Frequency regulation of geothermal power plant-integrated realistic power system with 3DOFPID controller

Abstract

In this article, a higher-order degree of freedom (DOF) proportional–integral–derivative (PID) (3DOFPID) controller optimized with the meta-heuristic method of the water cycle algorithm (WCA) is proposed. Initially, WCA-tuned 3DOFPID is designed to the widely accepted power system model of two-area simple hydro-thermal (TASHT) system and the presented controller efficacy is revealed with other techniques discussed in the literature. Later, another interconnected power system model of two areas nonlinear realistic hydro thermal (TANRHT) system is considered for the investigative purpose by subjugating area-1 with step load perturbation (SLP) of 10%. The proposed controller is implemented to TANRHT without and with deliberating the integration of a geothermal power plant (GTPP). Dynamical responses of TANRHT reveal the efficacy of 3DOFPID over PID and 2DOFPID. Further, the impact of GTPP integration on the performance of the TANRHT system is demonstrated. Furthermore, the coordinated territorial strategy of superconducting magnetic energy storage (SMES) and unified power flow controller (UPFC) is enacted with GTPP-integrated TANRHT system for performance improvement. Finally, the sensitivity analysis is conducted to reveal the robustness of proposed secondary and territorial control strategies.

Keywords:

• Water cycle algorithm
• 3DOFPID
• 10% SLP
• SMES-UPFC strategy
• GTPP integration

REVIEWING EDITOR:

• Ai Qingsong, Senior Editor, Wuhan University of Technology, China

SUBJECTS:

• Technology
• Engineering & Technology
• Electrical & Electronic Engineering
• Power & Energy
• Systems & Control Engineering
• Clean Tech

1. Introduction

The modern-day interconnected power system (IPS) employs diverse generation sources for electric power production. These diverse generation sources are interconnected with neighboring areas via tie-line to form a multi-area network. Moreover, the complexity of multi-area networks has been becoming large especially when it comes to the integration of intermittent power generating sources like renewable energy. Establishing security and stability of complex modern-day IPS has been a prominent task and can be safeguarded by the load frequency controller (LFC). LFC ensures an uninterrupted power supply and good-quality power to the consumer end. The ability to stabilize the frequency is a major measure of the power’s quality. LFC of a multi-area IPS network is more crucial than that of an isolated one (Srikanth Goud et al., 2022). Besides LFC, the other crucial task that is associated with the control of IPS is the regulation of real power exchange between the control regions. Further, the redistribution of generation with regards to the varying load demand on the multi-area IPS is the most significant job.

The real power mismatch that is the difference in real power demand and generation is the key parameter to be addressed in ensuring the stability of multi-area IPS. The real source of imbalance is directly related to frequency changes and LFC minimizes the real power mismatch by varying the power system operating point (PSOP). LFC comprises primary and secondary regulation loops (Kalyan & Rao, 2020). The impact of small load perturbations on the IPS performance is taken care of by the primary regulator through the speed governing action. However, the primary regulator could not able to handle the dynamic behavior of IPS under large load perturbations. As a result, a secondary regulator is required for the IPS network to ensure better performance. For the past four decades, researchers around the world are rigorously focused on designing secondary regulators for LFC of multi-area IPS networks.

Earlier researchers are concentrated on implementing traditional integral order (IO)-type regulators such as PI and PID (Padhan et al., 2014) and modified (M) IO regulators like MPID (Challapalli, Srikanth Goud, Kiran Kumar et al., 2022), PID plus acceleration (PIDA) (Kumar & Hote, 2018) and PID plus double derivative (DD) PIDD (Challapalli et al., 2022a) for the issues to be handled in the LFC. However, the operational efficacy of IO-type regulators is highly dependent on parametric values. Soft computing algorithms like particle swarm optimizer (PSO) (Panwar et al., 2018), coefficient diagram approach (CDA), backtracking search algorithm (BSA) (Challapalli et al., 2022b), symbiotic organism search (SOS) algorithm (Hasanien & El-Fergany, 2017), marine predator algorithm (MPA) (Kalyan, Srikanth Goud, Kiran Kumar, et al., 2022), grasshopper algorithm (GA), water cycle algorithm (WCA) (Harideep et al., 2022), bacterial foraging optimization (BFO) (Kalyan, Reddy, et al., 2023), selfish herd optimizer (SHO), dual-stage PSO, differential evolution (DE) (Ganji & Ramraj, 2021), elephant heard optimizer (EHO) (Dewangan et al., 2021), grey wolf optimization (GWO) (Kalyan, Reddy, et al., 2023), harmony search algorithm (HSA) (Shiva et al., 2022), mine blast optimization (MBO) (Kalyan, Goud, Muppoori, et al., 2023), cuckoo search algorithm (CSA) (Kalyan, Goud, Kumar, et al., 2023), imperialistic competitive algorithm (ICA) (Nayak et al., 2021), Harris Hawks optimization (HHO) (Sai Kalyan et al., 2023), population extremal optimization (PEO) (Sai Kalyan et al., 2022), seagull optimization algorithm (SOA) (Kalyan & Suresh, 2022), ant colony technique (ACT) (Dhanasekaran et al., 2020), gravitational search algorithm (GSA) and DE-artificial field algorithm (DE-AEFA) (Kalyan, Srikanth Goud, Reddy, et al., 2022) are reported for fine-tuning of IO-type regulators in the study of LFC. However, IO-type regulators are not effective for the power system models with nonlinearity constraints of generation rate constraint (GRC) and governor dead band (GDB).

Considering the limitations of traditional IO-type regulators, researchers are tried to adopt fractional order (FO) type IO regulators as a secondary regulator to IPS models to limit the control area frequency deviations. Regulators like FOPI, FOPID, tilt-integral-derivative (TID) and the FO cascaded with IO are available widely in the literature. However, researchers had considered population-based various optimizations like whale optimization algorithm (WOA) (Saha & Saikia, 2018), sine-cosine algorithm (SCA) (Tasnin et al., 2018), multi-verse optimization (MVO) (Kalyan, Goud, Bajaj, et al., 2022), volleyball algorithm (VBA) (Prakash et al., 2019), big-bang big-crunch (BBBC) (Kalyan, Goud, Reddy, et al., 2022), lion optimization technique (LOT) (Sharma & Yadav, 2019) and ant lion optimizer (ALO) (Kalyan, Goud, et al., 2021) in order to obtain optimal performance. A literature survey disclosed the supremacy of FO-type regulators over classical IO-based controllers. However, considering the aspects of implementing the FO-type regulators in realistic practice as secondary regulators getting the desired position of the PSOP might not be easy. Because the FO type involves additional knobs to be varied and also finding the optimal gains to all the parameters laid a considerable computational burden on optimization algorithms. Considering the aforementioned, fuzzy logic controllers (FLC) are widely implemented to LFC by the researchers. Fuzzy (F)-type controllers such as simulated annealing (SA) (Naga Sai Kalyan et al., 2022)-based FPI, MVO (Kouba et al., 2018), DE-pattern search (Belkhier et al., 2022), HSA (Shahzad et al., 2022), PSO (Bevrani et al., 2012), SCA (Rajesh & Dash, 2019) tuned FPID and Type-II FLC based on optimizations such as WCA (Goud et al., 2021), ICA (Pachauri et al., 2023) and GWO-SCA (Sahu et al., 2020). In addition to FLC, neural network (NN) (Khosravi et al., 2023) architectures and adaptive FLC (Jena et al., 2023) are reported in the LFC study. Designing FLC and NN is complex and also requires skillful technicians and experts; however, the selection of membership functions and rule-based inference system includes many assumptions. These assumptions might degrade the FLC performance and thereby, the operation of IPS.

Conversely, higher-order degree of freedom (DOF) controllers are becoming more popular and are used as an IPS for LFC secondary regulator. The benefit of accompanying independent closed-loop controls in DOF regulators encourages researchers all over the world to adopt for LFC study. Regulators like WOA (Simhadri et al., 2018), SOA (Kalyan, Syed, et al., 2021), DE (Sahu et al., 2013), JAYA (Guha et al., 2022)-based 2DOFPID, equilibrium optimizer (EO) (Srikanth Goud et al., 2023) and SOA (Sahoo et al., 2023) are reported. Moreover, the supremacy of DOF regulators over conventional IO, FO type and FLC regulators are demonstrated and validated in Biswas et al. (2021) and Rahman et al. (2015). As consequence, in this article, a 3DOFPID regulator is used to a nonlinear realistic multi-area IPS as secondary regulator.

Besides the selection of the regulator and the optimization technique, the researchers have shown diversity in adopting the test system models in order to exploit and validate the implementation issues of the suggested control approaches at the secondary and territory levels. Numerous test system models, as extensively reported in Fernández-Guillamón et al. (2022) and Obaid et al. (2019), such as one-area, two-area and three-area IPS networks, comprise traditional generation sources like thermal, hydro, gas and diesel units, of which only a few are examined with GRC and GDB constraints. Moreover, test system models with greater attention to nonconventional generation units are also reported. The nonconventional sources of solar photovoltaic, dish-stirling thermal and wind energy conversion systems are extensively considered by the research community in the domain of LFC to assess the IPS dynamic behavior. Geo-thermal energy is also a nonconventional type of source and is utilized in producing electricity, but it is not examined in LFC for frequency regulation studies. The United States stood first in harnessing electricity from geo-thermal sources, followed by Indonesia and the Philippines. Countries like El Salvador, Ice Land, Kenya and Costa Rica are also generating electricity from the geothermal sites. In India, there are several potential geothermal reservoirs that are situated in the provinces of Kashmir, Chhattisgarh and Jharkhand, and there is a proposal to set up a geothermal power plant (GTPP) in the Himalayan range of Kashmir province. In terms of electricity generation, the GTPP is a very reliable and potential energy source from a nonconventional source and differs from traditional thermal units by its particulate matter and size. Therefore, a detailed analysis of the GTPP’s dynamic behavior and the effects of its incorporation with the IPS thereafter are required. In Tasnin et al. (2018) and Tasnin and Saikia (2018), GTPP is considered for LFC analysis, and the study was limited to the consideration of FO controllers. A thorough investigation is to be carried out by considering the GTPP to examine the challenges that are to be incurred with the existing IPS network during integration. Hence, extensive investigations on the LFC of IPS with GTPP integration are to be examined to a wider extent. Thus, this work considered the test system model with the GTPP integration that was not rigorously investigated in the literature.

The contributions of this work are

• The WCA-based 3DOFPID is intended to serve as a supplementary regulator for IPS in order to achieve frequency control.

• The two-area simple hydro-thermal (TASHT) and two areas nonlinear realistic hydro thermal (TANRHT) power system models considered for study in this article are modeled in MATLAB/SIMULINK (R2016a) domain.

• Carried out the analysis on both the IPS models for 10% step load perturbation (SLP) on area-1.

• Efficacy of 3DOFPID based on WCA is revealed with DE-AEFA-based PID- and SOA-tuned PIDD techniques listed in the literature recently.

• Performance superiority of 3DOFPID is further showcased with PID and 2DOFPID regulators by testing them on the TANRHT system with and without GTPP integration.

• The effect of GTPP integration on TANRHT system performance is demonstrated.

• UPFC-SMES territorial strategy is implemented on GTPP-integrated TANRHT system for further performance enhancement.

• The sensitivity test is conducted with different load conditions and also with random loadings to validate the designed secondary and territory control mechanisms.

2. Power system under investigation

Two power system frameworks were explored in this work to evaluate the suggested secondary regulator for better frequency regulation. First, area-1 is subjected to 10% SLP in order to investigate the TASHT system shown in Figure 1. Subsequently, as shown in Figure 2, the proposed controller is put into practice in the TANRHT system. For both the power system frameworks, the modeling was created using the MATLAB/SIMULINK (R2016a) platform. The dynamical study of both power system models is performed on subjugating area-1 with a 10% SLP disturbance. Furthermore, the renewable-based power generation of GTPP is incorporated with the TANRHT system and its impact on IPS performance is analyzed. The necessary parameters to design TASHT and TANRHT models are considered from Kalyan and Suresh (2022), Choudhury et al. (2023) and Tasnin et al. (2018), respectively. TASHT and TANRHT parameters are shown in Appendix.

Figure 1. Transfer function model of TASHT system.

Figure 2. Transfer function model of TANRHT system with UPFC-SMES.

3. Controller and objective function

With the integration of sensing devices and remote terminal units with the IPS, the complexity has been increasing. Thus, an effective and supreme controller is necessitated to regulate the dynamical behavior of complex IPS with nonlinear realistic constraints. Traditional IO-type regulators fine-tuned with different stochastic-based and nature-inspired population-based optimization techniques are rigorously reported in the literature. However, meta-heuristic optimization techniques based on classical IO-type regulators are best suitable for simple linearized IPS and are not robust enough for complex nonlinear realistic models. Thus, this article focuses on designing soft computing techniques based on higher order DOF controllers for complex IPS to keep the power system indicators within specified limits under fluctuating load demands. The order of the DOF controller determines the number of closed-loop transfer functions that may be adjusted individually. Hence, this article designs 3DOFPID which enhances overall stability while eliminating the disturbance.

The structure of 3DOF (Rahman et al., 2015) is shown in Figure 3, where R(s) indicates the reference signal, C(s) indicates a single DOF controller, P(s) indicates plant, D(s) is the disturbance, FF(s) indicates feed-forward regulator and the output of investigative test system model is given as feedback to DOF regulator and is indicated with Y(s), RC(s) indicates input reference regulator. The structure of 3DOFPID is shown in Figure 4 and is modeled mathematically in the closed loop transfer function as given in (1).

Figure 3. Architecture of 3DOF controller.

Figure 4. Structure of 3DOFPID controller.

(1) $$Y(s)=\left[\frac{P(s)C(s)}{1+P(s)C(s)}\right]R_C(s)+\left[\frac{P(s)-P(s)C(s)\text{FF}(s)}{1+P(s)C(s)}\right]D(s)$$(1)

The enhancement in closed-loop stability is facilitated by the indicator C(s), the output response is influenced by R(s), and the elimination of disturbance is safeguarded by the indicator FF(s) subjected to the satisfaction of Equation (2)(2) $$P(s)-P(s)C(s)\text{FF}\mathrm{(}s\mathrm{)}=0$$(2) . (2) $$P(s)-P(s)C(s)\text{FF}\mathrm{(}s\mathrm{)}=0$$(2)

K_P, K_I and K_D parameters represents the gains of single DOF regulator C(s), K₁ and K₂ are the set-point weights reference for the controller, and K_ff indicates the gain parameter of the feed-forward regulator. The aforementioned parameters must be ideally determined utilizing a population-based nature-inspired optimization technique subjected to time domain objective function reduction. The integral square error (ISE) index given in Equation (3)(3) $$J_{\text{ISE}}=\underset{0}{\overset{T_{\text{Sim}}}{\int }}\left(\mathrm{\Delta }{f}_1^2+\mathrm{\Delta }{f}_2^2+\mathrm{\Delta }{P}_{\text{tie}12}^2\right)\mathit{\text{dt}}$$(3) is adopted to be minimized in finding the 3DOFPID parameters in this work. (3) $$J_{\text{ISE}}=\underset{0}{\overset{T_{\text{Sim}}}{\int }}\left(\mathrm{\Delta }{f}_1^2+\mathrm{\Delta }{f}_2^2+\mathrm{\Delta }{P}_{\text{tie}12}^2\right)\mathit{\text{dt}}$$(3)

4. Water cycle algorithm

WCA is a population-based algorithm presented by Mohsen et al. (2023) that was motivated from the actual water cycle process. Initially, the rivers/streams are formed by collecting the raindrops (RD) that are flown downhill. Rivers often flow downward and eventually merge into the sea. The formation of a cloud will happen by converting water into vapor and the cloud condensation releases water as either snow or raindrops which are later collected into streams/rivers. In this algorithm, RD has been initialized as the initial population by an array to mimic the natural water cycle process. In this approach, the sea is considered as the global solution of choice as the rivers or streams eventually meet the sea. An assumption has been made in this algorithm is streams flown into the rivers and rivers fly into the sea, if the stream’s fitness exceeds that of the river then their positions are swapped. The same criterion is applied to rivers and the sea. The completion of vaporization will be treated when all the rivers merged into the sea.

WCA works best for quickly and accurately determining the maximum and minimum values of a function. Therefore, this method is applied in this research to improve the 3DOFPID controller’s settings, which is used as a secondary regulator for IPS to change the PSOP and regulate the real power mismatch during load perturbations.

In this work, the WCA aims to optimizer 3DOFPID parameters (K_P, K_I, K_D, K₁, K₂, K_ff) and the searching process is initialized with the positions of RD. The searching mechanism will immediately be concluded up on locating the sea position. For a problem with ‘N’ number of variables (N_var) and every RD is an array of size, and every array is treated as a solution to the problem be put in the matrix form as (4) $$\begin{array}{c}R{D}_i=Y_i=[y_1,y_2\dots \dots \dots y_{N\text{var}}\text{]}\\ =\left[K_P{K}_I{K}_D{K}_1{K}_2{K}_{\text{ff}}\right]\end{array}$$(4) (5) $$\begin{array}{c}\text{RD Population}=\left[\begin{array}{c}{\text{RD}}_1\\ \begin{array}{c}\dots \\ {\text{RD}}_i\end{array}\\ \dots \\ {\text{RD}}_{N_{\text{POP}}}\end{array}\right]\\ =\left[\begin{array}{ccccccc}{y}_1^1& y_2^1& y_3^1& .& .& .& y_N^1\\ y_1^2& y_2^2& y_3^2& .& .& .& y_N^2\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ y_1^N& y_2^N& y_3^N& .& .& .& y_N^N\end{array}\right]\end{array}$$(5)

Later, using the cost function given in Equation (3)(3) $$J_{\text{ISE}}=\underset{0}{\overset{T_{\text{Sim}}}{\int }}\left(\mathrm{\Delta }{f}_1^2+\mathrm{\Delta }{f}_2^2+\mathrm{\Delta }{P}_{\text{tie}12}^2\right)\mathit{\text{dt}}$$(3) , the cost of each RD is calculated and the positions of the rivers/streams whose fitness value is close to the best solution are updated as (6) $${\text{Position}}_{\text{Stream}}^{\text{New}}=\hspace{0.17em}{\text{Position}}_{\text{Stream}}+\text{rand}\mathrm{(}\mathrm{)}\text{*}C\text{*}\left({\text{Position}}_{\text{River}}-{\text{Position}}_{\text{Sream}}\right)$$(6) (7) $${\text{Position}}_{\text{River}}^{\text{New}}=\hspace{0.17em}{\text{Position}}_{\text{River}}+\text{rand}\mathrm{(}\mathrm{)}\text{*}C\text{*}\left({\text{Position}}_{\text{Sea}}-{\text{Position}}_{\text{River}}\right)$$(7)

Where rand () is a uniformly generated number from [0–1] and C is a number between 1 and 2. The movement of steam and river toward the sea is illustrated in Equations (6)(6) $${\text{Position}}_{\text{Stream}}^{\text{New}}=\hspace{0.17em}{\text{Position}}_{\text{Stream}}+\text{rand}\mathrm{(}\mathrm{)}\text{*}C\text{*}\left({\text{Position}}_{\text{River}}-{\text{Position}}_{\text{Sream}}\right)$$(6) and (7)(7) $${\text{Position}}_{\text{River}}^{\text{New}}=\hspace{0.17em}{\text{Position}}_{\text{River}}+\text{rand}\mathrm{(}\mathrm{)}\text{*}C\text{*}\left({\text{Position}}_{\text{Sea}}-{\text{Position}}_{\text{River}}\right)$$(7) , respectively. When the stream’s solution is superior to that of its connecting river, their places are swapped (Goud et al., 2021). Proposes an evaporation and rain loop to WCA to prevent becoming caught in the local solution. WCA strategy is supposed to be designed subject to the assumption of rivers/streams merged with the sea, and Equation (8)(8) $$\left|{\text{Position}}_{\text{Sea}}-{\text{Position}}_{\text{River}}\right|\le d_{\mathrm{\text{Max}}}$$(8) illustrates the procedure involved in determining whether they are flown into the sea or not. (8) $$\left|{\text{Position}}_{\text{Sea}}-{\text{Position}}_{\text{River}}\right|\le d_{\mathrm{\text{Max}}}$$(8)

The value $d_{\mathrm{\text{max}}}$ is nearer to 0. In this regard, if the distance between the sea and river is smaller than $d_{\mathrm{\text{max}}}$ then the river is merged with the sea. Moreover, this $d_{\mathrm{\text{max}}}$ parameter regulates the intensity of the seeking pace as one gets closer to the sea and is modeled as given in Equation (9)(9) $$d_{\mathrm{\text{Max}}}^{\text{New}}=d_{\mathrm{\text{Max}}}-\left[\frac{d_{\mathrm{\text{Max}}}}{\mathrm{\text{Max}}\text{.Iteration}}\right]$$(9) . (9) $$d_{\mathrm{\text{Max}}}^{\text{New}}=d_{\mathrm{\text{Max}}}-\left[\frac{d_{\mathrm{\text{Max}}}}{\mathrm{\text{Max}}\text{.Iteration}}\right]$$(9)

After the completion of the evaporation stage, the rainy process will begin immediately. In this stage, the newly generated RD is again compared with the river that is adjoined to the sea once again. The new position of the steam is calculated after the generation of new RD is given in Equation (10)(10) $${\text{Position}}_{\text{Stream}}^{\text{New}}={\text{Position}}_{\text{Sea}}+\sqrt{U}\text{*rand}\mathrm{(}\text{1,}{N}_{\text{Var}}\mathrm{)}$$(10) . (10) $${\text{Position}}_{\text{Stream}}^{\text{New}}={\text{Position}}_{\text{Sea}}+\sqrt{U}\text{*rand}\mathrm{(}\text{1,}{N}_{\text{Var}}\mathrm{)}$$(10)

Figure 5 depicts the WCA flowchart, where the parameter ‘U’ denotes the exploration rate in proximity to the sea. In this article, the WCA optimizes the parameters of 3DOFPID for LFC study of multi-area realistic IPS subjected to the objective function of ISE.

Figure 5. WCA flowchart.

5. Coordinated SMES and UPFC strategy

Superconducting magnetic energy storage (SMES) device comprises the control unit, cryogenic system, a magnet with a superconducting coil and a power conditioning system (PCS) (Mishra et al., 2022). A literature survey discloses the application of SMES devices in enhancing IPS stability. SMES is an efficient ESD that charges up during off-peak hours demand and discharges swiftly when needed. To achieve superconductivity, the coil carrying current is kept at a cryogenic temperature, and energy is retained in DC state. The control unit of the SMES apparatus monitors the process of charging and discharging operation. Moreover, SMES are capable of storing bulk power hence they can be preferred for spinning reserve. SMES devices respond quickly and are having less cycle time. Owing to the above advantages, SMES devices are implemented in this article for minimizing the control area frequency in IPS. The transfer function modeling of SMES is given by (11) $$G_{\text{SMES}}=\frac{K_{\text{SMES}}}{1+s{T}_{\text{SMES}}}$$(11)

During uncertainties in load demand, the secondary controller alone is ineffective and the IPS might become highly unreliable. In modern IPS, FACTS devices had paved a path to attain enhancement in system dynamical behavior. In this work, the unified power flow controller (UPFC) device is placed with the tie-line to damping out the oscillations in tie-line power flow effectively. UPFC is among the most adaptable and effective compensating devices in the family of FACTS devices. It has two units of voltage source converters (VSC) that are coupled to a DC link. The VSCs are coupled to the line via the transformer, one in shunt and the other in series for compensation. Moreover, it facilitates damping over the oscillations significantly. The capacitor in UPFC makes it feasible for absorption and generation of real power. Hence, UPFC is implemented in this work as a part of a territorial control strategy and its architecture is shown in Figure 6 (Kalyan, 2021).

Figure 6. Architecture of UPFC as damping controller.

6. Simulation results

6.1. Case-1: Analysis of the TASHT system using several control strategies

Initially, the widely accepted power system model of TASHT is chosen to be investigated for the implementation of WCA-based 3DOFPID proposed regulator. In this context, area-1 of TASHT is subject to a 10% SLP perturbation. Dynamical responses of TASHT system under load perturbations with different secondary regulators like DE-AEFA-based PID (Kalyan, Srikanth Goud, Reddy, et al., 2022), WCA-based PID, SOA-based PIDD (Kalyan & Suresh, 2022), WCA-based 2DOFPID and WCA-based 3DOFPID are assessed one after the other in both the areas. Responses of TASHT under various regulators at the same load perturbations are rendered in Figure 7 for comparative analysis. Responses shown in Figure 7 are interpreted given settling time in seconds that are shown in Table 1. Observing the responses compared in Figure 7, and noticing the responses settling time tabulated in Table 1 concluded that the presented WCA-based 3DOFPID dominates the other control techniques with more ease. Moreover, with 3DOFPID, the magnitudes of the peak deviations are very finely shrunken and the responses are guided effectively to a steady condition in quick time. Further, the ISE index is more effectively reduced with WCA-based 3DOFPID and is improvised by 93.21% with DE-AEFA-tuned PID (Kalyan, Srikanth Goud, Reddy, et al., 2022), 89.97% with WCA-tuned PID, 81.65% with SOA-based PIDD (Kalyan & Suresh, 2022) and 64.51% with WCA-based 2DOFPID. Table 2 lists the ideal settings for several controllers that were optimized using WCA.

Figure 7. TASHT responses. (a) Δf₁, (b) ΔP_tie12 and (c) Δf₂.

Table 1. Responses settling time of TASHT system.

Settling time (s)	PID: DE-AEFA (Kalyan, Srikanth Goud, Reddy, et al., 2022)	PID: WCA	PIDD: SOA (Kalyan & Suresh, 2022)	2DOFPID: WCA	3DOFPID: WCA
Δf1	19.63	12.74	10.61	6.77	4.34
ΔPtie12	20.45	14.18	11.03	7.31	5.89
Δf2	15.66	13.11	10.13	6.15	4.07
ISE*10^–3	116.793	78.382	43.167	22.316	7.919

Table 2. Optimal gains of the controllers tested on TASHT system.

Parameters		PID: DE-AEFA (Kalyan, Srikanth Goud, Reddy, et al., 2022)	PID: WCA	PIDD: SOA (Kalyan & Suresh, 2022)	2DOFPID: WCA	3DOFPID: WCA
Area-1	KP	2.707	1.989	0.813	0.283	0.761
	KI	1.880	1.241	0.582	0.549	0.387
	KD	1.306	0.880	0.293	0.163	0.269
	KDD	–	–	0.179	–	–
	Kff	–	–	–	–	0.151
	K1	–	–	–	0.681	0.415
	K2	–	–	–	0.518	0.296
Area-2	KP	2.587	1.661	0.491	0.717	0.682
	KI	1.713	1.071	0.206	0.268	0.399
	KD	1.145	0.998	0.339	0.145	0.476
	KDD	–	–	0.113	–	–
	Kff	–	–	–	–	0.201
	K1	–	–	–	0.637	0.420
	K2	–	–	–	0.353	0.175

6.2. Case-2: Analysis of the TANRHT system without taking GTPP integration into account

Furthermore, the implementation of 3DOFPID based on the WCA mechanism is stretched out to the TANRHT system. Analysis is done after applying 10% SLP to region 1. In this case, the GTPP integration is not considered with TANRHT for analysis purposes. Regulators like PID, 2DOFPID and 3DOFPID are placed in each of the TANRHT system regions independently. The parameters of various regulators are finely tuned with the WCA algorithm, and the corresponding responses are rendered in Figure 8. It is clear from the responses compared in Figure 8 that the 3DOFPID dominates the PID and 2DOFPID in regulating the respective area frequency deviations as well as tie-line power flow during load perturbations. Nonetheless, the TANRHT responses have been extrapolated using the peak undershoot (PUS) and settling time given in Table 3. Noticing the responses settling time provided in Table 3, it has been concluded that the TANRHT performance is more enhanced under the monitoring of the proposed controller. Moreover, the deviations are very quickly settled down to a steady state with the presented WCA-based 3DOFPID regulator. Apart from the settling time point of view, the PUS is very finely mitigated with 3DOFPID (Δf₁ = 0.0164 Hz, ΔP_tie12 = 0.012 Pu.MW, Δf₂ = 0.0012 Hz) compared to that of 2DOFPID (Δf₁ = 0.0274 Hz, ΔP_tie12 = 0.0196 Pu.MW, Δf₂ = 0.0015 Hz) and (Δf₁ = 0.037 Hz, ΔP_tie12 = 0.026 Pu.MW, Δf₂ = 0.002 Hz) PID.

Figure 8. TANRHT responses for case-2. (a) Δf₁, (b) ΔP_tie12 and (c) Δf₂.

Table 3. Settling time of TANRHT system responses.

Settling time (s)	Case-2			Case-3
	PID	2DOFPID	3DOFPID	PID	2DOFPID	3DOFPID
Δf1	26.55	16.6	12.36	7.59	6.12	5.36
ΔPtie12	23.59	16.83	13.31	8.10	6.15	5.40
Δf2	24.23	17.8	12.19	8.14	7.31	5.27
ISE*10^–3	62.71	49.63	13.56	41.98	36.27	3.14

6.3. Case-3: Analysis of TANRHT system considering the GTPP integration

In this case, the GTPP integration with the TANRHT system is considered for investigation. TANRHT with the integration of GTPP is analyzed for the same perturbation of 10% SLP on area-1. The GTPP-integrated TANRHT performance is analyzed under WCA optimized PID/2DOFPID/3DOFPID regulators one at a time. Figure 9 compares the dynamic responses for this subsection, while Table 3 shows the settling time. Figure 9 and Table 3 clearly show that the 3DOFPID outperforms the traditional PID and 2DOFPID in reducing deviations to a stable position. Moreover, the PUS is also enhanced with 3DOFPID (Δf₁ = 0.0055 Hz, ΔP_tie12 = 0.0035 Pu.MW, Δf₂ = 0.00019 Hz) compared to that of 2DOFPID (Δf₁ = 0.0116 Hz, ΔP_tie12 = 0.0064 Pu.MW, Δf₂ = 0.0004 Hz) and (Δf₁ = 0.0127 Hz, ΔP_tie12 = 0.0088 Pu.MW, Δf₂ = 0.0008 Hz) PID. This is possible because of the independent control loops in 3DOFPID that facilitate more efficacious in damping out the oscillations and dampening PUS which makes it superior to other regulators. The optimal controller gains that are obtained with WCA for the TANRHT system are noted in Table 4.

Figure 9. TANRHT responses for case-3. (a) Δf₁, (b) ΔP_tie12 and (c) Δf₂.

Table 4. Optimal gains of the controllers tested on TANRHT system.

WCA optimized parameters	Area-1			Area-2
	PID	2DOFPID	3DOFPID	PID	2DOFPID	3DOFPID
KP	0.725	0.653	0.598	0.856	0.383	0.497
KI	0.481	0.382	0.407	0.531	0.517	0.364
KD	0.361	0.295	0.382	0.294	0.218	0.593
K1	–	0.105	0.019	–	0.082	0.018
K2	–	0.116	0.106	–	0.024	0.182
Kff	–	–	0.114	–	–	0.042

6.4. Case-4: Revealing the effect of GTPP integration on the TANRHT system performance

This subsection demonstrates the way GTPP integration affects the operation of the TANRHT system. The supremacy of the WCA-based 3DOFPID controller has been revealed in the aforementioned subsections. Under the same regulator, the dynamical responses of the TANRHT system are compared in Figure 10, both without and with the consideration of the integration of GTPP. Figure 10 shows that the incorporation of GTPP improves the performance of the TANRHT system significantly. Moreover, the magnitudes of the oscillation and PUS are greatly mitigated with GTPP integration and the responses also reached the steady condition in less time. GTPP is one of the renewable energy-based generation units that harness the power by utilizing geothermal energy. GTPP are having bulk power generation capacity and can be penetrated to IPS as that of other renewable-based generation units. With the capability of generating bulk power by the GTPP, its integration with the TANRHT system facilitates the capability in addressing the load perturbations thereby holding the system stability. Hence, the GTPP integration with the existing realistic IPS is having a very significant impact on system performance.

Figure 10. TANRHT responses for case-4. (a) Δf₁, (b) ΔP_tie12 and (c) Δf₂.

6.5. Case-5: UPFC-SMES-based coordinated strategy for GTPP-integrated TANRHT system with 3DOFPID controller based on WCA

To further substantiate the enhancement in GTPP-integrated TANRHT system performance, the coordinated strategy of UPFC-SMES is enacted in this work. For the first instance, the load perturbations of 10% SLP on area-1, SMES devices are included in both areas of the contemplated test system under the WCA-based 3DOFPID controller. Later, simply the UPFC device is connected to the tie-line, and the related dynamical reactions are shown in Figure 11. Furthermore, as shown in Figure 11, SMES devices are installed in each area, and UPFC is attached with the tie-line, and the behavioral responses are studied using the UPFC-SMES coordinated technique. Based on the responses presented in Figure 11 and the numerical data in Table 5, it has been determined that integrating just SMES and only UPFC resulted in a considerable improvement in GTPP-integrated TANRHT system. Furthermore, the use of a coordinated UPFC-SMES method results in a significant improvement in the system’s dynamical performance. This is due to SMES’s rapid reaction properties and superconductivity, as well as UPFC’s inherited nature in controlling actual power exchange via the tie-line.

Figure 11. TANRHT responses for case-5. (a) Δf₁, (b) ΔP_tie12 and (c) Δf₂.

Table 5. Settling time of TANRHT system responses under UPFC-SMES mechanism.

Parameters	Settling time (s)			Optimal parameters
	Δf1	ΔPtie12	Δf2	SMES	UPFC
Without device	5.36	5.40	5.27	–	–
With only SMES	4.98	5.11	4.45	KSMES = 0.891 TSMES = 0.901	–
With only UPFC	4.16	4.36	3.94	–	TUPFC = 0.891
With UPFC-SMES	3.61	3.7	3.48	KSMES = 0.783 TSMES = 0.893	TUPFC = 0.883

6.6. Case-6: Sensitivity analysis

The robustness of the presented 3DOFPID controller based on WCA optimization as well as UPFC-SMES-based territorial approach is disclosed from the sensitivity test. The GTPP-integrated TANRHT system under WCA-based 3DOFPID controller along with UPFC-SMES is targeted with different loadings of 10% SLP on only area-1, 10% SLP on both the areas and 20% SLP on both the areas and the corresponding responses are compared in Figure 12. Figure 12 shows that, despite the GTPP integrated TANRHT being subjected to various perturbations, there is little variation in the system responses as compared to the case of nominal loadings. Further, the TANRHT parameters are varied by aiming them at ±25% of their actual values, and the numerical results are placed in Table 6. Noticing Figure 12 and observing the numerical data in Table 6, it was elucidated that the TANRHT behavior under the suggested secondary and territory control methodologies is hardly changed under the parametric variations. In addition, the TANRHT system’s area-1 is loaded randomly, and Figure 13 displays the results. Figure 13 indicates that the deviations are significantly reduced when using UPFC-SMES devices as opposed to not using the territorial system. Hence, the presented WCA-based 3DOFPID secondary controller and UPFC-SMES territorial strategy are robust.

Figure 12. Sensitivity test on TANRHT for various loadings. (a) Δf₁, (b) ΔP_tie12 and (c) Δf₂.

Figure 13. Sensitivity test on TANRHT for random loadings. (a) Δf₁, (b) ΔP_tie12 and (c) Δf₂.

Table 6. Sensitivity analysis of TANRHT system for parametric variations.

		PUS			Settling time (s)
Parameter	% Change from actual parameter value	Δf1 × 10^-3(Hz)	ΔPtie12 × 10^-4 (Pu.MW)	Δf2 × 10^-4 (Hz)	Δf1	ΔPtie12	Δf2
	Actual parameter	3.14	13.65	1.16	3.61	3.7	3.48
Tt	+25%	4.57	15.32	1.87	4.17	4.25	3.95
	−25%	2.89	11.38	0.98	3.35	3.61	3.33
Tw	+25%	4.68	14.78	1.94	3.78	4.16	4.62
	−25%	2.16	12.43	0.986	3.29	3.11	2.83
B	+25%	2.54	12.87	1.06	3.18	2.47	2.41
	−25%	5.32	15.17	2.72	4.08	4.62	4.74
T12	+25%	1.98	9.36	0.786	3.18	2.47	2.41
	−25%	4.85	15.29	3.28	5.18	4.17	4.59

7. Conclusion

The 3DOFPID optimized with nature-inspired meta-heuristic optimization technique of WCA is designed as a regulator for LFC study. Primacy of WCA-tuned 3DOFPID is revealed with several controllers like DE-AEFA-based PID and SOA-based PIDD techniques listed in the literature recently by implementing on TASHT widely accepted system. The suggested controller is then evaluated on a realistic TANRHT IPS model for 10% SLP on area-1. The investigation on TANRHT is carried out while taking into account the situations without and with GTPP integration. Dynamical analysis of TANRHT without and with GTPP integration reveals the efficacy of 3DOFPID over 2DOFPID and conventional PID regulators. Moreover, the impact of GTPP integration with TANRHT system performance is showcased and also observed the enhancement in system performance. To ensure performance improvement in the TANRHT system further, a territorial strategy is implemented by incorporating SMES devices in every area and the tie-line with UPFC attachment. The findings of the simulation demonstrate how the coordinated approach of UPFC-SMES may further mitigate peak magnitudes, dampen inter-area oscillations, and quickly bring responses to a steady state. Finally, sensitivity analysis is conducted by targeting the TANRHT system having GTPP under WCA-tuned 3DOFPID with 10% SLP in only area-1, 10% SLP in area-1 and area-2, 20% SLP in area-1 and area-2 and random loadings. Even when the TANRHT system is subjected to substantial disturbances, sensitivity analysis demonstrates that the responses are not significantly altered. This demonstrates the resilience of the suggested secondary and territorial control system.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

CH. Naga Sai Kalyan

CH. Naga Sai Kalyan received his Ph.D degree from Acharya Nagarjuna University in the year 2021 and M.Tech degree from JNTUK, Kakinada, India in the year 2014. He is currently working as Associate Professor in EEE Department of Vasireddy Venkatadri Institute of Technology, Guntur, India. He published more than 90 publications in various International Journals and Conferences. He is the guest editor to the MDPI Energies Journal and also to the Computational Mathematics. He received several best paper awards in the conferences conducted by the IEEE and technically supported by the Springer Nature. He is the reviewer for various Taylor and Francis, Springer and MDPI journals. His research interest includes design of controllers for interconnected power system models using soft computing techniques and application of FACTS devices in power system operation and control.

G. Sambasiva Rao

G. Sambasiva Rao received his Doctoral degree from JNTUH, Hyderabad, India in 2014. His research interest includes controlling techniques for duel inverter fed open end winding induction motor, FACTs Controllers, Power quality improvement. Currently he is working as Professor in EEE Department of RVR&JC College of Engineering, India.

Mohit Bajaj

Dr. Mohit Bajaj is a Research Professor in the Department of Electrical Engineering at Graphic Era (Deemed to be University) in Dehradun, India. With a Ph.D. in Electrical Engineering from the prestigious National Institute of Technology in Delhi, he has established himself as a distinguished scholar and researcher in his field. Fueled by a passion for innovation and sustainability, Dr. Bajaj’s primary research interests revolve around electric vehicles, renewable energy sources, distributed generation, power quality, and smart grids. His extensive contributions to the field are evidenced by his numerous research publications, comprising impactful journal articles, international conference papers, and book chapters. With a commitment to international collaboration, Dr. Bajaj actively engages with researchers in the renewable energy domain, fostering partnerships with esteemed institutions and scholars from various countries. Furthermore, Dr. Bajaj’s exceptional contributions have garnered global recognition. He is ranked among the World’s Top 2% Scientists for the three consecutive years according to a recent study conducted by researchers from ICSR Lab, Elsevier B.V., and Stanford University in 2021, 2022 and 2023, reaffirming his status as a prominent figure in the field of Electrical Engineering. Through his relentless pursuit of knowledge, extensive research contributions, and commitment to academic collaboration, Dr. Mohit Bajaj continues to shape the future of renewable energy and electrical engineering, leaving an indelible impact on the scientific community and inspiring the next generation of researchers.

Baseem Khan

Baseem Khan received the B.Eng. degree in electrical engineering from Rajiv Gandhi Technological University, Bhopal, India in 2008, and the M.Tech and D.Phil. degrees in electrical engineering from the Maulana Azad National Institute of Technology, Bhopal, India, in 2010 and 2014, respectively. He is currently working as a Faculty Member at Hawassa University, Ethiopia. His research interest includes power system restructuring, power system planning, smart grid technologies, meta-heuristic optimization techniques, reliability analysis of renewable energy systems, power quality analysis, and renewable energy integration.

Majeed Rashid Zaidan

Majeed Rashid Zaidan holds both a BSc and MSc degree in Electrical Engineering from the University of Technology in Baghdad, Iraq, earned in 1986 and 2003, respectively. He currently serves as a lecturer at Baqubah Technical Institute, a part of Middle Technical University. His professional focus is on power systems and electrical machines. He has authored numerous papers for both local and international journals and has actively participated in several conferences, including the 2009 conference in Cairo on the Strategy of Technical Education in Iraq. Additionally, in 2011, he completed a management qualification program for Technical Education Leaders in London, UK.

Appendix

TASHT parameters: Thermal unit time constant of the governor T_g = 0.08 s and turbine T_t = 0.25 s, tie-line parameter T₁₂ = 0.454 s, biasing parameter B = 0.315 Pu.MW/Hz, hydro governor gain K₁ = 1 and time constant T₁ = 0.456 s, turbine time constant T_r = 20 s, penstock time T_w = 1.786 s.

TANRHT parameters: Thermal unit-time constant of governor T_sg = 0.06 s, turbine T_t = 1.1 s, reheat turbine T_r = 0.8 s, gain of rehear turbine K_r = 0.3. Hydro unit-time constant of governor T_gh = 0.2 s, turbine T_rh = 28.786 s, penstock T_w = 10.2 s, synchronizing coefficient T₁₂ = 0.086 Pu.MW/rad, power system gain and time parameters K_ps = 120, T_ps = 20 s. GTPP-governor and turbine time constant g = 3 s, t = 8 s.