Abstract
In this study, a natureinspired optimization tool called the water cycle algorithm (WCA) and its practical application to efficiently design a cascade controller for two area interconnected power system model is put forward to address the issues in load frequency control (LFC). The cascade control (CC) structure is one of the most effective controllers for improving the performance of a control scheme in power applications, particularly when disturbances occur. In this paper, a wellsystematized combination of the WCA and a welldesigned cascade tiltderivative tiltintegral (TDTI) cascade controller is introduced, and an error performance function, for example, the integral time absolute error, is taken. The proposed WCAbased effective TDTI, TID, and PID strategy are executed as one broadly two area multisource model with/without HVDC link under many scenarios to verify the effectiveness of the proposed system under a highload perturbation and some critical parameters associated with the interconnected power system. Simulation results reveal that the proposed technique provides superior performance to that of newly published schemes such as many objective/PID, TLBO/PID, IPA/TID and IGWO/FuzzyPID controllers. The dynamic investigation is also completed with consideration of the random load pattern, which sufficiently reveals the superior performance of the WCA/TDTI scheme.
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Abbreviations
 i :

Subscript associated \({\text{to area}}\) \(\left( {i = 1, 2} \right)\)
 f :

Nominal frequency \(\left( {{\text{Hz}}} \right)\)
 P _{R} :

Area \({\text{rated}}\) power \(\left( {{\text{MW}}} \right)\)
 P _{L} :

Nominal operative load \(\left( {{\text{MW}}} \right)\)
 ∆f _{i} :

Frequency deviations \(\left( {{\text{Hz}}} \right)\)
 ∆P _{Li} :

Step load change
 ∆P _{tie} :

Tie \({\text{  line deviation}}\) of power \(\left( {{\text{p}}.{\text{u}}.} \right)\)
 B _{ i } :

Frequency bias \(\left( {{\text{p}}.{\text{u}}.{\text{MW}}/{\text{Hz}}} \right)\)
 R _{ i } :

Speed regulation \(({\text{Hz}}/{\text{p}}.{\text{u}}.\))
 T _{ ti } :

Steam turbine \({\text{time constant}}\) \(\left( {\text{s}} \right)\)
 T _{ gi } :

Speed governor time constant \(\left( {\text{s}} \right)\)
 T _{12} :

Synchronizing coefficient \(\left( {{\text{p}}.{\text{u}}.} \right)\)
 T _{ RSi } :

Hydro \({\text{turbine speed governor}}\) reset time \(\left( {\text{s}} \right)\)
 T _{ GHi } :

Hydro \({\text{turbine speed governor}}\) time constant \(\left( {\text{s}} \right)\)
 T _{ RHi } :

\({\text{Hydro turbine speed governor transient}} {\text{droop}}\) Time constant (s)
 T _{ Wi } :

Nominal initial \({\text{time of water in penstock}}\left( {\text{s}} \right)\)
 K _{Ri} :

\({\text{Reheat coefficient of steam turbine}}\)
 T _{ri} :

\({\text{Reheat time constant of steam turbine }}\left( {\text{s}} \right)\)
 K _{pSi} :

\({\text{Power system gain }}\left( {{\text{Hz}}/{\text{p}}.{\text{u}}.} \right)\)
 T _{pSi} :

\({\text{Power system time constant }}\left( {\text{s}} \right)\)
 K _{T} :

Contribution factors of thermal unit
 K _{H} :

Contribution \({\text{factors of}}\) hydro unit
 K _{G} :

\({\text{Contribution factors of gas unit}}\)
 K _{DC} :

\({\text{HVDC gain of power system }}\left( {{\text{Hz}}/{\text{p}}.{\text{u}}.} \right)\)
 T _{DC} :

HVDC time constant \(\left( {\text{s}} \right)\)
 b _{g} :

Gas turbine constant of positioner \(\left( {\text{s}} \right)\)
 c _{g} :

Gas turbine valve positioner
 Y _{C} :

\({\text{Lag time of gas turbine governor }}\left( {\text{s}} \right)\)
 X _{C} :

Lead \({\text{time of gas turbine}}\) \({\text{governor }}\left( {\text{s}} \right)\)
 T _{fi} :

Gas \({\text{turbine fuel time}}\) constant \(\left( {\text{s}} \right)\)
 T _{CDi} :

\({\text{Gas turbine compressor discharge volume\; time constant (s)}}\)
 T_{CRi} :

Gas \({\text{turbine combustion reaction}}\;{\text{time delay }}\left( {\text{s}} \right)\)
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Appendix A (Mohanty et al. 2014)
Appendix A (Mohanty et al. 2014)
\({\text{P}}_{{{\text{rt}}}} = 2000{\text{ MW}};\;{\text{P}}_{{\text{L}}} = 1840{\text{ MW}}; \;B_{1} = B_{2} = 0.4312 \;{\text{p}}.{\text{u}}.{\text{ MW}}/{\text{H}}_{{\text{Z}}}\); \(R_{1} = R_{2} = R_{3} = 2.4{\text{ H}}_{Z} /{\text{p}}.{\text{u}}.\); \(T_{sg1} = T_{sg2} = 0.08{\text{ s}}\);
\(T_{t1} = T_{t2} = 0.3 s\); \(K_{r1} = K_{r2} = 0.3; \) \(T_{r1} = T_{r2} = 10 s; \) \(K_{PS1} = K_{PS2} = 68.9566{\text{ H}}_{Z} /{\text{p}}.{\text{u}}\); \(T_{PS1} = T_{PS2} = 11.49 {\text{ s}}\);
\(T_{12} = 0.0433 {\text{p}}.{\text{u}}.;{ }a_{12} =  1; \) \(T_{w1} = T_{w2} = 1{\text{ s}}; \) \(T_{RS1} = T_{RS2} = 5 {\text{ s}}\); \(T_{RH1} = T_{RH2} = 78.75 {\text{ s}}\); \(T_{GH1} = T_{GH2} = 0.2 {\text{ s}}\); \(X_{C} = 0.6 s\); \(Y_{C} = 1 {\text{s}};\) \(c_{g} = 1 s;\) \(b_{g} = 0.05 s;\) \(T_{F1} = T_{F2} = 0.23 {\text{s}}\); \(T_{CD1} = T_{CD2} = 0.2 {\text{s}}\); \(T_{CR1} = T_{CR2} = 0.01 {\text{s}}\);
\(K_{T} = 0.543478\); \(K_{H} = 0.326084\); \(K_{G} = 0.130438\); \(K_{DC} = 1\); \(T_{DC} = 0.2 s\);
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Barakat, M., Donkol, A., Hamed, H.F.A. et al. Controller parameters tuning of water cycle algorithm and its application to load frequency control of multiarea power systems using TDTI cascade control. Evolving Systems (2021). https://doi.org/10.1007/s12530020093630
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Keywords
 Interconnected power system
 Load frequency control
 Cascade control
 Water cycle algorithm
 And TID controller