Nonlinear Controller Design for Vehicle-to-Grid (V2G) Systems to Enhance Power Quality and Power System Stability

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1 Nonlinear Controller Design or Vehicle-to-Grid (V2G) Systems to Enhance Power Quality and Power System Stability Author Mahmud, M., Hossain, Jahangir, Pota, H., Roy, N. Published 214 Conerence Title Proceedings o the 19th World Congress The International Federation o Automatic Control DOI Copyright Statement 214 IFAC-PapersOnine. The attached ile is reproduced here in accordance with the copyright policy o the publisher. Please reer to the conerence's website or access to the deinitive, published version. Downloaded rom ink to published version Griith Research Online

2 Proceedings o the 19th World Congress The International Federation o Automatic Control Nonlinear Controller Design or Vehicle-to-Grid (V2G) Systems to Enhance Power Quality and Power System Stability M. A. Mahmud M. J. Hossain H. R. Pota N. K. Roy Faculty o Engineering & Industrial Sciences, Swinburne University o Technology, Hawthorn, VIC 3122, Australia ( mmahmud@swin.edu.au). Griith School o Engineering, Griith University, Gold Coast Campus, Gold Coast, QD 4222, Australia ( j.hossain@griith.edu.au). School o Engineering and Inormation Technology (SEIT), The University o New South Wales, Canberra, ACT 26, Australia ( h.pota@ada.edu.au). School o Engineering, Deakin University, Waurn Ponds, VIC 322, Australia ( naruttam.roy@deakin.edu.au). Abstract: A nonlinear controller design technique, or the enhancement o power quality and power system stability in a vehicle-to-grid (V2G) system, is proposed in this paper. The dynamical model o a V2G system is irst developed and then the controller is designed based on the partial eedback linearization o the developed model. The control scheme is developed in such a way that converters in V2G systems are capable o injecting both active and reactive power into the grid. The implementation o the proposed controller requires the stabilization o internal dynamics o V2G systems as it transorms the system into a partly linear and an autonomous system with internal dynamics. The stability o internal dynamics o V2G systems is also discussed in this paper. Finally, the perormance o the proposed control scheme is evaluated on a simple test system in terms o power quality and system stability enhancement. From the simulation result it is ound that the designed nonlinear controller provides excellence perormance in improving power quality and stability o whole system. Keywords: Power quality, power system stability, vehicle-to-grid (V2G) systems, partial eedback linearization, internal dynamics. 1. INTRODUCTION Plug-in hybrid electric vehicles (PHEVs), which can be recharged rom and discharged to the power grid by plugging into electrical outlets, are becoming increasingly popular in order to address energy and environmental issues as these vehicles reduce carbon emissions and provide ancillary services to the power grid. PHEVs can either be used as loads in charging phase o batteries rom the grid or as generators in discharging phase when they are not in use or driving which is also known as vehicle-togrid (V2G) operation. These eatures o PHEVs pose several opportunities and challenges in energy management strategies o modern power systems (Galus et al., 21). The integration o huge number o PHEVs into the grid as loads might cause several problems such as transormer or line overloading and voltage stability(papadopoulos et al., 212; Hilshey et al., 213). By considering these problems, several investigations have been perormed in (Das et al., 213; Yang et al., 213) so that PHEVs could be advantageous or power system operations. For example, eective charging and discharging schedules o PHEVs could support the integration o renewable energy sources by storing energy during the o-peak and deliver it back to the grid during the peak. Numerous research activities have been perormed eective charging and discharging schemesandsomemost recentcouldbe ound in (He et al., 213; Gunter et al., 213). In a V2G system, batteries o PHEVs act as distributed energy resources by locally meeting the demand during peak hours and thus, a V2G system reduces the stress on overloaded distribution systems. The amount o power delivered rom vehicles to the grid is estimated by the aggregator in which a communication link is used to communicate between vehicle owners and distribution network service providers (DNSPs) (Han et al., 21). A sudden discharge o batteries used in V2G systems may cause a voltage variation problem in distribution networks at which they are connected and this in turns causes voltage stability problems. Moreover, power electronic inverters are used as interacing units between the grid and batteries o PHEVs or which an eective switching scheme is essential to maintain the power quality and stability o whole system. Thereore, the design o a high perormance /214 IFAC 7659

3 controller is a prominent issue which has the capability to mitigate the voltage variation problem through reactive power management and enhances the power quality o distribution networks. Although a great deal o attention has been paid or the investigation o impacts o PHEVs on distribution networks and optimal scheduling o charging and discharging o PHEVs, a very little work has been done on the controller design or V2G operations o PHEVs. A uzzy-based requency controller is proposed in (Datta and Senjyu, 212) to alleviate requency luctuations and to reduce power luctuations in tie-lines with an application to V2G systems. The approach presented in (Datta and Senjyu, 212) provides satisactory results or controlling active power but the reactive power control is uncovered which is a key actor or maintaining voltage stability. The control o power low has been demonstrated using a uzzy logic controller in (Singhand et al., 212) or voltage compensations and peak shavings. However the main limitations o uzzy logic controllers are that a uzzy system cannot ully capture the dynamical model o V2G systems and require more ine tuning and simulation beore making it operational (Khayyam et al., 212). Thereore, it is essential to consider model-based control approach to enhance the power quality and stability o V2G systems. The design o linear and nonlinear controllers based on the detailed mathematical model o V2G systems could be worthy in order to maintain the stable operation o such systems with high power quality. Feedback linearization method is a widely used model-based nonlinear controller design technique which transorms a nonlinear system into a ully linear or a partly linear equivalent system by canceling the inherent nonlinearities within the system. inear control design techniques can be employed to design a suitable controller or the linearized system (Isidori, 2nd Edition, 1989; Slotine and i, 1991). When eedback linearization transorms a nonlinear system into ully linear system, the approach is called exact eedback linearization and i the system is transormed into a partially linearized system, the approach is known as partial eedback linearization (Isidori, 2nd Edition, 1989). Since eedback linearization cancels nonlinearities by introducing nonlinear term in the control law, the eedback linearized system is independent o operating points. The eedback linearization technique allows eective switching schemes or the interacing inverters with distributed energy resources (Mahmud et al., 212b,c) The aim o this paper is to design a partial eedback linearizing controller or a V2G system and the control objectives are set as both active and reactive power. Since the partial eedback linearization is a model-based approach, a comprehensive mathematical model o V2G systems is ormulated in this paper. The applicability and implementability o the proposed control scheme is tested through the eedback linearizability and stability o internal dynamics o V2G systems. The superiority o the proposed control scheme is investigated through simulation results under dierent operating scenarios and compared to that o a proportional-integral (PI) controller.. Em Im C1 R1 I 1 R 2 R I p(v p) Fig. 1. Equivalent circuit diagram o a battery Im Em I1 C1 R1 R Idc vdc _ Voltage Source Converter (VSC) Fig. 2. Schematic diagram o a V2G System R i I dc _ Grid Supply Point 2. MATHEMATICA MODEING OF V2G SYSTEM In this section, the mathematical model o a V2G system is developed. However beore designing the main V2G system, a battery model is briely reviewed as this is a major part o a V2G system. The most commonly used battery model is proposed in (Ceraolo, 2) and the electrical circuit model o this battery is shown in Fig.1. In the model as described in (Ceraolo, 2) and presented by Fig.1, the charge stored in the battery is the integral o only apart I m othe totalcurrent I dc enteringthe battery. The detailed o battery elements such as resistors (R, R 1, and R 2 ), capacitor (C 1 ), and internal voltage (E m ) can be seen in (Ceraolo, 2). Since parasitic reactions oten present in the battery, nonreversible parasitic branch models (with subscript p in Fig. 1) draw some current but does not participate in the main, reversible, reaction. It is noted that during discharge R 2 = and Ip = and when discharge behavior is to be simulated, the whole parasitic branch can be omitted (Ceraolo, 2). Thus, a V2G system with the revised battery model is shown in Fig. 2. From Fig. 2, it can be seen that in a V2G system I m = I dc. Now by applying Kirchho s current law (KC) at the node where the resistorr 1 and capacitorc 1 are connected in parallel, we can write dv C1 I dc = I 1 C 1 (1) dt wherev C1 is thevoltageacrossc 1 whichisalsothe voltage across R 1 and thus, V C1 = I 1 R 1. Using this relationship, equation (1) can be simpliied as di 1 dt = 1 τ 1 (I dc I 1 ) (2) where τ 1 = R 1 C 1. Now by applying Kirchho s voltage law (KV) at the output-side o the inverter, i.e., at the grid-side, we can write di dt = R m e (3) 766

4 where m represents the switching action o the converter which is a unction o modulation index and iring angle, R is the resistance o the connecting line, i is the output current o the inverter, is the combination o ilter and connecting line inductance. Equations (2) and (3) represent the time-variant model o a V2G system. But or the purpose oanalysisand control, it is essential to transorm the model into time-invariant system. To do this, the V2G system can be transormed into dq-rame which can be written as (Mahmud et al., 212a) with I 1 = 1 τ 1 (M d I d M q I q I 1 ) I d = R I d ωi q E d M d I q = ωi d R I q E q M q I dc = mi = M d I d M q I q where ω is the angular requency; M d and M q are the switching unctions in d and q rame respectively; I d and I q are the currents in d and q-rame respectively; and E d and E q are the grid voltages in d and q-rame respectively. In dq-rame, the active power (P) and reactive power (Q) delivered rom the vehicle into the grid can be written as (4) P = E q I q E d I d Q = E q I d E d I q (5) In dq rotating rame, it can be assumed that E d = (Kim, 26; Mahmud et al., 212c) and in this case, equation (5) can be simpliied as P = E q I q Q = E q I d (6) Equation (4) represents the completed dynamical model o a V2G system. The control objective is to design a nonlinear switching scheme or the V2G system as represented by equation (4) in order to deliver high quality active and reactive power into the grid. From equation (6), it can be seen that that quality o the active and reactive power depends on currents, I d and I q as there is nothing to do with the grid voltage components (E d & E q ) in dqrame. Thereore, the control objective can be achieved by regulating the currents, I d and I q which can be selected as output unctions o the V2G system. 3. FEEDBACK INEARIZATION AND FEEDBACK INEARIZABIITY OF V2G SYSTEM The mathematical model o a V2G system as represented by equation (4) can be written in the ollowing orm o a nonlinear multi-input multi-output (MIMO) system equation: where x = g(x) = I d τ1 ] 1 τ 1 I 1 I d, (x) = R I d ωi q E d, I q ωi d R I q Eq [ I1 I q τ 1, u = [ ] [ ] [ ] u1 Md Id =, and y = u 2 M q Iq Based on this nominal mathematical model, an overview o eedback linearizing controller design and eedback linearizability o V2G systems are discussed in the ollowing two subsections. 3.1 Overview o Feedback inearization The design o eedback linearizing controller depends on the eedback linearizability o the system and this eedback linearizability is deined by the relative degree o the system (Isidori, 2nd Edition, 1989). The relative degree o the system in turns depends on output unctions o the V2G system. The mathematical model o a V2G system as shown by equation (4) can be linearized using eedback linearization when some conditions as described latter are satisied. Consider the ollowing nonlinear coordinate transormation (z = φ(x)) or the aorementioned V2G system. [ ] T z = h 1 h 1 r1 1 h 1 h 2 h 2 r2 1 h 2 (8) where r 1 < n and r 2 < n are the relative degree corresponding to output unctions h 1 (x) and h 2 (x), respectively, h i (x) = hi x (x) is the ie derivative o h i (x), i = 1,2 along (x) (Isidori, 2nd Edition, 1989). The change o coordinate (8) transorms the nonlinear system (7) rom x to z coordinates provided that the ollowing conditions are satisied or: g k h i(x) = ; k < r i 1 g ri 1 h i (x) (9) N n = r i i=1 where g h i (x) is the ie derivative o h i (x) along g(x). The linearized system can be expressed as ollows: ż = Az Bv (1) where Ais the system matrix, B is the input matrix, and v is the new linear control input or the eedback linearized system. When (r 1 r 2 ) < n, only partial eedback linearization is possible, i.e., some states are transormed through nonlinear coordinate transormation and some are not. The new states o a partially eedback linearized system can be written as ẋ = (x)g 1 (x)u 1 g 2 (x)u 2 y 1 = h 1 (x) y 2 = h 2 (x) (7) z = φ(x) = [ z ẑ] T (11) where z represents the state vector obtained rom nonlinear coordinate transormation o order r 1 r 2 and ẑ the 7661

5 state vector o the nonlinear (remaining) part o order n (r 1 r 2 ). The dynamic o ẑ is called the internal dynamic o the system which needs to be stable in order to design and implement a partial eedback linearizing controller or the ollowing partially linearized system. z = à z Bṽ (12) where à is the system matrix, B is the input matrix, and ṽ is the new linear control input or the partially linearized system. The developed V2G system model could be exactly or partially linearized and the eedback linearizability o a V2G system is shown in the ollowing subsection. 3.2 Feedback inearizability o V2G Systems The eedback linearizability o the V2G system represented by equation (7) can be obtained by calculating the total relative degree (r) o the system. The relative degree corresponding to the irst output unction h 1 (x) = I d can be calculated as g 1 1 h 1 (x) = g h 1 (x) = (13) where r 1 = 1. Similarly, the relative degree corresponding to the other output unction h 2 (x) = I q can be calculated as ollows g 1 1 h 2 (x) = g h 2 (x) = (14) which indicates that r 2 = 1. Thereore, the total relative degree r = r 1 r 2 = 2 and this means that (r 1 r 2 ) < n as n = 3. From this, it can be said that the V2G system is partially linearized and partial eedback linearization approach needs to be used to design the controller or this system. The design o a partial eedback linearizing controller or V2G system is shown in the ollowing section. 4. PARTIA FEEDBACK INEARIZING CONTROER DESIGN FOR V2G SYSTEMS The essential steps to design the partial eedback linearizing controller or V2G systems can be discussed as ollows: Step 1: Nonlinear coordinate transormation and partial linearization o V2G systems A nonlinear coordinate transormation can be written as z= φ(x) (15) where φ is the unction o x. For a V2G system, we choose z 1 = R I d ωi q E d M d z 2 = ωi d R I q E q v (18) dc M q The above system can be written in the ollowing linearized orm: z 1 = ṽ 1 z 2 = ṽ 2 (19) where ṽ 1 and ṽ 2 are the linear control inputs which can be designed using any linear control technique and can be expressed as ṽ 1 = R I d ωi q E d M d ṽ 2 = ωi d R I q E q v (2) dc M q However beore designing and implementing controller through partial eedback linearization, it is essential to check the stability o internal dynamics o the V2G system which is discussed in the next step. Step 2: Stability o internal dynamics o V2G Systems In the previous step, the third-order V2G system is transormed into a second-order system representing the linear dynamics o the system. Desired perormance o the external dynamics can be obtained through design and implementation o a linear controller. However, to ensure stability, the control law needs to be chosen in such a way that lim h i(x) t which implies that the state o a linear system decays to zero as time approached to ininity, i.e., [ z 1 z 2 z r ] T ; t. For the V2G system considered in this work, this means that at steady-state z 1 = z 2 = (21) et the remaining nonlinear state be expressed by the ollowing nonlinear unction ẑ = ˆφ(x). To ensure stability, this needs to be selected in such a way that it must satisy the ollowing conditions (u et al., 21): and z 1 = φ 1 (x) = h 1 (x) = I q (16) g1ˆφ(x) = g2ˆφ(x) = (22) z 2 = φ 2 (x) = h 2 (x) = v (17) Using the above transormation, the partially linearized system can be obtained as ollows: z 1 = h 1(x) ẋ = h 1 (x) g1 h 1 (x)u 1 g2 h 1 (x)u 2 x z 2 = h 2(x) ẋ = h 2 (x) g1 h 2 (x)u 1 g2 h 2 (x)u 2 x For the V2G system, For the developed V2G system model, equation (22) will be satisied i we chose ˆφ(x) = ẑ = τ 1 I 1 1 Id 2 2v 1 Iq 2 (23) dc 2 Thus, the remaining dynamics o the V2G system can be expressed as ollows: ẑ = ˆφ(x) = τ1 1 I d 2 I q 3 (24) 7662

6 Since I d = h 1 = z 1 and I q = h 2 = z 2, equation (24) can be written as ẑ = ˆφ(x) = τ (25) z z Using equation (21), equation (25) can be simpliied as ˆz = I 1 (26) From equation (23), I 1 can be calculated as I 1 = 1 [ 1 Id 2 τ 1 2v 1 ] Iq 2 dc 2v ẑ (27) dc and replacing I d and I q with z 1 and z 2, respectively and using their values rom equation (21), equation (27) can be written as I 1 = 1 τ 1 ẑ (28) Thereore, substituting the value o I 1 rom equation (28) into equation (26), we obtain ẑ = 1 τ 1 ẑ (29) Equation (29) represents stable internal dynamics o the V2G system and thereore partial eedback linearizing controller can be designed or the V2G system. It is also clear that the proposed partial eedback linearizing scheme divides the dynamics o V2G systems into two parts: one is the external dynamics as described in the previous step, and the other is the internal dynamics which needs to be stable to design the controller. The derivation o the proposed control law is shown in the ollowing step. Step 3: Derivation o control law For the V2G system, the original control inputs in dqrame are M d and M q and the linear control inputs are ṽ 1 and ṽ 2. From equation (2), the original control laws M d and M q can be obtained as ollows M d = 1 [ṽ 1 RI d ωi q E d ] M q = 1 (3) [ṽ 2 ωi d RI q E q ] Equation (3) is the inal control law or the V2G system to deliver active and reactive power into the grid. At this point, the only issue to complete the controller design is to determine the linear control inputs, ṽ 1 and ṽ 2. In this paper, PI controllers are used and the structures o the two PI controllers are chosen as ollows t ṽ 1 = k 1p (I dre I d )k 1i (I dre I d )dt t ṽ 2 = k 2p (I qre I q )k 2i (I qre I q )dt (31) Thegainsneedtobeselectedinsuchawaythattheoutput ollows the reerence current to minimize the error. In this paper, the gains are set as ollows: and k 1p = 2I dre, k 1i = I 2 dre Grid Current (A) Time (s) Fig. 3. Grid current at unity power actor (Green line proposed controller and red line PI controller) k 2p = 2I qre, k 2i = I 2 qre The reerence values I dre and I qre can be calculated rom equation (6) as I qre = P re E q I dre = Q re E d The perormance o the designed controller is evaluated in the ollowing section. 5. CONTROER PERFORMANCE EVAUATION The perormance o the designed controller is evaluated on atestv2gsystemasshowninfig.2inwhichthevehicleis supplying a residential area, i.e., single-phase grid supply point. Since the main task o PHEVs are commutation, a minimum state o charge (SOC) needs to be maintained in order to deliver power into the grid. In this paper, the minimum SOC is considered as 3 per cent. The ollowing equation is used to calculate the total available energy o PHEVs during discharging (Singhand et al., 212) S discharging = P b N SOC min where S discharging is the total available energy or discharging to support the grid, P b is the kwh o batteries, N is the number o vehicles connected to the grid, and SOC min is the minimum SOC which is consideredas 3per cent. In this work, 15 PHEVs are connected to the grid and each o them with a battery rating o 4.4 kwh. Thereore the total available energy is 26.4 kwh. The other parameters o the battery and grid are provided in the Appendix A. The batteries o PHEVs are delivering power to the grid to supply a load o 5 KVA in a residential area and this inormation is provided by the aggregator. When the power actor o the load is considered as unity, no reactive power will be delivered into the grid as the grid voltage and current will be in phase with each other. In this case, 5 kw power will be delivered into the grid and the corresponding current into the grid will be A which is shown in Fig. 3. The output current o the inverter does not contain any harmonic with the designed controller as this is a pure sinusoidal signal which is shown bythe greenline in Fig. 3.But aconventionalproportional integral (PI) controller which is designed or the unity 7663

7 Grid Current (A) Time (s) Fig. 4. Grid current at.8 power actor (Green line proposed controller and red line PI controller) power actor operation o the V2G system, contains some harmonics (red line in Fig. 3). Now i the V2G system needs to operate at a power actor other than unity, the grid voltage and current will not be in phase. In this case, some reactive power will be delivered into the grid. I the power actor is considered as.8, the active power which needs to be delivered into the grid will be 4 kw and that o reactive power will be 3 kvar. In this case, the designed controller acts in a similar way as considered to the previous case (green line in Fig. 4). But the response o the conventional PI controller will be slower (red line in Fig. 4) as the reerence active and reactive power have been changed. 6. CONCUSIONS A new dynamical model o a V2G system has been developed and a partial eedback linearizing controller has been designed or improving the power quality and stability. The justiication, o using the proposed control approach, has also been provided or through the eedback linearizability o the developed V2G system model along with the inclusion o the stability o internal dynamics. Simulation results clearly indicate that the proposed approach improves the power quality signiicantly as compared to the conventional PI controller and enhance the stability o V2G systems as it is independent o operating conditions. The proposed controller acts aster than a PI controller during the changes in operating conditions which saves a huge amount o power. Future works will consider the design and implementation o such controller or a largescale operation. REFERENCES Ceraolo, M. (2). New dynamical models o lead-acid batteries. IEEE Trans. on Power Systems, 15(4), Das, R., Thirugnanam, K., Kumar, P., avudiya, R., and Singh, M. (213). Mathematical modeling or economic evaluation o electric vehicle to smart grid interaction. IEEE Trans. on Smart Grid, In Press, 1 1. Datta, M. and Senjyu, T. (212). Fuzzy control o distributed pv inverters/energy storage systems/electric vehicles or requency regulation in a large power system. IEEE Trans. on Smart Grid, 4(1), Galus, M.D., Zima, M., and Andersson, G. (21). On integration o plug-in hybrid electric vehicles into existing power system structures. Energy Policy, 38(11), Gunter, S.J., Aridi, K.K., and Perreault, D.J. (213). Optimal design o grid-connected PEV charging systems with integrated distributed resources. IEEE Trans. on Smart Grid, 4(2), Han, S., Han, S., and Sezaki, K. (21). Development o an optimal vehicle-to-grid aggregator or requency regulation. IEEE Trans. on Smart Grid, 1(1), He, Y., Venkatesh, B., and Guan,. (213). Optimal scheduling or charging and discharging o electric vehicles. IEEE Trans. on Smart Grid, 3(3), Hilshey, A.D., Hines, P.D.H., Rezaei, P., and Dowds, J.R. (213). Estimating the impact o electric vehicle smart charging on distribution transormer aging. IEEE Trans. on Smart Grid, 4(2), Isidori, A. (2nd Edition, 1989). Nonlinear Control Systems. Springer-Verlag, Berlin. Khayyam, H., Ranjbarzadeh, H., and Marano, V. (212). Intelligent control o vehicle to grid power. Journal o Power Sources, 21, 1 9. Kim, I.(26). Sliding mode controller or the single-phase grid-connected photovoltaic system. Applied Energy, 83(1), u,q.,sun,y.,andmei,s.(21). Nonlinear Control Systems and Power System Dynamics. Kluwer Academic Publishers, Boston. Mahmud, M.A., Hossain, M., and Pota, H.R. (212a). Nonlinear controller design or single-phase gridconnected photovoltaic systems using partial eedback linearization. In Australasian Control Conerence (AUCC), Sydney, Australia. Mahmud, M.A., Pota, H.R., and Hossain, M. (212b). Dynamic stability o three-phase grid-connected photovoltaic system using zero dynamic design approach. IEEE Journal o Photovoltaics, 2(4), Mahmud, M.A., Pota, H.R., and Hossain, M. (212c). Nonlinear DSTATCOM controller design or distribution network with distributed generation to enhance voltage stability. International Journal o Electrical Power and Energy Systems, 53, Papadopoulos, P., Skarvelis-Kazakos, S., Grau, I., Cipcigan,.M., and Jenkins, N. (212). Electric vehicles impact on British distribution networks. IET Electrical Systems in Transportation, 2(3), Singhand, M., Kumar, P., and Kar, I. (212). Implementation o vehicle to grid inrastructure using uzzy logic controller. IEEE Trans. on Smart Grid, 3(1), Slotine, J.J.E. and i, W. (1991). Applied Nonlinear Control. Prentice-Hall, New Jersey. Yang, H., Chung, C.Y., and Zhao, J. (213). Application o plug-in electric vehicles to requency regulation based on distributed signal acquisition via limited communication. IEEE Trans. on Power Systems, 28(2), Appendix A. SYSTEM PARAMETERS Battery Parameters: R 1 =.4 mω, τ 1 =72 s, R =2 mω Grid Parameters: Grid voltage (rms)=22 V, Frequency=5 Hz, R=.1 Ω, =1 mh 7664