A hybrid stochastic fractal search and pattern search technique based cascade PI-PD controller for automatic generation control of multi-source power systems in presence of plug in electric vehicles Academic research paper on "Electrical engineering, electronic engineering, information engineering"

CAAI Transactions on

Intelligence Technology

Accepted Manuscript

A hybrid stochastic fractal search and pattern search technique based cascade PI-PD controller for automatic generation control of multi-source power systems in presence of plug in electric vehicles

Sasmita Padhy, Sidhartha Panda

PII: S2468-2322(16)30077-4

DOI: 10.1016/j.trit.2017.01.002

Reference: TRIT 37

To appear in: CAAI Transactions on Intelligence Technology

Received Date: 4 November 2016 Revised Date: 11 January 2017 Accepted Date: 25 January 2017

Please cite this article as: S. Padhy, S. Panda, A hybrid stochastic fractal search and pattern search technique based cascade PI-PD controller for automatic generation control of multi-source power systems in presence of plug in electric vehicles, CAAI Transactions on Intelligence Technology (2017), doi: 10.1016/j.trit.2017.01.002.

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A hybrid stochastic fractal search and pattern search technique based cascade PI-PD controller for automatic generation control of multi-source power systems in presence of plug in electric vehicles

Sasmita Padhy and *Sidhartha Panda

Department of Electrical Engineering, VSSUT, Burla-768018, Odisha, India Corresponding author Phone no. : +91-9439702316, E-mail:panda_sidhartha@rediffmail.com

Abstract

A hybrid Stochastic Fractal Search plus Pattern Search (hSFS-PS) based cascade PI-PD controller is suggested in this paper for Automatic Generation Control (AGC) of thermal, hydro and gas power unit based power systems in presence of Plug in Electric Vehicles (PEV). Firstly, a single area multi-source power system consisting of thermal hydro and gas power plants is considered and parameters of Integral (I) controller is optimized by Stochastic Fractal Search (SFS) algorithm. The superiority of SFS algorithm over some recently proposed approaches such as optimal control, differential evolution and teaching learning based optimization techniques is demonstrated by comparing simulation results for the identical power system. To improve the system performance further, Pattern Search (PS) is subsequently employed. The study is further extended for different controllers like PI, PID, and cascaded PI-PD controller and the superiority of cascade PI-PD controller over conventional controllers is demonstrated. Then, cascade PI-PD controller parameters of AGC searched using the proposed hSFS-PS algorithm in presence of plug in electric vehicles. The study is also extended to an interconnected power system. It is seen from the comparative analysis that hSFS-PS tuned PI-PD controller in single and multi-area with multi sources improves the system frequency stability in complicated situations. Lastly, a three area interconnected system with PEVs with dissimilar cascade PI-PD controller in each area is considered and proposed hSFS-PS algorithm is used to tune the controller parameters in presence of nonlinearities like rate constraint of units, dead zone of governor and communication delay.

Keywords: Automatic Generation Control; cascade PI-PD controller; Stochastic Fractal Search; Pattern Search; Plug in Electric Vehicles.

1. Introduction

For stable and reliable operation of power systems, Automatic Generation Control (AGC) is necessary. AGC maintains balance between load and generation and hence minimizes frequency errors [1, 2]. In present day interconnected power system, the generation is usually made up of a combination of thermal units, hydro units as well as gas units. Gas bad units are suitable for supplying peak demands as they can be put into service quickly. When generation capacity is not sufficient to meet the increased load demand, other alternatives could be used to minimize the imbalance. Plugin Electric Vehicles (PEV) are projected to be used vigorously in the near future because of their low charging cost and less co2 emission level [3, 4]. PEVs offer an opportunity to use small distributed energy storage systems while they are plugged in [5, 6]. With large numbers of PEV and the communications and sensing associated with the power grid, they could offer ancillary services for the power grid. Frequency control is an ideal capability for PEV as the duration of energy supply is short and at the same time it is the highest priced ancillary service on the market which offers greater economic returns for vehicle owners [7-10]. Thus, PEVs have potential to contribute in the AGC to preserve the system frequency as per the load variations [11].

The conceptual frameworks for actively involving highly distributed loads in power system control actions has been presented in reference [12] where an overview of system control objectives, including economic dispatch, automatic generation control, and spinning reserve have been provided. Reviews of existing load control programs for the provision of power system services and challenges to achieve a load control scheme which balances devicelevel objectives with power system-level objectives have also been presented by the authors. Numerous control approaches have been proposed in literature for AGC of traditional interconnected systems. In this regard, Fuzzy Logic Controller (FLC) [13] and Adaptive Neuro Fuzzy Inference System (ANFIS) [14] based approaches have been proposed for AGC. However, these controllers require skilled operator for the design as well as application. Hence, these approaches are susceptible to the operator's understanding and skills. The classical Proportional Integral (PI) controller are still extensively used in industrial systems in spite of the substantial advances in recent years in modern control system as PI controllers provides satisfactory results for a variety of plants with varied

operating conditions. Besides, PI controllers can be realized and are well known to engineers. For improved system performance, a PD feedback loop can be added to a PI controller to modify the poles of the plants to required locations.

Many traditional approaches pertaining to the tuning of PID controllers and its variants are available in literature [15-19]. A modified PI-PD Smith predictor has been proposed in [20] for control of processes with large time constants or an integrator or unstable plant transfer functions plus long dead-time for reference inputs and disturbance rejections. However, these methods are time consuming and optimal parameters may not be obtained. Various intelligent technique based approaches have been recently proposed for controller design [21-23]. A Genetic Algorithm (GA) based fuzzy proportional-plus-integral-proportional-plus-derivative (PI/PD) controller has been proposed in [24] for an automotive active suspension system. In [25], the distribution of Spatio-temporal interest point is organized into a salient directed graph, reflecting the salient motions aiming at adding spatio-temporal discriminant to bag-of-visual words for real-time activity recognition. Frequency control in multi-source single and multi-area power systems by optimal controller [26], Differential Evolution (DE) [27] and Teaching Learning Based Optimization (TLBO) [28] have been reported in literature.

Stochastic Fractal Search (SFS) is a recently proposed metaheuristic algorithm motivated by the characteristics of growth using the concept of fractal [29]. SFS employs the diffusion feature that is commonly observed in random fractals, to explore the search space. The superiority of SFS over some well-known algorithms has been demonstrated in literature. However, SFS is a global optimizing technique which is intended to explore the search space. Hence, if only SFS is employed, an optimal/near-optimal solution may be obtained. Alternatively, local search techniques such as Pattern Search (PS) are intended to exploit a local area but not suitable for global optimization problems [30]. Because of their distinct strength and weakness, inspiration for the hybridization of SFS and PS arises. Therefore, a hybrid SFS and PS (hSFS-PS) based cascade PI-PD controller is suggested in this study for AGC of multi-source power systems in presence of PEVs. Initially, a single area thermal-hydro-gas units based power system is considered and SFS and hSFS-PS is used to tune the gains of conventional Integral (I) controller. The advantage of suggested hSFS-PS algorithm over SFS, DE and TLBO techniques is also established by comparative result analysis for the identical power system with identical controller. Then cascade PI-PD controller

is employed and the superiority of cascade PI-PD controller over, I, PI, PID controller is demonstrated. Then, PEVs are incorporated and the effect of PEVs in AGC is accessed. Finally, the study is extended to a three area interconnected non-linear power system with PEVs with dissimilar cascade PI-PD controller in each area. The main contributions of present work are:

• To apply a new hybrid optimization technique which takes the advantage of a recently proposed global SFS technique and local PS technique to tune the controller parameters for automatic generation control.

• To demonstrate the superiority of hybrid SFS-PS technique over similar recently proposed heuristic techniques such as DE and TLBO for the identical power system and controller.

• To verify the effectiveness of a cascade PI-PD controller compared to conventional PID controllers for AGC of power systems.

• To investigate the contribution of Plug in Electric Vehicles as an ancillary service for AGC of linear as well as nonlinear power systems.

2. System under study

At the first instance, a single area power system shown in Fig. 1 is considered. The system compromises of a hydro unit, a thermal and a gas unit. Initially integral controllers are considered for each unit. The individual generating units have their distinct regulation parameter and participation factor. According to these parameters the total load on the system is distributed among the units. The participation factors of all units should add up to unity. The details of each parameter can be found in reference [27, 28] and also provided in appendix A.

3. Modelling of plug in electric vehicle

Since a large number of PEVs are going to run on the road in near future, a lumped PEV model is considered in the present study. Each PEV is modeled as per its inverter capacity. The detail model of lumped PEV is provided in Fig. 2 [31] where AUE is the Load Frequency Control (LFC) signal given as an input to PEV and charging/discharging power of one PEV is the output. The capacity of battery is represented by ±BkW. The complex frequency is symbolized by s, the time constant of PEV is symbolized by T. The present energy of the battery is symbolized by E and controllable energy of battery is represented by limits iimax and Emm . The PEV energy remains within the

maximum and minimum limit of 90% and 80% of the controllable energy respectively. K1 and K 2 are calculated as K1 = E - Emax , K2 = E -Emin , as the energy differences. The PEV do not participate in AGC when the charge is above the maximum limit ( Emax ) of 90% and below the minimum limit ( Emin ) of 80%. The stored energy model in Fig. 2 computes the net energy stored in the batteries in one local control center. Local control center can act as a communicating link between power grid and the electric vehicles which control several EVs.

The stored energy model of one PEV is shown in Fig. 3. At any instant of time interval t, the number of controllable EVs NcontrollMe (t) which participate in AGC are calculated form information of the initial number of controllable

EVs at the beginning of the interval ( Ninitial (t) ), number of EVs moving from controllable state to driving state

during that time ( N plugout (t) )) and number of EVs moving from charging state to controllable state at that time

period ( Ncontrolin (t)) as given in Eq. (1). Hence, the number of controllable EVs ( Ncontrollable (t)) is varied as per the added number of the control in and plug out of the EVs.

N controllab le (t) = N initial (t) - N plugout (t) + N controlin (t) (1)

The energy expression is written as:

Econtrol (t) = Einitial (t) + Econtrolin (t) — Eplugout (t) — ELFC (t) (2)

Where, Einttial (t) is the initial energy, Econtrolin (t) is the increase in energy because of the EVs and Eplugout (t) is the

reduction in energy as a result of plug out. The increase in energy results in the change in the state of PEVs to controllable state from the charging state which is found by multiplying Ncontrolin (t) by the average charging energy

C*wh = 0.8 B*W ). The expression for Econtrolin (t)can be written as:

Econtrolin(t) = CkWh ' Ncontrolin (t) = °.8B*W ' Ncontrolin (t) [kWh] (3)

In Fig. 3, Elfc is the energy corresponding to the load frequency control signal and found by integrating local centre power ( PLFC ). ELFC can be expressed as:

Elfc (t) = J Plfc (t)dt (4)

4. Controller structure and objective function

4.1 Controller structure

In AGC, integral based controllers are generally used to minimize the Area Control Errors (ACE) which is a linear combination of frequency & tie-line power errors and bring them back to nominal values. However, the disadvantage of using only integral controller is that it might produce a closed loop system with significantly slower response times. Proportional Integral (PI) improves the system dynamic response and also offers the additional advantages like simple design, small cost, and their usefulness when designed for systems which are linear and stable process. At the same time, conventional PI controllers are generally not efficient when the higher order nonlinear unstable systems are involved.

Cascade control is one of the approaches which can be used to improve the performance of the system. As the number of tuning nubs is more in a cascade controller than a non-cascade controller, improved system performance may be obtained. Approaches for tuning of PID controller depending on process models and cascade PI-PD controller for control systems have been proposed in literature [32-34]. Because of its improved system performance, a cascade PI-PD controller shown in Fig. 4 is chosen in the present study for AGC. The control input signals are the respective ACEs and controller output are the reference power settings of individual generating units.

4.2 Objective function

For controller design using optimization techniques, the objective function is generally specified depending on some performance criteria such as Integral of Time multiplied Absolute Error (ITAE), Integral of Squared Error (ISE), Integral of Time multiplied Squared Error (ITSE) and Integral of Absolute Error (IAE). Detailed expression of various objective functions, their comparison on the system performance are available in literature [21-23, 27, 28]. It has also been shown in several studies that ITAE objective function provides better system performance

compared to other integral based alternatives [35. 36]. Hence ITAE is chosen in the present paper as objective function which is expressed as:

J = ITAE = || AF|.t.dt (5)

where, AF is deviation in frequency and tsim is simulation time.

5. Optimization technique

5.1 Stochastic fractal search

Stochastic Fractal Search (SFS) is a recently proposed optimization algorithm motivated by the process of growth using the concept of fractal. SFS employs the diffusion characteristic that is commonly observed in fractals, to explore the search space. Stochastic rules like Gaussian walks are used to change the iteration process to generate random fractals. Given an initial particle positioned at the beginning, new particles are then created arbitrarily in random manner around that point. Diffusion process enhances the ability of algorithm to find the global minima, as well as avoids to be struck in local minima. In the next update process, the positions of points are updated in the group depending on the other points position in the group. In this process, few best particles from the diffusing process are taken, and the remaining particles are rejected. Besides well-organized examination of the search space, the algorithm uses Gaussian random approaches to update thus introducing diversification properties in SFS algorithm.

The Stochastic Fractal Search algorithm can be explained with subsequent steps [29]:

A. Initialization: Each position of particles (point) is arbitrarily initialized depending on the problem constrains by specifying lower and upper bounds as:

P = LB + rand (UB - LB ) (6)

Where the P is the vector of points, UB and LB are the upper and lower bound vectors, rand creates evenly distributed number in the range [0, 1]. The fitness function of each particle is evaluated to find the Best Point (BP) among all particles.

B. Diffusion Process: Gaussian walk is employed to generate new points in the diffusion stage. The sequence of Gaussian Random Walks (GRW) used in diffusion stage are given by:

GRW1 = Gaussian (|BP|, SD) + {rand x BP - rand1 x P) (7)

GR W2 = Gaussian (| P |, SD) (8)

Where Pt is the i-th point, rand and rand1 are the random numbers as defined above, SD is the standard

deviation which is calculated as:

log(g)

X (P - BP)

Where g is the generation number. C. Updating Process: Every particle is ranked based on their fitness values and each particle i is given a probability value expressed as: rank ( Pi )

Where Ppi is the assigned probability of particle Pi, rank ( Pi) is the rank of Pi and N is the number particles. The j-th component of Pi is updated if Pai <rand, otherwise it remains same. The modified

position of Pi, Pi is calculated as:

Pi = Px (j) - rand [Py (j) - Pi (j)] Where Px and Py are arbitrary chosen points in the group.

All the points obtained from the first statistical procedure are ranked again and a probability value is assigned as before. The current position is modified to Pt if the condition Pai <rand is satisfied for a new point Pt , otherwise it remains same. The points are calculated:

P' = p.- rand[Px - BP] if rand £ 0.5

Pi = P. - rand [Px - Py] if rand g > 0.5

Where Px and Py are random chosen points found from the initial procedure, and randg are random numbers created by the Gaussian approach. The point Pi replaces p , if the fitness value of Pi is better than P ' .

5.2 Pattern search technique

Pattern search algorithm is an effective but simple technique applicable to the complex problems which cannot be solved by conventional optimization techniques. It has a flexible operator to fine tune the local explore capability. The PS technique involves a series of polls xk, k e N . A trial steps s'k with i = 1, 2,.. .p are added to the polls xk to get trial points xk = x k + s k at each poll. At these trial points the objective function value is calculated through a sequence of exploratory steps and compared with its previous value j(x ). The trial step s* corresponding to least value of J(xk + s'k) - J(xk) < 0 is then chosen to generate the subsequent point xk+1 = xk + s* . The trial steps s'k are created by a parameter A k e R+ known as step length parameter. The Ak value is modified in subsequent polls as per xk+1 value. The improvement of Ak , help the algorithm to converge. The detail of PS algorithm has been explained in [30]. 6. Results

6.1 Single area power system

Firstly, a single area power system with integral controllers illustrated in Fig. 1 is considered. The integral controller is initially chosen for better illustration of advantage of proposed optimization technique over some of the recently proposed technique such as Optimal controller [26] DE [27] and TLBO [28]. It is worthwhile to mention that for a fair comparison of optimization techniques, identical system and controller should be used. The integral gains are tuned using ITAE objective function by applying a 1% step load perturbation (SLP) employing SFS algorithm. The ranges of the gains are chosen as (2, -2). For the execution of SFS technique a series of runs were performed to properly choose the algorithm parameters. The following algorithm parameters are used: number of start points (initial populations) = 20, the maximum generations = 20, maximum diffusion =1. As suggested in literature, 25 independent algorithms are executed and the best values obtained in 25 runs are selected

as the integral gains. In the next step, PS is applied to fine tune controller parameter. The final controller parameters found by SFS algorithm are used in PS algorithm as starting points. The PS is implemented with following parameters: mesh size = 1, mesh expansion factor = 2, mesh contraction factor = 0.5, maximum number of objective function evaluations = 50, maximum generations = 10. The flow chart of the hSFS-PS algorithm is shown in Fig. 5. The final solutions for single area power system with integral controller as well as their performance are shown in Table 1 for SFS and hSFS-PS algorithm. For comparison, the corresponding values with TLBO [28], DE [27] and optimal control [26] for the identical system and controller are also given in Table 1. It is obvious from Table 1 that SFS outperforms TLBO [28], DE [27] and optimal control [26] approaches as less ITAE value is found by SFS algorithm (ITAE=45.21 x 10-2) compared to TLBO (ITAE=51.35 x 10-2), DE (ITAE=51.65 x 10-2) and optimal control (ITAE=99.34 x 10-2). The ITAE value is further reduced to 45.02 x 10-2 by hSFS-PS algorithm. Consequently, minimum settling time in frequency deviation (5% band) is attained with hSFS-PS compared to other approaches. It is also evident from Table 1 that less IAE, ITSE and ISE values are acquired with proposed hSFS-PS technique compared to other techniques. To further improve the system performance PI, PID and cascade PI-PD controllers are assumed and the parameters are tuned by hSFS-PS algorithm. The results are gathered in Table 2 from which is evident that less ITAE value is got by hSFS-PS optimized cascade PI-PD controller (ITAE=3.66 x 10-2) compared to PID (ITAE=4.45 x 10-2) and PI (ITAE=6.07 x 10-2) controllers. In the next step cascade PI-PD controllers are tuned by proposed hSFS-PS algorithm in presence of PEVs. The optimized parameters are given in Table 2 from which it is evident that ITAE value is decreased to 1.93 x 10-2 by the dynamic support of PEVs during the disturbance.

To examine the time-domain performance, a Step Load Perturbation (SLP) of 1 % is considered and system frequency response with proposed hSFS-PS optimized cascade PI-PD controller is provided in Fig. 6 from which it is clear that better system response is obtained with cascade PI-PD controller than conventional PI and PID controller. The system response is significantly improved with the inclusion of PEVs as evident from Fig. 6. 6.2 Extension to 2-area 6-units system

The study is also extended to a multi-area interconnected power system as shown in Fig. 7. The nominal system parameters are provided in appendix B.

The objective function is modified to include the tie-line power errors and expressed as:

J = ITAE = |(| AF1 | + | AF2 | + | APTle |). t.dt (14)

Where, AF1 and AF2 deviations in frequency of area 1 and area 2; APTie is the deviation in tie line power; t is the time at any instant and tsim is the simulation time.

Initially, both PID and cascade PI-PD controllers are assumed and the parameters are tuned employing hSFS-PS algorithm as explained earlier. Then PEVs are included in the system and the process is repeated. The optimized controller parameters are provided in Table 3. The various errors and settling times in frequency and tie-line power are also provided in Table 3. It is evident from Table 3 that less ITAE value is obtained with hSFS-PS optimized cascade PI-PD controller (ITAE=35.43 x10-2) compared to PID (ITAE=38.18 x10-2) and the ITAE value is further reduced to 19.63 x 10-2 when PEVs are included in the system model. It is also clear from Table 3 that minimum IAE, ITSE and ISE values as well as settling times are obtained with cascade PI-PD controller in presence of PEVs compared to individual PID controller and cascade PI-PD controller.

A 2% SLP in area 1 is applied at t = 0 sec and the results are shown in Figs. 8-10. It is clear from Figs. 8-10 that better system response is obtained with cascade PI-PD controller than conventional PID controller and the best system response is obtained with the inclusion of PEVs as shown in Figs. 8-10. The variation of powers of different units for the above SLP is illustrated in Fig. 11 from which it is evident that PEVs contribute in the LFC to maintain the system frequency as per the load variations.

To show the contributions made by PEVs, different step load disturbances are applied and power variation of PEVs are shown in Fig. 12. It is evident from Fig. 12 that as the size of load disturbance increases, PEVs contribute more during transient period to improve the system frequency response. 6.3 Extension to Three area system with nonlinearities

To prove the capability of the proposed approach to deal with interconnected power systems which have dissimilar controllers and nonlinearities a three area system [13, 35, 36] as shown in Fig. 13 is considered. The system comprises thermal and hydro units with PEVs and dissimilar controllers in each area. To get a precise understanding

of the AGC problem, it is essential to consider the vital physical constraints. The main physical constraints which have adverse impact on system performance are Generation Rate Constraint (GRC), Governor Dead Band (GDB) nonlinearity and time delay. Hence, the effect of GRC, GDB and time delay included in the system model. In a power system having thermal and hydro units, power generation can change only at a definite rate. Typical values of GRCs are: 3-10% p.u. MW/min for thermal [35], 270%/min for raising generation and 360%/min for lowering generation [36] for hydro. The speed governor dead band (GDB) effect rises the apparent steady-state speed regulation and makes the system oscillatory. In the present study, for thermal units a GRC of 3%/min is assumed. Along with these nonlinearities, a transport delay of 50 ms is introduced between the input and output of controllers in each area. The same procedure as presented earlier is followed to tune the controller parameters. The controller parameters found using hSFS-PS technique and are given in the Table 4.

A 1% step load disturbance is applied simultaneously in all the three areas at t=0 sec and the system responses are shown in Figs. 14-19. Critical analysis of the system dynamic responses clearly shows that performance of the system is significantly improved with proposed controller compared to conventional PID controller in presence of PEV.

7. Conclusion

Automatic Generation Control (AGC) of multi-unit systems with diverse power generation sources with plug in electric vehicles is addressed in this study. Firstly, a single area power system with thermal, hydro and gas units is considered and the superiority of SFS algorithm over some recently proposed approaches such as optimal control, DE and TLBO is demonstrated. The local Pattern search technique is then applied to improve the system performance further. Then PEVs are considered and a cascaded PI-PD controller is proposed. The controller parameters are tuned employing proposed hSFS-PS technique. It is demonstrated that best system performance is attained with cascade PI-PD controller in presence of PEVs. The approach is then applied in two area interconnected power system with PEVs in each area. It is found that better system response is obtained with hSFS-PS optimized cascade PI-PD controller in presence of PEVs than some recently proposed approaches like DE and TLBO. Lastly a three area nonlinear power system with PEVs dissimilar controllers is considered. It is seen that proposed hSFS-PS

optimized cascade PI-PD controller provides better system response compared to the conventional PID controllers in this case also. It is observed that, in all cases PEVs participate in the LFC to improve the system frequency response. Appendix A: Single area three unit system & Stored Energy model of One Local center

B= 0.4312 p.u. MW/Hz; Prl= 2000 MW; PL = 1840 MW; R1= R2 = R3 = 2.4 Hz/p.u.; TSG = 0.08 s; Tj= 0.3s; KR = 0.3 p.u.; TR= 10 s; KPS= 68.9566 Hz/p.u. MW; TPS = 11.49 s; T12 = 0.0433; a12= -1; TW = 1 s; TRS= 5 s; TRH= 28.75 s; TGH = 0.2 s; Xc= 0.6s; Yc = 1 s; cg = 1; bg= 0.05 s; TF = 0.23 s; TCR = 0.01s; TCD = 0.2 s; KT = 0. 543478 p.u.; KH = 0.326084 p.u.; KG = 0.130438 p.u.;

Ncontolin(t) = 12; Ninitial(t) = 90;NpiUgOMt(t) =20;Ncontrollable(t) = 82;

Appendix B: Two area six-unit system

B1= B2 = 0.4312 p.u. MW/Hz; Pr= 2000 MW; PL = 1840 MW; R1= R2 = R3 = 2.4 Hz/p.u.; TSG = 0.08 s; Tj= 0.3s; KR = 0.3 p.u.; TR= 10 s; KPS1= KPS2= 68.9566 Hz/p.u. MW; TPS1 = TPS2 = 11.49 s; T12 = 0.0433; a12= -1; TW = 1 s; TRS= 5 s; TRH= 28.75 s; TGH = 0.2 s; Xc= 0.6s; YC = 1 s; cg = 1; bg= 0.05 s; TF = 0.23 s; TCR = 0.01s; TCD = 0.2 s; KT = 0. 543478 p.u.; KH = 0.326084 p.u.; KG = 0.130438 p.u.; KDC= 1; TDC = 0.2 s.

Appendix C: Three-area hydro thermal power system with generation rate constraints dead band & transport delay [36]

Bj= B2= B3= 0.425 p.u. MW/Hz; Rj = R2 = R3 = 2.4 Hz/p.u. MW; TG1 = TG2=0.08 s; Tr1 = Tr2=10.0 s, Tt1 = Tt 2 = 0.3 s; Tw = 10 s; Tr = 5 s ; KpS1 = KpS 2 = KpS 3 = 120 Hz/p.u. MW; Tpg\ = TpS 2= TpS 3 =20 s; T12 = T23= T3!= °.°86 p.u.; a12= a23= a3i= -1. References

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Figures

1 1 1

R3 R2 R1

controller1

Thermal power plant withreheatturbine

1 + sTSG

1 + s KrTr

1 + sTr

1 + sTt

Hydrol power plant with governor

+ STGH

1 + sTrs

1 + sTrh

1 - sTw

1 + 5sT w

controller 2

controller3

cg+sbg

1+sTCR

1 + sTF

Kps 1+sTp

Gas turbine power plant

Fig. 1. Transfer function model of multi-source single area system with integral controller

LFC signal

~ Bkiv

1 + sT

A2 > 0

k2 < 0

Energy of one EV

Total Energy Model

Fig. 2 Model of Lumped Plug in Electric Vehicle [31]

Plfc (t )

Elfc (t )

N , (t )

-L * control in x 7

Econtrolin (t)

^^ •«,,,lllliii>^ controlm\ J

—► -►

NNinitial( )

^^ Einitial (t)

C^—► -*

Ckwh^ ^^

¿L.__I *

N Plug out( ) dX

Eplugout(t )

Econtrol(t)

Ncontrol( )

Input signal

Fig. 3. Stored energy model of one local control center

du + 4

Fig. 4. Structure of cascaded PI-PD controller

Fig. 5. Flowchart of hSFS-PS algorithm

Fig.6 Frequency deviation of single-area system for 1 % SLP with hSFS-PS optimized controllers

Fig. 7 Two area six unit interconnected power system with PEVs

Time (s)

Fig. 8 Frequency deviation of area 1for Two-area system with 2 % SLP with hSFS-PS optimized controllers

Time(s)

Fig. 9 Frequency deviation of area 2 for Two-area system with 2 % SLP with hSFS-PS optimized controllers

x 10-3

Fig. 10 Tie line power deviation of area 2 for Two-area system with 2 % SLP with hSFS-PS optimized controllers

Fig. 11 Variation of power in different units &PEV in 2area-6unit system with 2% step load perturbation

x 10-3

PEV with 2% disturbance PEV with 5% disturbance ■PEV with 10% disturbance

0 2 4 6 8 10 12 14 16 18 20

Time(s)

Fig. 12 Power variation of PEV at different disturbances in 2area-6unit system

Tg1.s+1 | | Tr1.s+1

Dead Zone Governor Steam Turbine (reheat)

, HtMÏKlH

Kp1 Tp1.s+1

Generation Rate Constraint

A Out1 In1 r SLP 1

DEL F1 (s)

I DeadZone! Governor

Area 2

Tg2.s+1 I Tr2.s+1

Steam Turbine (reheat)

Generation Rate Constraint

Kp2 Tp2.s+1

Tg3.s+1 | | Tr3.s+1 | | Tt3.s+1

Steam Turbine (reheat)

Generation Rate Constraint ---1 PEV3

Area 3

Fig. 13 Three area system with PEV considering GRC, dead band and transport delay

0.01 0 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06

20 25 Time(s)

Fig. 14 Frequency change of area 1 with 1 % SLP in all areas with hSFS-PS optimized controllers

< -0.02

0 5 10 15 20 25 30 35 40 45

Time(s)

Fig. 15 Frequency change of area 2 with 1 % SLP in all areas with hSFS-PS optimized controllers

Time(s)

Fig. 16 Frequency change of area 3 with 1 % SLP in all areas with hSFS-PS optimized controllers

x 10-3

Fig. 17 Tie line power change of Area 1 with 1 % SLP in all areas with hSFS-PS optimized controllers

Fig. 18 Tie line power deviation of Area 2 with 1 % SLP in all areas with hSFS-PS optimized controllers

x 10-3

Fig. 19 Tie line power deviation of Area 3 with 1 % SLP in all areas with hSFS-PS optimized controllers

Tables

Table 1: Integral controller parameters and performance of single area system with various optimization techniques

Controller parameters/ hSFS-PS SFS TLBO DE Optimal

performance/ technique [28] [27] Controller [26]

Parameter value Kii 0.0418 0.0417 0.0511 0.0516 0.1514

Ki2 0.0144 0.0143 0.0041 0.0071 0.0131

Ki3 0.2146 0.2129 0.1847 0.1701 0.0708

ITAE x 10-2 45.02 45.21 51.35 51.65 99.34

IAE x 10-2 18.96 18.98 19.24 19.54 23.01

ITSE x 10-3 17.32 17.28 17.72 18.2 17.84

ISE x 10-3 8.723 8.742 8.844 8.994 8.3

Settling time (sec) 4.74 4.75 4.89 5.01 8.84

Table 2: Controller parameters and performance of single area system with different controllers

Controllers parameters/ ITAE With PI Controller With PID controller With PIPD controller With EV & PIPD controller

Parameter Unit 1: Thermal Unit 1: Thermal Unit 1: Thermal Unit 1: Thermal

values KP1=1.8283 KP1=1.9663 KP1T=1.7376 KP1T=2.2950

K„=0.2290 KI1=0.2206 KIT=1.4439 KIT=2.3992

Unit 2: Hydro KD1=0.9861 KDT=0.8424 KDT=1.2592

KP2=0.0221 Unit 2: Hydro Kp2T=1 .7822 KP2T=1.9939

KI2=0.0120 KP2=1.5564 Unit 2: Hydro Unit 2: Hydro

Unit 3:Gas KI2=0.0672 KP1H=1.5093 KP1H=0.5906

KP3=0.4700 KD2=0.8125 KIH=0.3950 KIH=0.0405

KI3 =1.0746 Unit 2: Hydro KDH=0.0919 KDH=1.7872

KP3=0.5762 Kp2H=1.7822 KP2H=1.9939

KI3=1.6836 Unit 3:Gas Unit 3:Gas

KD3 =1.1549 KP1G=1.0574 KP1G=0.1177

KIG=1.6114 KIG=2.3650

Kdg=1.0018 KDG=0.7949

KP2G=1.7822 KP2G =1.9939

ITAE x 10-2 6.07 2.71 2.58 2.24

Table 3: Various controller parameters and performance of two area system with hSFS-PS optimization technique

Controller parameters/ PID Controller PID Controller PIPD Controller

performance/ technique without EV with EV with EV

Parameter values Unit 1: Thermal Unit 1: Thermal Unit 1: Thermal

KP1=-1.7074 KP1 = -1.6062 KP1T=1.2045

KI1=-1.9589 K„= -1.9258 KIT=1.435

KD1=-1.3934 KD1 = -1.9281 KDT=-1.9874

Unit 2: Hydro Unit 2: Hydro KP2T=-1.8746

KP2=-0.7453 KP2 = -1.6995 Unit 2: Hydro

KI2=0.1375 KI2 = -0.0148 KP1H=-1 4991

KD2=-0.9896 KD2 =1.0022 KIH= -1.0789

Unit 3: Gas Unit 3: Gas KDH=-1.1574

KP3=-1.8253 KP3 =-0.3612 KP2H=-0.4478

KI3=-1.6813 KI3 = -1.7917 Unit 3: Gas

KD3=-0.1628 KD3 =-1.6031 KP1G= 0.331 KIG= -1.9004 KDG=0.3906 Kp2G=1.917

ITAE x10-2 38.18 35.43 19.63

IAE x10 -2 14.71 8.855 6.123

ITSE x10-4 22.13 8.99 4.847

ISE x10 -4 20.48 9.362 5.415

Settling time A/1 0.49 0.2 0.18

in secs A/2 0.25 0.29 0.27

DPfie 0.4 0.2800 0.25

Table 4: Various controller parameters and performance of three area system with hSFS-PS optimization technique

Controller parameters/ PID Controller PIPD Controller

performance/ technique with EV with EV

Parameter values AREA 1: Thermal AREA 1: Thermal

KP1 = -1.6756 KP1 = -0.0568

KI1 = 0.1442 KI1 = 0.4784

KD1 =- 0.062 KD1 = -1.9918

AREA 2: Thermal KP11= 1.4542

KP2 =-0.3734 AREA 2: Thermal

KI2 = 0.4908 KP2 =0.7839

KD2 = 0.4878 KI2 = -1.1108

AREA 3: Hydro KD2 = 0.7807

KP3 =-0.461 KP22 =-0.5666

KI3 = 0.1867 AREA 3: Hydro

KD3 =0.011 KP3 =-0.0274

KI3 = -0.3259

KD3 =0.7304

KP33=-1.3726

ITAE 7.567 1.3524

• Hybrid SFS-PS based cascade PI-PD controller is proposed for AGC of power systems with PEV.

• The superiority of SFS algorithm over DE and TLBO is demonstrated for the same power system.

• The approach is applied to single area, two area and three area multisource power systems with PEV.

• Nonlinearities such as generation rate constraint, dead band and time delay are considered.

Sasmita Padhy was born on 29th June 1980 at Ganjam Odisha, India. She obtained her B.Engg (Electrical & Electronics) from National Institute of Science and Technology (NIST) Berhampur Odisha in 2003 and M.Tech (Power System) from BPUT in 2011. Currently She is pursuing Ph.D in VSSUT, Burla and her research interest lies in Power system stability, control and computational intelligence.

Sidhartha Panda is working as a Professor in the Department of Electrical Engineering, Veer Surendrai Sai University of Technology (VSSUT), Burla, Sambalpur, Odisha, India. He received Ph.D. degree from Indian Institute of Technology (IIT), Roorkee, India, M.E. degree from Veer Surendrai Sai University of Technology (VSSUT). His areas of research include Flexible AC Transmission Systems (FACTS), Power System Stability, Soft computing, Model Order Reduction, Distributed Generation and Wind Energy. Dr. Panda is a Fellow of Institution of Engineers (India).