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Grasshopper optimization algorithm optimized multistage controller for automatic generation control of a power system with FACTS devices
Protection and Control of Modern Power Systems volume 6, Article number: 8 (2021)
Abstract
This paper uses a Grasshopper Optimization Algorithm (GOA) optimized PDF plus (1 + PI) controller for Automatic generation control (AGC) of a power system with Flexible AC Transmission system (FACTS) devices. Three differently rated reheat turbine operated thermal units with appropriate generation rate constraint (GRC) are considered along with different FACTS devices. A new multistage controller design structure of a PDF plus (1 + PI) is introduced in the FACTS empowered power system for AGC while the controller gains are tuned by the GOA. The superiority of the proposed algorithm over the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithms is demonstrated. The dynamic responses of GOA optimized PDF plus (1 + PI) are compared with PIDF, PID and PI controllers on the same system. It is demonstrated that GOA optimized PDF plus (1 + PI) controller provides optimum responses in terms of settling time and peak deviations compared to other controllers. In addition, a GOAtuned PDF plus (1 + PI) controller with Interline Power Flow Controller (IPFC) exhibits optimal results compared to other FACTS devices. The sturdiness of the projected controller is validated using sensitivity analysis with numerous load patterns and a wide variation of parameterization. To further validate the realtime feasibility of the proposed method, experiments using OPALRT OP5700 RCP/HIL and FPGA based realtime simulations are carried out.
1 Introduction
In a multiarea power system, qualitative, reliable, secure, stable and economic action of the system requires stable frequency and power transmission across a tieline preserved at their nominal values. Symmetry in a power system will be maintained when proper coordination is established between power requirement and generation. Two control mechanisms are assigned, i.e., reactive power control (Automatic voltage regulator AVR) which maintains voltage profile and real power control through the AGC system [1] for frequency stabilization. The responsibility of AGC in a multiarea power network is to limit the transient frequency deviation, interline power exchange, and to reduce steadystate errors to zero [2]. An epidemic power system is an amalgamation of a large electrical network and within the network, each area is known as a control area and the areas are braided with one another over various tielines. In an electric network, the system operation must be proficient in establishing equilibrium in exchange power across a tieline and in securing frequency stabilization. Many nonlinear loads (equipped with power semiconductor devices) interlinked with a dispersed power system network introduce large transient disturbances in the electrical network resulting in a mismatch between generation and demand. Thus, the automatic control system has to be upgraded with modern techniques for stable, reliable and economical operation [3].
In a modern power system, the rapid development of power semiconductor devices gives opportunities to design fastacting FACTS devices [4]. Power system stability has reached a new height and power flow control becomes more flexible using modern FACTS devices. Much recent research explores the effect of FACTS devices in AGC, e.g., Thyristor controlled phase shifter (TCPS), Static Synchronous Series Compensator (SSSC) and various combinations equipped in series with a tieline integrated with SMES have been implemented to normalize frequency deviations under various restraints of a 2area system [5]. Steadiness of frequency oscillation is achieved by a fractional order based SSSC controller in [6] while TCPSSMES was implemented in DFIGbased wind farm integrated power systems in [7] [8, 9]. used redox flow batteries interlinked with IPFC and a Thyristor Controlled Series Capacitor (TCSC), while [10, 11] used TCSC for stability control in IPFC, and an SMESUPFC combination was used in a 2area 6unit system in [12].
Many have introduced various modern control strategies including modified structures of the classical controllers of I, PI and PID in the AGC system. The dynamic responses of classical controllers in AGC have been evaluated in [13, 14], while [15] proposed parallel 2DOFPID for LFC in a power system with GDB. The fuzzyPID controller was preferred to establish cohesion in power system dynamic behavior in [16,17,18], while cascaded PDPID and PIPD controllers were used in [19, 20] because of their adequate results, simplicity, reliability and performance. A 2DOF controller was implemented in [19] to minimize the steadystate error and to establish stability in the system, while [21, 22] satisfied a system necessity by introducing a metamorphic modern PDF+(1 + PI) controller which helped in developing the responses of transient and steadystate error to diminish with different dynamic responses with various parts.
In this paper, a PDF+(1 + PI) controller consisting of a PD controller with filter and a (1 + PI) controller connected in series, is examined with the influence of FACTS devices in an AGC multiarea thermal power system. Contemporary memetic natureinspired innovations have been evolved to carry out a comprehensive search. The efficacy of the memetic algorithm can be assessed by evidence that they emulate the finest outcome globally, specifically the excerpt of the competent in organic systems that have emerged by instinctive assortment over decades. From the literature survey, it is evident that many optimization techniques/ controllers have been applied to various problems but no metaheuristic method is exactly appropriate for all types of problems and there is scope for improvement by proposing new techniques/controller.
Conventional tuning methods are based on a single objective trial and error type. This often takes up more time and most often produces substandard results. Reference [13] used hybrid DEPS, while [15] adopted DE and [18] used PSO for optimization. However, these classical methods have the problem of getting trapped in local optima. Many methods have been used to try to address these problems, e.g., firefly algorithm (FA) [12], Symbiotic Organisms Search SOS [16], BAT [19], Grey Wolf Optimization GWO [20], and Cuckoo Search (CS) [23]. The efficacy of the sine cosine algorithm in the AGC system with FACTS devices was explored in [24], while better dynamic performance using GWO was obtained in [21] and in [22], the primacy of GOA with a 2stage controller was explored.
The GOA approach uses a node finite input for excitation and it has a simple user interface. It was extensively used in [25] for tuning controller gains. In this paper, the GOA algorithm is embedded with a PDF plus (1 + PI) controller in the AGC of a 3area thermal power network for the escalation of gains in the presence of contrasting FACTS devices.
Sensitivity investigation observed the robustness of the most favorable controller gains [21,22,23]. Similar investigation has been carried out for the optimum controller in the presence of FACTS devices in AGC, and the most convenient objective function for optimum controller and FACTS devices is investigated.
The main objectives of the present research work are:

Introduction of GOA for extensive modulation of controller gains of an AGC in a 3area thermal power network.

Introduction of a metamorphic PDF plus (1 + PI) controller in the AGC, consisting of a filter with PD and (1 + PI). The timevariant responses are equated with PI, PID and PIDF controllers for efficacy measurement.

Comparison of the dynamic performance of a 3area thermal power network with FACTS devices along with a metamorphic PDF plus (1 + PI) controller.

To compare the performance of GOA with PSO and GA for a controller design problem for the same test system.

Performance comparison of IPFC with SSSC, TCPS and TCSC for frequency regulation.

Sensitivity analysis of a 3area thermal power network with the best location of IPFC and optimum controller gains, by changing the percentage of step load perturbation (SLP) and system parameters.

Validation of simulation results by an OPALRT OP5700 realtime simulator.
2 Model investigated
A 3area thermal power network is proposed for analysis, where the size of area1 is 2000 MW, area2 is 6000 MW and area3 is 1200 MW. In this network model, nonlinearity constraints are extensively introduced by the implementation of GRC which is set at 3% with a reheat turbine in each control section. The nominal parameters of the model are given in Table 7 in Appendix. Several classic PI, PID and PDF controllers with the metamorphic PDF plus (1 + PI) controller are considered individually for study. Dynamic investigations of the 3area thermal power network with the independent influence of SSSC, TCSC, TCPS and IPFC are carried out in the presence of the GOA techniquetuned PDF plus (1 + PI) controller. The dynamic performance in each control area is estimated by setting SLP at 1%. The proposed control model of the 3area thermal network is presented in Fig. 1 and the relevant parameters are shown. The different possible combinations of various controllers with several FACT devices are optimized with GA, PSO and GOA for comparison with the proposed strategy.
2.1 Objective function
The objective functions, IAE, ITAE, ISE and ITSE are examined for obtaining optimum results in frequency stabilization and tieline power control. The corresponding objective function accepts ∆F_{i} and ∆P_{tie ij} as inputs and actions are taken to minimize them to zero by tuned controller gains.
Mathematical expressions for the objective functions are:
where ∆F_{i} is the frequency fluctuation in the i^{th} area and ∆P_{tie i − j} is the tieline power fluctuation in the i^{th} and j^{th} area.
2.2 Models of FACTS devices
For smooth management of tieline power control using fine adjustment of the relative phase angle between the two control areas is feasible using TCPS. This helps in the settlement of frequency oscillations as well as interexchange of active power across the tieline. Transient stability can be achieved by counteracting the oscillations with wellmanaged controller damping on the disrupted system. SSSC incorporates a voltage with adjustable magnitude in the quadrature with the current equivalent to a controllable inductive or capacitive reactance to influence the tieline power flow. The transfer function models of TCPS and SSSC are adapted from [5, 7]. IPFC provides reactive series compensation efficiently in inductive or capacitive fashion so that the tieline power flow can be effectively managed by the IPFC through the injection of an accurate series reactive compensating voltage [8, 9]. The control prototype of the IPFC has been acquired from [8]. TCSC can be employed in multitransmission lines to effectively introduce series compensation for dynamic change in transmission line reactance. The transfer function of TCSC is presented in [10, 11] while the criteria of TCPS, SSSC, TCSC and IPFC are taken from [5, 7,8,9,10,11, 21]. As shown in Fig. 1, IPFC is in series with the three control areas.
2.3 Proposed PDF plus (1 + PI) controller
Having a simple system interface makes the PID controller the most encouraging tool for many studies. The PID controller offers efficacy in most transient conditions and the minimization of steadystate error in dynamic analysis of any system is demonstrated in many studies. By the presence of integral gain, rapidity in minimization of steadystate error is achieved and system stability is reduced in the transient condition. For better response in the transient condition, the integral parameter must not be engaged in action all along the transient period. With the enhancement of prominent dynamic response of the system some refitted control structures have evolved which are proficient in transient stability establishment. This is accomplished by a metamorphic PDF plus (1 + PI) controller, which minimizes the error in the steadystate and at the same time manages speed and system stability. The controller consists of two stages, the 1st stage is a PD controller with filter and the 2nd stage is a 1 plus PI controller. To perform the corrective action ACE is accepted as input by the PDF controller and the output of this is endorsed by the PI controller. The structure of the proposed controller is shown in Fig. 2.
The mathematical expression of the PDF plus (1 + PI) controller is given as:
As shown, there are different elements of the PDF plus (1 + PI) controller, i.e., K_{P}, K_{I}, K_{D}, K_{PP} and N. The Area control error (ACE) is input to the controller and the output signal will be the input for the power network with the addition of changes in tieline power and frequency.
ACE is the difference between the actual power generation and the scheduled generation with the influence of frequency bias, and is given as:
3 Grasshopper optimization algorithm
The Grasshopper Optimization Algorithm (GOA) is a contemporary multifaceted anatomical method proposed in [25]. The GOA approach is based on the life cycle of the grasshopper, which consists of three stages of egg, nymph and adult going through a process called metamorphosis. Grasshoppers migrate from egg to nymph as sliding cylinders, and then when they migrate from nymph to metamorphosis, they damage crops. This nature is mathematically modeled to form an anatomical optimization technique named GOA. It has two aspects: first, during the investigation it searches for members, and then it moves nearby in the exploitation. This ensures the goal is accomplished logically.
The congregate behavior of ‘Grasshoppers’ is precisely articulated as follows:
where X_{m} is the location of the m^{th} Grasshopper, S_{m} is the correlation, G_{m} is the gravitational strength on the m^{th} Grasshopper, and A_{m} is the wind in abeyance. The equation can be upgraded to allow for arbitrary nature as:
where r_{1}, r_{2}, and r_{3} are arbitrary coefficients, and
where d_{mn} is the gap among the m^{th} and n^{th} Grasshoppers, d_{mn} =  x_{n}– x_{m} , s is the function of collective forces, and \( \hat{{\mathrm{d}}_{\mathrm{m}\mathrm{n}}}=\frac{{\mathrm{x}}_{\mathrm{n}}{\mathrm{x}}_{\mathrm{m}}}{{\mathrm{d}}_{\mathrm{m}\mathrm{n}}} \) is a unit vector from the m^{th} to n^{th} Grasshoppers.
The s function for the collective forces (dislike and like) is given as:
where f is the potential of likeness and l is the detachment of likeness force.
The G factor in (8) is evaluated as:
where g is the gravitational force constant and \( \hat{{\mathrm{e}}_{\mathrm{g}}} \) is a unity vector focused on along the earth’s center.
The A factor in (8) is evaluated as:
where u is a constant drift and \( \hat{{\mathrm{e}}_{\mathrm{w}}} \) is a unity vector for the wind course.
Replacing S, G, and A in (8) yields:
where n is the number of grasshoppers.
For optimization on the global horizon, (13) is altered as:
where ub_{d} is the D^{th} aspect upper bound, lb_{d} is the D^{th} aspect lower bound, \( \hat{{\mathrm{T}}_{\mathrm{d}}} \) is the D^{th} aspect of the objective bound, and c is a declining factor to minimize the comfort zone, dislike zone and like zone. Based on current place, GOA unceasingly updates the location of an investigation agent, global optimum and the location of all other investigation agents.
The comfort zone reduces, and coefficient c is proportional to the number of iterations and is evaluated as:
where cmax is the max value, cmin is the min value, l indicates the current iteration, and L is the number of iterations.
GOA is initiated by forming a collection of random results, and searching representatives upgrade their location at each iteration by (13). At the termination of every iteration, the finest marked location is upgraded. In addition, factor c is evaluated using (14) and the linearization of gaps among grasshoppers is carried out in every repetition. Adaptation is made iteratively until the final criterion is matched, and the global optimum comes out as the best approximation returned finally by the position and fitness of the best target. The flowchart of the GOA technique is given in Fig. 3.
3.1 Statistical analysis of GOA
Statistical analysis of the proposed PDF plus (1 + PI) controller with different algorithms of GOA, PSO and GA optimized for standard deviation, min, max and average values of fitness function is presented in Table 1. It is clear from Table 1 that functions F5, F6, F7, and F8 for GOA give good average results, and function F6 with SD = 2.5276 X10^{31} provides the best results in all respects out of the 23 predefined objective functions. Functions F2 with SD = 1.428 X10^{25} and F5 with SD = 6.2784 X10^{38} provide the best results in the cases of GA and PSO, respectively.
4 Results and discussions
The study is carried out using MATLAB R2019a, while the multithermal power system model is developed in SIMULINK with the reheat turbine, GRC and PDF plus (1 + PI) controller. The GOA, PSO and GA programs are in scriptfile and functionfile of MATLAB R2019a. The exploration is carried by 100 agents and 100 iterations are reserved for entire investigations. The efficacy authentication of the different objective functions is carried out by setting each control area with 1% SLP at t = 0 s.
4.1 Effectiveness of PDF plus (1 + PI) controller
In this segment, the 3area thermal power network fitted with reheat turbine, GRC and IPFC in each control area is examined by various controllers such as PI, PID, PIDF and PDF plus (1 + PI) optimized by the GOA technique. The obtained controller gains are as follows:
PI controller in each area:
PID controller in each area:
PIDF controller in each area:
PDF plus (1 + PI) controller in each area:
The comparative analysis of different objective functions with the various controllers with the GOA algorithm is shown in Fig. 4. Compared to PIDF, PID and PI, the improvements in the ITAE error with the proposed GOA tuned PDF plus (1 + PI) controller are 3.43%, 5.38% and 7.86%, respectively.
The dynamic behavior of the power system frequency and tieline power for each controller is compared in Fig. 5(a)(c). Performance indices such as the maximum overshoot and undershoot, and settling time of the dynamic responses, are given in Table 2. From Fig. 5 and Table 2, it is evident that the proposed PDF plus (1 + PI) controller is better than the classical PI, PID and PIDF controllers with lowest settling time of 34.22 s (∆f_{1}) and peak fluctuations.
4.2 Effectiveness of the GOA algorithm
In this section, the effectiveness of the structural algorithmbased GOA method is verified with the proposed PDF plus (1 + PI) controller. The thermal power system network is fitted with the IPFC controller in each area, while GRC is set at 3% and all SLP are fixed to 1%. Figure 6 shows the fitness of the best objective function algorithm, with GOA optimized PDF plus (1 + PI) controller with ITAE value 0.422 × 10–2 having the lowest among the entire statistical data.
Compared to PSO and GA, the improvements in the ITAE error with the proposed GOA tuned PDF plus (1 + PI) controller are 12.26% and 17.57%, respectively. Figure 7 provides complete information regarding the convergence of fitness function (ITAE) with PDF plus (1 + PI) controller for GOA, PSO and GA techniques. The dynamic frequency stabilization and tieline power flow is shown in Fig. 8(a)(c) and Table 3. The GOA method shows performance superior to that of GA and PSO methods with the same setting and strategy.
4.3 Effectiveness of several FACTS devices
In this section, four FACTS devices, i.e., TCPS, SSSC, TCSC, and IPFC are tested in the 3area thermal power system with PDF plus (1 + PI) controller optimized by GOA technique.
The dynamic responses of frequency deviation and power exchange across the tieline are given in Fig. 9(a)(f), while the performance indices are given in Table 4. From this analysis, it is noted that IPFC gives improved dynamic response (peak overshoot and undershoot and settling time) over other proposed FACTS devices. Compared to SSSC, TCPS and TCSC, the improved settling times of frequency deviation ∆f_{1} with IPFC and the proposed GOA tuned PDF plus (1 + PI) controller are 25.12%, 17.32% and 13.32%, respectively, while for ∆f_{2}, they are 19.11%, 13.97% and 4.40%, respectively. For ∆f_{3}, the corresponding settling time improvements are 14.72%, 12% and 5.36%, respectively. For ∆P_{tie1–2}, the improved settling times of frequency deviation with IPFC compared to SSSC, TCPS and TCSC are 10.02%, 3.38% and 1.8%, respectively, while the corresponding respective improvements are 15.68%, 11.21% and 8.39% for ∆P_{tie2–3}, and 13.25%, 7.66% and 1.91% for ∆P_{tie3–1}.
4.4 Effectiveness of IPFC at a different location with SLP
In this section, the multithermal power system network is tested with different locations of IPFC. It is also verified with hikes in SLP of 3% and 5% for the proposed controller and GOA technique. This allows examination of the robustness of the network when there is an uncertain nonlinearity, something that frequently occurs in a power system network.
The dynamic responses for GOAoptimized PDF plus (1 + PI) controller for an IPFC enabled AGC system is shown in Fig. 10(a)(c) with different locations of IPFC and SLP values. The performance attributes are given in Table 5. From these, it can be concluded that the IPFC with each area stabilizes the frequency and limits the oscillation of the power flow.
4.5 Sensitivity analysis
In this section, sensitivity analysis is carried out for the proposed GOA optimized PDF plus (1 + PI) controller for the IPFCenabled AGC system. The optimum controller gains are evaluated at nominal loading conditions with 1% SLP to the wide variation of system parameters. The GOA runs for each possibility of system parameter setting and with tuned parameters system performance index are evaluated. The dynamic response control indices are given in Table 6. The controller parameters are quite close to each other which validates the robustness of the complete framework as the proposed method. From every aspect it exhibits an effective response in every possible condition.
4.6 Validation by OP5700 RCP/HIL FPGA realtime simulator
The OPALRT OP5700 RCP/HIL FPGA realtime simulator is shown in Fig. 11 which is used for realtime validation of the proposed research. This is performed for practical feasibility testing. The OPALRT considers the delay and error nonlinearity disturbances which inherently exist but are neglected in conventional offline simulations [26]. The OPALRT allows researchers to authenticate their work in realtime irrespective of complexity. The important features of OPALRT are code parallelization, Simulink integration, customizable dashboard, communication protocols and I/O flexibility. The steps of realtime validation include the initialization of the Simulink model via OPALRT lab, the transformation of the model into RT application, running the model using multiple cores and finally data acquisition using the graphical interface. The frequency deviation (Δf_{1}) and tieline power response (ΔP_{tie 1–2}) from MATLAB/SIMULINK and OPALRT based RealTime Simulator (RTS) are shown in Fig. 12(a) and (b). It can be seen that the MATLAB/SIMULINK results match well with those from OPALRT realtime simulation.
5 Conclusion
A 3area thermal unit fitted with a reheat turbine is considered in this paper. The Grasshopper optimization algorithm is used in AGC to optimize the PI, PID, PIDF and the proposed PDF plus (1 + PI) controllers. First, statistical analysis is carried out to evaluate the effectiveness of GOA in test functions. Several FACTS devices such as SSSC, TCPS, TCSC and IPFC in association with PDF plus (1 + PI) optimized by GOA in AGC 3area systems are tested. Improvements in the ITAE error with the proposed GOA tuned PDF plus (1 + PI) controller compared to the PIDF, PID and PI are 3.43%, 5.38% and 7.86%, respectively. The effectiveness of GOA is justified by comparing the dynamic responses with GA and PSO, where respective improvements of 12.26% and 17.57% in the ITAE error with the proposed GOA tuned PDF plus (1 + PI) controller are achieved. It is also observed that the IPFC gives improved dynamic response (peak overshoot and undershoot, and settling time) in comparison with other considered FACTS devices.
The robustness of the proposed strategy is estimated by various sensitivity analyses. Dynamic behaviors due to different SLP and loading conditions are compared and sensitivity analysis reveals that a GOAtuned PDF plus (1 + PI) controllerfitted IPFC offers robustness in all respects. Finally, the proposed GOAtuned PDF plus (1 + PI) controller fitted IPFC approach is authenticated by OPALRT based simulations in a realtime environment.
Availability of data and materials
Not applicable.
Change history
11 May 2021
A Correction to this paper has been published: https://doi.org/10.1186/s4160102100196w
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Contributions
The first author developed the models and obtained the results. The second author implemented the optimization algorithm and tested on OPALRT. The third author suggested the controller and validated the manuscript. The author(s) read and approved the final manuscript.
Author’s information
Pratap Chabdra Nayak is a Ph.D research Scholar in the Department of Electrical Engineering, VSSUT, Burla, 768018, Odisha, India. Ramesh Chandra Prusty is working as Assistant Professor in the Department of Electrical Engineering, VSSUT, Burla, 768018, Odisha, India. Sidhartha Panda is working as Professor in the Department of Electrical Engineering, VSSUT, Burla, 768018, Odisha, India.
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Nayak, P.C., Prusty, R.C. & Panda, S. Grasshopper optimization algorithm optimized multistage controller for automatic generation control of a power system with FACTS devices. Prot Control Mod Power Syst 6, 8 (2021). https://doi.org/10.1186/s4160102100187x
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DOI: https://doi.org/10.1186/s4160102100187x