# A Coordinated Pumped Storage Dual Compensated Hydro Governor with PSS Action to Damp Electromechanical Power Oscillations

Authors: Narayan Nahak; Samarjeet Satapathy
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Subject to increasing penetrations of renewable sources like solar photovoltaic (SPV) and wind energy sources, power system oscillation damping is going to be a critical challenge for system operators. This work proposes a new dual compensated governor (DCG) in coordination with a power system stabilizer (PSS) of a pumped storage hydro plant for power oscillation damping subject to intermittent SPV and wind penetration for a hydro, wind, and SPV integrated power system. The phase lag provided by the hydro governor is compensated by additional phase lead contributed by the dual compensation, where speed and real power deviations brought by uncertain SPV and wind penetrations are simultaneously controlled by two lead-lag controllers before being applied to conventional Proportional-Integral-Derivative (PID) governor. Again, subject to critical oscillatory unstable conditions, the DCG is coordinated with PSS through a multiobjective function employing a new modified Differential Evolutionary-Particle swarm optimization (MDEPSO) algorithm. Different case studies with sudden and random SPV and wind penetrations being executed with the proposed controller considering a two area four machine and 39 bus multimachine system with pumped storage hydro units to observe system oscillations are considered. The proposed damping control action has been implemented to damp these oscillations, and the damped response has been analyzed with eigenvalue distributions and Bode plots with sensitivity analysis. The proposed action is found to be much more efficient in contrast to conventional PID governor and PSS damping action. Also, the usage of present hydro governors can be much improved by this coordinated controller action.


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## Body

## 1. Introduction

Renewable power generation (RPG) is going to be an integral part of bulk electric power generation, which includes generation from the hydropower plant (HPP), SPV, wind source, tidal, biomass, etc. [1]. For the integration of RPG, much more effort has been implemented worldwide including new transmission topology or technologies with PV generation [2, 3]. Out of several renewable sources, HPP is an important constituent in power generation sharing to counteract increasing load demands [4]. There are different categories of HPPs, including conventional, run of river, and pumped storage. A conventional HPP employs a dam for storing water. Run of river HPP usually has either no water storing or very less water storing capability. For HPP, proper storing and utilizing of water resources is an important issue for optimal power generation, which can be met by a pumped storage hydropower plant (PSHPP). In PSHPP the water resources can be efficiently utilized by storing the water and pumping as per load demand [5]. PSHPP has different states of operation, which are pumping and generating modes. There are upper and lower reservoirs in PSHPP. In the pumping state, the water is pumped to the upper reservoir from the lower reservoir, where the power demand is less. In the generation state, the water from the upper reservoir is utilized for power generation when the power demand increases. Therefore, PSHPP plays a very important role in power balancing. A battery energy storage system (BESS) is usually employed to meet the challenge of uncertainty and intermittence in RPG integration, like SPV and wind sources. But there are several drawbacks of BESS, like less current carrying capability of semiconductor switches, lower power handling capability, and short life time [6].


### 1.1. Literature Review

Due to randomness in SPV and wind generation, electromechanical oscillation (EMO) generated in the power system poses much more challenges to the system operator. In [7], an analysis has been presented depicting the impact of uncertain wind penetration on the stability of the power system. As per [8], the damping capability of wind sources can be imparted if wind turbines run at a constant speed. But as per [9], the small signal stability is a challenging issue with intermittent wind penetration, and the stability depends on the operating condition. The wind and synchronous generator may interact to provide positive or weak damping to EMO [10], and the stability may sacrifice if there is a strong coupling between wind and conventional generation [11]. So as per this research, variable wind integration creates a challenge to damping EMO. In a similar way, varying SPV also poses a challenge to EMO damping. In [12, 13], research have been conducted predicting the impact of undertrained SPV penetration on small signal stability of power system. The contribution to EMO depends on the characteristics of SPV, which have been analyzed in [14, 15]. Sudden and random SPV integration with the power system aggravated EMO [16]. As in [17], the mechanical mode of oscillation is more excited with heavy SPV penetration, and critical machines need to be identified to damp oscillations, which may be a difficult task. Time domain simulation and analysis have been performed in [18] with different RPGs subject to small signal stability, which explained optimal usage of different sources for stability improvement. Also, in [19], it has been observed that undertrained SPV penetration poses challenges for EMO damping. Therefore, as per the research stated above, damping EMO is a critical challenge for system operators when there are uncertain SPV and wind penetrations. A power system stabilizer (PSS) is usually employed to dampen EMO, which creates an electrical damping torque in the generator through an excitation system [20]. In [21], a criterion has been developed for selecting an optimal node to install PODs and PSSs, but the setting of parameters of the damping controller and its impact can be studied further. So, an important issue is selecting the proper PSS controller. The PSS control action may hamper regulating voltage and provides leading pf, which are demerits of PSS controller. Again, in the current state of deregulation in the power sector the optimal use of existing resources like mechanical torque control imparted by generator governor action would be an efficient technique if the governor's performance is improved. In [22], the efficiency of turbine governor action for oscillation damping has been presented, where it has been shown that speed control and excitation loop may be decoupled and do not influence each other. The governor can efficiently provide mechanical torque to stabilize frequency [23], but there may be a modification in turbine governor performance if additional phase compensation is provided with the governor [24]. But in the report of [25], it has been presented that hydro governors are generally blocked to damp interarea oscillation. So, although the governor can impact damping torque, its controllability needs to be improved much to counteract low interarea oscillations. The governor parameters need to be tuned efficiently to provide adequate damping torque. If steam valve control and excitation control are coordinated, then the control action would be enhanced as reported in [26], but using an efficient optimization technique may reduce a detailed mathematical model for efficient control action. In the current and future content of power system, HPP is going to take an important role so there can be a modification in hydro turbine governor action along with proper coordination by excitation system provided by PSS. This attempt has been performed in this work where the turbine governor action is coordinated with PSS to create damping torque with randomly changing loads, uncertain renewable penetration, varying operating condition, several disturbances, and interconnection of the power system network. The modern power system is going to face a lot of challenges penetrating to damping of EMO. Hence for optimal usage of turbine governor control to meet these challenges, a new modification in governor control action is performed in this work, in coordination with PSS action. Usually, the input to the governor is speed deviations, but if real power deviation can also be given simultaneously with additional phase compensation, the performance of the governor would be much enhanced. In this work, the hydro turbine governor is given dual inputs, which are speed and real power deviation, and both are fed simultaneously through different phase lead compensation which has been named here as dual compensated governor (DCG). The next aspect is setting control action gains optimally to enhance controller efficacy. In this context, currently, much research have been performed on advanced optimization processes. In [27], a low computational burden model predictive control based on a social ski driver algorithm has been presented for intelligent vehicular applications. In [28], arithmetic optimization algorithm (AOA) tuned model predictive control paradigm is proposed for automatic voltage regulators against uncertainty. So, on lightning search algorithm has been applied for variable structure control for a nuclear reactor power system in [29]. Whale optimization algorithm has been applied in [30] in contrast to other metaheuristics to design a new robust control method for wind energy conversion systems. Different researchers also have investigated the impact of a suitable control action and appropriate algorithm to regulate frequency in a power system. Genetic algorithm tuned fuzzy gain scheduling controller and optimal regulator are proposed in [31, 32] and an integrating layered recurrent ANN-based control action is proposed in [33] with various operating conditions including DFIG-based wind energy integration for automatic generation control. The system dynamic response can be regulated and improved with an energy storage device like a redox flow battery and an appropriate controller like fuzzy PID action as reported in [34], where the controller parameters are tuned with the SSA algorithm. In this work, different nonlinearities that resembled real world systems are also included to justify the control action. The coyote optimization algorithm is proposed in [35] with a fuzzy controller to improve frequency stability along with wind turbine units. Metaheuristic algorithms are justified to be much more efficient for handling different optimization problems, as reported by researchers. For this work, a new hybrid modified DE with PSO technique is proposed. DE and PSO are efficient evolutionary and swarm control laws being employed by many researchers for optimization. But, in contrast to DE, modified DE can choose suitable F and CR at the time of the program run, which exponentially decays from 1 to 0.01 and speeds up the computational time [36]. Due to lack of storage in MDE, the result may be local optima, which is the demerit of MDE. PSO provide a global best value and cover up the storage problem and can be easily implemented. Hence hybrid MDEPSO optimization technique has been developed here including the merits of both DE and PSO. This algorithm has been tested with some standard benchmarks.


### 1.2. Research Gap and Motivation

The research gap identified by the author is that hydro governors are under usage to damp EMO which is an important concern for modern power system networks subject to uncertain penetrations of renewable sources. Though researches focus on the utilization of the governor for frequency control still, there is not much for EMO damping as per the author knowledge. In [37], eigen analysis has been performed for hydraulic, mechanical, and electrical coupling systems but optimal coordinated control of the system may improve system dynamic response with modification in control action provided by the governor and PSS. For a modern power system, hydro plant is going to be an indispensable energy source; especially pumped storage units provide an additional advantage of addressing energy storage problems and challengeable to battery energy storage systems. But, the varying penetrations of renewable like solar and wind sources give rise to electromechanical oscillations in the power system, which need to be damped at an earlier stage, or else may lead to eventual loss of synchronism. So, to address this issue, a variable renewable penetrated PSHP dominated power system is considered in this work. Here the PSHP governor is modified with a dual compensated network and coordinated with PSS by a control strategy to impart an effective damping torque for power oscillations brought by random changes in solar and wind outputs. By this action, the utilization of governor action would be much improved so as to tackle critical oscillations in the power system. The prime contribution of the present work is a modification in PSHPP governor with PSS and coordination between them to handle electromechanical oscillations in power systems even to the critical oscillatory condition due to renewable penetrations. Also, the traditional governor needs to be much improved to provide effective damping torque for critical oscillations.


### 1.3. Research Contribution

As per the reviews of literature mentioned in previous sections, hydro governors need to be modified in contrast to existing models to counteract critical oscillatory conditions. In this model, compensation networks are implemented in the path of speed and real power signals to impart effective damping torque by the governor. Also, as per existing works, PSS are not properly coordinated so as to handle critical system oscillations, but in this model, PSS have been coordinated with a modified governor so that sufficient damping torque can be contributed for system oscillations. So, the proposed approach can enhance the effective damping torque contribution of both the governor and PSS.The prime contribution of this work can be stated in brief as follows:(i)
A new dual compensated pumped storage hydro governor (DCG) is proposed.(ii)
A new coordinated control of DCG with PSS is proposed for efficient damping torque contribution.(iii)
Intermittent and sudden SPV/wind penetration is executed to observe electromechanical low frequency oscillations and proposed control action being implemented to damp oscillations.(iv)
A new hybrid modified DE with PSO is proposed to tune control action parameters.(v)
This control action can prevent underutilizing governor action to dampen EMO as well as enhance the efficacy of pumped storage hydro plant.


### 1.4. Paper Organization

The rest part of this manuscript has been organized as follows: Section 2 presents the modeling of PSHPP with PSS and governor action, Section 3 illustrates modified governor and proposed control action, Section 4 describes the multiobjective function and proposed optimization technique. The case studies and analysis with proposed control action are presented in Section 5 and the conclusion in the conspectus is presented in Section 6.


## 1.1. Literature Review

Due to randomness in SPV and wind generation, electromechanical oscillation (EMO) generated in the power system poses much more challenges to the system operator. In [7], an analysis has been presented depicting the impact of uncertain wind penetration on the stability of the power system. As per [8], the damping capability of wind sources can be imparted if wind turbines run at a constant speed. But as per [9], the small signal stability is a challenging issue with intermittent wind penetration, and the stability depends on the operating condition. The wind and synchronous generator may interact to provide positive or weak damping to EMO [10], and the stability may sacrifice if there is a strong coupling between wind and conventional generation [11]. So as per this research, variable wind integration creates a challenge to damping EMO. In a similar way, varying SPV also poses a challenge to EMO damping. In [12, 13], research have been conducted predicting the impact of undertrained SPV penetration on small signal stability of power system. The contribution to EMO depends on the characteristics of SPV, which have been analyzed in [14, 15]. Sudden and random SPV integration with the power system aggravated EMO [16]. As in [17], the mechanical mode of oscillation is more excited with heavy SPV penetration, and critical machines need to be identified to damp oscillations, which may be a difficult task. Time domain simulation and analysis have been performed in [18] with different RPGs subject to small signal stability, which explained optimal usage of different sources for stability improvement. Also, in [19], it has been observed that undertrained SPV penetration poses challenges for EMO damping. Therefore, as per the research stated above, damping EMO is a critical challenge for system operators when there are uncertain SPV and wind penetrations. A power system stabilizer (PSS) is usually employed to dampen EMO, which creates an electrical damping torque in the generator through an excitation system [20]. In [21], a criterion has been developed for selecting an optimal node to install PODs and PSSs, but the setting of parameters of the damping controller and its impact can be studied further. So, an important issue is selecting the proper PSS controller. The PSS control action may hamper regulating voltage and provides leading pf, which are demerits of PSS controller. Again, in the current state of deregulation in the power sector the optimal use of existing resources like mechanical torque control imparted by generator governor action would be an efficient technique if the governor's performance is improved. In [22], the efficiency of turbine governor action for oscillation damping has been presented, where it has been shown that speed control and excitation loop may be decoupled and do not influence each other. The governor can efficiently provide mechanical torque to stabilize frequency [23], but there may be a modification in turbine governor performance if additional phase compensation is provided with the governor [24]. But in the report of [25], it has been presented that hydro governors are generally blocked to damp interarea oscillation. So, although the governor can impact damping torque, its controllability needs to be improved much to counteract low interarea oscillations. The governor parameters need to be tuned efficiently to provide adequate damping torque. If steam valve control and excitation control are coordinated, then the control action would be enhanced as reported in [26], but using an efficient optimization technique may reduce a detailed mathematical model for efficient control action. In the current and future content of power system, HPP is going to take an important role so there can be a modification in hydro turbine governor action along with proper coordination by excitation system provided by PSS. This attempt has been performed in this work where the turbine governor action is coordinated with PSS to create damping torque with randomly changing loads, uncertain renewable penetration, varying operating condition, several disturbances, and interconnection of the power system network. The modern power system is going to face a lot of challenges penetrating to damping of EMO. Hence for optimal usage of turbine governor control to meet these challenges, a new modification in governor control action is performed in this work, in coordination with PSS action. Usually, the input to the governor is speed deviations, but if real power deviation can also be given simultaneously with additional phase compensation, the performance of the governor would be much enhanced. In this work, the hydro turbine governor is given dual inputs, which are speed and real power deviation, and both are fed simultaneously through different phase lead compensation which has been named here as dual compensated governor (DCG). The next aspect is setting control action gains optimally to enhance controller efficacy. In this context, currently, much research have been performed on advanced optimization processes. In [27], a low computational burden model predictive control based on a social ski driver algorithm has been presented for intelligent vehicular applications. In [28], arithmetic optimization algorithm (AOA) tuned model predictive control paradigm is proposed for automatic voltage regulators against uncertainty. So, on lightning search algorithm has been applied for variable structure control for a nuclear reactor power system in [29]. Whale optimization algorithm has been applied in [30] in contrast to other metaheuristics to design a new robust control method for wind energy conversion systems. Different researchers also have investigated the impact of a suitable control action and appropriate algorithm to regulate frequency in a power system. Genetic algorithm tuned fuzzy gain scheduling controller and optimal regulator are proposed in [31, 32] and an integrating layered recurrent ANN-based control action is proposed in [33] with various operating conditions including DFIG-based wind energy integration for automatic generation control. The system dynamic response can be regulated and improved with an energy storage device like a redox flow battery and an appropriate controller like fuzzy PID action as reported in [34], where the controller parameters are tuned with the SSA algorithm. In this work, different nonlinearities that resembled real world systems are also included to justify the control action. The coyote optimization algorithm is proposed in [35] with a fuzzy controller to improve frequency stability along with wind turbine units. Metaheuristic algorithms are justified to be much more efficient for handling different optimization problems, as reported by researchers. For this work, a new hybrid modified DE with PSO technique is proposed. DE and PSO are efficient evolutionary and swarm control laws being employed by many researchers for optimization. But, in contrast to DE, modified DE can choose suitable F and CR at the time of the program run, which exponentially decays from 1 to 0.01 and speeds up the computational time [36]. Due to lack of storage in MDE, the result may be local optima, which is the demerit of MDE. PSO provide a global best value and cover up the storage problem and can be easily implemented. Hence hybrid MDEPSO optimization technique has been developed here including the merits of both DE and PSO. This algorithm has been tested with some standard benchmarks.


## 1.2. Research Gap and Motivation

The research gap identified by the author is that hydro governors are under usage to damp EMO which is an important concern for modern power system networks subject to uncertain penetrations of renewable sources. Though researches focus on the utilization of the governor for frequency control still, there is not much for EMO damping as per the author knowledge. In [37], eigen analysis has been performed for hydraulic, mechanical, and electrical coupling systems but optimal coordinated control of the system may improve system dynamic response with modification in control action provided by the governor and PSS. For a modern power system, hydro plant is going to be an indispensable energy source; especially pumped storage units provide an additional advantage of addressing energy storage problems and challengeable to battery energy storage systems. But, the varying penetrations of renewable like solar and wind sources give rise to electromechanical oscillations in the power system, which need to be damped at an earlier stage, or else may lead to eventual loss of synchronism. So, to address this issue, a variable renewable penetrated PSHP dominated power system is considered in this work. Here the PSHP governor is modified with a dual compensated network and coordinated with PSS by a control strategy to impart an effective damping torque for power oscillations brought by random changes in solar and wind outputs. By this action, the utilization of governor action would be much improved so as to tackle critical oscillations in the power system. The prime contribution of the present work is a modification in PSHPP governor with PSS and coordination between them to handle electromechanical oscillations in power systems even to the critical oscillatory condition due to renewable penetrations. Also, the traditional governor needs to be much improved to provide effective damping torque for critical oscillations.


## 1.3. Research Contribution

As per the reviews of literature mentioned in previous sections, hydro governors need to be modified in contrast to existing models to counteract critical oscillatory conditions. In this model, compensation networks are implemented in the path of speed and real power signals to impart effective damping torque by the governor. Also, as per existing works, PSS are not properly coordinated so as to handle critical system oscillations, but in this model, PSS have been coordinated with a modified governor so that sufficient damping torque can be contributed for system oscillations. So, the proposed approach can enhance the effective damping torque contribution of both the governor and PSS.The prime contribution of this work can be stated in brief as follows:(i)
A new dual compensated pumped storage hydro governor (DCG) is proposed.(ii)
A new coordinated control of DCG with PSS is proposed for efficient damping torque contribution.(iii)
Intermittent and sudden SPV/wind penetration is executed to observe electromechanical low frequency oscillations and proposed control action being implemented to damp oscillations.(iv)
A new hybrid modified DE with PSO is proposed to tune control action parameters.(v)
This control action can prevent underutilizing governor action to dampen EMO as well as enhance the efficacy of pumped storage hydro plant.


## 1.4. Paper Organization

The rest part of this manuscript has been organized as follows: Section 2 presents the modeling of PSHPP with PSS and governor action, Section 3 illustrates modified governor and proposed control action, Section 4 describes the multiobjective function and proposed optimization technique. The case studies and analysis with proposed control action are presented in Section 5 and the conclusion in the conspectus is presented in Section 6.


## 2. Modeling of PSHPP with PSS and Governor Action

The PSHPP has an upper and a lower reservoir and can meet the requirement of energy storage. It can operate in generating or pumping mode. Generating mode is initiated for high energy demand and the pumping mode is for low energy demand. When demand for energy is less, the PSHPP turbine works in pumping mode, thereby pumping water from the low to the upper reservoir, and so, during the hereby demand of energy period, the turbine works in generating mode thereby utilizing upper reservoir water for generation purpose so as to meet the load. Figure1 depicts a PSHPP connected to the grid.Figure 1
PSHPP with PSS.


### 2.1. PSHPP Modeling with PSS

The hydro generator is modeled here in terms of transfer function pertained to small signal analysis, whereK1 to K6 are constants of the generator model dependent on operating conditions [19]. The real power, output voltage, and field emfs can be presented by the following equations:(1)ΔPe=K1Δδ+K2ΔEq′,(2)ΔEq=K4Δδ+K3ΔEq′,(3)ΔVt=K5Δδ+K6ΔEq′.The linearized equation of the machine is given below:(4)Δδ.=ω0Δω,(5)Δω⋅=−K1MΔδ−DMΔω−K2MΔEq′+ΔPMM,(6)ΔEq′.=−K4Td0′Δδ−K3Td0′ΔEq′+ΔEfdTd0′,(7)ΔE.fd=−K5KaTaΔδ−K6KaTaΔEq′−ΔEfdTa+ΔVpssKaTa,(8)ΔV1.=−K1KpsΔδ−DKpsΔω−K2KpsΔEq′+KpsΔPm−ΔV1TW.The PSS is connected through an excitation system to the generator and change in PSS output voltage is depicted by ΔVpss by equation (9), where Kps,T1,T2 are PSS tuning parameters.(9)ΔVpss.=−K1KpsT1T2Δδ−DKpsT1T2Δω−K2KpsT1T2ΔEq′+KpsT1T2ΔPM+ΔV1T21−T1TW−ΔVpssT2.Governor Δωref and ΔPeref are not considered here. The gate opening ΔY can be presented by Equation (10). ΔY1, and ΔY2 are outputs of the integrator and servo system. ΔX1, ΔX2 are integral and derivative outputs. The governor dynamics are presented by the following equations [38] in the required form:(10)ΔY.=ΔY1−ΔYta,(11)ΔY1.=KsmΔY2,(12)ΔY2.=K1KpKCRPTCΔδ−KpKCTCΔω+K2KpKCRPTCΔEq′+KCTCΔX1+KCTCΔX2−KCTCΔY−ΔY2TC,(13)ΔX.1=K1RPKiΔδ−KiΔω+K2KiRPΔEq′,(14)ΔX.2=K1KdMTd−K2K4RPKdTdo′TdΔδ+DMKdTd+RPKdK1ω0TdΔω.+K2KdMTd−K2K3RPKdTdo′TdΔEq′+K2RPKdTdo′TdΔEfd−KdΔPmMTd−ΔX2Td.Taking the length of penstock asL (cm), c. s area (m2), water discharge q (m3/sec), and static head hs (m), the discharge rate is given by equation (15) and in pu in equation (16):(15)dqdt=hs−h−hpgAL,(16)dqdt=1−h−hpTtw,where Ttw is water time constant given by equation (17) and the output prime mover power is presented by equation (18) on the MVA base of the hydro generator.(17)Ttw=LAqbhbg,(18)Pm=Athq−qn−DtY0Δω,(19)At=Turbine MW ratingGenerator MVA ratinghratedqrated−qn.The linearized prime mover output power are given in the following:(20)ΔPm=At1−Z1s1−Z2sΔY−DtY0Δω,where Z1=q0−qn/TtW,, Z2=Y0TtW/2.Figure 2
Modeling of SPV generation.The transfer function of the linearized turbine is given by equation (21) by taking Y0 = q0 and neglecting the damping coefficient.(21)GT=ΔPmΔY=1−Y0TtWs1+Y0TtWs/2×At,(22)ΔPm.=DtY0MK1Δδ+DtY01Z2+DMΔω+DtY0K2MΔEq′−DtY0M−1Z2ΔPm−AtZ21+Z1taΔY−AtZ1Z2taΔY1.


### 2.2. Modeling of SPV and Wind Energy Generation

Pspv is SPV generation in watt can be presented as follows [18]:(23)Pv=Pspv=ηcSaϕv1−0.005Ta+25,Here Pspv depends on Ta and ϕv, which are temperature and radiation and ηc and Sa are constants, which are efficiency and area. Temperature Ta is taken as 25°C. Figure 2 shows the SPV modeling.Figure 3
Modeling of wind generation.For wind energy generation, the natural wind speed is employed to rotate the turbine. The speed of rotation of the shaft is raised by gear box. The wind mechanical energy is transformed into electrical energy through the grid and fed to transformers.Models of wind speed: the different wind types are classified as random, gradient, gusty, and basic types [18].Random type: here, Gaussian noise is employed to express the random speed of the wind as given by the following equation:(24)VR=2∑i=1NSRωiΔωwcosωi+ϕi,(25)ωi=i−o.5Δωw,SRωi=2KNF2ωi∏21+Fωi/μ∏234.Gradient wind can be expressed as follows:(26)VG=0,tTGs,VG,maxt−TGsTG1,TGs≤t≤TGs+TG1,VGmax,TGs+TG1≤t≤TGe−TG2,VG,maxTGe−tTG2,TGe−TG2≤t≤TGe,0,t>TGe.Gusty wind can be expressed as follows:(27)Vs0,t<Tis,Vsmax21−cos2∏tTSe−TSs−TSSTSe−TSS,0,t>T2s.Equation (28) shows the wind turbine power output as presented by the following:(28)Pw=12ρdAbCpVW3,where Pw varies with ρd = 1.25 kgm−3 and Ab = 1735 m2, which are the density of air and sweeping blade area, respectively. VW in ms−1 is the velocity of wind, which depends on Cp, which varies with λp and βp, which are tip ratio and blade pitch angle, respectively. Blade radius and speed are 23.5 m and 3.14 rads−1, respectively. Cp is given by the following:(29)CP=0.44−0.0167βpsinπλp−315−0.3βp−0.0184λp−3βp,Figure3 represents the output power in pu versus VW and model of wind power generation, respectively. This model is given by the following:Figure 4
Phasor diagram of governor torque.


## 2.1. PSHPP Modeling with PSS

The hydro generator is modeled here in terms of transfer function pertained to small signal analysis, whereK1 to K6 are constants of the generator model dependent on operating conditions [19]. The real power, output voltage, and field emfs can be presented by the following equations:(1)ΔPe=K1Δδ+K2ΔEq′,(2)ΔEq=K4Δδ+K3ΔEq′,(3)ΔVt=K5Δδ+K6ΔEq′.The linearized equation of the machine is given below:(4)Δδ.=ω0Δω,(5)Δω⋅=−K1MΔδ−DMΔω−K2MΔEq′+ΔPMM,(6)ΔEq′.=−K4Td0′Δδ−K3Td0′ΔEq′+ΔEfdTd0′,(7)ΔE.fd=−K5KaTaΔδ−K6KaTaΔEq′−ΔEfdTa+ΔVpssKaTa,(8)ΔV1.=−K1KpsΔδ−DKpsΔω−K2KpsΔEq′+KpsΔPm−ΔV1TW.The PSS is connected through an excitation system to the generator and change in PSS output voltage is depicted by ΔVpss by equation (9), where Kps,T1,T2 are PSS tuning parameters.(9)ΔVpss.=−K1KpsT1T2Δδ−DKpsT1T2Δω−K2KpsT1T2ΔEq′+KpsT1T2ΔPM+ΔV1T21−T1TW−ΔVpssT2.Governor Δωref and ΔPeref are not considered here. The gate opening ΔY can be presented by Equation (10). ΔY1, and ΔY2 are outputs of the integrator and servo system. ΔX1, ΔX2 are integral and derivative outputs. The governor dynamics are presented by the following equations [38] in the required form:(10)ΔY.=ΔY1−ΔYta,(11)ΔY1.=KsmΔY2,(12)ΔY2.=K1KpKCRPTCΔδ−KpKCTCΔω+K2KpKCRPTCΔEq′+KCTCΔX1+KCTCΔX2−KCTCΔY−ΔY2TC,(13)ΔX.1=K1RPKiΔδ−KiΔω+K2KiRPΔEq′,(14)ΔX.2=K1KdMTd−K2K4RPKdTdo′TdΔδ+DMKdTd+RPKdK1ω0TdΔω.+K2KdMTd−K2K3RPKdTdo′TdΔEq′+K2RPKdTdo′TdΔEfd−KdΔPmMTd−ΔX2Td.Taking the length of penstock asL (cm), c. s area (m2), water discharge q (m3/sec), and static head hs (m), the discharge rate is given by equation (15) and in pu in equation (16):(15)dqdt=hs−h−hpgAL,(16)dqdt=1−h−hpTtw,where Ttw is water time constant given by equation (17) and the output prime mover power is presented by equation (18) on the MVA base of the hydro generator.(17)Ttw=LAqbhbg,(18)Pm=Athq−qn−DtY0Δω,(19)At=Turbine MW ratingGenerator MVA ratinghratedqrated−qn.The linearized prime mover output power are given in the following:(20)ΔPm=At1−Z1s1−Z2sΔY−DtY0Δω,where Z1=q0−qn/TtW,, Z2=Y0TtW/2.Figure 2
Modeling of SPV generation.The transfer function of the linearized turbine is given by equation (21) by taking Y0 = q0 and neglecting the damping coefficient.(21)GT=ΔPmΔY=1−Y0TtWs1+Y0TtWs/2×At,(22)ΔPm.=DtY0MK1Δδ+DtY01Z2+DMΔω+DtY0K2MΔEq′−DtY0M−1Z2ΔPm−AtZ21+Z1taΔY−AtZ1Z2taΔY1.


## 2.2. Modeling of SPV and Wind Energy Generation

Pspv is SPV generation in watt can be presented as follows [18]:(23)Pv=Pspv=ηcSaϕv1−0.005Ta+25,Here Pspv depends on Ta and ϕv, which are temperature and radiation and ηc and Sa are constants, which are efficiency and area. Temperature Ta is taken as 25°C. Figure 2 shows the SPV modeling.Figure 3
Modeling of wind generation.For wind energy generation, the natural wind speed is employed to rotate the turbine. The speed of rotation of the shaft is raised by gear box. The wind mechanical energy is transformed into electrical energy through the grid and fed to transformers.Models of wind speed: the different wind types are classified as random, gradient, gusty, and basic types [18].Random type: here, Gaussian noise is employed to express the random speed of the wind as given by the following equation:(24)VR=2∑i=1NSRωiΔωwcosωi+ϕi,(25)ωi=i−o.5Δωw,SRωi=2KNF2ωi∏21+Fωi/μ∏234.Gradient wind can be expressed as follows:(26)VG=0,tTGs,VG,maxt−TGsTG1,TGs≤t≤TGs+TG1,VGmax,TGs+TG1≤t≤TGe−TG2,VG,maxTGe−tTG2,TGe−TG2≤t≤TGe,0,t>TGe.Gusty wind can be expressed as follows:(27)Vs0,t<Tis,Vsmax21−cos2∏tTSe−TSs−TSSTSe−TSS,0,t>T2s.Equation (28) shows the wind turbine power output as presented by the following:(28)Pw=12ρdAbCpVW3,where Pw varies with ρd = 1.25 kgm−3 and Ab = 1735 m2, which are the density of air and sweeping blade area, respectively. VW in ms−1 is the velocity of wind, which depends on Cp, which varies with λp and βp, which are tip ratio and blade pitch angle, respectively. Blade radius and speed are 23.5 m and 3.14 rads−1, respectively. Cp is given by the following:(29)CP=0.44−0.0167βpsinπλp−315−0.3βp−0.0184λp−3βp,Figure3 represents the output power in pu versus VW and model of wind power generation, respectively. This model is given by the following:Figure 4
Phasor diagram of governor torque.


## 3. Modified Governor and Proposed Control Action

Generally, the governors are not associated with interarea oscillation damping because their parameters are not set properly [25]. So, to enhance the usefulness of conventional hydro governor, a modification is proposed in the present work. The dynamics of conventional governor provide negative damping to oscillations, and the system eigenvalues are shifted to the right half of s-plane. Hence as a remedy to this, a damping torque can be created by the governor if a signal in phase with angular rotor frequency variations is applied. As shown in Figure 4 the mechanical power Pm0 is shifted to Pm and the damping component shifted to Pd from Pdo, thereby creating a +ve damping torque. In this work, the input to the governor is both speed and electrical power deviation signal. In dual controlled governor, two simultaneously controlled phase compensation networks are inserted in parallel with the speed and real power variation signals, as shown in Figure 5, where the PID governor is supplemented by dual phase compensation network.(30)ΔC3.=−Δω−ΔC310.05,(31)ΔC2.=−ΔωKw0.05−ΔC2TW−ΔC3Kw0.05,(32)ΔC1.=−ΔωTp1Tp2Kw0.05−ΔC3Tp1Tp2Kw0.05−1TWTp1Tp2+1Tp2ΔC2−1Tp2ΔC1,(33)ΔU2.=−K2K4KpeTdo′Δδ+KpK1ω0Δω−K3KpeK2Tdo′ΔEq′+KpeK2Tdo′ΔEfd−ΔU2TW,(34)ΔU1.=−KpeK2K4Tdo′Te1Te2Δδ+KpeK1ω0Te1Te2Δω−KpeK2K3Tdo′Te1Te2ΔEq′+KpeK2Tdo′Te1Te2ΔEfd−ΔU1Te2+ΔU2Te2Te1TW+1,(35)ΔY2.=KCKpTCΔC1−KCKpRPTCΔU1+KCTCΔX1+KCTCΔX2−ΔYKCTC−1TCΔY2,(36)ΔX.1=KiΔC1+RPKiΔU1,(37)ΔX2.=KdTdTp1Tp2Kw0.05−Δω−ΔC3−ΔC2TW+ΔC2−ΔC1+RPKdTdKpeK1ω0Δω+K2ΔEfdTdo′−K2Tdo′K4Δδ+K3ΔEq′−ΔU2TWTe1Te2+ΔU2Te2−ΔU1Te2−ΔX2Td.Figure 5
Small signal model of PSHPP with proposed control action.In the above equations, ΔC1,ΔC2&ΔC3 are the lead-lag compensator, washout block& delay outputs, respectively, for angular speed variation, which is given in equations (30)–(32). ΔU1&ΔU2 are the lead-lag compensator & washout block outputs, respectively, for real power variations, which are given in equations (33)–(34). Modification of ΔY2, ΔX1&ΔX2 due to DCG are given in equations (35)–(37).Figure5 shows the proposed control action with turbine and synchronous generator small signal modeling. In the proposed controller, dual compensated governor (DCG) and PSS are coordinately tuned and the strategy of coordination is presented in Figure 6. A multiobjective function is utilized to coordinate DCG and PSS by a modified DE and PSO control algorithm. Now governor provides mechanical damping torque and PSS provides electrical torque, so proper coordination between them is performed in the proposed control action. A time delay is incorporated with a speed deviation signal for the governor system as it is a remote signal. Equation (38) presents state-space model of PSHPP with the proposed controller. The elements of matrix [A] are given in the appendix.(38)ΔX.=AΔX,where ΔX.=Δδ.Δω.ΔEq′.ΔE.fdΔV1.ΔVpss.ΔP.mΔY.ΔY.1ΔY.2ΔX1.ΔX2.ΔC.1ΔC.2ΔC.3ΔU.1ΔU.2.Figure 6
Strategy of proposed control action.


## 4. Multiobjective Function and Optimization Technique

### 4.1. Multiobjective Function

A multiobjective function in the time domain has been implemented here to damp system oscillations by minimizing speed and real power variation, overshoot, undershoot, and settling time simultaneously. The objective of the proposed work is to damp power system oscillations, for which two different objectivesJ1 and J2 are considered here. The objective J1 is of ITAE type to damp variations is speed and real power as shown by equation (39). For multimachine systems, Δωe and ΔPe are sum of speed and real power variations of all generators. The range of gain values Kps,Kw, Kpe are taken from 0 to 100. PID parameters Kp, Ki, and Kd gain values range from 0 to 50, 0–2, and 0–5, respectively. The range of time constants T1, T2, Te1, Te2, Tp1, and Tp2 are taken from 0 to 1.(39)J1=∫0tsimtΔωedt+∫0tsimtΔPedt.For objective functionJ2 the system response characteristics such as undershoot (US), overshoot (OS), and settling time (Tse) have been considered with the same constraints as for J1. Equation (40) shows function J2, where normalized values of 4000 and 1000 are taken for US and OS, respectively.(40)J2=4000×US2+1000×OS2+Tse2.The multiobjective functionJ3 represented by equation (41) combines both J1 and J2 through weighing factor w1 and w2 and both are taken 0.5 in this study.(41)J3=w1×J1+w2×J2.


### 4.2. Modified DE Algorithm

Differential evolution technique mainly depends upon the mutation strategies and control parameters, scaling factor (F), crossover rate (CR), Population (NP), and generation (G). For convergence in the modified differential evolution technique, F and CR are selected by the following expressions [36]:(42)FG=Fmaxe−a1G/Gmax,(43)CRG=CRmaxe−a2G/Gmax.InitiallyG = 0 which gives FG = FMAX and CRG = CRMAX and in last generation when G = GMAX, FG = FMIN and CRG = CRMIN, where FG and CRG = Generation value of F and CR. FMAX and FMIN = maximum and minimum values of F, which are taken as 1 and 0, respectively. CRMAX and CRMIN = maximum and minimum values of CR, which are taken as 1 and 0, respectively. a1 and a2 = constants taken as 0.5 & 0.6, respectively.


### 4.3. PSO Algorithm

Velocity and position of swarms are the two main parameters of particle swarm optimization in a particular area. Equations (44) and (45) represent the velocity and the position of swarms, where acceleration coefficients and inertia weight are c1, c2, and w, respectively, whose limits are between 0.4 to 0.9. Two random values are rand1 and rand2, whose range is (0-1). Equation (45) represents the next iteration for the best solution.(44)vik+1=wvik+c1rand1Pi,pbestk−xik+c2rand2Pi,gbestk−xik,(45)xinew=xi+vi,(46)xik+1=xi,newiffxi,new≤fxixiotherwise.


### 4.4. Proposed Hybrid MDEPSO Algorithm

MDE has the advantage over DE that it can choose suitableF and CR at the time of the program run, which exponentially decays from 1 to 0.01 and speeds up the computational time. Due to lack of storage in MDE, the result may be local optima, which is the demerit of MDE. PSO provides the global best value and can be easily implemented. Hence hybrid MDEPSO optimization technique has been developed considering the advantages of both MDE and PSO. The pseudocode of MDEPSO is presented in the following subsection and minimizations with different benchmarks taken from [39] as presented in Figure 7 are shown in Figure 8. Minimization data with different benchmarks are depicted in Table 1.Figure 7
Representation of benchmarks.Figure 8
Representation of minimizations with benchmarks.Table 1
Minimization data with different benchmarks.
Test functionMethodBestWorstMeanMedianStdModeF1x=∑i=1nxi2DE7.7076×10−2389.68141.82842.0515×10−109.10872.5660×10−24PSO8.6825×10−2659.05230.37153.2881×10−052.26020.8170MDE1.5296×10−17197.04580.28734.6855×10−853.95921.5296×10−171MDEPSO2.3716×10−25279.57380.17521.5736×10−1252.96965.6962×10−207F2x=∑i=1nxi+∏i=1nxiDE7.5011×10−1337.45821.07575.5487×10−64.36434.5889PSO1.8587×10−1329.14770.63610.00541.69662.1191MDE7.1634×10−10444.31170.18331.1278×10−512.14937.1634×10−104MDEPSO7.6077×10−15232.71410.10876.6201×10−761.45451.2815×10−79F3x=∑i=1n∑j=1ixj2DE7.4006122.866019.456717.738814.80769.3429PSO1.2930×10−7100.09190.91530.09033.97961.8530MDE2.1968×10−21131.551.45663.6139×10−108.52651.7430×10−18MDEPSO1.9980×10−51113.83150.93225.3824×10−256.91571.9269×10−42F4x=maxxi,1≤i≤xDE0.00284.13330.54140.12410.87110.0053PSO6.6978×10−089.45540.97840.08643.97561.5098MDE1.6120×10−374.39520.04931.0167×10−180.32919.9964×10−23MDEPSO2.6549×10−463.41570.03315.0452×10−230.24591.3978×10−21F5x=−20exp−0.21n∑i=1nxi2−exp1n∑i=1ncos2πxi+20+eDE8.3391×10−128.47470.42901.0178×10−51.37452.5207×10−6PSO1.4655×10−137.35760.44710.00460.80840.9592MDE7.9936×10−159.10440.16128.1599×10−90.68097.9936×10−15MDEPSO4.4409×10−158.08350.06574.4409×10−150.58844.4409×10−15F6x=∏n10sin2∏yi+∑i=1nyi−121+10sin23∏yi+1+∑i=1nuxi,10,100,4DE1.0362×10−234.93030.10109.6834×10−120.49910.0086PSO8.7535×10−283.83360.01551.5919×10−70.15630.0099MDE2.4163×10−325.65290.01163.8120×10−200.15662.4163×10−32MDEPSO2.3558×10−323.31280.01762.3558×10−320.24262.3558×10−32F7x=0.1sin23∏xi+∑i=1nxi−121+sin23∏xi+1+xn−121+sin22∏xn+∑i=1nuxi,8,100,4DE4.2714×10−2312.31920.24602.9953×10−111.24541.3498×10−32PSO2.1554×10−278.15810.05963.5052×10−60.34160.1303MDE1.4730×10−3216.56530.05301.0710×10−200.46521.4730×10−32MDEPSO1.3498×10−329.03890.06331.3498×10−320.83761.3498×10−32Pseudocode of MDEPSO:(a)
X1are the initialized random particle.(b)
Generation starts atG = 0.(c)
Evaluate Fit_1 by using equation (41).(d)
MDE algorithm starts(i)
Calculation ofFG and CRG by using equations (42) and (43).(ii)
Construct the mutant vectorX2 by performing mutation and crossover.(iii)
Evaluate Fit_2 by using equation (41).(e)
PSO algorithm starts.(i)
Present population isX2.(ii)
If Fit_1 > Fit_2 then Pbest isX1 otherwise X2.(iii)
Gbest is evaluated from all the best values.(iv)
By using equations (44) and (45), a new velocity and a new position X3 are updated.(v)
Evaluate Fit_3 by using equation (41).(vi)
Best particle for the next generation is by comparing Fit_1, Fit_2, and Fit_3.XG+1 = X1 if Fit_1 is greater.=X2 if Fit_2 is greater.=X3 if Fit_3 is greater.(vii)
GenerationG = G+1(viii)
Maximum generation is checked. If no, then repeat again from step (C).


## 4.1. Multiobjective Function

A multiobjective function in the time domain has been implemented here to damp system oscillations by minimizing speed and real power variation, overshoot, undershoot, and settling time simultaneously. The objective of the proposed work is to damp power system oscillations, for which two different objectivesJ1 and J2 are considered here. The objective J1 is of ITAE type to damp variations is speed and real power as shown by equation (39). For multimachine systems, Δωe and ΔPe are sum of speed and real power variations of all generators. The range of gain values Kps,Kw, Kpe are taken from 0 to 100. PID parameters Kp, Ki, and Kd gain values range from 0 to 50, 0–2, and 0–5, respectively. The range of time constants T1, T2, Te1, Te2, Tp1, and Tp2 are taken from 0 to 1.(39)J1=∫0tsimtΔωedt+∫0tsimtΔPedt.For objective functionJ2 the system response characteristics such as undershoot (US), overshoot (OS), and settling time (Tse) have been considered with the same constraints as for J1. Equation (40) shows function J2, where normalized values of 4000 and 1000 are taken for US and OS, respectively.(40)J2=4000×US2+1000×OS2+Tse2.The multiobjective functionJ3 represented by equation (41) combines both J1 and J2 through weighing factor w1 and w2 and both are taken 0.5 in this study.(41)J3=w1×J1+w2×J2.


## 4.2. Modified DE Algorithm

Differential evolution technique mainly depends upon the mutation strategies and control parameters, scaling factor (F), crossover rate (CR), Population (NP), and generation (G). For convergence in the modified differential evolution technique, F and CR are selected by the following expressions [36]:(42)FG=Fmaxe−a1G/Gmax,(43)CRG=CRmaxe−a2G/Gmax.InitiallyG = 0 which gives FG = FMAX and CRG = CRMAX and in last generation when G = GMAX, FG = FMIN and CRG = CRMIN, where FG and CRG = Generation value of F and CR. FMAX and FMIN = maximum and minimum values of F, which are taken as 1 and 0, respectively. CRMAX and CRMIN = maximum and minimum values of CR, which are taken as 1 and 0, respectively. a1 and a2 = constants taken as 0.5 & 0.6, respectively.


## 4.3. PSO Algorithm

Velocity and position of swarms are the two main parameters of particle swarm optimization in a particular area. Equations (44) and (45) represent the velocity and the position of swarms, where acceleration coefficients and inertia weight are c1, c2, and w, respectively, whose limits are between 0.4 to 0.9. Two random values are rand1 and rand2, whose range is (0-1). Equation (45) represents the next iteration for the best solution.(44)vik+1=wvik+c1rand1Pi,pbestk−xik+c2rand2Pi,gbestk−xik,(45)xinew=xi+vi,(46)xik+1=xi,newiffxi,new≤fxixiotherwise.


## 4.4. Proposed Hybrid MDEPSO Algorithm

MDE has the advantage over DE that it can choose suitableF and CR at the time of the program run, which exponentially decays from 1 to 0.01 and speeds up the computational time. Due to lack of storage in MDE, the result may be local optima, which is the demerit of MDE. PSO provides the global best value and can be easily implemented. Hence hybrid MDEPSO optimization technique has been developed considering the advantages of both MDE and PSO. The pseudocode of MDEPSO is presented in the following subsection and minimizations with different benchmarks taken from [39] as presented in Figure 7 are shown in Figure 8. Minimization data with different benchmarks are depicted in Table 1.Figure 7
Representation of benchmarks.Figure 8
Representation of minimizations with benchmarks.Table 1
Minimization data with different benchmarks.
Test functionMethodBestWorstMeanMedianStdModeF1x=∑i=1nxi2DE7.7076×10−2389.68141.82842.0515×10−109.10872.5660×10−24PSO8.6825×10−2659.05230.37153.2881×10−052.26020.8170MDE1.5296×10−17197.04580.28734.6855×10−853.95921.5296×10−171MDEPSO2.3716×10−25279.57380.17521.5736×10−1252.96965.6962×10−207F2x=∑i=1nxi+∏i=1nxiDE7.5011×10−1337.45821.07575.5487×10−64.36434.5889PSO1.8587×10−1329.14770.63610.00541.69662.1191MDE7.1634×10−10444.31170.18331.1278×10−512.14937.1634×10−104MDEPSO7.6077×10−15232.71410.10876.6201×10−761.45451.2815×10−79F3x=∑i=1n∑j=1ixj2DE7.4006122.866019.456717.738814.80769.3429PSO1.2930×10−7100.09190.91530.09033.97961.8530MDE2.1968×10−21131.551.45663.6139×10−108.52651.7430×10−18MDEPSO1.9980×10−51113.83150.93225.3824×10−256.91571.9269×10−42F4x=maxxi,1≤i≤xDE0.00284.13330.54140.12410.87110.0053PSO6.6978×10−089.45540.97840.08643.97561.5098MDE1.6120×10−374.39520.04931.0167×10−180.32919.9964×10−23MDEPSO2.6549×10−463.41570.03315.0452×10−230.24591.3978×10−21F5x=−20exp−0.21n∑i=1nxi2−exp1n∑i=1ncos2πxi+20+eDE8.3391×10−128.47470.42901.0178×10−51.37452.5207×10−6PSO1.4655×10−137.35760.44710.00460.80840.9592MDE7.9936×10−159.10440.16128.1599×10−90.68097.9936×10−15MDEPSO4.4409×10−158.08350.06574.4409×10−150.58844.4409×10−15F6x=∏n10sin2∏yi+∑i=1nyi−121+10sin23∏yi+1+∑i=1nuxi,10,100,4DE1.0362×10−234.93030.10109.6834×10−120.49910.0086PSO8.7535×10−283.83360.01551.5919×10−70.15630.0099MDE2.4163×10−325.65290.01163.8120×10−200.15662.4163×10−32MDEPSO2.3558×10−323.31280.01762.3558×10−320.24262.3558×10−32F7x=0.1sin23∏xi+∑i=1nxi−121+sin23∏xi+1+xn−121+sin22∏xn+∑i=1nuxi,8,100,4DE4.2714×10−2312.31920.24602.9953×10−111.24541.3498×10−32PSO2.1554×10−278.15810.05963.5052×10−60.34160.1303MDE1.4730×10−3216.56530.05301.0710×10−200.46521.4730×10−32MDEPSO1.3498×10−329.03890.06331.3498×10−320.83761.3498×10−32Pseudocode of MDEPSO:(a)
X1are the initialized random particle.(b)
Generation starts atG = 0.(c)
Evaluate Fit_1 by using equation (41).(d)
MDE algorithm starts(i)
Calculation ofFG and CRG by using equations (42) and (43).(ii)
Construct the mutant vectorX2 by performing mutation and crossover.(iii)
Evaluate Fit_2 by using equation (41).(e)
PSO algorithm starts.(i)
Present population isX2.(ii)
If Fit_1 > Fit_2 then Pbest isX1 otherwise X2.(iii)
Gbest is evaluated from all the best values.(iv)
By using equations (44) and (45), a new velocity and a new position X3 are updated.(v)
Evaluate Fit_3 by using equation (41).(vi)
Best particle for the next generation is by comparing Fit_1, Fit_2, and Fit_3.XG+1 = X1 if Fit_1 is greater.=X2 if Fit_2 is greater.=X3 if Fit_3 is greater.(vii)
GenerationG = G+1(viii)
Maximum generation is checked. If no, then repeat again from step (C).


## 5. Case Studies and Analysis

In this work, the electromechanical oscillations are to be damped by the proposed control action. So, different cases are experimented with to justify the controller objective. A four-machine, two-area, and 39-bus new England system is considered for study. The system data is presented in Table2. At first, the governor performance was compared with dual compensated governor and the coordinated DCG-PSS actions are observed with different operating conditions of hydro generators are considered equipped with DCG and PSS. MDEPSO algorithm is employed to tune controller parameters with multiobjective function J3.Table 2
System data.
Hydro generatorRated = 100 MVA, rated turbineo/p = 90.94 MW, turbine discharge rate = 71.43 m3/s, turbine head = 138.9 m, gate position = 0.9 pu, discharge without load = 4.3 m3/s, permanent droop Rp = 0.05 pu, pilot time constant = 0.02 s, servo time constant = 0.5 s, penstock length = 465 m and cross-sectional area = 15.2 m2SPV and wind generationKWG = 1.0, TWG = 1.5, KV = 1.0, TV = 1.8Trans lineVnominal = 230 kV, L1 = 25 km, L2 = 10 km, L3 = 110 kmR = 1.0 × 10−4 pu/km, XL = 1.0 × 10−3 pu/km, BC = 1.75 × 10−3 pu/km


### 5.1. Case-I. Performance Analysis of Dual Compensated Governor

Here a two-area system with four hydro generators is considered with sudden penetration of SPV and wind sources. The system is shown in Figure9 and the initial operating state of hydro generators is in Table 3. With this operating condition, three different conditions are executed with sudden SPV and wind variations. In condition-I, SPV output is raised suddenly to 0.5 pu, in condition-II, wind output is suddenly raised to 0.5 pu, and in condition-III, both SPV and wind output are raised suddenly to 0.3 pu and 0.7 pu, respectively. The system response comparisons for DCG and uncompensated governors are presented in Figures 10 and 11, subject to local oscillations of all generators.Figure 9
(a) Two area system under study. (b) Control unit block.
(a)(b)Table 3
Initial operating condition for hydro generators for four m/c system.
Real (P0)/reactive power (Q0)G1G2G3G4P0 (pu)0.90.60.80.71Q0 (pu)0.120.250.170.20Figure 10
Angular frequency variation forG1 and G2.Figure 11
Angular frequency variation forG3 and G4.Table4 presents optimal parameters for all generators for different conditions. The system response predicts that DCG provides a better response as compared to only governor action to damp oscillations.Table 4
Optimal parameters.
ParametersSPV output raised by 0.5 puWind output raised by 0.5 puSPV output raised by 0.3 pu with wind output raised by 0.7 pu simultaneouslyCGovGovCGovGovCGovGovKp133.87243.1168.97336.3541.8517.67Kp237.47625.68510.27342.587.8725.47Kp317.07135.44714.46539.6115.8140.88Kp425.17117.85137.26728.5619.231.91Ki11.6320.3230.4921.341.310.904Ki21.6151.3181.5981.411.341.67Ki31.2910.5140.9220.5790.5620.281Ki40.2621.3730.5221.111.841.11Kd14.8713.6384.2354.312.563.45Kd22.4341.6984.6443.742.271.29Kd34.5183.3883.9542.962.951.15Kd42.9514.5332.3514.871.6738.767Kw193.684---------37.821---------7.23---------Kw274.798---------76.046---------86.51---------Kw345.984---------93.696---------68.16---------Kw462.819---------44.671---------65.44---------Kpe19.896---------90.787---------94.31---------Kpe243.763---------62.061---------71.34---------Kpe351.271---------22.152---------25.48---------Kpe422.092---------73.416---------48.92---------Te10.739---------0.728---------0.703---------Te20.197---------0.195---------0.375---------Te30.119---------0.341---------0.774---------Te40.816---------0.642---------0.568---------Te50.531---------0.257---------0.245---------Te60.697---------0.637---------0.248---------Te70.606---------0.132---------0.655---------Te80.259---------0.847---------0.598---------Tp10.921---------0.668---------0.687---------Tp20.491---------0.435---------0.394---------Tp30.781---------0.607---------0.952---------Tp40.504---------0.335---------0.445---------Tp50.677---------0.359---------0.782---------Tp60.159---------0.638---------0.404---------Tp70.845---------0.268---------0.803---------Tp80.208---------0.262---------0.866---------


### 5.2. Case-II. Sudden Variation in SPV and Wind Penetration

#### 5.2.1. Time and Frequency Domain Analysis

In this case, sudden SPV and wind penetration are executed subject to different operating conditions. A two-area four hydro generator system is shown in Figure9 and has been taken for this case. The initial operating state of all generators is given in Table 1. With these generators, sudden SPV and wind penetration are executed at Bus-1 to Bus-4 at different instants. The SPV and wind penetrations are suddenly raised by 0.3 pu and 0.7 pu, respectively. The local oscillations for all generators are examined independently with only PSS, Gov-PSS, Single compensated governor with PSS (CG-PSS), and proposed dual compensated governor with PSS (DCG-PSS) tuned by DE, PSO, and multiobjective MDEPSO algorithms. The local oscillations for G1 and G2 are shown in Figure 12, for G3 and G4 are shown in Figure 13, and interarea oscillations are shown in Figure 14. Figure 15 depicts settling time comparisons with different control actions. These interarea oscillations are observed when sudden SPV and wind penetrations are applied to machine-1, machine-2, machine-3, and machine-4 separately and presented for ω14, ω23,ω32, and ω41, respectively. Tables 5 and 6 present mechanical oscillatory mode and optimized gains, respectively. In Table 5, the oscillatory mode with governor and excitation system as reported in [37] has also been compared with the proposed control action, and the eigenvalues are found to move towards a more stable region with the proposed control action. In [37], the governor and excitation control action has been implemented for a single machine system, but in this work, this action has been implemented for all four generators separately for analysis purposes. Stability analysis in the frequency domain has also been performed in this case, subject to simultaneous solar and wind penetration. For this analysis, Bode plots have been performed and Table 7 represents the Bode plot for local oscillations of all the generators. The positive gain margin and phase margin in the Bode plots signify the stability of the system with the proposed control action. The higher synchronous generation contribution led to a better stability region in frequency analysis via Bode plots. It is found that oscillations are more excited with fewer generator output contributions. Oscillations are damped heavily with a higher operating state of generators with more active power contributions. Also, dual compensation of the governor in coordination with PSS can provide efficient damping to these oscillations, which has been justified by system oscillatory responses.Figure 12
Angular frequency variation forG1 and G2.Figure 13
Angular frequency variation forG3 and G4.Figure 14
Inter-area oscillation ofω14, ω41, ω23 and ω32.Figure 15
Settling time comparisons with different control actions.Table 5
Mechanical mode for local oscillations.
SystemPSSGov-PSS [37]Coordinated Gov-PSSCoordinated CG-PSSProposed coordinated DCG-PSSG1−3.9265 + 4.6293i−1.9265 + 7.6296i−3.9426 + 4.6197i−4.0322 + 4.6055i−3.9324 + 4.6244i−3.9265 − 4.6293i−1.9265 − 7.6296i−3.9426 − 4.6197i−4.0322 − 4.6055i−3.9324 − 4.6244i−0.6168 + 3.0837i−0.0668 + 3.0131i−0.0853 + 3.2578i−0.0671 + 3.6037i−1.808 + 3.2894i−0.6168 − 3.0837i−0.0668 − 3.0131i−0.0853 − 3.2578i−0.0671 − 3.6037i−1.808 − 3.2894iG2−3.9370 + 4.6245i−1.9371 + 9.8871i−3.9614 + 4.6290i−3.9666 + 4.6666i−3.9729 + 4.6247i−3.9370 − 4.6245i−1.9371 − 9.8871i−3.9614 − 4.6290i−3.9666 − 4.6666i−3.9729 − 4.6247i−1.0144 + 2.0551i−0.0132 + 2.0523i−1.3807 + 2.3670i−0.0913 + 3.6233i−1.2890 + 2.9189i−1.0144 − 2.0551i−0.0132 − 2.0523i−1.3807 − 2.3670i−0.0913 − 3.6233i−1.2890 − 2.9189iG3−3.9744 + 4.6789i−1.9751 + 7.6661i−4.0268 + 4.7275i−3.9674 + 4.6382i−4.0947 + 4.7168i−3.9744 − 4.6789i−1.9751 − 7.6661i−4.0268 − 4.7275i−3.9674 − 4.6382i−4.0947 − 4.7168i−0.5998 + 2.7791i−0.0991 + 4.2111i−0.1806 + 3.6584i−0.5016 + 3.0458i−1.4459 + 2.5127i−0.5998 − 2.7791i−0.0991 − 4.2111i−0.1806 − 3.6584i−0.5016 − 3.0458i−1.4459 − 2.5127IG4−4.0207 + 4.6712i−1.0727 + 8.6712i−3.9548 + 4.5862i−3.9464 + 4.6296i−3.9508 + 4.6214i−4.0207 − 4.6712i−1.0727 − 8.6712i−3.9548 − 4.5862i−3.9464 − 4.6296i−3.9508 − 4.6214i−0.2019 + 3.2541i−0.2028 + 3.2577i−0.0611 + 3.2038i−0.0011 + 3.6178i−1.3135 + 3.1889i−0.2019 − 3.254i−0.2028 − 3.2577i−0.0611 − 3.2038i−0.0011 − 3.6178i−1.3135 − 3.1889iTable 6
Optimized gains.
ParametersPSSCoordinated Gov-PSSCoordinated CG-PSSCoordinated DCG-PSS (DE)Coordinated DCG-PSS (PSO)Proposed coordinated DCG-PSS (MDEPSO)Kps170.6896.5573.1781.5451.8540.68Kps256.7389.6758.4548.3365.2217.47Kps371.4391.9339.9885.0931.4854.32Kps454.4876.6268.2992.3790.9670.00T10.8790.3360.3240.9010.4810.269T20.6660.2110.2860.6570.3110.676T30.4620.4720.6010.7710.6270.231T40.3070.2990.6780.8460.9270.492T50.6330.2160.8240.2810.6420.657T60.3610.3370.8410.4610.8380.986T70.6470.7930.7880.1230.1010.167T80.7210.6080.8580.9320.6290.777Kp1-------7.63841.0230.8632.1117.33Kp2-------8.81535.5136.0122.0513.24Kp3-------13.0523.2933.6211.3715.87Kp4-------46.0438.1637.8126.2044.72ki1-------1.5961.5421.0511.3741.087Ki2-------0.1710.0260.0810.6971.197Ki3-------1.1711.6131.3590.3270.901Ki4-------0.5941.6961.3840.7281.296kd1-------3.0114.5852.9462.1541.063Kd2-------3.7551.9963.3543.4884.452Kd3-------1.5273.3431.0982.6753.015Kd4-------2.4911.7542.7274.8313.731Kw1--------------49.3166.3688.8033.28Kw2--------------91.1955.1217.3468.06Kw3--------------75.2411.126.52190.05Kw4--------------19.5075.9358.0799.91Tp1--------------0.4450.1830.3730.589Tp2--------------0.1840.5550.7910.123Tp3--------------0.6840.5350.8870.995Tp4--------------0.5430.3580.6170.432Tp5--------------0.3750.2440.5180.107Tp6--------------0.6410.5150.7370.515Tp7--------------0.1450.4770.8610.241Tp8--------------0.5410.1070.2060.438Kpe1---------------------93.5856.7631.52Kpe2---------------------58.4134.8370.68Kpe3---------------------86.0352.7790.90Kpe4---------------------35.4279.1588.71Te1---------------------0.8620.2940.383Te2---------------------0.1480.4240.692Te3---------------------0.9510.2690.683Te4---------------------0.1480.3050.121Te5---------------------0.9860.4230.257Te6---------------------0.3470.2720.735Te7---------------------0.1620.1450.688Te8---------------------0.9460.7260.457Table 7
Bode plot.


#### 5.2.2. Sensitivity Analysis for Parametric Variations

The robustness of the system with the proposed control action can be analyzed with different uncertainties occurring in a practical power system. Besides changes in system operating conditions and variation in renewable power generation, as considered earlier, the parametric variation has been considered in this section. Sensitivity analysis has been performed in this case subject to variation in excitation system, governor, and prime mover parameters considering G1 in a multimachine system as shown in Figure9. The system local eigenvalues, settling time, and minimum damping ratios are presented in Table 8. In this case, the excitation system parameter Ta, the governor servo motor parameter Tc and prime mover water time constant Ttw are raised and lowered by 50%. From the system eigen-distribution, it is observed that subject to parametric variation, which may occur in a practical power system, all the eigenvalues have negative real part predicting stability of the system. So, with the proposed controller, the stability of the system can be justified pertaining to parameter variation, which signifies robustness of the control action. Also, the minimum damping ratio with less settling time within 5 s predicts that even though system parameters are largely varied, the system becomes stable within less time.Table 8
Eigen distributions for parametric variations.
Parameter changeEigen valueSettling timeMinimum damping ratioTa decreased by 50%1.0e + 02∗−1.9965, −0.5000, −0.2733,−0.1969, −0.0007 + 0.0569i, −0.0007 − 0.0569i, −0.0434 + 0.0490i, −0.0434 − 0.0490i, −0.0332,−0.0278, −0.0180, −0.0015 + 0.0006i, −0.0015 − 0.0006i, −0.0009, −0.0010, −0.0067, −0.00564.22580.0122Ta raised by 50%−66.7194, −49.9829, −27.5268, −19.3836, −0.1002 + 6.4346i, −0.1002 − 6.4346i, −4.4724 + 5.0343i, −4.4724 − 5.0343i, −2.5694, −1.9417, −1.6843, −0.1474 + 0.0625i, −0.1474 − 0.0625i, −0.0901, −0.0017, −0.1000, −0.6667, −0.55564.33020.0156Tc decreased by 50%−99.7238, −50.0381, −31.0300, −19.1870, −7.5659 + 3.2935i, −7.5659 − 3.2935i, −0.0297 + 5.6774i, −0.0297 − 5.6774i, −1.4702, −1.9512, −1.9280, −0.1606 + 0.0442i, −0.1606 − 0.0442i, −0.0981, −0.0017, −0.1000, −0.6667, −0.55564.50320.0522Tc raised by 50%−99.7515, −50.0006, −26.4410, −19.7465, −0.1563 + 5.6422i, −0.1563 − 5.6422i, −3.0743 + 4.5920i, −3.0743 − 4.5920i, −1.7397, −1.7127, −1.6187, −0.1467 + 0.0616i, −0.1467 − 0.0616i, −0.0911, −0.0017, −0.1000, −0.6667, −0.55564.41310.0277Ttw decreased by 50%−99.7217, −50.0170, −27.1666, −19.8390, −0.1018 + 5.5947i, −0.1018 − 5.5947i, −4.1998 + 4.6267i, −4.1998 − 4.6267i, −2.5689, −1.9972, −1.4085, −0.1443 + 0.0628i, −0.1443 − 0.0628i, −0.0975, −0.0009, −0.1000, −0.6667, −0.55564.62440.0182Ttw raised by 50%−99.7296, −49.9994, −27.3071, −19.7186, −4.2943 + 4.8820i, −4.2943 − 4.8820i, −0.0408 + 5.4871i, −0.0408 − 5.4871i, −2.3378, −1.4841, −1.1960, −0.1705 + 0.0200i, −0.1705 − 0.0200i, −0.0926, −0.0025, −0.1000, −0.6667, −0.55564.69960.00743


### 5.3. Case-III. Intermittent Variation in SPV and Wind Penetration

In this case, the four-machine system, as taken in the previous case and a modified new-England 39 bus system have been investigated for random SPV and wind penetrations penetrating to electromechanical oscillations. The pattern of this penetration is given in Figure16. For a 4-machine system, this variation in SPV and wind generations have been applied independently and shown in Figures 17 and 18 for G1, G2, and G3, G4, respectively, for SPV variations. Similarly, Figures 19 and 20 for G1, G2, and G3, G4, respectively, for wind variations. The 39-bus system is being shown in Figure 21 with SPV and wind penetrations are executed at bus-6 and bus-25, respectively. The initial operating state of 10 machines is given in Table 9. These SPV and wind perturbations are executed separately at different timings. Figure 22 presents local oscillations for G4, G5, G6, G7, and interarea oscillations ω46, ω58 when random SPV penetrations are executed at bus-6 and Figure 23 presents similar oscillations with random wind penetration is executed at bus-25. For this case, the proposed multiobjective coordinated dual compensated to damp oscillations. The effectiveness of the proposed controller is observed with oscillations for generators with different initial states subject to intermittent SPV and wind penetrations at bus-6 and bus-25. For the practical implementation of the proposed work, the hardware control action and complexity of the model are mainly responsible. Also, there may be chances of instability during the running of the model for new parameters, and to tackle this, the flow of the MDEPSO algorithm can terminate simulation under this condition. Real time digital simulator (RTDS) can be implemented for testing the system in real-time. It is found from experimentations that intermittency in SPV and wind penetration excites local and interarea oscillations and the proposed controller can efficiently dampen these oscillations.Figure 16
Pattern of solar/wind power variations.Figure 17
Speed variation for SPV change.Figure 18
Speed variation for SPV change.Figure 19
Speed variation for wind change.Figure 20
Speed variation for wind change.Figure 21
39 bus system.Table 9
Initial operating condition for hydro generators for 39 bus system.
Real power (P0)/Reactive power (Q0)G1G2G3G4G5G6G7G8G9G10P0 (pu)0.710.80.60.90.80.60.710.90.60.8Q0 (pu)0.200.170.250.120.170.250.200.120.250.17Figure 22
Angular frequency variation ofG4, G5,G6, and G7.Figure 23
Angular frequency variation ofG4, G5,G6, and G7.


## 5.1. Case-I. Performance Analysis of Dual Compensated Governor

Here a two-area system with four hydro generators is considered with sudden penetration of SPV and wind sources. The system is shown in Figure9 and the initial operating state of hydro generators is in Table 3. With this operating condition, three different conditions are executed with sudden SPV and wind variations. In condition-I, SPV output is raised suddenly to 0.5 pu, in condition-II, wind output is suddenly raised to 0.5 pu, and in condition-III, both SPV and wind output are raised suddenly to 0.3 pu and 0.7 pu, respectively. The system response comparisons for DCG and uncompensated governors are presented in Figures 10 and 11, subject to local oscillations of all generators.Figure 9
(a) Two area system under study. (b) Control unit block.
(a)(b)Table 3
Initial operating condition for hydro generators for four m/c system.
Real (P0)/reactive power (Q0)G1G2G3G4P0 (pu)0.90.60.80.71Q0 (pu)0.120.250.170.20Figure 10
Angular frequency variation forG1 and G2.Figure 11
Angular frequency variation forG3 and G4.Table4 presents optimal parameters for all generators for different conditions. The system response predicts that DCG provides a better response as compared to only governor action to damp oscillations.Table 4
Optimal parameters.
ParametersSPV output raised by 0.5 puWind output raised by 0.5 puSPV output raised by 0.3 pu with wind output raised by 0.7 pu simultaneouslyCGovGovCGovGovCGovGovKp133.87243.1168.97336.3541.8517.67Kp237.47625.68510.27342.587.8725.47Kp317.07135.44714.46539.6115.8140.88Kp425.17117.85137.26728.5619.231.91Ki11.6320.3230.4921.341.310.904Ki21.6151.3181.5981.411.341.67Ki31.2910.5140.9220.5790.5620.281Ki40.2621.3730.5221.111.841.11Kd14.8713.6384.2354.312.563.45Kd22.4341.6984.6443.742.271.29Kd34.5183.3883.9542.962.951.15Kd42.9514.5332.3514.871.6738.767Kw193.684---------37.821---------7.23---------Kw274.798---------76.046---------86.51---------Kw345.984---------93.696---------68.16---------Kw462.819---------44.671---------65.44---------Kpe19.896---------90.787---------94.31---------Kpe243.763---------62.061---------71.34---------Kpe351.271---------22.152---------25.48---------Kpe422.092---------73.416---------48.92---------Te10.739---------0.728---------0.703---------Te20.197---------0.195---------0.375---------Te30.119---------0.341---------0.774---------Te40.816---------0.642---------0.568---------Te50.531---------0.257---------0.245---------Te60.697---------0.637---------0.248---------Te70.606---------0.132---------0.655---------Te80.259---------0.847---------0.598---------Tp10.921---------0.668---------0.687---------Tp20.491---------0.435---------0.394---------Tp30.781---------0.607---------0.952---------Tp40.504---------0.335---------0.445---------Tp50.677---------0.359---------0.782---------Tp60.159---------0.638---------0.404---------Tp70.845---------0.268---------0.803---------Tp80.208---------0.262---------0.866---------


## 5.2. Case-II. Sudden Variation in SPV and Wind Penetration

### 5.2.1. Time and Frequency Domain Analysis

In this case, sudden SPV and wind penetration are executed subject to different operating conditions. A two-area four hydro generator system is shown in Figure9 and has been taken for this case. The initial operating state of all generators is given in Table 1. With these generators, sudden SPV and wind penetration are executed at Bus-1 to Bus-4 at different instants. The SPV and wind penetrations are suddenly raised by 0.3 pu and 0.7 pu, respectively. The local oscillations for all generators are examined independently with only PSS, Gov-PSS, Single compensated governor with PSS (CG-PSS), and proposed dual compensated governor with PSS (DCG-PSS) tuned by DE, PSO, and multiobjective MDEPSO algorithms. The local oscillations for G1 and G2 are shown in Figure 12, for G3 and G4 are shown in Figure 13, and interarea oscillations are shown in Figure 14. Figure 15 depicts settling time comparisons with different control actions. These interarea oscillations are observed when sudden SPV and wind penetrations are applied to machine-1, machine-2, machine-3, and machine-4 separately and presented for ω14, ω23,ω32, and ω41, respectively. Tables 5 and 6 present mechanical oscillatory mode and optimized gains, respectively. In Table 5, the oscillatory mode with governor and excitation system as reported in [37] has also been compared with the proposed control action, and the eigenvalues are found to move towards a more stable region with the proposed control action. In [37], the governor and excitation control action has been implemented for a single machine system, but in this work, this action has been implemented for all four generators separately for analysis purposes. Stability analysis in the frequency domain has also been performed in this case, subject to simultaneous solar and wind penetration. For this analysis, Bode plots have been performed and Table 7 represents the Bode plot for local oscillations of all the generators. The positive gain margin and phase margin in the Bode plots signify the stability of the system with the proposed control action. The higher synchronous generation contribution led to a better stability region in frequency analysis via Bode plots. It is found that oscillations are more excited with fewer generator output contributions. Oscillations are damped heavily with a higher operating state of generators with more active power contributions. Also, dual compensation of the governor in coordination with PSS can provide efficient damping to these oscillations, which has been justified by system oscillatory responses.Figure 12
Angular frequency variation forG1 and G2.Figure 13
Angular frequency variation forG3 and G4.Figure 14
Inter-area oscillation ofω14, ω41, ω23 and ω32.Figure 15
Settling time comparisons with different control actions.Table 5
Mechanical mode for local oscillations.
SystemPSSGov-PSS [37]Coordinated Gov-PSSCoordinated CG-PSSProposed coordinated DCG-PSSG1−3.9265 + 4.6293i−1.9265 + 7.6296i−3.9426 + 4.6197i−4.0322 + 4.6055i−3.9324 + 4.6244i−3.9265 − 4.6293i−1.9265 − 7.6296i−3.9426 − 4.6197i−4.0322 − 4.6055i−3.9324 − 4.6244i−0.6168 + 3.0837i−0.0668 + 3.0131i−0.0853 + 3.2578i−0.0671 + 3.6037i−1.808 + 3.2894i−0.6168 − 3.0837i−0.0668 − 3.0131i−0.0853 − 3.2578i−0.0671 − 3.6037i−1.808 − 3.2894iG2−3.9370 + 4.6245i−1.9371 + 9.8871i−3.9614 + 4.6290i−3.9666 + 4.6666i−3.9729 + 4.6247i−3.9370 − 4.6245i−1.9371 − 9.8871i−3.9614 − 4.6290i−3.9666 − 4.6666i−3.9729 − 4.6247i−1.0144 + 2.0551i−0.0132 + 2.0523i−1.3807 + 2.3670i−0.0913 + 3.6233i−1.2890 + 2.9189i−1.0144 − 2.0551i−0.0132 − 2.0523i−1.3807 − 2.3670i−0.0913 − 3.6233i−1.2890 − 2.9189iG3−3.9744 + 4.6789i−1.9751 + 7.6661i−4.0268 + 4.7275i−3.9674 + 4.6382i−4.0947 + 4.7168i−3.9744 − 4.6789i−1.9751 − 7.6661i−4.0268 − 4.7275i−3.9674 − 4.6382i−4.0947 − 4.7168i−0.5998 + 2.7791i−0.0991 + 4.2111i−0.1806 + 3.6584i−0.5016 + 3.0458i−1.4459 + 2.5127i−0.5998 − 2.7791i−0.0991 − 4.2111i−0.1806 − 3.6584i−0.5016 − 3.0458i−1.4459 − 2.5127IG4−4.0207 + 4.6712i−1.0727 + 8.6712i−3.9548 + 4.5862i−3.9464 + 4.6296i−3.9508 + 4.6214i−4.0207 − 4.6712i−1.0727 − 8.6712i−3.9548 − 4.5862i−3.9464 − 4.6296i−3.9508 − 4.6214i−0.2019 + 3.2541i−0.2028 + 3.2577i−0.0611 + 3.2038i−0.0011 + 3.6178i−1.3135 + 3.1889i−0.2019 − 3.254i−0.2028 − 3.2577i−0.0611 − 3.2038i−0.0011 − 3.6178i−1.3135 − 3.1889iTable 6
Optimized gains.
ParametersPSSCoordinated Gov-PSSCoordinated CG-PSSCoordinated DCG-PSS (DE)Coordinated DCG-PSS (PSO)Proposed coordinated DCG-PSS (MDEPSO)Kps170.6896.5573.1781.5451.8540.68Kps256.7389.6758.4548.3365.2217.47Kps371.4391.9339.9885.0931.4854.32Kps454.4876.6268.2992.3790.9670.00T10.8790.3360.3240.9010.4810.269T20.6660.2110.2860.6570.3110.676T30.4620.4720.6010.7710.6270.231T40.3070.2990.6780.8460.9270.492T50.6330.2160.8240.2810.6420.657T60.3610.3370.8410.4610.8380.986T70.6470.7930.7880.1230.1010.167T80.7210.6080.8580.9320.6290.777Kp1-------7.63841.0230.8632.1117.33Kp2-------8.81535.5136.0122.0513.24Kp3-------13.0523.2933.6211.3715.87Kp4-------46.0438.1637.8126.2044.72ki1-------1.5961.5421.0511.3741.087Ki2-------0.1710.0260.0810.6971.197Ki3-------1.1711.6131.3590.3270.901Ki4-------0.5941.6961.3840.7281.296kd1-------3.0114.5852.9462.1541.063Kd2-------3.7551.9963.3543.4884.452Kd3-------1.5273.3431.0982.6753.015Kd4-------2.4911.7542.7274.8313.731Kw1--------------49.3166.3688.8033.28Kw2--------------91.1955.1217.3468.06Kw3--------------75.2411.126.52190.05Kw4--------------19.5075.9358.0799.91Tp1--------------0.4450.1830.3730.589Tp2--------------0.1840.5550.7910.123Tp3--------------0.6840.5350.8870.995Tp4--------------0.5430.3580.6170.432Tp5--------------0.3750.2440.5180.107Tp6--------------0.6410.5150.7370.515Tp7--------------0.1450.4770.8610.241Tp8--------------0.5410.1070.2060.438Kpe1---------------------93.5856.7631.52Kpe2---------------------58.4134.8370.68Kpe3---------------------86.0352.7790.90Kpe4---------------------35.4279.1588.71Te1---------------------0.8620.2940.383Te2---------------------0.1480.4240.692Te3---------------------0.9510.2690.683Te4---------------------0.1480.3050.121Te5---------------------0.9860.4230.257Te6---------------------0.3470.2720.735Te7---------------------0.1620.1450.688Te8---------------------0.9460.7260.457Table 7
Bode plot.


### 5.2.2. Sensitivity Analysis for Parametric Variations

The robustness of the system with the proposed control action can be analyzed with different uncertainties occurring in a practical power system. Besides changes in system operating conditions and variation in renewable power generation, as considered earlier, the parametric variation has been considered in this section. Sensitivity analysis has been performed in this case subject to variation in excitation system, governor, and prime mover parameters considering G1 in a multimachine system as shown in Figure9. The system local eigenvalues, settling time, and minimum damping ratios are presented in Table 8. In this case, the excitation system parameter Ta, the governor servo motor parameter Tc and prime mover water time constant Ttw are raised and lowered by 50%. From the system eigen-distribution, it is observed that subject to parametric variation, which may occur in a practical power system, all the eigenvalues have negative real part predicting stability of the system. So, with the proposed controller, the stability of the system can be justified pertaining to parameter variation, which signifies robustness of the control action. Also, the minimum damping ratio with less settling time within 5 s predicts that even though system parameters are largely varied, the system becomes stable within less time.Table 8
Eigen distributions for parametric variations.
Parameter changeEigen valueSettling timeMinimum damping ratioTa decreased by 50%1.0e + 02∗−1.9965, −0.5000, −0.2733,−0.1969, −0.0007 + 0.0569i, −0.0007 − 0.0569i, −0.0434 + 0.0490i, −0.0434 − 0.0490i, −0.0332,−0.0278, −0.0180, −0.0015 + 0.0006i, −0.0015 − 0.0006i, −0.0009, −0.0010, −0.0067, −0.00564.22580.0122Ta raised by 50%−66.7194, −49.9829, −27.5268, −19.3836, −0.1002 + 6.4346i, −0.1002 − 6.4346i, −4.4724 + 5.0343i, −4.4724 − 5.0343i, −2.5694, −1.9417, −1.6843, −0.1474 + 0.0625i, −0.1474 − 0.0625i, −0.0901, −0.0017, −0.1000, −0.6667, −0.55564.33020.0156Tc decreased by 50%−99.7238, −50.0381, −31.0300, −19.1870, −7.5659 + 3.2935i, −7.5659 − 3.2935i, −0.0297 + 5.6774i, −0.0297 − 5.6774i, −1.4702, −1.9512, −1.9280, −0.1606 + 0.0442i, −0.1606 − 0.0442i, −0.0981, −0.0017, −0.1000, −0.6667, −0.55564.50320.0522Tc raised by 50%−99.7515, −50.0006, −26.4410, −19.7465, −0.1563 + 5.6422i, −0.1563 − 5.6422i, −3.0743 + 4.5920i, −3.0743 − 4.5920i, −1.7397, −1.7127, −1.6187, −0.1467 + 0.0616i, −0.1467 − 0.0616i, −0.0911, −0.0017, −0.1000, −0.6667, −0.55564.41310.0277Ttw decreased by 50%−99.7217, −50.0170, −27.1666, −19.8390, −0.1018 + 5.5947i, −0.1018 − 5.5947i, −4.1998 + 4.6267i, −4.1998 − 4.6267i, −2.5689, −1.9972, −1.4085, −0.1443 + 0.0628i, −0.1443 − 0.0628i, −0.0975, −0.0009, −0.1000, −0.6667, −0.55564.62440.0182Ttw raised by 50%−99.7296, −49.9994, −27.3071, −19.7186, −4.2943 + 4.8820i, −4.2943 − 4.8820i, −0.0408 + 5.4871i, −0.0408 − 5.4871i, −2.3378, −1.4841, −1.1960, −0.1705 + 0.0200i, −0.1705 − 0.0200i, −0.0926, −0.0025, −0.1000, −0.6667, −0.55564.69960.00743


## 5.2.1. Time and Frequency Domain Analysis

In this case, sudden SPV and wind penetration are executed subject to different operating conditions. A two-area four hydro generator system is shown in Figure9 and has been taken for this case. The initial operating state of all generators is given in Table 1. With these generators, sudden SPV and wind penetration are executed at Bus-1 to Bus-4 at different instants. The SPV and wind penetrations are suddenly raised by 0.3 pu and 0.7 pu, respectively. The local oscillations for all generators are examined independently with only PSS, Gov-PSS, Single compensated governor with PSS (CG-PSS), and proposed dual compensated governor with PSS (DCG-PSS) tuned by DE, PSO, and multiobjective MDEPSO algorithms. The local oscillations for G1 and G2 are shown in Figure 12, for G3 and G4 are shown in Figure 13, and interarea oscillations are shown in Figure 14. Figure 15 depicts settling time comparisons with different control actions. These interarea oscillations are observed when sudden SPV and wind penetrations are applied to machine-1, machine-2, machine-3, and machine-4 separately and presented for ω14, ω23,ω32, and ω41, respectively. Tables 5 and 6 present mechanical oscillatory mode and optimized gains, respectively. In Table 5, the oscillatory mode with governor and excitation system as reported in [37] has also been compared with the proposed control action, and the eigenvalues are found to move towards a more stable region with the proposed control action. In [37], the governor and excitation control action has been implemented for a single machine system, but in this work, this action has been implemented for all four generators separately for analysis purposes. Stability analysis in the frequency domain has also been performed in this case, subject to simultaneous solar and wind penetration. For this analysis, Bode plots have been performed and Table 7 represents the Bode plot for local oscillations of all the generators. The positive gain margin and phase margin in the Bode plots signify the stability of the system with the proposed control action. The higher synchronous generation contribution led to a better stability region in frequency analysis via Bode plots. It is found that oscillations are more excited with fewer generator output contributions. Oscillations are damped heavily with a higher operating state of generators with more active power contributions. Also, dual compensation of the governor in coordination with PSS can provide efficient damping to these oscillations, which has been justified by system oscillatory responses.Figure 12
Angular frequency variation forG1 and G2.Figure 13
Angular frequency variation forG3 and G4.Figure 14
Inter-area oscillation ofω14, ω41, ω23 and ω32.Figure 15
Settling time comparisons with different control actions.Table 5
Mechanical mode for local oscillations.
SystemPSSGov-PSS [37]Coordinated Gov-PSSCoordinated CG-PSSProposed coordinated DCG-PSSG1−3.9265 + 4.6293i−1.9265 + 7.6296i−3.9426 + 4.6197i−4.0322 + 4.6055i−3.9324 + 4.6244i−3.9265 − 4.6293i−1.9265 − 7.6296i−3.9426 − 4.6197i−4.0322 − 4.6055i−3.9324 − 4.6244i−0.6168 + 3.0837i−0.0668 + 3.0131i−0.0853 + 3.2578i−0.0671 + 3.6037i−1.808 + 3.2894i−0.6168 − 3.0837i−0.0668 − 3.0131i−0.0853 − 3.2578i−0.0671 − 3.6037i−1.808 − 3.2894iG2−3.9370 + 4.6245i−1.9371 + 9.8871i−3.9614 + 4.6290i−3.9666 + 4.6666i−3.9729 + 4.6247i−3.9370 − 4.6245i−1.9371 − 9.8871i−3.9614 − 4.6290i−3.9666 − 4.6666i−3.9729 − 4.6247i−1.0144 + 2.0551i−0.0132 + 2.0523i−1.3807 + 2.3670i−0.0913 + 3.6233i−1.2890 + 2.9189i−1.0144 − 2.0551i−0.0132 − 2.0523i−1.3807 − 2.3670i−0.0913 − 3.6233i−1.2890 − 2.9189iG3−3.9744 + 4.6789i−1.9751 + 7.6661i−4.0268 + 4.7275i−3.9674 + 4.6382i−4.0947 + 4.7168i−3.9744 − 4.6789i−1.9751 − 7.6661i−4.0268 − 4.7275i−3.9674 − 4.6382i−4.0947 − 4.7168i−0.5998 + 2.7791i−0.0991 + 4.2111i−0.1806 + 3.6584i−0.5016 + 3.0458i−1.4459 + 2.5127i−0.5998 − 2.7791i−0.0991 − 4.2111i−0.1806 − 3.6584i−0.5016 − 3.0458i−1.4459 − 2.5127IG4−4.0207 + 4.6712i−1.0727 + 8.6712i−3.9548 + 4.5862i−3.9464 + 4.6296i−3.9508 + 4.6214i−4.0207 − 4.6712i−1.0727 − 8.6712i−3.9548 − 4.5862i−3.9464 − 4.6296i−3.9508 − 4.6214i−0.2019 + 3.2541i−0.2028 + 3.2577i−0.0611 + 3.2038i−0.0011 + 3.6178i−1.3135 + 3.1889i−0.2019 − 3.254i−0.2028 − 3.2577i−0.0611 − 3.2038i−0.0011 − 3.6178i−1.3135 − 3.1889iTable 6
Optimized gains.
ParametersPSSCoordinated Gov-PSSCoordinated CG-PSSCoordinated DCG-PSS (DE)Coordinated DCG-PSS (PSO)Proposed coordinated DCG-PSS (MDEPSO)Kps170.6896.5573.1781.5451.8540.68Kps256.7389.6758.4548.3365.2217.47Kps371.4391.9339.9885.0931.4854.32Kps454.4876.6268.2992.3790.9670.00T10.8790.3360.3240.9010.4810.269T20.6660.2110.2860.6570.3110.676T30.4620.4720.6010.7710.6270.231T40.3070.2990.6780.8460.9270.492T50.6330.2160.8240.2810.6420.657T60.3610.3370.8410.4610.8380.986T70.6470.7930.7880.1230.1010.167T80.7210.6080.8580.9320.6290.777Kp1-------7.63841.0230.8632.1117.33Kp2-------8.81535.5136.0122.0513.24Kp3-------13.0523.2933.6211.3715.87Kp4-------46.0438.1637.8126.2044.72ki1-------1.5961.5421.0511.3741.087Ki2-------0.1710.0260.0810.6971.197Ki3-------1.1711.6131.3590.3270.901Ki4-------0.5941.6961.3840.7281.296kd1-------3.0114.5852.9462.1541.063Kd2-------3.7551.9963.3543.4884.452Kd3-------1.5273.3431.0982.6753.015Kd4-------2.4911.7542.7274.8313.731Kw1--------------49.3166.3688.8033.28Kw2--------------91.1955.1217.3468.06Kw3--------------75.2411.126.52190.05Kw4--------------19.5075.9358.0799.91Tp1--------------0.4450.1830.3730.589Tp2--------------0.1840.5550.7910.123Tp3--------------0.6840.5350.8870.995Tp4--------------0.5430.3580.6170.432Tp5--------------0.3750.2440.5180.107Tp6--------------0.6410.5150.7370.515Tp7--------------0.1450.4770.8610.241Tp8--------------0.5410.1070.2060.438Kpe1---------------------93.5856.7631.52Kpe2---------------------58.4134.8370.68Kpe3---------------------86.0352.7790.90Kpe4---------------------35.4279.1588.71Te1---------------------0.8620.2940.383Te2---------------------0.1480.4240.692Te3---------------------0.9510.2690.683Te4---------------------0.1480.3050.121Te5---------------------0.9860.4230.257Te6---------------------0.3470.2720.735Te7---------------------0.1620.1450.688Te8---------------------0.9460.7260.457Table 7
Bode plot.


## 5.2.2. Sensitivity Analysis for Parametric Variations

The robustness of the system with the proposed control action can be analyzed with different uncertainties occurring in a practical power system. Besides changes in system operating conditions and variation in renewable power generation, as considered earlier, the parametric variation has been considered in this section. Sensitivity analysis has been performed in this case subject to variation in excitation system, governor, and prime mover parameters considering G1 in a multimachine system as shown in Figure9. The system local eigenvalues, settling time, and minimum damping ratios are presented in Table 8. In this case, the excitation system parameter Ta, the governor servo motor parameter Tc and prime mover water time constant Ttw are raised and lowered by 50%. From the system eigen-distribution, it is observed that subject to parametric variation, which may occur in a practical power system, all the eigenvalues have negative real part predicting stability of the system. So, with the proposed controller, the stability of the system can be justified pertaining to parameter variation, which signifies robustness of the control action. Also, the minimum damping ratio with less settling time within 5 s predicts that even though system parameters are largely varied, the system becomes stable within less time.Table 8
Eigen distributions for parametric variations.
Parameter changeEigen valueSettling timeMinimum damping ratioTa decreased by 50%1.0e + 02∗−1.9965, −0.5000, −0.2733,−0.1969, −0.0007 + 0.0569i, −0.0007 − 0.0569i, −0.0434 + 0.0490i, −0.0434 − 0.0490i, −0.0332,−0.0278, −0.0180, −0.0015 + 0.0006i, −0.0015 − 0.0006i, −0.0009, −0.0010, −0.0067, −0.00564.22580.0122Ta raised by 50%−66.7194, −49.9829, −27.5268, −19.3836, −0.1002 + 6.4346i, −0.1002 − 6.4346i, −4.4724 + 5.0343i, −4.4724 − 5.0343i, −2.5694, −1.9417, −1.6843, −0.1474 + 0.0625i, −0.1474 − 0.0625i, −0.0901, −0.0017, −0.1000, −0.6667, −0.55564.33020.0156Tc decreased by 50%−99.7238, −50.0381, −31.0300, −19.1870, −7.5659 + 3.2935i, −7.5659 − 3.2935i, −0.0297 + 5.6774i, −0.0297 − 5.6774i, −1.4702, −1.9512, −1.9280, −0.1606 + 0.0442i, −0.1606 − 0.0442i, −0.0981, −0.0017, −0.1000, −0.6667, −0.55564.50320.0522Tc raised by 50%−99.7515, −50.0006, −26.4410, −19.7465, −0.1563 + 5.6422i, −0.1563 − 5.6422i, −3.0743 + 4.5920i, −3.0743 − 4.5920i, −1.7397, −1.7127, −1.6187, −0.1467 + 0.0616i, −0.1467 − 0.0616i, −0.0911, −0.0017, −0.1000, −0.6667, −0.55564.41310.0277Ttw decreased by 50%−99.7217, −50.0170, −27.1666, −19.8390, −0.1018 + 5.5947i, −0.1018 − 5.5947i, −4.1998 + 4.6267i, −4.1998 − 4.6267i, −2.5689, −1.9972, −1.4085, −0.1443 + 0.0628i, −0.1443 − 0.0628i, −0.0975, −0.0009, −0.1000, −0.6667, −0.55564.62440.0182Ttw raised by 50%−99.7296, −49.9994, −27.3071, −19.7186, −4.2943 + 4.8820i, −4.2943 − 4.8820i, −0.0408 + 5.4871i, −0.0408 − 5.4871i, −2.3378, −1.4841, −1.1960, −0.1705 + 0.0200i, −0.1705 − 0.0200i, −0.0926, −0.0025, −0.1000, −0.6667, −0.55564.69960.00743


## 5.3. Case-III. Intermittent Variation in SPV and Wind Penetration

In this case, the four-machine system, as taken in the previous case and a modified new-England 39 bus system have been investigated for random SPV and wind penetrations penetrating to electromechanical oscillations. The pattern of this penetration is given in Figure16. For a 4-machine system, this variation in SPV and wind generations have been applied independently and shown in Figures 17 and 18 for G1, G2, and G3, G4, respectively, for SPV variations. Similarly, Figures 19 and 20 for G1, G2, and G3, G4, respectively, for wind variations. The 39-bus system is being shown in Figure 21 with SPV and wind penetrations are executed at bus-6 and bus-25, respectively. The initial operating state of 10 machines is given in Table 9. These SPV and wind perturbations are executed separately at different timings. Figure 22 presents local oscillations for G4, G5, G6, G7, and interarea oscillations ω46, ω58 when random SPV penetrations are executed at bus-6 and Figure 23 presents similar oscillations with random wind penetration is executed at bus-25. For this case, the proposed multiobjective coordinated dual compensated to damp oscillations. The effectiveness of the proposed controller is observed with oscillations for generators with different initial states subject to intermittent SPV and wind penetrations at bus-6 and bus-25. For the practical implementation of the proposed work, the hardware control action and complexity of the model are mainly responsible. Also, there may be chances of instability during the running of the model for new parameters, and to tackle this, the flow of the MDEPSO algorithm can terminate simulation under this condition. Real time digital simulator (RTDS) can be implemented for testing the system in real-time. It is found from experimentations that intermittency in SPV and wind penetration excites local and interarea oscillations and the proposed controller can efficiently dampen these oscillations.Figure 16
Pattern of solar/wind power variations.Figure 17
Speed variation for SPV change.Figure 18
Speed variation for SPV change.Figure 19
Speed variation for wind change.Figure 20
Speed variation for wind change.Figure 21
39 bus system.Table 9
Initial operating condition for hydro generators for 39 bus system.
Real power (P0)/Reactive power (Q0)G1G2G3G4G5G6G7G8G9G10P0 (pu)0.710.80.60.90.80.60.710.90.60.8Q0 (pu)0.200.170.250.120.170.250.200.120.250.17Figure 22
Angular frequency variation ofG4, G5,G6, and G7.Figure 23
Angular frequency variation ofG4, G5,G6, and G7.


## 6. Conclusion

The present work employed a coordinated damping control action of mechanical torque provided by hydro governor and electrical torque provided by PSS through excitation system by the help of a multiobjective function with a modified DE-PSO control algorithm for a hydro, wind, and SPV integrated power system. The experimentations with the findings of this study can be presented as follows:(1)
At first, the governor performances with dual compensation are compared with only conventional PID action, and the oscillations due to sudden SPV and wind variations are found to be damped better by additional dual phase lead incorporated with the governor.(2)
The PSS has been traditionally employed to damp oscillation, but when coordinated with a dual compensated governor (DCG), the damping capability is further enhanced. The multiobjective function employs minimization of speed and real power deviations, US, OS, and settling time for efficient damping action.(3)
The proposed control action is justified considering a four-machine two-area and 39-bus 10 m/c system as compared with conventional PID governor and PSS action. The local and remote signals, which are real power and speed deviations undergone through phase compensation and coordination of governor with PSS, are found to provide heavy damping action for critical oscillatory conditions.(4)
This work can be further extended to a large-scale extended power system with more renewable penetrations. For future work, multiple hydro governors with PSS can be optimally coordinated with time delay coordination to handle governor and excitation system dynamics.



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*Source: 8802143-2022-10-19.xml*