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Frequency stabilisation of a hybrid two‐area power system by a novel quasi‐oppositional harmony search algorithm

2015; Institution of Engineering and Technology; Volume: 9; Issue: 15 Linguagem: Inglês

10.1049/iet-gtd.2014.0913

1751-8695

Tarkeshwar Mahto, V. Mukherjee,

Power System Optimization and Stability

IET Generation, Transmission & DistributionVolume 9, Issue 15 p. 2167-2179 Research ArticleFree Access Frequency stabilisation of a hybrid two-area power system by a novel quasi-oppositional harmony search algorithm Tarkeshwar Mahto, Tarkeshwar Mahto Department of Electrical Engineering, Indian School of Mines, Dhanbad, Jharkhand, IndiaSearch for more papers by this authorVivekananda Mukherjee, Corresponding Author Vivekananda Mukherjee vivek_agamani@yahoo.com Department of Electrical Engineering, Indian School of Mines, Dhanbad, Jharkhand, IndiaSearch for more papers by this author Tarkeshwar Mahto, Tarkeshwar Mahto Department of Electrical Engineering, Indian School of Mines, Dhanbad, Jharkhand, IndiaSearch for more papers by this authorVivekananda Mukherjee, Corresponding Author Vivekananda Mukherjee vivek_agamani@yahoo.com Department of Electrical Engineering, Indian School of Mines, Dhanbad, Jharkhand, IndiaSearch for more papers by this author First published: 01 November 2015 https://doi.org/10.1049/iet-gtd.2014.0913Citations: 15AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Modelling, simulation and performance analysis of a two-area thermal-hybrid distributed generation (HDG) power system having different sources of power generation has been carried out in this study. The thermal power plant is consisting of re-heat type thermal system, whereas the HDG system includes the combination of wind turbine generator and diesel generator. In the studied model, superconducting magnetic energy storage (SMES) device is considered in both the areas. Additionally, a flexible ac transmission system (FACTS) device such as static synchronous series compensator (SSSC) is also considered in the tie-line. The different tunable parameters of the proportional-integral-derivative (PID) controllers, SMES and SSSC are optimised using a novel quasi-oppositional harmony search (QOHS) algorithm. Optimisation performance of the novel QOHS algorithm is established while comparing its performance with binary coded genetic algorithm. From the simulation work it is observed that with the inclusion of SMES in both the areas, the system performances toward the achievement of minimal frequency and tie-line power oscillations are promising under different types of input loading perturbations. It is further revealed from the simulation results that the installation of an expensive FACTS device such as SSSC does not yield any significant improvement to the system performance. Nomenclature Ar swept area of blade A12 area capacity ratio ACEi area control error for area i Bi frequency bias of area i, pu MW/h Cp power co-efficient EGD energy generated from diesel generator FOD figure of demerit GPID(s) PID controller gain ID0 inductor rated current of SMES unit KD1 governor gain Ki generator gain constant of area i feedback gain of ΔID in the SMES unit fluid coupling gain KPC blade characteristic KP1 gain of pitch actuator KP2 gain of hydraulic pitch actuator KP3 gain of data fit the pitch response KR1 re-heat co-efficient of steam turbine for thermal area KSMES gain for SMES loop control KSSSC gain for SSSC L inductance value of SMES PGD power output deviation of diesel side PW mechanical power output of the wind turbine RDi governor speed regulation of area i, Hz/pu MW TDi time constant of speed governor control system for diesel generator, s TDC converter time constant of SMES unit, s TG1 time constant of speed governor control system for thermal area, s Ti generator time constant of area i, s TP1 time constant of pitch actuator, s TP2 time constant of hydraulic pitch actuator, s TP3 time constant of data fit pitch response, s TR1 re-heat time constant of thermal area, s TSSSC time constant of SSSC, s TT1 time constant of steam turbine for thermal area, s T12 tie-line synchronising co-efficient VW wind speed, m/s ΔED convertor voltage derivative applied to the inductor of SMES ΔFi frequency deviation of area i, Hz ΔFW speed deviation of the wind turbine induction generator ΔFTIE frequency deviation of tie-line, Hz ΔID inductor current deviation in SMES, pu ΔPCD control signal of the diesel governor, pu ΔPCT speed changer position deviation for thermal area, pu ΔPCW control signal of pitch controller, pu ΔPGD power output deviation of diesel side, pu ΔPGW power output deviation of wind side, pu ΔPHW control signal of data fit pitch response, pu ΔPIW input wind power deviation, pu ΔPLi real power demand deviation for area i, pu ΔPPD signal for speed governor of diesel generator, pu ΔPPT signal for governor of thermal unit, pu ΔPPW power output deviation of wind side, pu ΔPSMESi output real power deviation of SMES unit in area i, pu ΔPSSSC output real power deviation of SSSC, pu ΔPTD signal for diesel engine of diesel generator, pu ΔPTIE power output deviation of tie-line, pu ΔPTT power deviation of non-rehear turbine, pu ΔwTH rotor speed deviation of thermal unit, pu ηGD efficiency of diesel generator 1 Introduction Beyond any doubt, 21st century may be considered as the one devoted to renewable energy system (RES) [1]. Energy companies are considering installation of distributed generation (DG) as the energy sector is being restructured. DGs are small-scale power generating units that, usually, combine one or more RES together with non-renewable ones and/or with storage devices to form isolated hybrid DG (IHDG) power system when not connected to the distribution system [1, 2]. IHDGs may be incorporated within the distribution system or at a customers' site for power supply or improved and reliable power supply. Interconnection of two power systems (that is, main grid with IHDG) results in (a) reduced environmental danger from grid point of view and (b) enhanced reliability and capacity. Power supply of diesel-based IHDG grids may be integrated with the main grid energy sources such as thermal, hydro or nuclear [3]. In [4], simulation for grid-connected wind turbines with fluctuation has been studied. Caballero et al. [5] have studied optimal design of a grid-connected hybrid photovoltaic (PV)-wind energy system without energy storage for an Easter Island's block. Intelligent PV farm for robust frequency stabilisation in multi-area interconnected power system has been presented in [6]. However, connection of IHDG energy sources with the main grid power system increases the complexity of controlling, protecting and maintaining the distribution systems. Connection of IHDG to the weak parts of the power network [7, 8] will (a) increase fault levels, (b) induce voltage variations, (c) degrade network transient stability, (d) reverse the power flow and (e) increase losses depending on the relative size of the plant and the local loads. Therefore, in order to increase RES penetration, IHDG must be, properly, activated in order to keep system frequency and power deviation within admissible minimum level during dynamic transients. Literature survey reveals that most of the previous works in two-area power system are pertaining to an interconnected hydro–thermal, thermal–thermal and hydro–hydro etc. systems and relatively lesser attention has been devoted to an interconnected hybrid two-area power system. Thus, this paper addresses two-area interconnected power system having one area as thermal system, whereas the other area is HDG system and named as thermal-HDG system. To cope up with the challenges imposed by modern power systems, fast responding energy storage devices and/or power electronic-based controllers may be considered. In recent years, it has been observed that energy storage devices such as superconducting magnetic energy storage (SMES) [9, 10], which is able to control both active and reactive powers simultaneously, has been expected as one of the most effective stabilisers for both frequency and as well as power oscillations. Conventional generating units continue to generate constant power output even at the instant of occurrence of some disturbances in the system because SMES possesses the capability to follow system load demand almost instantaneously. It has the ability to damp out low-frequency power oscillation and to stabilise frequency deviation arising out of system transients. Moreover, SMES has high-power ramp ratio which allows it to smoothen the wind turbine power output. In turn, it favours the mitigation of voltage and frequency variations at the connection point of wind power plant. Other aspects related to the system stability issue under perturbations, such as oscillation damping and low-voltage ride through capability, become clearly improved with energy storage support. Moreover, energy technologies with high ramp rates are required features for such integration. All these characteristics of SMES make it an attractive device towards its implementation in power system [11]. The recent developments in the field of power electronics have introduced the use of flexible ac transmission system (FACTS) controllers in power systems [12]. FACTS controllers are capable of controlling the network conditions in a very fast manner and this feature of FACTS devices may be exploited to improve the stability of power system under load and wind perturbation. Static synchronous series compensator (SSSC) is an important member in the FACTS family which may be installed in series with the transmission lines. With the capability to change its reactance characteristic from capacitive to inductive, SSSC is very effective in controlling power flow of power systems [13]. Feasibility of SSSC in the studied hybrid two-area power system model is going to be addressed in this paper. A new derivative-free real parameter optimisation algorithm, which draws inspiration from the musical improvisation process of searching for a perfect state of harmony is, recently, introduced in the literature and is termed as harmony search (HS) algorithm [14]. In comparison with other meta-heuristics reported in the literature, HS algorithm imposes fewer mathematical requirements and may be easily adopted for solving various kinds of engineering optimisation problems [15]. HS algorithm does not require the setting of initial values of decision variables. HS algorithm may solve a continuous variable problem as well as combinatorial problem and outperforms other existing mathematical and heuristic methods. HS algorithm has faster convergence ability in lesser number of iterations. HS algorithm achieves this by making a new vector after considering all existing vectors, rather than considering only two (parents) as it is in genetic algorithm (GA). These features help HS in increasing flexibility and in finding better solutions [14]. The HS algorithm is good at identifying the high-performance regions of solution space within a reasonable time. A few modified variants of HS were proposed in the literature for enhancing its solution accuracy and convergence rate. Mahdavi et al. [16] have presented an improved HS algorithm, by introducing a strategy to, dynamically, tune its key parameters. Omran and Mahdavi [17] have proposed a global best HS algorithm by borrowing the concept from swarm intelligence. Pan et al. [18] have proposed a self-adaptive global best HS algorithm for solving continuous optimisation problems. Banerjee et al. [19] have proposed opposition-based HS algorithm for engineering optimisation problem with special emphasis on reactive power compensation of an autonomous hybrid power system model. Hybridisation of evolutionary optimisation techniques is still going on with the basic intension to formulate an effective and efficient optimisation technique for handling real-life engineering applications. In the view of the above, the main objectives of this paper are: (a) modelling of two-area thermal-HDG system to supply more reliable electricity and to meet its growing need for industries and remote rural areas, (b) investigating the impact on frequency and power deviation of the studied model by installing SMES in both thermal and HDG units, (c) checking the compatibility of SSSC in series with the tie-line and investigating its impact on frequency and power deviation under different perturbations for the studied two-area thermal-HDG power system model, (d) examining the effect of different perturbations such as application of step load disturbance (SLD), sinusoidal loading pattern and outage of tie-line on the transient performance of the test power system model, (e) initiating the robustness study of the system model, (f) evaluating the performance of the studied model considering the effect of generation rate constraint (GRC), (g) comparing the performance of SMES and battery as a storage device, (h) obtaining the optimised tunable parameters of the studied model by employing a novel quasi-oppositional HS (QOHS) algorithm, (i) establishing the optimal compatibility of the proposed QOHS algorithm over binary coded GA (BGA) and (j) evaluating the comparative computational cost of the deployed evolutionary optimisation techniques (i.e. QOHS and BGA). The rest of this paper is organised as follows. In Section 2, system modelling is presented. The mathematical problem of the present work is formulated in Section 3. Section 4 concentrates on evolutionary optimisation techniques employed vis-à-vis proposed QOHS algorithm. Simulation results are presented and discussed in Section 5. Finally, conclusions and scope of future work are focused in Section 6. 2 Proposed system modelling The block diagram representation of the studied interconnected two-area thermal IHDG system is presented in Fig. 1. In this figure, area 1 is a re-heat type thermal system, whereas area 2 is HDG system which is a combination of diesel and wind power generation system. These two power generating units are interconnected by a tie-line. HDG system is exposed to small changes in load demand and wind speed during its normal operation. To stabilise the frequency and power oscillations generated in the system due to the disturbances, SMES is installed in both the areas, whereas an SSSC is connected in series with the tie-line. Fig. 1Open in figure viewerPowerPoint Block diagram representation of an interconnected two-area thermal-HDG system 2.1 Modelling of thermal power system unit Thermal power system consists of electrical generator, steam turbine, speed governor and re-heater. Speed governor and turbine of the thermal power system is a first-order system. Drop characteristic of the generator governs the mechanical output–generator speed relationship. From Fig. 1, (1)–(4) follow (1) (2) (3) (4)The governing equations for frequency deviation of thermal (ΔFTH) power system (Fig. 1) may be expressed by (5) (5) 2.2 Modelling of proportional-integral-derivative (PID) controller In this paper, the transfer function of the considered PID controller considered may be given by (6) [20] (6)In the studied model (Fig. 1), three PID controllers are used. 2.3 Modelling HDG power system unit The various energy resources such as wind turbine generator (WTG) and diesel engine generator (DEG) units are incorporated to form the HDG system of the present work. The intermittent wind speed, due to unpredictable weather variation, may diminish the capacity of energy unit. Hence, SMES is integrated with such HDG system to overcome the issues related to stability. 2.3.1 Modelling of DEG In DEG, the value of EDG is calculated by using (7) [21, 22] (7)From Fig. 1, the model equation for power generated by DEG may be expressed by (8) (8)The equation for speed governor of the DEG may expressed by (9) (9)The controlling signal for the speed governor, generated by the droop characteristics and the controller, may be stated as by (10) (10)When a sudden change in load occurs, the immediate requirement of change in power generation has to come from the inertia of the generator rotor [21, 22]. Consequently, the generator frequency changes and its governing equation may be stated by (11) (11) 2.3.2 Modelling of WTG The generated power of the WTG depends on the value of VW. The mechanical power output of the wind turbine is expressed by (12) (12)The fluid coupling block transfers the speed difference between the turbine and generator frequency into power following (13) (13)The speed of wind turbine induction generator is represented by (14) (14)The 'data fit pitch response' block of Fig. 1 acts as a simple lag compensator which is required to match the phase/gain characteristic of the model. Thus, the wind turbine input power may be represented by (15) (15)Hydraulic pitch actuator controls the pitch angle of the turbine. The pitch angle is very finely selected to maximise the output power of WTG. The transfer function block for hydraulic pitch actuator may be given by (16) (16) 2.4 Modelling of SMES unit The superconducting coil may be charged to a set value during normal operation of the power system. When there is a sudden rise in the load demand, the stored energy is almost released through the converter to the power system as alternating current. As the governor and other control mechanisms start working to set the power system to the new equilibrium condition, the coil current changes back to its initial value and vice-versa action takes place during sudden release of load condition [23]. Fig. 2 shows the block diagram of SMES unit. The equations of output real power deviation, inductor current deviation and voltage deviation of SMES unit are as in (17)–(19), in sequence (17) (18) (19) Fig. 2Open in figure viewerPowerPoint Block diagram of SMES unit From Fig. 1, it may be noted that input signal to the SMES unit is the area control error signal of the respective area in power system (namely, ACETH and ACEHDG) and these two may be expressed by (20) and (21), respectively (20) (21) 2.5 Modelling of SSSC unit The dynamic characteristic of SSSC controller for the frequency stabilisation is shown in Fig. 3. The theory of operation of SSSC and its control fundamentals are extensively elaborated in [12, 24]. The input signal of the proposed controller is per unit ΔwTH. Thus, ΔPSSSC may be expressed by (22) (Fig. 3) (22) Fig. 3Open in figure viewerPowerPoint Structure of SSSC as a frequency controller The tunable parameters of SSSC are KSSSC, TSSSC, T1, T2, T3 and T4. 2.6 Modelling of tie-line Tie-lines have the benefits of providing inter-area support under abnormal conditions as well as the transmission parts for contractual energy exchanges between the areas. The basic equations related to ΔPTIE are given in (23) and (24) (Fig. 1) (23) (24)The deviation in tie-line frequency during the power exchange may be expressed by (25) (Fig. 1) (25) 3 Mathematical problem formulation The objective of this work is to ensure minimal deviation in terminal frequencies (ΔF) and tie-line power flow (ΔPTIE) response profiles. This may be achieved by minimising overshoot (MP), minimising settling time (ts), reducing rising time (tr) and narrowing down steady-state error (ESS) of ΔF and ΔPTIE response profiles. Thus, a time-domain performance index, termed as figure of demerit (FOD), is designed as in (26) (26)In the present work, the value of FOD is minimised by employing an optimisation technique. 4 Evolutionary optimisation techniques employed vis-à-vis proposed A novel HS algorithm is proposed in the present work for the tuning of the different tunable parameters of the studied power system model and BGA is employed for the sake of comparison. These two algorithms are explained in the next two sections. 4.1 BGA GA [25], motivated by Darwin's theories of evaluation and the concept of 'survival of the fittest', is an increasingly popular optimisation technique and is being applied to many fields of endeavour. 4.2 QOHS algorithm 4.2.1 HS algorithm HS algorithm has been developed in 2001 [14], inspired by the natural musical performance of the musicians while trying for creation of better harmony, HS algorithm is a new variant of derivative-free meta-heuristic algorithm. In HS algorithm, the solution vector is analogous to the harmony in music and the local and global search schemes are analogous to the musicians' improvisations. On the basis of the work reported by Banerjee et al. [19], the computational procedure on the basic HS algorithm may be summarised as in Algorithm 1 (see Fig. 4). The notations used in Algorithm 1 (Fig. 4) are explained in [19]. Fig. 4Open in figure viewerPowerPoint Pseudo-code for HS algorithm 4.2.2 Proposed QOHS algorithm The pseudo-code for the proposed QOHS approach is presented in Algorithm 2 (see Fig. 5). It is to be noted here that step 6 of Algorithm 2 (Fig. 5) describes the implementation of quasi-oppositional generation jumping for the proposed QOHS algorithm. Fig. 5Open in figure viewerPowerPoint Pseudo-code for the proposed QOHS algorithm 5 Simulation results and discussion The nominal model parameters used in the two-area thermal-HDG power system are presented in Table 6. In the present work, the following mentioned three configurations of the studied two-area power system model are considered: (a) Only model: Only PID-based governor control for thermal unit and diesel section of HDG along with PID-based pitch controller of wind generator in HDG section is termed as 'only model'. Comparative responses of PID controller-based 'only model' and integral (I) controller-based 'only model' (i.e. all the considered PID controllers of 'only model' are replaced by I controllers) are presented in Section 8.2 of Appendix which justifies the selection of PID controller for the studied 'only model' configuration. (b) Model+SMES: The 'only model' configuration of the studied power system model along with SMES system in both the areas is considered as 'model+SMES'. (c) Model+SMES+SSSC: The 'model+SMES' configuration of the studied power system model along with SSSC for tie-line control (Fig. 1) is considered as 'model+SMES+SSSC'. All the above-mentioned two-area thermal-HDG power system models are subjected to step and sinusoidal load disturbance. For the simulation work, the values for area participation factor (APF) considerations in Fig. 1 are taken as APFDEG = 0.2 and APFWTG = 0.8. Results of interest are 'bold faced' in the respective tables. The major observations of the present work are presented below. 5.1 Comparison of employed optimisation techniques Comparative BGA and the proposed QOHS algorithm-based responses of ΔFHDG(Hz), ΔFTH(Hz) and ΔPTIE(pu) of the studied three power system configurations, namely, 'only model', 'model+SMES' and 'model+SMES+SSSC' are shown in Fig. 6 with 1% SLD in area 2 (i.e. HDG). Comparative convergence profiles of FOD values as yielded by the BGA and the proposed QOHS algorithm for these three power system models are shown in Fig. 7. From Figs. 6 and 7 it may be concluded that the proposed QOHS algorithm-based optimisation approach offers superior results than BGA counterpart. These pictorial proofs are also supported by mathematical calculation of FOD value. Model parameters along with FOD values, as yielded by BGA and the proposed QOHS optimisation algorithm, are given in Tables 1–3 under different set of input parameters such as of RD1, RD2 and T12. From these tables, it may be observed that the proposed QOHS algorithm yields better performance than the BGA for all the test systems. Thus, the proposed QOHS algorithm may be accepted as a better optimising technique for this application and, hence, subsequent optimisation tasks of the present work are based on the application of the proposed QOHS algorithm. Table 1. Optimised parameters for 'only model' configuration Parameter Input set of parameters RD1 = 2.4, RD2 = 5,T12 = 0.0707 RD1 = 1.2, RD2 = 2.5,T12 = 0.0373 RD1 = 1.2, RD2 = 5,T12 = 0.02 RD1 = 1.2, RD2 = 2.5,T12 = 0.0707 QOHS BGA QOHS BGA QOHS BGA QOHS BGA KTP 43.163 51.958 36.215 51.567 45.612 49.224 11.477 52.349 KTI 86.866 99.609 95.151 99.609 19.533 92.188 30.056 99.609 KTD 26.853 51.958 20.519 51.567 23.056 49.224 26.201 52.349 KDP 97.635 51.958 99.671 51.567 96.575 9.2238 99.547 52.348 KDI 98.962 99.609 98.159 99.609 97.439 92.188 87.796 99.609 KDD 10.867 51.958 6.8820 51.567 13.234 49.224 10.734 52.349 KWP 30.158 99.609 38.557 99.609 27.165 92.188 26.632 99.609 KWI 3.2952 51.958 4.6592 51.567 3.5599 49.224 3.0377 52.349 KWD 98.811 99.609 92.998 99.609 99.954 92.188 97.666 99.609 FOD 7.4 × 10−12 6.9× 10−11 6.6 × 10−12 1.1E-11 9.7 × 10−13 3.1× 10−11 7.4 × 10−13 5.5× 10−11 Table 2. Optimised parameters for 'model+SMES' configuration Parameter Input set of parameters RD1 = 2.4, RD2 = 5,T12 = 0.0707 RD1 = 1.2, RD2 = 2.5,T12 = 0.0373 RD1 = 1.2, RD2 = 5,T12 = 0.02 RD1 = 1.2, RD2 = 2.5,T12 = 0.0707 QOHS BGA QOHS BGA QOHS BGA QOHS BGA KTP 25.567 93.360 73.219 93.360 93.810 99.609 18.663 99.609 KTI 9.2133 99.609 82.699 99.609 58.828 99.609 39.585 99.609 KTD 25.914 93.360 54.082 93.360 40.603 99.609 31.101 99.609 KDP 77.235 93.360 81.011 93.360 46.470 99.609 77.617 99.609 KDI 99.027 99.609 99.469 99.609 99.552 99.609 99.201 99.609 KDD 94.129 93.360 63.113 93.360 50.446 99.609 98.921 99.609 KWP 38.867 99.609 6.5972 99.609 89.965 99.609 38.449 99.609 KWI 6.6309 93.360 20.940 93.360 77.261 99.609 94.708 99.609 KWD 26.603 99.609 87.824 99.609 49.380 99.609 15.067 99.609 KSMES1 23.299 48.242 42.983 24.809 49.730 49.805 46.059 49.805 TDC1 0.5985 0.1493 0.4453 0.0049 0.7692 0.0010 0.2777 0.0010 KID1 0.0652 0.2053 2.1459 0.7911 3.4092 3.3296 2.0163 25.005 KSMES 49.999 49.804 50.000 49.805 50.000 49.805 49.998 9.805 TDC2 0.9607 0.9922 1.0000 0.9883 0.9375 0.9961 0.8809 0.9961 KID2 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 FOD 1.8 × 10−16 1.9× 10−14 1.5 × 10−16 1.8× 10−14 1.5 × 10−17 1.9× 10−14 1.5 × 10−17 2.1× 10−15 Table 3. Optimised parameters for 'model+SMES+SSSC' configuration Parameter Input set of parameters RD1 = 2.4, RD2 = 5,T12 = 0.0707 RD1 = 1.2, RD2 = 2.5,T12 = 0.0373 RD1 = 1.2, RD2 = 5,T12 = 0.02 RD1 = 1.2, RD2 = 2.5,T12 = 0.0707 QOHS BGA QOHS BGA QOHS BGA QOHS BGA KTP 17.966 99.609 84.805 49.614 98.826 99.609 81.294 99.609 KTI 19.632 99.609 37.249 99.609 38.384 99.609 93.567 99.609 KTD 71.632 99.609 54.229 49.614 26.919 99.609 46.902 99.609 KDP 93.540 9.609 82.231 49.614 22.979 99.609 76.219 99.6094 KDI 98.752 99.609 95.462 99.609 99.303 99.609 99.813 99.609 KDD 95.989 99.609 78.962 49.614 33.693 99.609 21.422 99.609 KWP 14.182 99.609 61.368 99.609 66.737 99.609 94.938 99.609 KWI 3.7401 99.609 5.0650 49.614 54.165 99.609 53.011 99.609 KWD 18.474 99.609 36.235 99.609 91.014 99.609 84.048 99.609 KSMES1 86.792 99.609 88.277 99.609 83.203 99.219 76.074 96.094 TDC1 0.2923 0.0010 0.0968 0.0049 0.2748 0.3210 0.3859 0.0986 KID1 0.0107 0.4006 25.690 6.6500 3.3376 0.0100 15.125 0.0100 KSMES2 100.00 9.609 99.913 9.609 99.705 99.609 99.084 93.360 TDC2 0.9992 0.7424 0.1357 0.9961 0.9246 0.9571 0.7276 0.9922 KID2 0.0100 1.5723 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 KSSSC 0.0100 0.0100 0.0101 0.0100 0.0101 0.0100 0.0106 0.0100 TSSSC 0.1550 9.9219 0.1608 9.9609 0.9367 1.6415 2.2238 9.9219 T1 0.5693 0.0283 0.8605 0.0322 0.9587 0.8400 0.2269 0.0244 T2 0.8660 0.5512 0.0248 0.9298 0.9237 0.4459 0.6562 0.9337 T3 0.3270 0.0166 0.2755 0.1571 0.0267 0.9961 0.0311 0.0166 T4 0.7244 0.9805 0.5929 0.9766 0.0529 0.6137 0.7908 0.9415 FOD 4.8 × 10−14 1.9× 10−13 3.9 × 10−15 1.6× 10−14 3.9 × 10−15 1.9× 10−13 4.5 × 10−14 1.8× 10−13 Fig. 6Open in figure viewerPowerPoint Comparative QOHS and BGA-based profiles of ΔFHDG(Hz), ΔFTH(Hz) and ΔPTIE(pu) with 1% SLD in area 2 fora 'Only model'b 'Model+SMES'c 'Model+SMES+SSSC' Fig. 7Open in figure viewerPowerPoint Comparative QOHS and BGA-based convergence profiles of FOD fora 'Only model'b 'Model+SMES'c 'Model+SMES+SSSC' 5.2 Performance evolution Transient performance evolution of 'only model', 'model+SMES' and 'model+SMES+SSSC' system configurations have been carried out to justify the compatibility of the system configurations under different input perturbation conditions in order to present the superiority of one model over the others. For these purposes, system configurations with different load perturbations have been tested. The three case studies considered here are: Case 1: increase of 10% SLD in area 2, Case 2: application of sinusoidal load change in area 2 and Case 3: simulation under tie-line outage. 5.2.1 Case 1: increase of 10% SLD in area 2 A 10% SLD in area 2 at t = 0 s is applied for this case. The comparative transient responses of 'only model', 'model+SMES' and 'model+SMES+SSSC' system configurations are shown in Fig. 8