time constant

\(\Delta {P}_{t}\) :

Incremental change in turbine output power generation

\({T}_{cd}\) :

Gas turbine compressor discharge volume-time constant

\(\Delta {P}_{D}\) :

Incremental change in load demand

\({K}_{dc}\) :

Gain constant of HVDC link

\(\Delta f\) :

Incremental change in area frequency

\({T}_{dc}\) :

Time constant of HVDC link

\(\Delta {P}_{tie}\) :

Incremental change in tie-line power

\({K}_{T}\) :

Participation factor for thermal unit

\({ACE}_{i}\) :

Area control error

\({K}_{H}\) :

Participation factor for hydro unit

\({T}_{sg}\) :

Speed governor time constant of thermal unit

\({K}_{G}\) :

Participation factor for gas unit

\({K}_{r}\) :

Reheat gain constant

\({K}_{p}\) :

Controller proportional gain

\({T}_{r}\) :

Reheat time constant

\({K}_{i}\) :

Controller integral gain

\({T}_{gh}\) :

Hydro turbine speed governor main servo time constant

\({K}_{d}\) :

Controller derivative gain

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Engineering Faculty, Duzce University, Düzce, Turkey

    Emre Çelik

  2. Department of Electrical and Electronics Engineering, Technology Faculty, Gazi University, Ankara, Turkey

    Nihat Öztürk

  3. Department of Electrical Engineering, J.C. Bose University of Science and Technology, YMCA, Faridabad, Haryana, India

    Yogendra Arya

  4. Department of Electrical and Energy, Ostim Vocational School, Gazi University, Ankara, Turkey

    Cemil Ocak

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  1. Emre Çelik
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  3. Yogendra Arya
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  4. Cemil Ocak
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Correspondence to Emre Çelik.

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Appendices

Appendix

Nominal parameters of test systems in order

Test system-1 [1, 2, 7, 33, 71];

\(f=60\) Hz, \(B=0.425\) p.u MW/Hz, \(R=2.4\) Hz/pu, \({T}_{\mathrm{g}}=0.03\) s, \({T}_{\mathrm{t}}=0.3\) s, \({K}_{\mathrm{ps}}=120\) Hz/pu, \({T}_{\mathrm{ps}}=20\) s, \({T}_{12}=0.545\) p.u MW/rad.

Test system-2 [2, 7, 15, 71];

\(f=60\) Hz, \(B=0.425\) p.u MW/Hz, \(R=2.4\) Hz/pu, \({T}_{\mathrm{g}}=0.2\) s, \({T}_{\mathrm{t}}=0.3\) s, \({K}_{\mathrm{ps}}=120\) Hz/pu, \({T}_{\mathrm{ps}}=20\) s, \({T}_{12}=0.444\) p.u MW/rad.

Test system-3 [19, 45, 47, 68];

\(f=60\) Hz, \(R=2.4\) Hz/pu, \({T}_{\mathrm{sg}}=0.08\) s, \({K}_{\mathrm{r}}=0.3\), \({T}_{\mathrm{r}}=10\) s, \({T}_{\mathrm{t}}=0.3\) s, \({T}_{\mathrm{gh}}=0.2\) s, \({T}_{\mathrm{rs}}=5\) s, \({T}_{\mathrm{rh}}=28.75\) s \({T}_{\mathrm{w}}=1\) s, \({b}_{\mathrm{g}}=0.05\) s, \({c}_{\mathrm{g}}=1\), \({X}_{\mathrm{c}}=0.6\) s, \({Y}_{\mathrm{c}}=1\) s, \({T}_{\mathrm{cr}}=0.01\) s, \({T}_{\mathrm{f}}=0.23\) s, \({T}_{\mathrm{cd}}=0.2\) s, \({K}_{\mathrm{T}}=0.543478\) pu, \({K}_{\mathrm{H}}=0.326084\) pu, \({K}_{\mathrm{G}}=0.130438\) pu, \({K}_{\mathrm{ps}}=68.9566\) Hz/pu MW, \({T}_{\mathrm{ps}}=11.49\) s.

Test system-4 [19, 45, 47, 49];

\(f=60\) Hz, \(B=0.4312\) pu, \(R=2.4\) Hz/pu, \({T}_{\mathrm{sg}}=0.08\) s, \({K}_{\mathrm{r}}=0.3\), \({T}_{\mathrm{r}}=10\) s, \({T}_{\mathrm{t}}=0.3\) s, \({T}_{\mathrm{gh}}=0.2\) s, \({T}_{\mathrm{rs}}=5\) s, \({T}_{\mathrm{rh}}=28.75\) s \({T}_{\mathrm{w}}=1\) s, \({b}_{\mathrm{g}}=0.05\) s, \({c}_{\mathrm{g}}=1\), \({X}_{\mathrm{c}}=0.6\) s, \({Y}_{\mathrm{c}}=1\) s, \({T}_{\mathrm{cr}}=0.01\) s, \({T}_{\mathrm{f}}=0.23\) s, \({T}_{\mathrm{cd}}=0.2\) s, \({K}_{\mathrm{T}}=0.543478\) pu, \({K}_{\mathrm{H}}=0.326084\) pu, \({K}_{\mathrm{G}}=0.130438\) pu, \({T}_{12}=0.0433\), \({K}_{\mathrm{ps}}=68.9566\) Hz/pu MW, \({T}_{\mathrm{ps}}=11.49\) s.

Test system-5 [10, 19, 68];

\(f=60\) Hz, \(B=0.4312\) pu, \(R=2.4\) Hz/pu, \({T}_{\mathrm{sg}}=0.08\) s, \({K}_{\mathrm{r}}=0.3\), \({T}_{\mathrm{r}}=10\) s, \({T}_{\mathrm{t}}=0.3\) s, \({T}_{\mathrm{gh}}=0.2\) s, \({T}_{\mathrm{rs}}=5\) s, \({T}_{\mathrm{rh}}=28.75\) s \({T}_{\mathrm{w}}=1\) s, \({b}_{\mathrm{g}}=0.05\) s, \({c}_{\mathrm{g}}=1\), \({X}_{\mathrm{c}}=0.6\) s, \({Y}_{\mathrm{c}}=1\) s, \({T}_{cr}=0.01\) s, \({T}_{\mathrm{f}}=0.23\) s, \({T}_{\mathrm{cd}}=0.2\) s, \({K}_{\mathrm{T}}=0.543478\) pu, \({K}_{\mathrm{H}}=0.326084\) pu, \({K}_{\mathrm{G}}=0.130438\) pu, \({T}_{12}=0.0433\), \({K}_{\mathrm{ps}}=68.9566\) Hz/pu MW, \({T}_{\mathrm{ps}}=11.49\) s, \({K}_{dc}=1\), \({T}_{\mathrm{dc}}=0.2\) s.

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Çelik, E., Öztürk, N., Arya, Y. et al. (1 + PD)-PID cascade controller design for performance betterment of load frequency control in diverse electric power systems. Neural Comput & Applic 33, 15433–15456 (2021). https://doi.org/10.1007/s00521-021-06168-3

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