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Salp swarm algorithm-based model predictive controller for frequency regulation of solar integrated power system

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Abstract

Global analysis of power system markets project frequency regulation as one of the most profitable ancillary services. It is associated with second-to-second balance of load and frequency within a control area and acquires a principal role in enabling power interchanges while offering better conditions for electricity exchange. In the light of the above, a novel control strategy, namely salp swarm algorithm (SSA)-based model predictive controller, is proposed for frequency regulation of an unequal two-area realistic power system, incorporating solar thermal power plant and conventional thermal plant. Governor dead band, generation rate constraint and transport delay are considered in each control area. Over the past few years, model predictive controller (MPC) has come forward as a prediction-based control strategy for stabilizing dynamical systems while considering non-linearities, system uncertainties and constraints. The MPC parameters are optimized using SSA. The performance of the proposed approach is validated by comparing the dynamic time responses of SSA-optimized MPC with the other SSA-optimized conventional controllers, namely PID, FOPID and cascade PIDN-FOPID controller. The simulation result analysis shows that the proposed optimal MPC outpaces the conventional controllers with respect to peak overshoot, undershoot and settling time of the time responses. A comparative study of various objective functions indicates that, as compared to other indices, integral square error is better for the considered test system. Further, sensitivity analysis reveals the robustiousness of MPC parameters obtained at nominal values and hence is not required to be retuned, against variations in system loading and inertia constant.

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Abbreviations

\( f \) :

Considered system frequency (Hz)

\( i \) :

Referred subscript to area i, \( i \) = 1, 2

\( T_{12} \) :

Synchronizing coefficient

\( \Delta P_{Di} \) :

Load variation in area \( i \) (p.u.)

\( T \) :

Simulation time (s)

\( \Delta f_{i} \) :

Frequency change in ith area (Hz)

\( D_{i} \) :

ΔPDi/Δfi (p.u. MW/Hz)

\( K_{si} \) :

Gain of solar field of ith area

\( B_{i} \) :

Frequency bias constant of ith area

\( \pi \) :

pi

\( K_{pi} \) :

1/Di (Hz/p.u. MW)

\( H_{i} \) :

Inertia constant of area \( i \) (s)

\( \beta_{i} \) :

(Di + 1/Ri); area frequency response characteristics of ith area

\( R_{i} \) :

Speed regulation parameter of governor of ith area (Hz/p.u. MW)

\( \Delta P_{\text{tie}} \) :

Incremental tie-line power deviation amid area 1 and area 2

\( T_{gi} \) :

Time constant of steam governor for thermal power plant in ith area

\( K_{pfi} \) :

Proportional gain of FOPID part of PIDN-FOPID cascade controller for ith area, i = 1, 2

\( \mu_{i} \) :

Order of differentiator of cascade PIDN-FOPID controller in ith area, i = 1, 2

\( T_{ti} \) :

Time constant of steam turbine for thermal power plant in ith area

\( T_{gsi} \) :

Time constant of steam governor for STPP in ith area

\( a_{12} \) :

Area capacity ratio

T pi :

2H i /f/D i

T o :

Working fluid outlet temperature of solar field (°C)

T i :

Working fluid inlet temperature of solar field (°C)

T e :

Environmental temperature (°C)

I :

Solar irradiance (W/m2)

v :

Pump flow rate (m3/s)

A :

Surface area of the collector

C :

Heat capacity of the working fluid (J/K)

η 0 :

Solar field collector efficiency

U L :

Total heat loss coefficient (W/m2 K)

T ri :

Reheat steam turbine time constant of ith area (s)

K ri :

Reheat coefficient of steam turbine of ith area

K pri :

PID, FOPID, PIDN-FOPID proportional gain for ith area, i = 1, 2

K ini :

PID, FOPID, PIDN-FOPID integral gain for ith area, i = 1, 2

K dei :

PID, FOPID, PIDN-FOPID derivative gain for ith area, i = 1, 2

N i :

PIDN-FOPID derivative filter coefficient for ith area, i = 1, 2

K dfi :

Derivative gain of FOPID part of PIDN-FOPID cascade controller for ith area, i = 1, 2

K ifi :

Integral gain of FOPID part of PIDN-FOPID cascade controller for ith area, i = 1, 2

λ i :

Order of integrator of cascade PIDN-FOPID controller in ith area, i = 1, 2

T si :

Solar collector time constant of ith area

T tsi :

Time constant of steam turbine for STPP in ith area

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Acknowledgements

This research work is sponsored by the Council of Scientific & Industrial Research, New Delhi, India, under the Research and Development Project Grant 22(0692)/15/EMR-II.

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Authors and Affiliations

  1. Electrical Engineering Department, National Institute of Technology Hamirpur, Hamirpur, Himachal Pradesh, India

    Amita Singh & Veena Sharma

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  1. Amita Singh
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  2. Veena Sharma
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Correspondence to Amita Singh.

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Appendix

Appendix

Nominal parameters considered for the test system are [7, 10, 13]: f = 60 Hz; 1% step load disturbance in area 1; Tts = 3.0 s; Tgs = 1.0 s; Tg1 = 0.08 s, Tg2 = 0.08 s; Tt1= 0.3 s, Tt2 = 0.3 s; Kri = 0.5 s; Tri = 10 s; Tpi = 20 s; Kpi = 120 Hz/p.u. MW; T12 = 0.08 p.u. MW/rad; Di = 8.33 × 10−3 p.u. MW/Hz; Ri = 2.4 Hz/p.u. MW; Bi = 0.425 p.u. MW/Hz; Hi = 5 s; Ts = 1.8 s; Ks = 1.8.

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Singh, A., Sharma, V. Salp swarm algorithm-based model predictive controller for frequency regulation of solar integrated power system. Neural Comput & Applic 31, 8859–8870 (2019). https://doi.org/10.1007/s00521-019-04422-3

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