Implementation of combined hydrogen aqua electrolyser-fuel cell and redox-flow-battery under restructured situation of AGC employing TSA optimized PDN(FOPI) controller

Abstract

This work addresses the automatic-generation-control of multiple-area and sources under a restructured-situation. Sources within area-1 represent geothermal power plant, thermal, and gas, and area-2 sources represent thermal, hydro, and wind. An original endeavour is brought about to execute a controller with an admixture of proportional-derivative with filter (PDN) (integer-order) besides fractional-order proportional–integral (FOPI). Examination manifests excellence of PDN(FOPI) over integer order controllers likely integral, proportional–integral, proportional–integral–derivative-filter from perspective concerning depleted status of peak aberrations, extent-of-oscillations, and duration of settlement. To attain the controller’s attributes bioinspired meta-heuristic tunicate swarm algorithm is exercised. The occurrence of renewable sources makes arrangements meaningfully improved related to base thermal-gas-hydro arrangement. The action of hydrogen aqua electrolyzer-fuel cell and redox flow battery is examined using a PDN(FOPI) controller, providing noteworthy outcome in dynamic performance. The analysis is conducted under all the schemes of restructured situations.

KEYWORDS:

• Automatic generation control
• fuel cell
• hydrogen aqua electrolyzer
• PDN(FOPI) controller
• redox flow battery
• tunicate swarm algorithm

Nomenclature

I	=	Subscript refers to area-i (i = 1, 2) for two areas
*	=	Superscript denotes optimum value
Bi	=	Frequency bias coefficient of area-i
Di	=	ΔPDi /Δfi (p.u. MW/Hz)
Ri	=	Governor speed regulation parameter of area-i (Hz/p.u. MW)
βi	=	Area frequency response characteristics of area-i ( = Di + 1/Ri)
ΔPDi	=	Incremental load change in area-i (p.u. MW)
ΔPgi	=	Incremental generation change in area-i (p.u. MW)
F	=	Nominal frequency (Hz)
Pi	=	π
ΔPtie i-j	=	Incremental change in tie-line power in the line connecting area-i and area-j (i≠j)
Δfi	=	Deviation in the frequency of area-i (Hz)
Tij	=	Synchronizing coefficients
T	=	Simulation time (s)
Hi	=	Inertia constant of area-i (s)
Kpi	=	1/Di (Hz /p.u. MW)
Tpi	=	(2×Hi) / (fi × Di) (s)
Pri	=	Rated power of area-i (MW)
aij	=	Pri/Prj)
N	=	Number of search agents
Tgi	=	Steam governor time constant for thermal power plant of area-i(s)
Tti	=	Turbine time constant for thermal power plant of area-i(s)
Tri	=	Reheat turbine time constant for thermal power plant of area-i(s)
Kri	=	Reheat turbine gain for thermal power plant of area-i
Bgi	=	Time constant of valve position of the gas plant of area-i(s)
Cgi	=	Gas turbine valve position of the gas plant of area-i
Xgi	=	Lead time constant of gas turbine governor of the gas plant of area-i(s)
Ygi	=	Lag time constant of gas turbine governor of the gas plant of area-i(s)
Tcri	=	Gas turbine combustion reaction time delay of the gas plant of area-i(s)
Tfi	=	Gas turbine fuel time constant of the gas plant of area-i(s)
Tcdi	=	Compressor discharge volume time constant of the gas plant of area-i(s)
Kp	=	Proportional gain of the electric governor of the hydro plant
Ki	=	Integral gain of the electric governor of the hydro plant
Kd	=	Derivative gain of the electric governor of the hydro plant
Tw	=	Water starting time of hydro turbine (s)
AGC	=	Automatic generation control
ALFC	=	Automatic load frequency control
Apf	=	Area participation factor
BESS	=	Battery energy storage system
Cpf	=	Contract participation factor
DEG	=	Diesel engine generator
DG	=	Distributed generation
DISCO	=	Distribution company
DPM	=	DISCO participation matrix
DSTS	=	Dish-Stirling solar thermal system
EV	=	Electric vehicle
FO	=	Fractional order
GDB	=	Governor dead band
GENCOm	=	Generation company
GRC	=	Generation rate constraint
IO	=	Integer order.
I	=	Integral
ISE	=	Integral squared error
PI	=	Proportional-integral controller
PIDN	=	Proportional-integral-derivative with controller
RFB	=	Redox flow battery
SLP	=	Step load perturbation
WPP	=	Wind power plant

1. Introduction

The automatic generation control (AGC) plays an important role in balancing the generation with respect to load demand in the power system. As long as imbalance is not looked upon this may lead towards serious issues from the perspective of errors in frequency plus power in the tie line. To date an ample amount of tasks are being stated in the domain of AGC. Researchers initially concentrate on isolated and two-area thermal systems mostly and in the current era the work has been extended to three, four and five areas [1–7]. Apart from the traditional system, many works are also reported under the restructured situation of AGC or load frequency control (LFC) [8–14]. Under the restructured situation there exist three commercial participants, namely generating companies (GENCOms), distributing companies (DISCOms) and also transmission companies. Thus, the bidding processes among them are maintained by the independent system operator. Under deregulated environment, the research work has been carried out in three-area thermal systems [8–10], while later on five-area restructured system incorporating thermal-hydro-gas [11], the thermal-hydro deregulated system by considering the area participation factor [12,15], three area system having thermal and gas [16] and two-area thermal gas system [17].

With concern to major environmental issues, renewable sources (RnS) have made a major contribution to the world’s power generation. Authors have reported the application of solar thermal in a deregulated situation [13], the details of dish-Stirling solar thermal [18–20], geo thermal power plant (GPP) [14], incorporation of wind [21], dish-Stirling solar and GPP [22] in the restructured situation of AGC. However, the combination of systems comprising of GPP, thermal, gas, hydro and wind under restructured situations has not been yet reported. So this mentioned system needs to be assessed.

In an interconnected system, the energy storage devices (ESD) boost the system stability by compensating the surged load demand. Authors have reported on the use of hydrogen aqua electrolyser-fuel cells (HAE(FC)) [23]. HAE and FC are incorporated together to enhance the reliability and quality of power. HAE(FC) act as a power plant during peak load as it supplies power during peak load and stores energy during normal duration. Another ESD redox flow battery (RFB) [24] has a longer runtime and facilitates with large power ability. RFB has assured benefits like rapid small-duration excess capability, large efficiency, open from self-discharge issues, cheap and not messed up by unexpected charging or discharging. So, the inclusion of HAE(FC) along with RFB in this GPP-thermal-gas-hydro-wind system is a fresh attempt in LFC under a restructured scenario.

To mitigate the system nonlinearities by reducing the area control errors, a highly developed and competent second controller is desired in interconnected power systems. The use of integer order controllers such as integral (I), integral proportional–integral (PI), and proportional–integral–derivative (PID) are very common in the field of LFC. Apart from them, several literatures point out the use of fractional order (FO) as well as cascade controllers (CCs). The FO controllers have been introduced in AGC as FOIDF in a three-area multi-source LFC system restructured [10], applied FOPID in the multi-area multi-source system of LFC [25] and FOIDDF in the combination of frequency and voltage control system [26]. CCs are done in multiple ways like IO-IO CCs, FO-FO CCs and IO-FO CCs. Puja et al. [27] have reported the use of IO-IO CCs named PD-PID in a three-area thermal system. Tasnin et al. [14] reported the use of FO-FO CCs termed FOPI-FOPID as secondary controllers for a three-area system. Saha et al. [13] utilized the IO-FO CCs like PIDN-FOPD in a two-area solar-thermal system under a restructured situation.

Saha et al. [16] have reported the use of another combination of controllers. The authors have used the combination of PID with derivative filter (PIDN) cascaded with fractional order integrator (FOI). The authors utilized both PIDN-FOI controller as well a two-degree-of-freedom PIDN-FOI (2DOF-PIDN-FOI) controller. Apart from all such controllers mentioned above the IO-FO CCs combination like proportional-derivative with filter (PDN) along with FO proportional–integral (FOPI) is a new controller. Moreover, this controller PDN(FOPI) has not yet found its application in either traditional or restructured situations of power systems. Thus, this controller can be taken into account for analysis.

The better performance of secondary controllers is marked with best-obtained values for gains and parameters with the help of different meta-heuristic algorithms. Few of them are Bacterial foraging [4], Quasi oppositional harmony search algorithm [6], Particle swarm optimization (PSO) [25], firefly algorithm (FA) [5], cuckoo search (CS) [27], lightning search algorithm (LSA) [26], Sine Cosine algorithm [14], Whale optimization algorithm [13], whale optimization algorithm (WOA) [16], Imperialist competitive algorithm (ICA) [15], dragonfly algorithm (DA) [17], Gaussian arithmetic [28], symbiotic search [29], salp swarm [30–35], boosted sooty tern [36], centre line concept [37], human psychology optimization [38] and so on. Kaur et al. [39] developed a bioinspired meta-heuristic algorithm designated as the tunicate swarm algorithm (TSA). It mimics jet propulsion plus swarm behaviour of tunicates within steering as well as the foraging method. TSA was developed after being motivated by the swarm nature of tunicates to sustain deep under the sea. TSA’s application is the first time noticed here in the present work for a GPP-thermal-gas-hydro-wind system under a restructured scenario.

The novelty and main contributions are as follows:

1. A two-area system with unequal area capacity under restructured situations with non-linearities is studied. Area-1 comprises GPP, thermal and gas as generating sources. Area-2 comprises thermal, hydro and wind as generating sources.

2. A new controller PDN(FOPI) is proposed for the AGC study under the restructured situation.

3. The best values of controller gains and parameters are obtained using the TSA algorithm.

4. The effectiveness of controller performance is compared with various classical controllers (I/PI/PIDN) as well as with recently published controllers like FOPID and PIDN-FOI under Poolco, bilateral and contract violation schemes of a restructured scenario of power system individually.

5. The impact of GPP and wind on system dynamics is studied for all three schemes.

6. The impact of HAE(FC) and RFB on system dynamics is studied for all three schemes.

7. DPM sensitivity is carried out to examine the robustness of the best controller’s gains with varied DPMs.

8. Sensitivity analysis for changing system loading and inertia constant is examined for robustness assessment.

The entire work has been represented in a pictorial form in Figure 1 for easy understanding.

Figure 1. Pictorial representation of the entire work.

2. Investigated systems, HAE(FC) and RFB

2.1 Investigated systems

A two-area system of unequal type is taken into account for the survey under restructured (deregulated) situation. The area capacity ratio is 1:5. Area-1 has three generating companies (GENCOms), namely geothermal power plant (GPP), thermal and gas. Similarly, the three GENCOms of area-2 are thermal, hydro and wind.

Geothermal energy is a potential renewable source of energy where underground thermal energy is transformed into electricity. The transfer function (Trfn) modelling of GPP is similar to thermal plants but it does not have a boiler for reheating steam [14]. The first-order Trf of the governor and turbine of GPP is given by (1) and (2), respectively. (1) $\begin{array}{rl}\text{Trf}{\text{n}}_{\text{GPP}}& =\frac{1}{1+s{G}_{\text{GPP}}}\end{array}$(1) (2) $\begin{array}{rl}\text{Trf}{\text{n}}_{T_{\text{GPP}}}& =\frac{1}{1+s{T}_{\text{GPP}}}\end{array}$(2) G_GPP and T_GPP are the time constants of the governor and turbine of GPP, respectively. The governor time constant value (G_GPP) is around 0.1 s and a typical value of turbine time constant (T_GPP) is within 0.1−0.5 s [22]. The exact values are obtained by the optimization technique TSA and for T_GPP within the limits 0.1−0.5 s. Analysis is also performed considering the hydrogen aqua electrolyser fuel cell (HAE(FC)) (details in Section 2.2) and redox flow battery (RFB) (details in Section 2.3). Three different systems are analysed here:

• System A: Area-1 is inclusive of thermal, thermal and gas. Area-2 is inclusive of thermal, hydro and thermal.

• System B: Area-1 is inclusive of GPP, thermal and gas. -2 is inclusive of thermal, hydro and wind.

• System C: Area-1 is inclusive of GPP, thermal, gas and HAE(FC). Area-2 is inclusive of thermal, hydro, wind and RFB.

The Trfn model is provided in Figure 2(a).

Figure 2. System’s Tf model, proposed controller, TSA’s flowchart and linearized RFB model: (a) Tf of considered system with GPP, wind, HAE(FC) and RFB, (b) Arrangement of the proposed controller, (c) flowchart of TSA algorithm and (d) linearized RFB model.

2.1.1 Short outline of AGC as part of restructured situation:

The reflected two-area system of unequal form is inclusive of three GENCOms and three DISCOms in every single area. They relate to each other by contract participation factors (cpfs) as demonstrated in the basic DISCO participation matrix (DPM_basic) displayed in (3). (3) $\begin{array}{rl}\text{DP}{\text{M}}_{\text{basic}}& =[\begin{array}{ccc}\text{cpf11}& \text{cpf12}& \text{cpf13}\\ \text{cpf21}& \text{cpf22}& \text{cpf23}\\ \text{cpf31}& \text{cpf32}& \text{cpf33}\\ \text{cpf41}& \text{cpf42}& \text{cpf43}\\ \text{cpf51}& \text{cpf52}& \text{cpf53}\\ \text{cpf61}& \text{cpf62}& \text{cpf63}\end{array}\\ & \begin{array}{ccc}\text{cpf14}& \text{cpf15}& \text{cpf16}\\ \text{cpf24}& \text{cpf25}& \text{cpf26}\\ \text{cpf34}& \text{cpf35}& \text{cpf36}\\ \text{cpf44}& \text{cpf45}& \text{cpf46}\\ \text{cpf54}& \text{cpf55}& \text{cpf56}\\ \text{cpf64}& \text{cpf65}& \text{cpf66}\end{array}]\end{array}$(3) where (4) $\begin{array}{r}\text{cp}{\text{f}}_{\mathrm{kl}}=\frac{\text{Deal}\text{ demand}\text{ of}\text{ load}\text{ for}k\text{th }\text{GENCO}}{\text{Complete }\text{demand}\text{ of}\text{ load}\text{ the }l\text{th }\text{DISCO}}\end{array}$(4) In the matrix, the rows and columns represent the GENCOms and DISCOms, respectively. The off-diagonal terms reveal the connection of DISCOms of one area to GENCOms of another area, whereas diagonal terms reveal the connection of DISCOm and GENCOms of the same area. The area participation factors (APFs) are computed based on generation ability.

The common format for the scheduled tie power flow within areas for a two-area system is as given by (5) (5) $\begin{array}{rl}\mathrm{\Delta }{P}_{\text{tie - scheduled}}& =[\text{Demands }\text{of }\text{DISCOms }\text{in }\text{area}\\ & -2\text{from }\text{GENCOms }\text{in }\text{area - }1]\\ & -[\text{Demands }\text{of}\text{ DISCOms }\text{in}\text{ area}\\ & -1\text{ from }\text{GENCOms}\text{ in}\text{ area - 2}]\end{array}$(5) (6) $\begin{array}{rl}\mathrm{\Delta }{P}_{\text{tie - scheduled}}& =P_{\text{exp}}-P_{\text{imp}}\end{array}$(6) where (7) $\begin{array}{rl}{P}_{\text{exp}}& =\text{Power}\text{ demanded}\text{ from}\text{ GENCOms }\text{in }\text{area}\\ & -2\text{by}\text{ DISCOms }\text{in }\text{area - 1}\end{array}$(7) (8) $\begin{array}{rl}{P}_{\text{imp}}& =\text{Power}\text{ demanded}\text{ from }\text{GENCOms }\text{in area - 1 }\\ & \text{by }\text{DISCOms }\text{in }\text{area - 2}\end{array}$(8) The exact power variation in the tie line and erroneousness in tie power interchange are given by (9) and (10), respectively. (9) $\begin{array}{rl}\mathrm{\Delta }{P}_{i-j\text{ actual}}& =\frac{2\pi T_{12}}{s}\left[\mathrm{\Delta }{f}_1\left(s\right)-\mathrm{\Delta }{f}_2\left(s\right)\right]=\mathrm{\Delta }{P}_{\text{tie - actual}}\end{array}$(9) (10) $\begin{array}{rl}\mathrm{\Delta }{P}_{i-j\text{error}}& =\mathrm{\Delta }{P}_{i-j\text{actual}}-\mathrm{\Delta }{P}_{i-j\text{scheduled}}\end{array}$(10) Area control error (ACE) is an amalgamation of signals as a consequence of frequency and tie-power erroneousness given by (11). (11) $\begin{array}{r}\text{AC}{\text{E}}_i=B_i\mathrm{\Delta }{f}_i+\mathrm{\Delta }{P}_{i-j\text{error}}\end{array}$(11)

2.2 Hydrogen aqua electrolyser fuel cell (HAE(FC))

The association of hydrogen aqua electrolyser (HAE), and hydrogen tank along fuel cell (FC) is expected to provide power when there is a large demand for power for a long period. During normal conditions, the HAE is used to produce hydrogen (H₂) by the process of water electrolysis through electricity and storing H₂ by compression. The FC has a proton exchange membrane that produces electricity by using the above-mentioned H₂ to meet the instant load.

• The actual process of delivering power back to the grid is as follows:

• At first, an AC/DC converter feeds direct current (D.C.) power to HAE.

• HAE breaks water into H₂ and oxygen (O₂).

• H₂ is stored in the form of energy in a reservoir by the process of compression. The main purpose of storing H₂ is to generate electricity with the help of FC.

• FC is used because it directly converts the chemical energy present in H₂ into electricity.

• This DC power is fed back in the form of AC (alternating current) power to the grid by using a DC/AC converter.

HAE and FC in actual systems are of higher order along with non-linearities. But, the present work is in lower frequency domain so the first-order transfer functions are considered for both HAE and FC [23].

The Trfn of HAE is given by (12) (12) $\begin{array}{r}\text{Trf}{\text{n}}_{\text{HAE}}=\frac{K_{\text{HAE}}}{1+s{T}_{\text{HAE}}}\end{array}$(12) K_HAE and T_HAE are the gain along with the time constant of HAE, respectively.

The Trfn of FC is given by (13). (13) $\begin{array}{r}\text{Trf}{\text{n}}_{\text{FC}}=\frac{K_{\text{FC}}}{1+s{T}_{\text{FC}}}\end{array}$(13) K_FC and T_FC are the gain along with the time constant of FC, respectively. The numerical values are given in the Appendix.

2.3 Redox flow battery

Redox flow battery (RFB) is type of flow battery which is developed on the basis of stationary energy-storing techniques. RFB has found a large number of applications in the field of AGC. In this type of battery, the reactive substantial is absent in the structure rather it is aided by an outer provision of storing tanks. Thus, the whole energy capability is dependent on the quantity of electrolyte in outer storing tanks and output power is related to the organization of electrodes. The electrolyte is a solution of sulphuric acid in combination with vanadium ions. A pair of pumps are associated with flow of the solution through cells of the battery. The chemical reactions which occur inside the battery cell during charging as well as discharging are provided by (14)−(15).

At the positive electrode: (14) $\begin{array}{r}{V}^{\text{4 + }}\underset{\text{Discharge}}{\overset{\text{Charge}}{\stackrel{⟶}{⟵}}}{V}^{\text{5 + }}+{\text{e}}^{-}\end{array}$(14) At the negative electrode: (15) $\begin{array}{r}{V}^{\text{3 + }}+{\text{e}}^{-}\underset{\text{Discharge}}{\overset{\text{Charge}}{\stackrel{⟶}{⟵}}}{V}^{\text{2 + }}\end{array}$(15) RFB is mentioned with the benefits of longer runtime and facilitates large power ability. Even has assured benefits like rapid small-duration excess capability, large efficiency, open from self-discharge issues, cheap and not messed up by unexpected charging or discharging. The nominal parameters for RFB are given in the Appendix. The linearized model of RFB for this study is provided in Figure 2(d).

3. Proposed control approach

The present section provides information on the proposed controller (PDN(FOPI)), the objective function used, and the TSA technique used for various assessments.

3.1 Problematic statement

The existing understanding is important for implementing a frequency excursion approach and an advanced metaheuristic strategy to improve the merging controller for InOd and FrOd inside an interconnected power system that includes renewable sources. The major aim is to remove frequency anomalies and create effective control mechanisms for tie-line power interactions in various locations.

3.2 Recommended PDN(FOPI) controller

The proposed controller is the combination of an integer order (IO) controller along with a fractional order (FO) controller. The proposed controller is proportional-derivative with filter (PDN) with FO proportional–integral (FOPI), hence PDN(FOPI). The block outline of PDN(FOPI) is demonstrated in Figure 1(b). Block-1 (B1) and Block-2 (B2) are the arrangement of PDN and FOPI, respectively. Rs_i(s) and Os_i(s) are the reference (area control error (ACE)) and output signal for the PDN(FOPI) controller, respectively. ACE is an amalgamation of signals as a consequence of frequency and tie-power erroneousness. The ACE signals for area-1 and area-2 are given by (16) and (17), respectively. (16) $\begin{array}{rl}\text{AC}{\text{E}}_{\text{1}}& ={\text{β}}_{\text{1}}\mathrm{\Delta }{f}_{\text{1}}+\mathrm{\Delta P}\text{ti}{\text{e}}_{\text{1}-\text{2}}\end{array}$(16) (17) $\begin{array}{rl}\text{AC}{\text{E}}_{\text{2}}& ={\text{β}}_{\text{2}}\mathrm{\Delta }{f}_{\text{2}}+a_{\text{12}}\mathrm{\Delta }P\text{ti}{\text{e}}_{\text{1}-\text{2}}\end{array}$(17) where β₁, β₂ = frequency response characteristics of area-1 and 2, respectively; Δf₁, Δf₂ = frequency aberration of area-1 and 2, respectively; ΔPtie_1-2= deviation in tie line power connecting both areas and a₁₂= ratio of power rating of areas.

The Tf of B1_i(s) (controller PDN) is given by (18). (18) $\begin{array}{r}\text{B}{\text{1}}_i\text{(}s\text{) = }\frac{K_{\text{Pi}}s+K_{\mathrm{Di}}{N}_i}{\text{(}s+N_i\text{)}}\left(\text{Controller}\text{ PDN}\right)\end{array}$(18) K_Pi, K_Di: proportional and derivative gain of IO of related area and N_i: filter.

The Riemann−Liouville (R-L) description for the FO integrator can be acquired from the equation given by (19). (19) $\begin{array}{r}\alpha D_t^{-\alpha }f\left(t\right)=\frac{1}{\mathrm{\Gamma }\left(n\right)}{\int }_{\alpha }^t{(t-\tau )}^{\alpha -1}f\left(\tau \right)\mathrm{d\tau }\end{array}$(19) In (30) n−1≤ α <n, n is an integer, $\alpha D_t^{\alpha }$is the fractional operator and Γ(.) is Euler’s gamma function. The Laplace transformation of (17) is given by (20). (20) $\begin{array}{r}L\left\{\alpha D_t^{\alpha }f\left(t\right)\right\}=s^{\alpha }F\left(s\right)-\sum _{k=0}^{n-1}{s}^k\alpha D_t^{\alpha -k-1}f\left(t\right){|}_{t=0}\end{array}$(20) The disadvantage of infinite count of poles and zeros due to perfect approximation is overwhelmed as mentioned by Oustaloup et al. [40]. In [40] a proper Tf is suggested which can be estimated FO derivatives as well integrators via recursive distribution about poles and zeros demonstrated by (21). (21) $\begin{array}{r}{s}^{\alpha }=K\prod _{n=1}^M\frac{1+\left(s/\phantom{s{\omega }_{Z,n}}{\omega }_{Z,n}\right)}{1+\left(s/\phantom{s{\omega }_{p,n}}{\omega }_{p,n}\right)}\end{array}$(21) If K = 1 (attuned gain) then gain = zero db with 1 rad/s frequency, M = number of poles as well as zeros (already set) and frequencies range for poles and zeros are provided by (22)−(26). (22) $\begin{array}{rl}{\omega }_{Z,l}& ={\omega }_l\sqrt{n}\end{array}$(22) (23) $\begin{array}{rl}{\omega }_{p,n}& ={\omega }_{Z,n}ϵ,n=1,\dots .,M\end{array}$(23) (24) $\begin{array}{rl}{\omega }_{Z,n+1}& ={\omega }_{p,n}\sqrt{\eta }\end{array}$(24) (25) $\begin{array}{rl}ϵ& =({\omega }_h/{\omega }_l{)}^{v/\phantom{\mathrm{vM}}M}\end{array}$(25) (26) $\begin{array}{rl}\eta & =({\omega }_n/{\omega }_l{)}^{(1-v)/\phantom{(1-v)M}M}\end{array}$(26)

The Trfn of B2_i(s) (controller FOPI) is given by (27). (27) $\begin{array}{r}\text{B}{\text{2}}_i(s\text{) = }{K}_{\text{FPi}}+\frac{K_{\text{FIi}}}{s^{{\lambda }_i}}\text{(Controller}\in \text{ FOPI)}\end{array}$(27) where λ is the noninteger order of the FO integrator part. K_FPi, K_FIi: Proportional and integral gain of FO part of related area.

The Trfn of the proposed PDN(FOPI) controller is given by (28). (28) $\begin{array}{r}\text{T}{\text{f}}_{\text{PD(FOID)}}\text{(}s\text{) = }\left(\frac{K_{\mathrm{Pi}}s+K_{\mathrm{Di}}{N}_i}{\text{(}s+N_i\text{)}}\right)\times \left(K_{\text{FPi}}+\frac{K_{\text{FIi}}}{s^{{\lambda }_i}}\right)\end{array}$(28) The controller structure is provided in Figure 2(b).

The action of the controller solely depends on gain/ parameter values of controllers. The obtained values suggest the control action near about the operating point. But a sudden disturbance in the power system causes the operating point to shift and hence it becomes tedious to regain an optimum value by such a conventional hit and trial process. In order to overcome such a situation, the support of optimization techniques is taken. They have provision of both exploration and exploitation which provides optimum values during disturbances with ease. In the present research work, the tunicate swarm algorithm (TSA) is applied to optimize gain/parameter values of the controller to have an optimal solution. The controller I/PI/PIDN/PDN(FOPI) are utilized on an individual basis. The controller receives ACE as its input signal and provides with an action which leads to the reduction of ACE. Performance indices (Pi) are considered as objective functions to provide with the least value of ACE. The various Pi are integral square error (Pi_ISE), integral time square error (Pi_ITSE), integral absolute error (Pi_IAE) and integral time absolute error (Pi_ITAE) given by (29)−(32) respectively. (29) $\begin{array}{rl}\text{P}{\text{i}}_{\text{ISE}}& ={\int }_{\text{0}}^T\{\mathrm{\Delta }{f_{\text{1}}}^{\text{2}}+\mathrm{\Delta }{f_{\text{2}}}^{\text{2}}+\mathrm{\Delta }\text{Pti}{{\text{e}}_{\text{1}-\text{2}}}^{\text{2}}\}\text{ d}t\end{array}$(29) (30) $\begin{array}{rl}\text{P}{\text{i}}_{\text{ITSE}}& ={\int }_{\text{0}}^T\{\mathrm{\Delta }{f_{\text{1}}}^{\text{2}}+\mathrm{\Delta }{f_{\text{2}}}^{\text{2}}+\mathrm{\Delta }\text{Pti}{{\text{e}}_{\text{1}-\text{2}}}^{\text{2}}\}t\text{ d}t\end{array}$(30) (31) $\begin{array}{rl}\text{P}{\text{i}}_{\text{IAE}}& ={\int }_{\text{0}}^T\{|\mathrm{\Delta }{f}_{\text{1}}|+|\mathrm{\Delta }{f}_{\text{2}}|+|\mathrm{\Delta }\text{Pti}{\text{e}}_{\text{1}-\text{2}}|\}\text{ d}t\end{array}$(31) (32) $\begin{array}{rl}\text{P}{\text{i}}_{\text{ITAE}}& ={\int }_{\text{0}}^T\{|\mathrm{\Delta }{f}_{\text{1}}|+|\mathrm{\Delta }{f}_{\text{2}}|+|\mathrm{\Delta }\text{Pti}{\text{e}}_{\text{1}-\text{2}}|\}t\text{ d}t\end{array}$(32)

3.3 Objective function

The foremost determination of the controller proposal is appropriate optimization mission counting deprecation of a specific cost function given the restraints of controller attributes with limits. Here, in the current AGC knowledge, ISE is intricated as the cost function. The scientific appearance of ISE as PI (PI_ISE) is reflected in (29).

The adjusting parameters of PDN(FOPI) are obtained using TSA by Pi_ISE subject to (33). (33) $\begin{array}{r}\begin{array}{l}{K}_P^{min}\le K_P\le K_P^{max}\\ K_D^{min}\le K_D\le K_D^{max}\\ N^{min}\le N\le N^{max}\\ K_{\mathrm{FP}}^{min}\le K_{\mathrm{FP}}\le K_{\mathrm{FP}}^{max}\\ K_{\mathrm{FI}}^{min}\le K_{\mathrm{FI}}\le K_{\mathrm{FI}}^{max}\\ {\lambda }^{min}\le \lambda \le {\lambda }^{max}\end{array}\}\end{array}$(33) The min and max are the minimum and maximum values of the adjusting parameters of the controller. The gains of controllers are maintained within the range of 0−1 and the derivative coefficient filter within 0−100. These boundaries are fixed by practice, the diverse numeral of trials and by referring to different literature.

3.4 Optimization approach-tunicate swarm algorithm (TSA)

The bioinspired meta-heuristic algorithm designated as the tunicate swarm algorithm (TSA) was developed by Kaur et al. [39]. Tunicates are bio-luminescent in nature having acylindrical shape and size of a few millimetres. It emits powerful light which is visible from more than many metres. Their cylindrical shape has one open end and the other closed. This open end contributes to jet propulsion by drawing surrounding water. This algorithm mimics the jet propulsion plus swarm behaviour of tunicates within navigation as well as foraging procedures. TSA was developed after being motivated by the swarm nature of tunicates to exist deep under the sea. The common gelatinous substance of each tunicate binds them together. In [39] two behaviours of tunicates are considered to seek the position of food which is the optimum value. They are jet propulsion along with swarm intelligence. Jet propulsion action is mathematically modelled when three conditions are satisfied like avoiding dispute between each search agent, motioning towards the direction of nearby superior search agent and remaining not far from the superior search agent. And the swarm behaviour will upgrade the spot of other search agents with respect to the best-obtained value.

The stages of TSA are as follows:

1. Initialize the population of tunicates.

2. Decide initial parameters, as well as, the highest count of iterations.

3. Compute the fitness value corresponding to each search agent.

4. After that the finest search agent is examined in the provided search space.

5. Upgrade the position of each search agent.

6. Modify the upgraded search agents which go outside the considered search space.

7. Now, compute the fitness value of the upgraded search agent. If an improved solution is obtained then replace the previous value with it.

8. If stopping requirements are fulfilled, then the algorithm stops or else repeats the stages 5−8.

The best solution obtained so far is returned.

The flowchart of TSA is provided in Figure 2(c).

4. Outcome and evaluation

4.1 Evaluation of dynamic outcomes in the Poolco scheme

4.1.1 Dynamic responses along with GPP and wind for a system with I, PI, PIDN and PDN(FOPI) controllers in the Poolco scheme

In accordance with various schemes available in the restructured situation of the power system, the total count of GENCOms and DISCOms is not rigid. Where DISCOms can select any number of GENCOms. Therefore, there lies a link between them delineated as a matrix entitled DPM. Each term of the matrix is called cpf’s (as shown in Section 2.1.1).

In the Poolco scheme, the GENCOms of the concerned area can maintain contact with DISCOms of the same area. Over here the GENCOms of area-1 (GPP, thermal, gas) or area-2 (thermal, hydro, wind) can perform depending on which areas DISCOm is demanding. Here, analysis is done using System B. So, now for assessment it is considered that DISCOms of area-1 are demanding 0.01p.u. MW each which needs to be accomplished by GENCOms of area-1. The considered DPM is provided by (34) where zero represents the non-participating DISCOms. Thus, the apf’s are apf₁₁= 0.33, apf₂₁= 0.37, apf₃₁= 0.30. (34) $\begin{array}{r}\text{DP}{\text{M}}_{\text{poolco}}=\left[\begin{array}{cccccc}0.33& 0.33& 0.33& 0& 0& 0\\ 0.37& 0.37& 0.37& 0& 0& 0\\ 0.3& 0.3& 0.3& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]\end{array}$(34) Initially the system is fed with I controller to obtain its gain values as well as the parameters of GPP (G_GPP and T_GPP) using TSA. The governor and turbine time constants (G_GPP and T_GPP) obtained are 0.1 s for both cases and are kept the same for the rest of the work. The system is then introduced with PI/PIDN/ PDN(FOPI) on an individual basis. The best available values of each of the controller gains and parameters are acquired using TSA by using Pi_ISE (equation given by (29)). The best possible values are marked down in Table 1 and with these dynamic responses are acquired as shown in Figure 3(a,b). The simulation is carried forward for the analysis of area control error (ACE) and amount of power deviation of GENCOm. The comparison of the amount of power deviations of GENCOm₁ and GENCOm₃ (here GENCOm is wind) of area-1 and 2 is shown in Figure 3(c,d). And ACE corresponding to area-1 (i.e. ACE₁) is reflected in Figure 3(e). Analysis of Figure 3(a−e) reflects the excellence of PDN(FOPI) over other controllers regarding lessened levels of P_O, P_U as well as S_T. The values of Pi_ISE for I, PI, PIDN and PDN(FOPI) controllers are provided in Table 6 which says the PDN(FOPI) controller provides the least value of error. The performance of the PDN(FOPI) controller is with few recently published controllers in the field of AGC. So, the considered controllers are fractional order proportional integral derivative (FOPID) [25] and cascade combination of proportional–integral–derivative with filter and fractional order integrator (PIDN-FOI) [16]. The dynamic response comparison is provided in Figure 3(f) which reflects the better performance of the PDN(FOPI) controller.

Figure 3. Assessment of responses of controllers I, PI, PIDN and PDN(FOPI) under the Poolco scheme and performance comparison of PDN(FOPI) with recently published controllers: (a) frequency abnormalities of area-1 Vs. time, (b) tie line power error aberration Vs. time, (c) aberration in power output of GENCOm₁₁ Vs. time, (d) aberration in power output of GENCOm₂₃ Vs. time, (e) area control error of area-1 Vs. time and (f) area-1 frequency aberration Vs. time (comparison with recently published controllers).

Table 1. Attributes of I, PI, PIDN and PDN(FOPI) controllers for poolco scheme.

Controller	Gains/Parameter	Area-1	Area-2
I	KIi*	0.9975	0.9987
PI	KPi*	0.0014	0.0026
	KIi*	0.8986	0.9387
PIDN	KPi*	0.0859	0.0973
	KIi*	0.6677	0.6937
	KDi*	0.5795	0.3523
	Ni*	26.93	11.08
PDN(FOPI)	KPi*	0.9859	0.9950
	KDi*	0.5085	0.5858
	Ni*	49.55	54.48
	KFPi*	0.9997	0.9867
	KFIi*	0.9975	0.7663
	λi*	1.0011	1.0299

4.1.2 Selection of performance index (Pi)

The leading performance index (Pi) amongst integral squared error (Pi_ISE), integral time squared error (Pi_ITSE), integral absolute error (Pi_IAE) and integral time absolute error (Pi_ITAE) are acquired by facilitating System-B with each of these Pi on individual terms using the PDN(FOPI) controller. The best values of PDN(FOPI) controller gains and parameters are obtained using the TSA algorithm. The expressions for Pi_ISE, Pi_ITSE, Pi_IAE, and Pi_ITAE are given by (27)−(30), respectively. Using the best values obtained for the PDN(FOPI) controller in each case the dynamic responses are contrasted in Figure 4(a, b). A critical view of the responses says responses considering Pi_ISE as a performance index have better performance compared to others with respect to lessened P_U and S_T. Further, the values of Pi are Pi_ISE = 0.0007, Pi_ITSE = 0.0012, Pi_IAE = 0.1381 and Pi_ITAE  = 0.8982, which says about better performance of system with Pi_ISE.

Figure 4. Assessment for the nomination of performance index (Pi) and algorithm separately for using PDN(FOPI) controller using System-B under the Poolco scheme: (a) area-2 frequency aberration Vs. time (Pi selection), (b)tie line power aberration for line interconnecting area-1 and area-2 Vs. time(Pi selection), (c) area-2 frequency aberration Vs. time (algorithm selection), and (d) convergence curve (algorithm selection).

4.1.3 Selection of algorithm

For the selection of algorithm, the system-B is provided with different algorithms separately using the PDN(FOPI) controller under the Poolco scheme. The algorithms used here are particle swarm optimization (PSO), cuckoo search algorithms (CS), firefly algorithm (FA), lightning search algorithm (LSA) and TSA. For PSO the tuned parameters values are w = 1, w_damp = 0.99, c1 = 1.4, c2 = 1.98, population size  = 50, maximum generation number = 1000. The tuned values for FA are β₀ = 0.3, α = 0.5, γ = 0.4, count of fireflies = 50 and the maximum number of generation = 1000. For CS, nest count = 50, rate of discovery = 0.5, exponent of levy = 1.5, maximum generation  = 1000 and count of dimensions = 10. For LSA, the tuned parameters are number of search agents = 50, channel time = 10 and maximum number of iterations = 1000. For each of the algorithm, the best values for the PDN(FOPI) controller are obtained. The values are not provided here. With these values, the responses of different algorithms are contrasted in Figure 4(c). The analysis reflects the better performance of TSA regarding P_U and S_T. Further, the supremacy is judged by the convergence curve provided in Figure 4(d), where it is observed that the response with TSA-optimized PDN(FOPI) controller is converging faster and has the least value of Pi_ISE. Therefore, further analysis iscarried out using the TSA algorithm.

4.2 Evaluation of dynamic outcomes in the bilateral scheme

In a bilateral scheme, the GENCOms of the concerned area can maintain contact with DISCO of any area.

This is maintained by the DPM_A mentioned in (35). (35) $\begin{array}{r}\text{DP}{\text{M}}_A=\left[\begin{array}{cccccc}0.2& 0.1& 0.2& 0.2& 0.1& 0.2\\ 0.2& 0.2& 0.1& 0.2& 0.2& 0.1\\ 0.2& 0.1& 0.2& 0.1& 0.2& 0.2\\ 0.1& 0.2& 0.1& 0.1& 0.2& 0.1\\ 0.1& 0.2& 0.2& 0.2& 0.2& 0.2\\ 0.2& 0.2& 0.2& 0.2& 0.1& 0.2\end{array}\right]\end{array}$(35) The addressed apf’s for analysis are fixed by the approach highlighted by Parida and Nanda in [12]. So, now for assessment, it is considered that DISCOms of area-1 are demanding 0.02 p.u. MW and area-2 are demanding 0.03 p.u. MW. Thus, the apf’s of GENCOms of area-1 are apf₁₁= 0.33, apf₂₁= 0.34 and apf₃₁= 0.33 and for GENCOms of area-2 are apf₁₂= 0.267, apf₂₂= 0.367 and apf₃₂= 0.366. Here, analysis is done for System B. The system is introduced with controllers I/PI/PIDN/PDN(FOPI) on an individual basis. The best feasible values of each of the controller gains and parameters are acquired by employing TSA, by using Pi_ISE. The best possible values are marked down in Table 2 and with these dynamic responses are acquired as shown in Figure 5(a−c). The comparison of amount of power deviations of GENCOm₃ of area-1 is displayed in Figure 5(b). And ACE corresponding to area-2 (i.e. ACE₂) is reflected in Figure 5(c). Analysis of Figure 5(a−c) reflects the excellence of PDN(FOPI) over other controllers regarding lessened level of P_O, P_U as well as S_T under the bilateral scheme for system-B. Again the values of Pi_ISE for I, PI, PIDN and PDN(FOPI) controllers provided in Table 6 say that _the PDN(FOPI) controller is providing the least value of error. According to theoretical calculation, the aberration of power of GENCOM₃ of area-1 should be around 0.02 p.u. MW which is obtained by simulation as visible in Figure 5(b). Also, the ACE₂ (Figure 5(c)) is brought back to zero. The performance comparison of the PDN(FOPI) controller with FOPID [25] and PIDN-FOI [16] is provided in Figure 5(d) which reflects the better performance of the PDN(FOPI) controller.

Figure 5. Assessment of responses of controllers I, PI, PIDN and PDN(FOPI) without HAE(FC) and RFB under the bilateral scheme: (a) area-1 frequency irregularity contradiction time, (b) area-2 frequency irregularity contradiction time, (c) tie line power error irregularity contradiction time and (d) aberration in power output of GENCOm₁₃ contradiction time.

Table 2. Best values of attributes of I, PI, PIDN and PDN(FOPI) controllers aimed at the bilateral scheme.

Controllers	Gains/Parameters	Area-1	Area-2
I	KIi*	0.9740	0.9852
PI	KPi*	0.4714	0.5121
	KIi*	0.5684	0.5074
PIDN	KPi*	0.0086	0.0085
	KIi*	0.7578	0.6846
	KDi*	0.1883	0.3965
	Ni*	18.23	17.45
PDN(FOPI)	KPi*	0.9852	0.9963
	KDi*	0.8509	0.9852
	Ni*	48.42	71.70
	KFPi*	0.5659	0.9885
	KFIi*	0.9761	0.9796
	λi*	1.1332	1.1360

4.3 Evaluation of dynamic outcomes in the contract violation scheme

In this instance of contract violation, it is considered that DISCOm₃ of area-1 demands supplementary power of 0.02 p.u. MW. This amount of add-on demand necessitates being managed by GENCOms of area-1 itself (i.e. by GENCOm₁, GENCOm₂, GENCOm₃). Thus, the total local load along with the uncontract load of area-1 is given by (36). (36) $\begin{array}{r}\mathrm{\Delta }{P}_{\text{local,1}}=\left(\right(0.02+0.02+0.02)+0.02)=0.08\text{p}\text{.u}\text{.}\text{MW}\end{array}$(36) Thus, this interaction of DISCOms and GENCOms along with the uncontracted load is given by the DPM_B mentioned in (37). (37) $\begin{array}{r}\text{DP}{\text{M}}_B=\left[\begin{array}{cccccc}0.1& 0.25& 0.1& 0.1& 0.25& 0.2\\ 0.1& 0.1& 0.2& 0.25& 0.25& 0.1\\ 0.1& 0.2& 0.25& 0.1& 0.2& 0.1\\ 0.2& 0.1& 0.25& 0.1& 0.1& 0.1\\ 0.25& 0.1& 0.1& 0.2& 0.1& 0.25\\ 0.25& 0.25& 0.1& 0.25& 0.1& 0.25\end{array}\right]\end{array}$(37) The apf’s are apf₁₁=2 0.33, apf₂₁= 0.34 and apf₃₁= 0.33 for area-1 and for area-2 the apf’s are apf₁₂= 0.258, apf₂₂= 0.379 and, apf₃₂= 0.363. The analysis is performed for System B. The scheme is imported with controllers I/PI/PIDN/PDN(FOPI) on the respective base. The outstanding obtainable values of any of the controller attributes are attained by employing TSA, by adopting Pi_ISE. The outstanding achievable values are manifested in Table 3 and outcomes are accomplished as revealed in Figure 6(a,b). The theoretical value for power deviations of GENCOm₁ of area-1 is given by (38). (38) $\begin{array}{rl}\mathrm{\Delta P}{g}_{11}& =\left(\right(0.1+0.25+0.1+0.1+0.25+0.2)\times 0.02)\\ & +(0.33\times 0.02))=0.0266\text{p}\text{.u}\text{.}\text{MW}\end{array}$(38) The comparison of the amount of power deviations of GENCOm₁ of area-1 is demonstrated in Figure 6(c). And ACE corresponding to area-1 (i.e. ACE₁) is reflected in Figure 6(c).

Figure 6. Assessment of results of controllers alike I, PI, PIDN and PDN(FOPI) deprived of HAE(FC) besides RFB under contract violation scheme: (a) area-1 frequency irregularity contradiction time, (b) area-2 frequency irregularity contradiction time, (c) tie line power error aberration Vs. time and (d) aberration in power output of GENCOm₁₁ Vs. time.

Table 3. Finest values of attributes of I, PI, PIDN and PDN(FOPI) controllers for the contract violation scheme.

Controllers	Gains/Parameters	Area-1	Area-2
I	KIi*	0.8728	0.8624
PI	KPi*	0.0954	0.0165
	KIi*	0.6936	0.6405
PIDN	KPi*	0.0958	0.0985
	KIi*	0.5306	0.6449
	KDi*	0.2013	0.3965
	Ni*	11.74	10.51
PDN(FOPI)	KPi*	0.9891	0.9616
	KDi*	0.8639	0.8612
	Ni*	28.26	32.01
	KFPi*	0.8390	0.7123
	KFIi*	0.9728	0.9831
	λi*	1.0508	1.0979

The analysis of Figure 6(a−c) reflects the excellence of PDN(FOPI) over other controllers regarding the lessened level of P_O, P_U as well as S_T under the contract violation scheme for system-B. Again the values of Pi_ISE for I, PI, PIDN and PDN(FOPI) controllers provided in Table 6 say that the PDN(FOPI) controller is providing the least value of error. According to theoretical calculation, the aberration of power of GENCOM₁ of area-1 should be 0.0266 p.u. MW which is obtained near about by simulation as visible in Figure 6(b). Also, ACE₁ (Figure 6(c)) is brought back to zero. The performance comparison of the PDN(FOPI) controller with FOPID [25] and PIDN-FOI [16] is provided in Figure 6(d) which reflects the better performance of the PDN(FOPI) controller.

4.4 Impact of renewables (GPP and wind) on system dynamics under different schemes

Now, the impact of GPP and wind is examined by comparing dynamic responses (system with GPP and wind) with the responses of the two-area system having thermal, thermal and gas in area-1, thermal, hydro, thermal in area-2 under the restructured situation. This system is entitled System A. The GPP and wind source are replaced by a thermal source of the same capacity to perform analysis. PDN(FOPI) is considered a secondary controller and its gains best values are noted in Table 4 separately for Poolco, bilateral and contract violation. With these values the responses are contrasted in Figure 7 (Figure 7(a) for Poolco, Figure 7(b) for bilateral and Figure 7(c) for contract violation) for systems with and without GPP and wind. A critical view of each response says about the excellence of system dynamics in the presence of GPP and wind regarding the lessened level of peak_overshoot, extent-of-oscillations, peak_undershoot as well as settling_time using the PDN(FOPI) controller under each scheme of Poolco, bilateral and contract violation. The system without GPP and wind degrades to a great extent. Only one response is provided here for each schemes.

Figure 7. Assessment of impact of GPP and wind on system dynamics using PD(FOPI)controller: (a) tie line power error aberration Vs. time under the poolco scheme, (b) area-2 frequency aberration Vs. time under the bilateral scheme, and (c) area-1 frequency aberration Vs. time under the contract violation scheme.

Table 4. Best values of gains and parameters of PDN(FOPI) controllers for the system without GPP and Wind under poolco, bilateral and contract violation schemes separately.

System without GPP and wind for Poolco scheme
Controller	Gains/Parameters	Area-1	Area-2
PDN(FOPI)	KPi*	0.7012	0.8428
	KDi*	0.9585	0.7435
	Ni*	89.66	79.24
	KFPi*	0.7417	0.8201
	KFIi*	0.8484	0.8474
	λi*	1.1026	1.1493
System without GPP and wind for Bilateral scheme
Controller	Gains/Parameters	Area-1	Area-2
PDN(FOPI)	KPi*	0.4378	0.2104
	KDi*	0.8527	0.9342
	Ni*	85.09	71.37
	KFPi*	0.4703	0.8030
	KFIi*	0.5398	0.8526
	λi*	1.0933	1.0988
System without GPP and wind for Contract violation scheme
Controller	Gains/Parameters	Area-1	Area-2
PDN(FOPI)	KPi*	0.4896	0.5272
	KDi*	0.8580	0.4836
	Ni*	35.53	20.67
	KFPi*	0.0828	0.0729
	KFIi*	0.3049	0.3645
	λi*	1.1925	1.0997

4.5 Impact of HAE(FC) and RFB on system dynamics under different schemes

Here, the impact of energy-storing devices HAE(FC) (described in Section 2.2) and RFB (described in Section 2.3) is examined by comparing its responses with the responses of two-area systems named as system B. System B is incorporated with HAE(FC) in area-1 and RFB in area-2. This system is entitled as system C (Figure 2(a)). The main purpose of AGC is to maintain frequency as well as tie power at a scheduled value. These values deviate even with minute changes in load due to the transformation of kinetic energy to electrical energy. An energy-storing device if incorporated will draw some amount of surplus power, which leads to lesser utilization of kinetic energy while mitigating small demand in load. So energy storing devices are used. PDN(FOPI) is considered a secondary controller and its gains best values are noted in Table 5 separately for Poolco, bilateral and contract violation. With these values, the responses are contrasted in Figure 8 (Figure 8(a) for Poolco, Figure 8(b) for bilateral and Figure 8(c) for contract violation) for systems with and without HAE(FC) and RFB. A critical view of each response says about the excellence of system dynamics in the presence of HAE(FC) and RFB regarding lessened level of P_O, P_U, S_T using the PDN(FOPI) controller under each scheme of Poolco, bilateral and contract violation. Only one response is provided here for each scheme. The linearized model of RFB used for the study is provided in Figure 8(d).

Figure 8. Assessment of the impact of HAE(FC) and RFB on system dynamics using PDN(FOPI)controller: (a) area-2 frequency aberration Vs. time under the poolco scheme, (b) tie line power error aberration Vs. time under the bilateral scheme, and (c) area-2 frequency aberration Vs. time under the contract violation scheme.

Table 5. Best values of gains and parameters of PDN(FOPI) controllers for system with HAE(FC) and RFB under poolco, bilateral and contract violation scheme separately.

System with HAE(FC) and RFB for Poolco scheme
Controller	Gains/Parameters	Area-1	Area-2
PDN(FOPI)	KPi*	0.9097	0.9057
	KDi*	0.9953	0.9986
	Ni*	98.53	98.25
	KFPi*	1.2888	1.2474
	KFIi*	1.3219	1.2447
	λi*	1.0152	1.0049
System with HAE(FC) and RFB for the bilateral scheme
Controller	Gains/Parameters	Area-1	Area-2
PDN(FOPI)	KPi*	0.9898	0.9750
	KDi*	0.9629	0.9960
	Ni*	76.86	73.32
	KFPi*	0.7995	0.9988
	KFIi*	0.9965	0.9859
	λi*	1.1097	1.2309
System with HAE(FC) and RFB for the contract violation scheme
Controller	Gains/Parameters	Area-1	Area-2
PDN(FOPI)	KPi*	0.9888	0.9999
	KDi*	0.5984	0.2959
	Ni*	47.92	51.30
	KFPi*	1.2955	1.0022
	KFIi*	1.1550	1.1258
	λi*	1.0200	1.1909

4.6 Convergence profile of different studies

In this section, the Pi_ISE value is compared for all the cases and the values are provided in Table 6. From Table 6 it is visible that under all the schemes (i.e. Poolco, bilateral, contract violation) of the restructured power system, the value of performance index ISE (Pi_ISE) is least when the PDN(FOPI) controller is used as a secondary controller compared to I/PI/PIDN/FOPID/PIDN-FOI controllers. Amongst all case studies, the system incorporated with HAE(FC) and RFB using the PDN(FOPI) controller is providing the least value of Pi_ISE for Poolco, bilateral as well as contract violation.

Table 6. Convergence profile of different studies.

Section	Value of PiISE
4.1.1	I	PI	PIDN	PDN(FOPI)	FOPID	PIDN-FOI
	0.0021	0.0020	0.0015	0.0007	0.0011	0.0013
4.2	I	PI	PIDN	PDN(FOPI)	FOPID	PIDN-FOI
	0.0377	0.0506	0.0274	0.0093	0.0155	0.0167
4.3	I	PI	PIDN	PD(FOPI)	FOPID	PIDN-FOI
	0.0451	0.0509	0.0371	0.0130	0.0248	0.0370
4.4	PDN(FOPI)in Poolco	PDN(FOPI)in Bilateral	PDN(FOPI)in Contract violation
	0.0141	5.5533	7.8737
4.5	PDN(FOPI)in Poolco	PD(FOPI)in Bilateral	PDN(FOPI)in Contract violation
	0.0004	0.0062	0.0079

*Bold signify best values.

4.7 Assessment of DPM sensitivity

Here analysis is done to evaluate the behaviour of the system during variations in market demands considering different DPMs. Utilizing the same best values of PDN(FOPI) in the presence of HAE and FC under the bilateral scheme (given in Table 3 of Section 4.2.3), the system is provided with other DPMs like DPM_B (given by (37)) and DPM_C given by (39). (39) $\begin{array}{r}\text{DP}{\text{M}}_C=\left[\begin{array}{cccccc}0.4& 0.4& 0.2& 0.05& 0.25& 0.05\\ 0.2& 0.25& 0.25& 0.05& 0.2& 0.2\\ 0.25& 0.05& 0.05& 0.05& 0.4& 0.25\\ 0.05& 0.05& 0.4& 0.4& 0.05& 0.05\\ 0.05& 0.05& 0.05& 0.2& 0.05& 0.05\\ 0.05& 0.2& 0.05& 0.25& 0.05& 0.4\end{array}\right]\end{array}$(39) The assessment of responses corresponding to DPM_A, DPM_B and DPM_C reflected in Figure 9 shows that all the responses are almost identical. Thus, the system behaviour does not undergo alteration unfavourably when DPMs are different. So, the influence of altering DPMs is insignificant.

Figure 9. Assessment of dynamic responses with best values of PD(FOPI) controller using DPM_A (with HAE(FC) and RFB) when exposed to diverse DPMs: (a) frequency abnormalities of area-1 Vs. time, (b) frequency abnormalities of area-2 Vs. time and (c) tie line power error aberration Vs. time.

4.8 Robustness assessment

To examine the durability of TSA-optimized controller gains, a sensitivity analysis is performed using a  ± 25% difference in loading circumstances and inertia constant (H). The controller gains and settings are individually tuned for each changed situation, however precise values of optimal gains for the various changed circumstances are not supplied in this context. The answers acquired under changing conditions, together with their corresponding optimized controller gain levels, are then compared to those produced under nominal settings. As seen in Figure 10, the answers behave remarkably identically under both modified and nominal settings. As a result, it can be concluded that the TSA-optimized gains and parameters of the PDN(FOPI) controller are resilient under nominal circumstances and do not require revisions to account for fluctuations in loads and system factors.

Figure 10. Comparison of dynamic responses for the changed condition of ±25% of system loading and inertia constant (H) under bilateral scenario: (a) frequency abnormalities of area-1 Vs. time for +25% loading condition, (b) frequency abnormalities of area-2 Vs. time for -25% loading condition, (c) tie line power error aberration Vs. time for +25% of inertia constant, and (d) tie line power error aberration Vs. time for −25% of inertia constant.

5. Conclusion

The studied research focuses on the novel integration of HAE(FC) in the area of load frequency control (LFC) in restructured situations. Under Poolco, bilateral and contract violation situations, the combined efficacy of HAE(FC) and RFB in the analysed system results in lower peak anomalies, a larger range of oscillations and faster settling time. A novel technique is used to create a hybrid controller in LFC, which combines proportional-derivative with filter (PDN) (integer-order) and fractional order proportional–integral (FOPI). The tunicate swarm algorithm (TSA), a recently created meta-heuristic algorithm inspired by tunicates’ biological properties, is effectively used to find gains and settings for various controllers.

PDN(FOPI) performance is compared to standard controllers in a variety of settings. In addition, a PDN(FOPI) controller is used to assess the influence of geothermal power plants and wind. The PDN(FOPI) controller's robustness is evaluated using various Disco Participation Matrix (DPMs), system loads and inertia constants. The results show that the ideal values for PDN(FOPI) gains and parameters are adequate, indicating that no changes are required despite differences in disturbance rejection mechanisms.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Appendix

Thermal component: T_r1 = 10 s, K_r1 = 5, T_t1 = 0.3 s, T_g1 = 0.08 s;

Gas component: C_g1 = 1, X_g1 = 0.6 s, B_g1= 0.049 s, T_cd1 = 0.2 s, Y_g1 = 1.1 s, T_f1= 0.239 s,

T_cr1= −0.01 s;

RFB: K_r1= 1,T_r1=  0.78 s, T_d1= 0, K_RFB1 = 1.8;

Wind: K_wp1 = 1.25, T_wp1= 6 s, K_wp2 = 1.4, T_wp1= 0.041 s;

Hydro: T_R= 5 s, T_RH = 48.7 s, T_W = 1 s, T_GH = 0.513 s;

HAE(FC): K_HAE= 0.002, T_HAE= 0.5 s, K_FC= 0.01, T_AE= 4.0 s.