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Nonlinear Controller Design for Vehicle-to-Grid Systems with Output LCL Filters
9th 9th IFAC IFAC symposium symposium on on Control Control of of Power Power and and Energy Energy Systems Systems 9th IFAC symposium on Control of Power and Energy Systems Indian Institute of Technology Indian Institute of Technology 9th IFAC symposium on Control of Power and Energy Systems Indian Institute of Technology December 9-11, 2015. 2015. Delhi, India India Available online at www.sciencedirect.com December 9-11, Delhi, Indian Institute of Technology December 9-11, 2015. Delhi, India December 9-11, 2015. Delhi, India
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IFAC-PapersOnLine 48-30 (2015) 529–534
Nonlinear Nonlinear Nonlinear Vehicle-to-Grid Vehicle-to-Grid Vehicle-to-Grid
Controller Design for Controller Design for Controller Design for LCL Systems with Output Systems with Output LCL Systems Filters with Output LCL Filters Filters ∗∗ ∗ ∗∗∗
∗ M. M. A. A. Mahmud Mahmud ∗ H. H. R. R. Pota Pota ∗∗ A. A. M. M. T. T. Oo Oo ∗∗ R. R. C. C. Bansal Bansal ∗∗∗ ∗∗∗ M. A. Mahmud ∗∗ H. R. Pota ∗∗ ∗∗ A. M. T. Oo ∗ R. C. Bansal ∗∗∗ M. A. Mahmud H. R. Pota A. M. T. Oo R. C. Bansal ∗ ∗ School of Engineering, Deakin University, Waurn Ponds, VIC 3220, ∗ School of Engineering, Deakin University, Waurn Ponds, VIC 3220, of Engineering, Deakin University, Waurn Ponds, VIC 3220, Australia (e-mail: {apel.mahmud {apel.mahmud and aman.m}@deakin.edu.au). aman.m}@deakin.edu.au). ∗ School Australia (e-mail: and School of Engineering, Deakin University, Waurn Ponds, VIC 3220, ∗∗ Australia (e-mail: {apel.mahmud and aman.m}@deakin.edu.au). ∗∗ School of Engineering and Information Technology School of(e-mail: Engineering and Information Technology (SEIT), (SEIT), The The Australia {apel.mahmud and aman.m}@deakin.edu.au). ∗∗ School of Engineering and Information Technology (SEIT), The University of New South Wales, Canberra, ACT 2600, Australia ∗∗ University New Southand Wales, Canberra, ACT 2600, Australia School of of Engineering Information Technology (SEIT), The University of New(e-mail: South Wales, Canberra, ACT 2600, Australia [email protected]). (e-mail: [email protected]). University of New South Wales, Canberra, ACT 2600, Australia ∗∗∗ (e-mail: [email protected]). ∗∗∗ Department of Electrical, Electronic and and Computer Computer Engineering, Engineering, Electronic (e-mail: [email protected]). ∗∗∗ Department of Electrical, of Electrical, and Computer Engineering, University of Pretoria, Pretoria, Africa ∗∗∗ Department UniversityofofElectrical, Pretoria,Electronic Pretoria, South South Africa (e-mail: (e-mail: Department Electronic and Computer Engineering, University of Pretoria, Pretoria, South Africa (e-mail: [email protected]). [email protected]). University of Pretoria, Pretoria, South Africa (e-mail: [email protected]). [email protected]). Abstract: This paper presents a nonlinear Abstract: This paper presents a nonlinear controller controller design design for for vehicle-to-grid vehicle-to-grid (V2G) (V2G) systems systems Abstract: This paper presents a nonlinear controller design for vehicle-to-grid (V2G) systems with LCL output filters. The V2G systems are modeled with LCL output filters in to with LCL output filters. The V2G systemscontroller are modeled with output filters in order order to Abstract: This paper presents a nonlinear design forLCL vehicle-to-grid (V2G) systems with LCLharmonics output filters. The V2Gpower systems are modeled with LCLcontroller output filters in order to eliminate harmonics for improving power qualities and the nonlinear controller is designed based eliminate for improving qualities and the nonlinear is designed based with LCL output filters. The V2G systems are modeled with LCL output filters in order to eliminate harmonics for improving qualities and the nonlinear controller is designed based on linearization. The feasibility of the appropriate feedback linearization on the the feedback feedback linearization. Thepower feasibility of using using the appropriate feedback linearization eliminate harmonics for improving power qualities and the nonlinear controller is designed based on the feedback linearization. The feasibility of using the appropriate feedback linearization approaches, either partial or exact, is also investigated through the feedback linearizability of approaches, eitherlinearization. partial or exact, is also investigated through the feedback linearizability of on the feedback The feasibility of using the appropriate feedback linearization approaches, either partial or exact, is also investigated through the feedback linearizability of V2G systems. In this paper, partial feedback linearization is used to design the controller with V2G systems. In this paper, feedback linearization is usedthe to feedback design thelinearizability controller with approaches, either partial or partial exact, is also investigated through of V2G systems. this paper, partialand feedback linearization is used to design the controllerof with a capability capability of In sharing both active active reactive power in in V2G V2G systems. The performance performance the a of sharing both reactive power systems. The the V2G systems. In this paper, partialand feedback linearization is used to design the controllerofwith aproposed capability of sharing both active and reactive power in V2G systems. The performance of the controller controller is evaluated on a single-phase full-bridge converter-based V2G controller controller is evaluated on apower single-phase full-bridge converter-based aproposed capability of sharing both active and reactive in V2G systems. The performance ofV2G the proposed controller is evaluated on ato single-phase full-bridge converter-based V2G system an output and that any Simulation system with with an LCL LCL controller output filter filter and compared compared that of of without without any filter. filter. Simulation results results proposed controller controller is evaluated on atosingle-phase full-bridge converter-based V2G system with an LCL the output filter and comparedcapabilities to that of without any filter. Simulation results clearly demonstrate the harmonic elimination capabilities of the proposed V2G structure with clearly demonstrate harmonic elimination of the proposed V2G structure with system with an LCL output filter and compared to that of without any filter. Simulation results clearly demonstrate the harmonic elimination capabilities of the proposed V2G structure with the proposed control scheme. the proposed control scheme. clearly demonstrate the harmonic elimination capabilities of the proposed V2G structure with the proposed control scheme. the proposed control scheme. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Harmonic Harmonic elimination, elimination, LCL LCL filters, filters, partial partial feedback feedback linearization, linearization, power power quality, quality, Keywords: Keywords: Harmonic elimination, LCL filters, partial feedback linearization, power quality, V2G systems. systems. V2G Keywords: Harmonic elimination, LCL filters, partial feedback linearization, power quality, V2G systems. V2G systems. 1. INTRODUCTION INTRODUCTION connected solar solar photovoltaic photovoltaic (PV) (PV) systems systems to to eliminate eliminate 1. connected 1. INTRODUCTION connected solarand photovoltaic (PV) systems to eliminate the harmonics and improve power quality. Though the the harmonics improve power quality. Though the 1. INTRODUCTION connected solar photovoltaic (PV) systems to eliminate the harmonics improve power distribution quality. Though the impacts of V2G V2Gand systems on power power networks Vehicle-to-grid (V2G) systems provide ancillary services to impacts of systems on distribution networks the harmonics and improve power quality. Though the Vehicle-to-grid (V2G) systems provide ancillary services to impacts of V2G systems on power distribution networks have been been well-studied (Galus et al., al.,distribution 2010; Papadopoulos Papadopoulos Vehicle-to-grid systems power providein ancillary services to impacts power networks networks(V2G) by delivering delivering case of of emergency emergency have (Galus et 2010; of well-studied V2G systems on power networks power by case Vehicle-to-grid (V2G) systems power provideinancillary services to have been well-studied (Galus et al., 2010; Papadopoulos et al., 2012; Fernandez et al., 2011; Das et al., 2014) 2014) but but power networks by delivering power in case of emergency situations. In V2G systems, power electronic converters et al.,been 2012;well-studied Fernandez (Galus et al., 2011; et Papadopoulos al., et al.,Das 2010; situations. In V2G systems, power converters have power networks by delivering power electronic in case of emergency et al., 2012;conversion Fernandeztechnologies et al., 2011;with Das different et al., 2014) but the power conversion technologies with different types of situations. In V2G systems, power electronic converters play a key role to supply electric power from plug-in the power types of al., 2012; Fernandez et al., 2011; Das et al., 2014) but play a keyInrole to systems, supply electric power from plug-in et situations. V2G power electronic converters the power conversion technologies different of control techniques along with power powerwith quality issuestypes are still still play a key role to supply electric power from plug-in electric vehicles (EVs) into the grids as the stored direct control techniques along with quality issues are the power conversion technologies with different types of electric vehicles into the grids power as the from storedplug-in direct control techniques along with power quality issues are still play a key role (EVs) to supply electric at early earlytechniques stages. electric vehicles (EVs) intoto the grids into as the stored direct current (DC) (DC) power needs convert alternating cur- control at stages. along with power quality issues are still current power needs convert alternating curelectric vehicles (EVs) intotothe grids into as the stored direct at early stages. current (DC) power needs to convert into alternating current (AC) power. The power needs to be supplied in a early stages. rent (AC) power. power needs into to bealternating supplied in a at Fuzzy logic controllers used for for power power current (DC) powerThe needs to convert curFuzzy logic controllers have have been been widely widely used rent (AC) power with needsthe tolocal be supplied in a Fuzzy manner thatpower. it can can The can match match demand durdurlogic controllers have been widely used for power manner that it can demand conversion in V2G systems (Khayyam et al., 2012; Datta rent (AC) power. The power with needsthe tolocal be supplied in a Fuzzy conversion V2G systems et al., Datta logicincontrollers have(Khayyam been widely used2012; for power manner it of canoverloaded can matchdistribution with the local demand ing peak hours networks as durwell conversion in 2012; V2G systems (Khayyam et al.,et 2012; Datta ing peakthat hours networks as well and Senjyu, 2012; Datta, 2014; Singhand et al., 2012; manner that it of canoverloaded can matchdistribution with the local demand durand Senjyu, Datta, 2014; Singhand al., 2012; in V2G systems (Khayyam et al., 2012; Datta ing of overloaded networks as well conversion as in inpeak casehours of power power blackoutsdistribution or any any other other unpredictable Senjyu, 2012; Datta, 2014; Singhand et al.,is 2012; as case of blackouts or unpredictable Thirugnanam et al., 2014). A fuzzy logic controller is used ing peak hours of overloaded distribution networks as well and Thirugnanam et al., 2014). A fuzzy logic controller used and Senjyu, 2012; Datta, 2014; Singhand et al., 2012; as in case of powerpower blackouts or any other unpredictable event. Otherwise, imbalances will into al., 2014). A fuzzy logic and controller is used event. Otherwise, imbalances will occur occur into the the Thirugnanam in (Datta (Datta and andet Senjyu, 2012) for V2G V2G and PV applicaapplicaas in case of powerpower blackouts or any other unpredictable in Senjyu, 2012) for PV Thirugnanam et al., 2014). A fuzzy logic controller is used event. Otherwise, power imbalancesand willvoltage occur into the in (Datta and Senjyu, 2012) for V2G and PV applicagrid which which are prone prone to frequency frequency stability grid are to stability tions to power fluctuations in which event. Otherwise, power imbalancesand willvoltage occur into the in tions to reduce reduce active power fluctuations in tie-lines tie-lines which (Datta and active Senjyu, 2012) for V2G and PV applicagrid which are prone to frequency and voltage stability problems. Moreover, power electronic converters are the tions to reduce active power fluctuations in tie-lines which problems. electronic are the in turn alleviates the frequency fluctuations. In (Datta, grid whichMoreover, are pronepower to frequency andconverters voltage stability in turn alleviates the frequency fluctuations. In (Datta, tions to reduce active power fluctuations in tie-lines which problems. Moreover, power electronic converters are the main sources sources of harmonics harmonics which deteriorates theare power turn an alleviates the frequency In (Datta, main of deteriorates the power 2014), aggregator has been been fluctuations. designed based based on the the problems. Moreover, power which electronic converters the in 2014), aggregator has designed on turn an alleviates the frequency fluctuations. In (Datta, main sources of harmonics which to deteriorates thesystems power in quality. Therefore, it is is essential essential design V2G V2G an aggregator has been designed based on the quality. Therefore, it design fuzzy logic control to maintain communication between main sources of harmonics which to deteriorates thesystems power 2014), fuzzy logic control to has maintain an aggregator been communication designed based between on the quality. Therefore, it isfilters essential design V2G systems along with with appropriate and to control schemes in such such 2014), fuzzy logic control to maintain along appropriate and control schemes in the utilities utilities and vehicles vehicles with an ancommunication aim to to control control between the grid grid quality. Therefore, it isfilters essential to design V2G systems the and with aim the fuzzy logic control to maintain communication between along with appropriate filters and control schemes in such way with that harmonics harmonics can easily becontrol eliminated and in desired utilitiesHowever, and vehicles withvoltage an aimis to control the issue grid aa way that easily be eliminated and desired frequency. However, the grid voltage is an important issue along appropriatecan filters and schemes such the frequency. the grid an important utilities and vehicles with an aim to control the grid apower way that harmonics easily be eliminated and desired the sharing can be be can maintained. However, the grid voltage is an important issue sharing can maintained. as this this needs needs to be be kept kept within specified level (Mahmud (Mahmud apower way that harmonics can easily be eliminated and desired frequency. as to within aa specified level frequency. However, the grid voltage is an important issue power sharing can be maintained. as this needs to be kept within a specified level (Mahmud et al., 2013). A V2G controller along with a charging power sharing can be maintained. The power power quality quality in in V2G V2G systems systems can can be be improved improved by by as et this al., needs 2013).toAbeV2G along with charging keptcontroller within a specified levela(Mahmud The al., 2013). A V2G controller along withet a al., charging station controller is proposed proposed in (Singhand (Singhand 2012; The qualityfilters in V2G systems can be improved by et usingpower appropriate which can the station controller is in 2012; al., 2013). A V2G controller along witheta al., charging using appropriate which can eliminate eliminate the harmonharmonThe power qualityfilters in V2G systems can be improved by et station controller is proposed in (Singhand et al., 2012; Thirugnanam et al., 2014) by considering both voltage using appropriate filters which can eliminate the harmonics. LCL filters are the most popular for grid-connected Thirugnanam et al., 2014) by considering both voltage controller is proposed in (Singhand et al., 2012; ics. LCL filters are the which most popular for grid-connected using appropriate filters can eliminate the harmon- station et al., 2014) by considering both voltage and frequency frequency stability. stability. The combination combination of adaptive adaptive neuics. LCL filters are the most popular for have grid-connected power electronic converters as these these filters the better better Thirugnanam and The of neuThirugnanam et al., 2014) by considering both voltage power electronic converters as filters the ics. LCL filters are the most popular for have grid-connected and frequency stability. The combination of adaptive neural network (ANN) and adaptive neural fuzzy inference power electronic converters as these filters have the better attenuation capability of switching switching frequency harmonics ral network (ANN) andThe adaptive neural offuzzy inference frequency stability. combination adaptive neuattenuation capability of frequency power electronic converters as these filters have harmonics the better and ral network (ANN) and adaptive neural inference system (ANFIS) is used used in (Kaushal (Kaushal andfuzzy Verma, 2014) attenuation capability frequency and lower lower cost cost (Liu et et of al.,switching 2009; Shen Shen et al., al., harmonics 2010). An system (ANFIS) is in and Verma, 2014) network (ANN) and adaptive neural fuzzy inference and (Liu 2009; et 2010). An ral attenuation capability ofal., switching frequency harmonics (ANFIS) is used (Kaushal and in Verma, 2014) to control control both active active andin reactive power V2G appliappliand (Liu et in al., 2009; Shen et2014b) al., 2010). An system LCL lower filter is iscost considered (Mahmud et for to both and power V2G (ANFIS) is used inreactive (Kaushal and in Verma, 2014) LCL filter considered (Mahmud et al., al., for gridgridand lower cost (Liu et inal., 2009; Shen et2014b) al., 2010). An system control both active and reactive power in V2G appliLCL filter is considered in (Mahmud et al., 2014b) for grid- to LCL filter is considered in (Mahmud et al., 2014b) for grid- to control both active and reactive power in V2G appli-
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cations where the control of reactive power ensures the voltage stability. These intelligent controllers (both fuzzy and ANN with ANFIS) provide good performance in terms of power sharing but the power quality issues have not been taken into account. Moreover, the fuzzy controllers have the limitations of capturing full dynamics of V2G systems and require more fine tuning before making them operational (Khayyam et al., 2012). The shortcomings of intelligent controllers can be overcome by considering model-based controllers which require a dynamical model of V2G systems. A static model of V2G system is proposed in (Madawala and Thrimawithana, 2011) where a proportional integral (PI) controller is used for V2G applications. However, a dynamical model-based controller will provide better solution for V2G applications in term of power sharing and power quality enhancement. Since the major part of a V2G system includes a battery energy storage system (BESS), the mathematical model can be developed by incorporating a BESS model along with a grid-connected converter model. Based on this concept, the dynamical model of a V2G system has been developed in (Mahmud et al., 2014a) and a nonlinear feedback linearizing controller is designed for appropriate power (both active and reactive) sharing. However, the dynamics of the filter is not considered in the development of V2G systems. This paper aims to design a feedback linearizing controller for V2G system by considering the dynamics of an LCL filter which is connected at the output of the inverter. The controller is designed based on the partial feedback linearization of V2G system models as the V2G system with an LCL filter is partially linearized which is also discussed in this paper. Finally the performance of the proposed controller is tested on a residential V2G applications to illustrate the effectiveness as compared to that of as presented in (Mahmud et al., 2014a) where no LCL filters are used. 2. MODELING OF V2G SYSTEMS WITH LCL FILTERS A V2G system comprises a BESS, a voltage source converter (VSC), an LCL output filter, connecting lines, and a grid supply point as shown in Fig. 1. The battery model, used in this paper, is developed based on the electrochemical phenomenon as presented in (Ceraolo, 2000). Based on the equivalent circuit diagram of a V2G system as shown in Fig. 1, the dynamical model of V2G system can be developed in a similar manner as presented in (Mahmud et al., 2014a) by simply applying the circuit theory. If Kirchhoff’s current law (KCL) is applied at the battery of EV where the resistor and capacitor are connected together, then it can be written as dVC1 (1) dt where Idc = mii is the output DC current of the battery, m represents the switching signal of the converter which is a function of modulation index and firing angle, I1 is the current flowing through the resistor R1 , C1 is the capacitor, VC1 is the voltage across both C1 and R1 as Idc = I1 + C1
530
they are connected in parallel which implies VC1 = I1 R1 and simplifies equation (1) as 1 dI1 (2) = (mii − I1 ) dt τ1 where τ1 = R1 C1 is the time constant of the battery. If Kirchhoff’s voltage law (KVL) is applied at the first loop of the inverter output, the following relationship will be obtained: R vdc vC dii (3) = − ii + m − dt L1 L1 L1 where R is the line resistance, ii is the input current to the filter, and L1 is the filter inductance. Again by applying KCL at the node where the filter capacitor C is connected, it can be written as 1 dvC (4) = (ii − io ) dt C where vC is the voltage across the filter capacitor and io is the output current of the filter. Finally, by applying KVL at the output loop of the filter; it can be written as 1 dio (5) = (vC − e) dt L2 where L2 is the filter inductance and e is the grid voltage. Equations (2)–(5) represent an instantaneous model of the V2G system with an LCL filter. For the purpose of controller design, equations (2)–(5) need to be written in the dq-frame which can be done in the same way as presented in (Mahmud et al., 2014a) and in this case, the V2G system can be written as 1 I˙1 = (Md Iid + Mq Iiq − I1 ) τ1 R vCd vdc + Md I˙id = − Iid + ωIiq − L1 L1 L1 R vCq vdc Iiq − + Mq I˙iq = −ωIid − L1 L1 L1 1 (6) v˙ cd = ωvcq + (Iid − Iod ) C 1 v˙ cq = −ωvcd + (Iiq − Ioq ) C 1 (vCd − Ed ) I˙od = ωIoq + L2 1 (vCq − Eq ) I˙oq = −ωIod + L2 where the subscripts d and q denote the corresponding variables in d- and q-frame, respectively. Since the paper is aimed to design a controller for the V2G system used in a residential area, the converter model is considered as a single-phase. In this case, the active and reactive power delivered into the grid can be written as P = Eq Ioq
(7) Q = Eq Iod Therefore, the injection of active and reactive power in V2G systems can be controlled by controlling Ioq and Iod , respectively. However, it is essential to analyze the feedback linearizability of V2G systems which is shown in the following section.
IFAC CPES 2015 December 9-11, 2015. Delhi, India
Im
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C1 R1
+
Em
R0
R
Idc
ii
+
I1
L1
vC
io
+ e
C
Grid Supply Point
_
_
_ Battery of EV
L2 +
vdc
531
LCL Filter
Converter
Fig. 1. V2G system with LCL filter 3. FEEDBACK LINEARIZABILITY OF V2G SYSTEMS
degree of the system. To calculate the relative degree corresponding to the first output Iod , lets start with
The V2G system model as represented by equation (6) has two inputs (Md and Mq ) and two outputs Ioq and Iod . Therefore, the mathematical model of V2G system can be represented by the following generalized equation of nonlinear systems:
Lg h1 = Lg L1−1 Iod = 0 f
y1 = h1 (x)
Since = 0, it is essential to proceed one step further. To do that, it is essential to obtain the following: 1 (vCd − Ed ) L2 which in turn helps to calculate L2−1 Iod = ωIoq + f
x˙ = f (x) + g1 (x)u1 + g2 (x)u2 (8)
y2 = h2 (x) where
I 1
Iid Iiq x= vcd , vcq Iod Ioq
I
id
τ1 vdc L1 g(x) = 0 0 0 0 0
(9)
Lg L1−1 Iod f
Lg Lf h1 = Lg L2−1 Iod = 0 f
(10)
(11)
From equation (11), it can be seen that Lg L2−1 Iod = 0 f which requires to move one step forward and in this case, we need to calculate
1 I1 τ1 R − Iid + ωIiq − vCd + vdc Md L L1 L1 1 vCq vdc R −ωIid − Iiq − + Mq L1 L1 L1 1 , f (x) = ωvcq + (Iid − Iod ) C 1 −ωvcd + (Iiq − Ioq ) C 1 ωI + (v − E ) oq Cd d L2 1 −ωIod + (vCq − Eq ) L2 −
Iod = L3−1 f
2ω ω 1 Iid − µIod + vCq − Eq L2 C L2 L2
(12)
where µ=
�
1 + ω2 L2 C
�
and vdc = D �= 0 (13) L1 L2 C where is D is a constant. This implies that the relative degree corresponding to the first output function is three. At this point, the relative degree corresponding to the second output function needs to be determined. In order to determine the relative degree for the second output, we need to follow the same steps as presented above. At the beginning, we need to calculate Lg L1−1 Iod which is also f zero in this case. Therefore, lets start as follows: Iod = Lg L2f h1 = Lg L3−1 f
Iiq τ1 0 � � � � � � vdc u1 Md Iod , u = = , and y = . L1 Ioq u2 Mq 0 0 0 0
The feedback linearizability of nonlinear V2G systems determines whether the systems are exactly or partially linearized. The V2G systems will be partially linearized if the relative degree of the system is less than the order (which is seven for the considered model) of the system and exactly linearized if relative degree and order are equal to each other. The definition of relative degree can be seen in (Mahmud et al., 2012). Since there are two outputs of the V2G system, it is essential to calculate the relative degree for each output and then sum up together to calculate the total relative 531
L2−1 Ioq = −ωIod + f
1 (vCq − Eq ) L2
(14)
and Lg Lf h2 = Lg L2−1 Ioq = 0 f
(15)
Since Lg L2−1 Ioq = 0, we need to move one step ahead, f i.e., Ioq = L3−1 f and
ω 1 2ω Iiq − µIoq − vCd + Ed L2 C L2 L2
(16)
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vdc = D �= 0 (17) L1 L2 C which implies that the relative degree corresponding to the second output is also three. Therefore, the total relative degree of the system is six which is less than than order of the system and the V2G system is said to be partially linearized. Since the V2G system is partially linearized, partial feedback linearization technique needs to be used to design the controller which is shown in the following section. Lg L2f h1 = Lg L3−1 Iod = f
4. NONLINEAR CONTROLLER DESIGN FOR V2G SYSTEMS WITH LCL FILTERS The design of partial feedback linearizing controller for V2G system with LCL filters requires to follow some steps such as nonlinear coordinate transformation, stability analysis of internal dynamics of V2G systems, and the derivation of final control law. These steps are discussed in the following: • Step 1: Nonlinear coordinate transformation for obtaining partially linearized of V2G systems From Section 3, it can be seen that the relative degree of the V2G system is six whereas the order of the system is seven which means that the seventh order system will be transformed into a sixth order system. Therefore, six new coordinates will be obtained from nonlinear coordinate transformation which can be written as z 1 = L0f h1 = Iod
1 (vCd − Ed ) L2 2ω ω Iid − µIod + vCq − = L2 C L2 = Ioq 1 = −ωIod + (vCq − Eq ) L2 2ω 1 Iiq − µIoq − vCd + = L2 C L2
z 2 = L1f h1 = ωIoq + z 3 =
L2f h1
z 4 = L0f h2
z 5 = L1f h2
z 6 = L2f h2
ω Eq L2
(18)
ω Ed L2
+
v 2 = L3f h2 + Lg L2f h2 Mq
which means that the transformed states become zero as the time is increased, i.e., z i → 0 with i = 1, 2, · · · , 6 as t → ∞. In order to obtain the remaining dynamic equation, the nonlinear coordinate transformation (ˆ z = ˆ φ(x)) needs to be selected in a manner that it satisfies the following condition (Lu et al., 2001): ˆ Lg φ(x) =0
(19)
(21)
The condition as represented by equation (21) will be satisfied for the considered V2G system, if the following nonlinear coordinate transformation is chosen:
ˆ zˆ˙ = Lf φ(x) = L2 Iod f6 + L2 Ioq f7
(23)
As Since Iod = z 1 and Ioq = z 4 , equation (23) can be written as
Lg L2f h1 Md
= −αIid + βIiq − γvCd − ηIoq
Since the V2G system is transformed into a sixth order system, there will be only one remaining dynamic equation whose characteristics need to be investigated. The desired performance of the transformed dynamics is ensured with the linear controllers where the linear control laws are chosen as
1 1 2 2 ˆ (22) φ(x) = zˆ = L2 Iod + L2 Ioq 2 2 With this nonlinear coordinate transformation, the remaining dynamic of V2G system can be written as follows:
z ˙ 4 = z 5 z ˙ 5 = z 6 z ˙ 6 = v 2
v 1 =
• Step 2: Analysis of internal dynamics of V2G systems
lim hi (x) → 0
z ˙ 1 = z 2 z ˙ 2 = z 3 z ˙ 3 = v 1
L3f h1
R L1 L2 C 3ω β= L2 C µ 2ω 2 1 + + γ= L1 L2 C L2 L2 2ω η = µω + L2 C The original control laws (Md and Mq ) of the V2G system can be derived from equation (20). Before obtaining the original control laws, the internal dynamics of the V2G systems, which do not transform through feedback linearization, need to be analyzed and this has been discussed in the following steps. α=
t→∞
Using the nonlinear coordinate transformation as represented by equation (18), the following feedback linearized V2G system can be obtained:
with
where v 1 and v 2 are linear control laws which can be obtained by using any linear technique; α, β, γ, and η are are the constant and function of V2G system parameters which can be written as
γ + Ed + DMd L2
= −βIid − αIiq − γvCq + ηIod +
(20)
zˆ˙ = L2 z 1 f6 + L2 z 4 f7
(24)
zˆ˙ = 0
(25)
Since z i → 0 with i = 1, 2, · · · , 6; equation (24) can be simplified as From equation (25), it can be seen that the internal dynamic of the V2G system with an LCL filter is zero
γ Eq + DMq L2 532
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and this is different from to that as presented in (Mahmud et al., 2014a). For the considered V2G system, the internal dynamic does not have any effect on the overall stability and thus, partial feedback linearizing control laws can be designed and implemented for this system which is shown in the following step.
20 10
0
The gains have been selected arbitrarily as a function of the reference values and in this paper, the gains are used as 2 2 k1p = 2Iodref , k1i = Iodref , k2p = 2Ioqref , k2i = Ioqref
With the designed controller, the performance of a V2G system in residential applications is evaluated in the following section. 5. SIMULATION RESULTS The proposed V2G structure is considered for a residential application where the key objective is to deliver appropriate active and reactive power sharing into the grid supply point with high power quality. The batteries of EVs need to maintain a minimum state of charge (SOC) for delivering the power into the grid which can be calculated in a similar manner as presented in (Mahmud et al., 2014a; Singhand et al., 2012). In this paper, it is assumed that the residential area consists of 15 PHEVs where each EV has a battery capacity of 4.4 kWh and these EVs are connected to the grid in order to supply a load of 5 KVA. The performance of the controller is evaluated in terms of delivering active and reactive power without any harmonic. When the consumers consume only active power, the controller needs to act in such a way that the V2G system can supply only active power. In this case, the voltage and current will be in phase with each other and 5 kW power will be delivered from the batteries of the V2G system. If the 533
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0.205
0.21
0.215
0.22
0.225 Time (s)
0.23
0.235
0.24
0.245
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Fig. 2. Grid current at unity power factor for V2G system without LCL filter 30 20 10 Current (A)
Equation (26)represents the final control law for the V2G system with an LCL filter which has the capability of delivering both active and reactive power into the grid. Since v 1 and v2 are linear control inputs and can be determined using any linear techniques, PI controllers can be used to achieve the desired control objectives which can be obtained as follows t v 1 = k1p (Iodref − Iod ) + k1i (Iodref − Iod )dt 0 (27) t (Ioqref − Ioq )dt v 2 = k2p (Ioqref − Ioq ) + k2i
0 −10
• Step 3: Formulation of partial feedback linearizing control laws Since the internal dynamic of the V2G system with an LCL filter does not have any affect, the original control law in dq-frame (Md and Mq ) can be obtained from equation (20) as γ 1 v1 + αIid − βIiq + γvCd + ηIoq − Md = Ed D L2 (26) 1 γ v2 + βIid + αIiq + γvCq − ηIod − Eq Mq = D L2
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30
Current (A)
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0.205
0.21
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0.22
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0.23
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Fig. 3. Grid current at unity power factor for V2G system with LCL filter grid voltage is 220 V, the output current will be 22.72 A. Though the output current with the designed controller does not contain any harmonic as shown in Fig. 3 but the current with the same controller for the V2G system without an LCL filter as presented in (Mahmud et al., 2014a) contains some harmonics which can be seen in Fig. 2. The designed controller will perform in a similar way for all other operating conditions as it is designed in a manner that the linearization of the V2G system with an LCL filter is independent of operating conditions. 6. CONCLUSIONS A partial feedback linearizing controller has been designed for a V2G system with an output LCL filter where the dynamical model has also been developed for similar structures. The partial feedback linearizability of the whole V2G system determines the applicability of the proposed control scheme. Simulation results clearly indicate the superiority of the designed scheme over the existing one where the system model was mainly developed without any filter. Simulation results also reflect the harmonic rejection capability of the proposed V2G system structure along with the designed control scheme. The designed controller enhances the power quality in a much better way as compared to the existing controller. Since feedback linearization is sensitive to the variations in system parameters, future works will consider these parameter variations into the controller design. REFERENCES Ceraolo, M. (2000). New dynamical models of lead-acid batteries. IEEE Trans. on Power Systems, 15(4), 1184– 1190.
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Das, R., Thirugnanam, K., Kumar, P., Lavudiya, R., and Singh, M. (2014). Mathematical modeling for economic evaluation of electric vehicle to smart grid interaction. IEEE Transactions on Smart Grid, 5(2), 712–721. Datta, M. (2014). Fuzzy logic based frequency control by V2G aggregators. In 2014 IEEE 5th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 1–8. Datta, M. and Senjyu, T. (2012). Fuzzy control of distributed PV inverters/energy storage systems/electric vehicles for frequency regulation in a large power system. IEEE Transactions on Smart Grid, 4(1), 479–488. Fernandez, L.P., Roman, T.G.S., Cossent, R., Domingo, C.M., and Frias, P. (2011). Assessment of the impact of plug-in electric vehicles on distribution networks. IEEE Transactions on Power Systems, 26(1), 206–213. Galus, M.D., Zima, M., and Andersson, G. (2010). On integration of plug-in hybrid electric vehicles into existing power system structures. Energy Policy, 38(11), 6736–6745. Kaushal, A. and Verma, N. (2014). Implementation of vehicle to grid concept using ANN and ANFIS controller. In 2014 IEEE 9th Conference on Industrial Electronics and Applications (ICIEA), 960–965. Khayyam, H., Ranjbarzadeh, H., and Marano, V. (2012). Intelligent control of vehicle to grid power. Journal of Power Sources, 201, 1–9. Liu, F., Zhou, Y., Duan, S., Yin, J., Liu, B., and Liu, F. (2009). Parameter design of a two-current-loop controller used in a grid-connected inverter system with LCL filter. IEEE Transactions on Industrial Electronics, 56(11), 4483–4491. Lu, Q., Sun, Y., and Mei, S. (2001). Nonlinear Control Systems and Power System Dynamics. Kluwer Academic Publishers, Boston. Madawala, U. and Thrimawithana, D. (2011). A bidirectional inductive power interface for electric vehicles in v2g systems. IEEE Transactions on Industrial Electronics, 58(10), 4789–4796. Mahmud, M.A., Hossain, M.J., and Pota, H.R. (2013). Voltage variation on distribution networks with distributed generation: Worst case scenario. IEEE Systems Journal, In Press, 1–8. Mahmud, M.A., Hossain, M.J., Pota, H.R., and Roy, N.K. (2014a). Implementation of vehicle to grid concept using ANN and ANFIS controller. In 2014 IFAC World Congress, 7659–7664. Mahmud, M.A., Hossain, M.J., Pota, H.R., and Roy, N.K. (2014b). Robust nonlinear controller design for three-phase grid-connected photovoltaic systems under structured uncertainties. IEEE Transactions on Power Delivery, 29(3), 1221–1230. Mahmud, M.A., Pota, H.R., and Hossain, M. (2012). Dynamic stability of three-phase grid-connected photovoltaic system using zero dynamic design approach. IEEE Journal of Photovoltaics, 2(4), 564–571. Papadopoulos, P., Skarvelis-Kazakos, S., Grau, I., Cipcigan, L.M., and Jenkins, N. (2012). Electric vehicles’ impact on British distribution networks. IET Electrical Systems in Transportation, 2(3), 91–102. Shen, G., Zhu, X., Zhang, J., and Xu, D. (2010). A new feedback method for PR current control of LCL-filterbased grid-connected inverter. IEEE Transactions on 534
Industrial Electronics, 57(6), 2033–2041. Singhand, M., Kumar, P., and Kar, I. (2012). Implementation of vehicle to grid infrastructure using fuzzy logic controller. IEEE Transactions on Smart Grid, 3(1), 565–577. Thirugnanam, K., Joy, T.P.E.R., Singh, M., and Kumar, P. (2014). Modeling and control of contactless based smart charging station in V2G scenario. IEEE Transactions on Smart Grid, 5(1), 337–348. Appendix A. SYSTEM PARAMETERS Battery Parameters: R1 =0.4 mΩ, τ1 =7200 s, R0 =2 mΩ Grid Parameters: Grid voltage (rms)=220 V, Frequency=50 Hz, R=0.1 Ω, L=10 mH
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Nonlinear Nonlinear Nonlinear Vehicle-to-Grid Vehicle-to-Grid Vehicle-to-Grid
Controller Design for Controller Design for Controller Design for LCL Systems with Output Systems with Output LCL Systems Filters with Output LCL Filters Filters ∗∗ ∗ ∗∗∗
∗ M. M. A. A. Mahmud Mahmud ∗ H. H. R. R. Pota Pota ∗∗ A. A. M. M. T. T. Oo Oo ∗∗ R. R. C. C. Bansal Bansal ∗∗∗ ∗∗∗ M. A. Mahmud ∗∗ H. R. Pota ∗∗ ∗∗ A. M. T. Oo ∗ R. C. Bansal ∗∗∗ M. A. Mahmud H. R. Pota A. M. T. Oo R. C. Bansal ∗ ∗ School of Engineering, Deakin University, Waurn Ponds, VIC 3220, ∗ School of Engineering, Deakin University, Waurn Ponds, VIC 3220, of Engineering, Deakin University, Waurn Ponds, VIC 3220, Australia (e-mail: {apel.mahmud {apel.mahmud and aman.m}@deakin.edu.au). aman.m}@deakin.edu.au). ∗ School Australia (e-mail: and School of Engineering, Deakin University, Waurn Ponds, VIC 3220, ∗∗ Australia (e-mail: {apel.mahmud and aman.m}@deakin.edu.au). ∗∗ School of Engineering and Information Technology School of(e-mail: Engineering and Information Technology (SEIT), (SEIT), The The Australia {apel.mahmud and aman.m}@deakin.edu.au). ∗∗ School of Engineering and Information Technology (SEIT), The University of New South Wales, Canberra, ACT 2600, Australia ∗∗ University New Southand Wales, Canberra, ACT 2600, Australia School of of Engineering Information Technology (SEIT), The University of New(e-mail: South Wales, Canberra, ACT 2600, Australia [email protected]). (e-mail: [email protected]). University of New South Wales, Canberra, ACT 2600, Australia ∗∗∗ (e-mail: [email protected]). ∗∗∗ Department of Electrical, Electronic and and Computer Computer Engineering, Engineering, Electronic (e-mail: [email protected]). ∗∗∗ Department of Electrical, of Electrical, and Computer Engineering, University of Pretoria, Pretoria, Africa ∗∗∗ Department UniversityofofElectrical, Pretoria,Electronic Pretoria, South South Africa (e-mail: (e-mail: Department Electronic and Computer Engineering, University of Pretoria, Pretoria, South Africa (e-mail: [email protected]). [email protected]). University of Pretoria, Pretoria, South Africa (e-mail: [email protected]). [email protected]). Abstract: This paper presents a nonlinear Abstract: This paper presents a nonlinear controller controller design design for for vehicle-to-grid vehicle-to-grid (V2G) (V2G) systems systems Abstract: This paper presents a nonlinear controller design for vehicle-to-grid (V2G) systems with LCL output filters. The V2G systems are modeled with LCL output filters in to with LCL output filters. The V2G systemscontroller are modeled with output filters in order order to Abstract: This paper presents a nonlinear design forLCL vehicle-to-grid (V2G) systems with LCLharmonics output filters. The V2Gpower systems are modeled with LCLcontroller output filters in order to eliminate harmonics for improving power qualities and the nonlinear controller is designed based eliminate for improving qualities and the nonlinear is designed based with LCL output filters. The V2G systems are modeled with LCL output filters in order to eliminate harmonics for improving qualities and the nonlinear controller is designed based on linearization. The feasibility of the appropriate feedback linearization on the the feedback feedback linearization. Thepower feasibility of using using the appropriate feedback linearization eliminate harmonics for improving power qualities and the nonlinear controller is designed based on the feedback linearization. The feasibility of using the appropriate feedback linearization approaches, either partial or exact, is also investigated through the feedback linearizability of approaches, eitherlinearization. partial or exact, is also investigated through the feedback linearizability of on the feedback The feasibility of using the appropriate feedback linearization approaches, either partial or exact, is also investigated through the feedback linearizability of V2G systems. In this paper, partial feedback linearization is used to design the controller with V2G systems. In this paper, feedback linearization is usedthe to feedback design thelinearizability controller with approaches, either partial or partial exact, is also investigated through of V2G systems. this paper, partialand feedback linearization is used to design the controllerof with a capability capability of In sharing both active active reactive power in in V2G V2G systems. The performance performance the a of sharing both reactive power systems. The the V2G systems. In this paper, partialand feedback linearization is used to design the controllerofwith aproposed capability of sharing both active and reactive power in V2G systems. The performance of the controller controller is evaluated on a single-phase full-bridge converter-based V2G controller controller is evaluated on apower single-phase full-bridge converter-based aproposed capability of sharing both active and reactive in V2G systems. The performance ofV2G the proposed controller is evaluated on ato single-phase full-bridge converter-based V2G system an output and that any Simulation system with with an LCL LCL controller output filter filter and compared compared that of of without without any filter. filter. Simulation results results proposed controller controller is evaluated on atosingle-phase full-bridge converter-based V2G system with an LCL the output filter and comparedcapabilities to that of without any filter. Simulation results clearly demonstrate the harmonic elimination capabilities of the proposed V2G structure with clearly demonstrate harmonic elimination of the proposed V2G structure with system with an LCL output filter and compared to that of without any filter. Simulation results clearly demonstrate the harmonic elimination capabilities of the proposed V2G structure with the proposed control scheme. the proposed control scheme. clearly demonstrate the harmonic elimination capabilities of the proposed V2G structure with the proposed control scheme. the proposed control scheme. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Harmonic Harmonic elimination, elimination, LCL LCL filters, filters, partial partial feedback feedback linearization, linearization, power power quality, quality, Keywords: Keywords: Harmonic elimination, LCL filters, partial feedback linearization, power quality, V2G systems. systems. V2G Keywords: Harmonic elimination, LCL filters, partial feedback linearization, power quality, V2G systems. V2G systems. 1. INTRODUCTION INTRODUCTION connected solar solar photovoltaic photovoltaic (PV) (PV) systems systems to to eliminate eliminate 1. connected 1. INTRODUCTION connected solarand photovoltaic (PV) systems to eliminate the harmonics and improve power quality. Though the the harmonics improve power quality. Though the 1. INTRODUCTION connected solar photovoltaic (PV) systems to eliminate the harmonics improve power distribution quality. Though the impacts of V2G V2Gand systems on power power networks Vehicle-to-grid (V2G) systems provide ancillary services to impacts of systems on distribution networks the harmonics and improve power quality. Though the Vehicle-to-grid (V2G) systems provide ancillary services to impacts of V2G systems on power distribution networks have been been well-studied (Galus et al., al.,distribution 2010; Papadopoulos Papadopoulos Vehicle-to-grid systems power providein ancillary services to impacts power networks networks(V2G) by delivering delivering case of of emergency emergency have (Galus et 2010; of well-studied V2G systems on power networks power by case Vehicle-to-grid (V2G) systems power provideinancillary services to have been well-studied (Galus et al., 2010; Papadopoulos et al., 2012; Fernandez et al., 2011; Das et al., 2014) 2014) but but power networks by delivering power in case of emergency situations. In V2G systems, power electronic converters et al.,been 2012;well-studied Fernandez (Galus et al., 2011; et Papadopoulos al., et al.,Das 2010; situations. In V2G systems, power converters have power networks by delivering power electronic in case of emergency et al., 2012;conversion Fernandeztechnologies et al., 2011;with Das different et al., 2014) but the power conversion technologies with different types of situations. In V2G systems, power electronic converters play a key role to supply electric power from plug-in the power types of al., 2012; Fernandez et al., 2011; Das et al., 2014) but play a keyInrole to systems, supply electric power from plug-in et situations. V2G power electronic converters the power conversion technologies different of control techniques along with power powerwith quality issuestypes are still still play a key role to supply electric power from plug-in electric vehicles (EVs) into the grids as the stored direct control techniques along with quality issues are the power conversion technologies with different types of electric vehicles into the grids power as the from storedplug-in direct control techniques along with power quality issues are still play a key role (EVs) to supply electric at early earlytechniques stages. electric vehicles (EVs) intoto the grids into as the stored direct current (DC) (DC) power needs convert alternating cur- control at stages. along with power quality issues are still current power needs convert alternating curelectric vehicles (EVs) intotothe grids into as the stored direct at early stages. current (DC) power needs to convert into alternating current (AC) power. The power needs to be supplied in a early stages. rent (AC) power. power needs into to bealternating supplied in a at Fuzzy logic controllers used for for power power current (DC) powerThe needs to convert curFuzzy logic controllers have have been been widely widely used rent (AC) power with needsthe tolocal be supplied in a Fuzzy manner thatpower. it can can The can match match demand durdurlogic controllers have been widely used for power manner that it can demand conversion in V2G systems (Khayyam et al., 2012; Datta rent (AC) power. The power with needsthe tolocal be supplied in a Fuzzy conversion V2G systems et al., Datta logicincontrollers have(Khayyam been widely used2012; for power manner it of canoverloaded can matchdistribution with the local demand ing peak hours networks as durwell conversion in 2012; V2G systems (Khayyam et al.,et 2012; Datta ing peakthat hours networks as well and Senjyu, 2012; Datta, 2014; Singhand et al., 2012; manner that it of canoverloaded can matchdistribution with the local demand durand Senjyu, Datta, 2014; Singhand al., 2012; in V2G systems (Khayyam et al., 2012; Datta ing of overloaded networks as well conversion as in inpeak casehours of power power blackoutsdistribution or any any other other unpredictable Senjyu, 2012; Datta, 2014; Singhand et al.,is 2012; as case of blackouts or unpredictable Thirugnanam et al., 2014). A fuzzy logic controller is used ing peak hours of overloaded distribution networks as well and Thirugnanam et al., 2014). A fuzzy logic controller used and Senjyu, 2012; Datta, 2014; Singhand et al., 2012; as in case of powerpower blackouts or any other unpredictable event. Otherwise, imbalances will into al., 2014). A fuzzy logic and controller is used event. Otherwise, imbalances will occur occur into the the Thirugnanam in (Datta (Datta and andet Senjyu, 2012) for V2G V2G and PV applicaapplicaas in case of powerpower blackouts or any other unpredictable in Senjyu, 2012) for PV Thirugnanam et al., 2014). A fuzzy logic controller is used event. Otherwise, power imbalancesand willvoltage occur into the in (Datta and Senjyu, 2012) for V2G and PV applicagrid which which are prone prone to frequency frequency stability grid are to stability tions to power fluctuations in which event. Otherwise, power imbalancesand willvoltage occur into the in tions to reduce reduce active power fluctuations in tie-lines tie-lines which (Datta and active Senjyu, 2012) for V2G and PV applicagrid which are prone to frequency and voltage stability problems. Moreover, power electronic converters are the tions to reduce active power fluctuations in tie-lines which problems. electronic are the in turn alleviates the frequency fluctuations. In (Datta, grid whichMoreover, are pronepower to frequency andconverters voltage stability in turn alleviates the frequency fluctuations. In (Datta, tions to reduce active power fluctuations in tie-lines which problems. Moreover, power electronic converters are the main sources sources of harmonics harmonics which deteriorates theare power turn an alleviates the frequency In (Datta, main of deteriorates the power 2014), aggregator has been been fluctuations. designed based based on the the problems. Moreover, power which electronic converters the in 2014), aggregator has designed on turn an alleviates the frequency fluctuations. In (Datta, main sources of harmonics which to deteriorates thesystems power in quality. Therefore, it is is essential essential design V2G V2G an aggregator has been designed based on the quality. Therefore, it design fuzzy logic control to maintain communication between main sources of harmonics which to deteriorates thesystems power 2014), fuzzy logic control to has maintain an aggregator been communication designed based between on the quality. Therefore, it isfilters essential design V2G systems along with with appropriate and to control schemes in such such 2014), fuzzy logic control to maintain along appropriate and control schemes in the utilities utilities and vehicles vehicles with an ancommunication aim to to control control between the grid grid quality. Therefore, it isfilters essential to design V2G systems the and with aim the fuzzy logic control to maintain communication between along with appropriate filters and control schemes in such way with that harmonics harmonics can easily becontrol eliminated and in desired utilitiesHowever, and vehicles withvoltage an aimis to control the issue grid aa way that easily be eliminated and desired frequency. However, the grid voltage is an important issue along appropriatecan filters and schemes such the frequency. the grid an important utilities and vehicles with an aim to control the grid apower way that harmonics easily be eliminated and desired the sharing can be be can maintained. However, the grid voltage is an important issue sharing can maintained. as this this needs needs to be be kept kept within specified level (Mahmud (Mahmud apower way that harmonics can easily be eliminated and desired frequency. as to within aa specified level frequency. However, the grid voltage is an important issue power sharing can be maintained. as this needs to be kept within a specified level (Mahmud et al., 2013). A V2G controller along with a charging power sharing can be maintained. The power power quality quality in in V2G V2G systems systems can can be be improved improved by by as et this al., needs 2013).toAbeV2G along with charging keptcontroller within a specified levela(Mahmud The al., 2013). A V2G controller along withet a al., charging station controller is proposed proposed in (Singhand (Singhand 2012; The qualityfilters in V2G systems can be improved by et usingpower appropriate which can the station controller is in 2012; al., 2013). A V2G controller along witheta al., charging using appropriate which can eliminate eliminate the harmonharmonThe power qualityfilters in V2G systems can be improved by et station controller is proposed in (Singhand et al., 2012; Thirugnanam et al., 2014) by considering both voltage using appropriate filters which can eliminate the harmonics. LCL filters are the most popular for grid-connected Thirugnanam et al., 2014) by considering both voltage controller is proposed in (Singhand et al., 2012; ics. LCL filters are the which most popular for grid-connected using appropriate filters can eliminate the harmon- station et al., 2014) by considering both voltage and frequency frequency stability. stability. The combination combination of adaptive adaptive neuics. LCL filters are the most popular for have grid-connected power electronic converters as these these filters the better better Thirugnanam and The of neuThirugnanam et al., 2014) by considering both voltage power electronic converters as filters the ics. LCL filters are the most popular for have grid-connected and frequency stability. The combination of adaptive neural network (ANN) and adaptive neural fuzzy inference power electronic converters as these filters have the better attenuation capability of switching switching frequency harmonics ral network (ANN) andThe adaptive neural offuzzy inference frequency stability. combination adaptive neuattenuation capability of frequency power electronic converters as these filters have harmonics the better and ral network (ANN) and adaptive neural inference system (ANFIS) is used used in (Kaushal (Kaushal andfuzzy Verma, 2014) attenuation capability frequency and lower lower cost cost (Liu et et of al.,switching 2009; Shen Shen et al., al., harmonics 2010). An system (ANFIS) is in and Verma, 2014) network (ANN) and adaptive neural fuzzy inference and (Liu 2009; et 2010). An ral attenuation capability ofal., switching frequency harmonics (ANFIS) is used (Kaushal and in Verma, 2014) to control control both active active andin reactive power V2G appliappliand (Liu et in al., 2009; Shen et2014b) al., 2010). An system LCL lower filter is iscost considered (Mahmud et for to both and power V2G (ANFIS) is used inreactive (Kaushal and in Verma, 2014) LCL filter considered (Mahmud et al., al., for gridgridand lower cost (Liu et inal., 2009; Shen et2014b) al., 2010). An system control both active and reactive power in V2G appliLCL filter is considered in (Mahmud et al., 2014b) for grid- to LCL filter is considered in (Mahmud et al., 2014b) for grid- to control both active and reactive power in V2G appli-
Copyright © 2015, 2015 529 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2015 IFAC IFAC 529 Hosting by Elsevier Ltd. All rights reserved. Copyright 2015 responsibility IFAC 529Control. Peer review©under of International Federation of Automatic Copyright © 2015 IFAC 529 10.1016/j.ifacol.2015.12.434
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cations where the control of reactive power ensures the voltage stability. These intelligent controllers (both fuzzy and ANN with ANFIS) provide good performance in terms of power sharing but the power quality issues have not been taken into account. Moreover, the fuzzy controllers have the limitations of capturing full dynamics of V2G systems and require more fine tuning before making them operational (Khayyam et al., 2012). The shortcomings of intelligent controllers can be overcome by considering model-based controllers which require a dynamical model of V2G systems. A static model of V2G system is proposed in (Madawala and Thrimawithana, 2011) where a proportional integral (PI) controller is used for V2G applications. However, a dynamical model-based controller will provide better solution for V2G applications in term of power sharing and power quality enhancement. Since the major part of a V2G system includes a battery energy storage system (BESS), the mathematical model can be developed by incorporating a BESS model along with a grid-connected converter model. Based on this concept, the dynamical model of a V2G system has been developed in (Mahmud et al., 2014a) and a nonlinear feedback linearizing controller is designed for appropriate power (both active and reactive) sharing. However, the dynamics of the filter is not considered in the development of V2G systems. This paper aims to design a feedback linearizing controller for V2G system by considering the dynamics of an LCL filter which is connected at the output of the inverter. The controller is designed based on the partial feedback linearization of V2G system models as the V2G system with an LCL filter is partially linearized which is also discussed in this paper. Finally the performance of the proposed controller is tested on a residential V2G applications to illustrate the effectiveness as compared to that of as presented in (Mahmud et al., 2014a) where no LCL filters are used. 2. MODELING OF V2G SYSTEMS WITH LCL FILTERS A V2G system comprises a BESS, a voltage source converter (VSC), an LCL output filter, connecting lines, and a grid supply point as shown in Fig. 1. The battery model, used in this paper, is developed based on the electrochemical phenomenon as presented in (Ceraolo, 2000). Based on the equivalent circuit diagram of a V2G system as shown in Fig. 1, the dynamical model of V2G system can be developed in a similar manner as presented in (Mahmud et al., 2014a) by simply applying the circuit theory. If Kirchhoff’s current law (KCL) is applied at the battery of EV where the resistor and capacitor are connected together, then it can be written as dVC1 (1) dt where Idc = mii is the output DC current of the battery, m represents the switching signal of the converter which is a function of modulation index and firing angle, I1 is the current flowing through the resistor R1 , C1 is the capacitor, VC1 is the voltage across both C1 and R1 as Idc = I1 + C1
530
they are connected in parallel which implies VC1 = I1 R1 and simplifies equation (1) as 1 dI1 (2) = (mii − I1 ) dt τ1 where τ1 = R1 C1 is the time constant of the battery. If Kirchhoff’s voltage law (KVL) is applied at the first loop of the inverter output, the following relationship will be obtained: R vdc vC dii (3) = − ii + m − dt L1 L1 L1 where R is the line resistance, ii is the input current to the filter, and L1 is the filter inductance. Again by applying KCL at the node where the filter capacitor C is connected, it can be written as 1 dvC (4) = (ii − io ) dt C where vC is the voltage across the filter capacitor and io is the output current of the filter. Finally, by applying KVL at the output loop of the filter; it can be written as 1 dio (5) = (vC − e) dt L2 where L2 is the filter inductance and e is the grid voltage. Equations (2)–(5) represent an instantaneous model of the V2G system with an LCL filter. For the purpose of controller design, equations (2)–(5) need to be written in the dq-frame which can be done in the same way as presented in (Mahmud et al., 2014a) and in this case, the V2G system can be written as 1 I˙1 = (Md Iid + Mq Iiq − I1 ) τ1 R vCd vdc + Md I˙id = − Iid + ωIiq − L1 L1 L1 R vCq vdc Iiq − + Mq I˙iq = −ωIid − L1 L1 L1 1 (6) v˙ cd = ωvcq + (Iid − Iod ) C 1 v˙ cq = −ωvcd + (Iiq − Ioq ) C 1 (vCd − Ed ) I˙od = ωIoq + L2 1 (vCq − Eq ) I˙oq = −ωIod + L2 where the subscripts d and q denote the corresponding variables in d- and q-frame, respectively. Since the paper is aimed to design a controller for the V2G system used in a residential area, the converter model is considered as a single-phase. In this case, the active and reactive power delivered into the grid can be written as P = Eq Ioq
(7) Q = Eq Iod Therefore, the injection of active and reactive power in V2G systems can be controlled by controlling Ioq and Iod , respectively. However, it is essential to analyze the feedback linearizability of V2G systems which is shown in the following section.
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Im
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C1 R1
+
Em
R0
R
Idc
ii
+
I1
L1
vC
io
+ e
C
Grid Supply Point
_
_
_ Battery of EV
L2 +
vdc
531
LCL Filter
Converter
Fig. 1. V2G system with LCL filter 3. FEEDBACK LINEARIZABILITY OF V2G SYSTEMS
degree of the system. To calculate the relative degree corresponding to the first output Iod , lets start with
The V2G system model as represented by equation (6) has two inputs (Md and Mq ) and two outputs Ioq and Iod . Therefore, the mathematical model of V2G system can be represented by the following generalized equation of nonlinear systems:
Lg h1 = Lg L1−1 Iod = 0 f
y1 = h1 (x)
Since = 0, it is essential to proceed one step further. To do that, it is essential to obtain the following: 1 (vCd − Ed ) L2 which in turn helps to calculate L2−1 Iod = ωIoq + f
x˙ = f (x) + g1 (x)u1 + g2 (x)u2 (8)
y2 = h2 (x) where
I 1
Iid Iiq x= vcd , vcq Iod Ioq
I
id
τ1 vdc L1 g(x) = 0 0 0 0 0
(9)
Lg L1−1 Iod f
Lg Lf h1 = Lg L2−1 Iod = 0 f
(10)
(11)
From equation (11), it can be seen that Lg L2−1 Iod = 0 f which requires to move one step forward and in this case, we need to calculate
1 I1 τ1 R − Iid + ωIiq − vCd + vdc Md L L1 L1 1 vCq vdc R −ωIid − Iiq − + Mq L1 L1 L1 1 , f (x) = ωvcq + (Iid − Iod ) C 1 −ωvcd + (Iiq − Ioq ) C 1 ωI + (v − E ) oq Cd d L2 1 −ωIod + (vCq − Eq ) L2 −
Iod = L3−1 f
2ω ω 1 Iid − µIod + vCq − Eq L2 C L2 L2
(12)
where µ=
�
1 + ω2 L2 C
�
and vdc = D �= 0 (13) L1 L2 C where is D is a constant. This implies that the relative degree corresponding to the first output function is three. At this point, the relative degree corresponding to the second output function needs to be determined. In order to determine the relative degree for the second output, we need to follow the same steps as presented above. At the beginning, we need to calculate Lg L1−1 Iod which is also f zero in this case. Therefore, lets start as follows: Iod = Lg L2f h1 = Lg L3−1 f
Iiq τ1 0 � � � � � � vdc u1 Md Iod , u = = , and y = . L1 Ioq u2 Mq 0 0 0 0
The feedback linearizability of nonlinear V2G systems determines whether the systems are exactly or partially linearized. The V2G systems will be partially linearized if the relative degree of the system is less than the order (which is seven for the considered model) of the system and exactly linearized if relative degree and order are equal to each other. The definition of relative degree can be seen in (Mahmud et al., 2012). Since there are two outputs of the V2G system, it is essential to calculate the relative degree for each output and then sum up together to calculate the total relative 531
L2−1 Ioq = −ωIod + f
1 (vCq − Eq ) L2
(14)
and Lg Lf h2 = Lg L2−1 Ioq = 0 f
(15)
Since Lg L2−1 Ioq = 0, we need to move one step ahead, f i.e., Ioq = L3−1 f and
ω 1 2ω Iiq − µIoq − vCd + Ed L2 C L2 L2
(16)
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vdc = D �= 0 (17) L1 L2 C which implies that the relative degree corresponding to the second output is also three. Therefore, the total relative degree of the system is six which is less than than order of the system and the V2G system is said to be partially linearized. Since the V2G system is partially linearized, partial feedback linearization technique needs to be used to design the controller which is shown in the following section. Lg L2f h1 = Lg L3−1 Iod = f
4. NONLINEAR CONTROLLER DESIGN FOR V2G SYSTEMS WITH LCL FILTERS The design of partial feedback linearizing controller for V2G system with LCL filters requires to follow some steps such as nonlinear coordinate transformation, stability analysis of internal dynamics of V2G systems, and the derivation of final control law. These steps are discussed in the following: • Step 1: Nonlinear coordinate transformation for obtaining partially linearized of V2G systems From Section 3, it can be seen that the relative degree of the V2G system is six whereas the order of the system is seven which means that the seventh order system will be transformed into a sixth order system. Therefore, six new coordinates will be obtained from nonlinear coordinate transformation which can be written as z 1 = L0f h1 = Iod
1 (vCd − Ed ) L2 2ω ω Iid − µIod + vCq − = L2 C L2 = Ioq 1 = −ωIod + (vCq − Eq ) L2 2ω 1 Iiq − µIoq − vCd + = L2 C L2
z 2 = L1f h1 = ωIoq + z 3 =
L2f h1
z 4 = L0f h2
z 5 = L1f h2
z 6 = L2f h2
ω Eq L2
(18)
ω Ed L2
+
v 2 = L3f h2 + Lg L2f h2 Mq
which means that the transformed states become zero as the time is increased, i.e., z i → 0 with i = 1, 2, · · · , 6 as t → ∞. In order to obtain the remaining dynamic equation, the nonlinear coordinate transformation (ˆ z = ˆ φ(x)) needs to be selected in a manner that it satisfies the following condition (Lu et al., 2001): ˆ Lg φ(x) =0
(19)
(21)
The condition as represented by equation (21) will be satisfied for the considered V2G system, if the following nonlinear coordinate transformation is chosen:
ˆ zˆ˙ = Lf φ(x) = L2 Iod f6 + L2 Ioq f7
(23)
As Since Iod = z 1 and Ioq = z 4 , equation (23) can be written as
Lg L2f h1 Md
= −αIid + βIiq − γvCd − ηIoq
Since the V2G system is transformed into a sixth order system, there will be only one remaining dynamic equation whose characteristics need to be investigated. The desired performance of the transformed dynamics is ensured with the linear controllers where the linear control laws are chosen as
1 1 2 2 ˆ (22) φ(x) = zˆ = L2 Iod + L2 Ioq 2 2 With this nonlinear coordinate transformation, the remaining dynamic of V2G system can be written as follows:
z ˙ 4 = z 5 z ˙ 5 = z 6 z ˙ 6 = v 2
v 1 =
• Step 2: Analysis of internal dynamics of V2G systems
lim hi (x) → 0
z ˙ 1 = z 2 z ˙ 2 = z 3 z ˙ 3 = v 1
L3f h1
R L1 L2 C 3ω β= L2 C µ 2ω 2 1 + + γ= L1 L2 C L2 L2 2ω η = µω + L2 C The original control laws (Md and Mq ) of the V2G system can be derived from equation (20). Before obtaining the original control laws, the internal dynamics of the V2G systems, which do not transform through feedback linearization, need to be analyzed and this has been discussed in the following steps. α=
t→∞
Using the nonlinear coordinate transformation as represented by equation (18), the following feedback linearized V2G system can be obtained:
with
where v 1 and v 2 are linear control laws which can be obtained by using any linear technique; α, β, γ, and η are are the constant and function of V2G system parameters which can be written as
γ + Ed + DMd L2
= −βIid − αIiq − γvCq + ηIod +
(20)
zˆ˙ = L2 z 1 f6 + L2 z 4 f7
(24)
zˆ˙ = 0
(25)
Since z i → 0 with i = 1, 2, · · · , 6; equation (24) can be simplified as From equation (25), it can be seen that the internal dynamic of the V2G system with an LCL filter is zero
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and this is different from to that as presented in (Mahmud et al., 2014a). For the considered V2G system, the internal dynamic does not have any effect on the overall stability and thus, partial feedback linearizing control laws can be designed and implemented for this system which is shown in the following step.
20 10
0
The gains have been selected arbitrarily as a function of the reference values and in this paper, the gains are used as 2 2 k1p = 2Iodref , k1i = Iodref , k2p = 2Ioqref , k2i = Ioqref
With the designed controller, the performance of a V2G system in residential applications is evaluated in the following section. 5. SIMULATION RESULTS The proposed V2G structure is considered for a residential application where the key objective is to deliver appropriate active and reactive power sharing into the grid supply point with high power quality. The batteries of EVs need to maintain a minimum state of charge (SOC) for delivering the power into the grid which can be calculated in a similar manner as presented in (Mahmud et al., 2014a; Singhand et al., 2012). In this paper, it is assumed that the residential area consists of 15 PHEVs where each EV has a battery capacity of 4.4 kWh and these EVs are connected to the grid in order to supply a load of 5 KVA. The performance of the controller is evaluated in terms of delivering active and reactive power without any harmonic. When the consumers consume only active power, the controller needs to act in such a way that the V2G system can supply only active power. In this case, the voltage and current will be in phase with each other and 5 kW power will be delivered from the batteries of the V2G system. If the 533
−20 −30 0.2
0.205
0.21
0.215
0.22
0.225 Time (s)
0.23
0.235
0.24
0.245
0.25
Fig. 2. Grid current at unity power factor for V2G system without LCL filter 30 20 10 Current (A)
Equation (26)represents the final control law for the V2G system with an LCL filter which has the capability of delivering both active and reactive power into the grid. Since v 1 and v2 are linear control inputs and can be determined using any linear techniques, PI controllers can be used to achieve the desired control objectives which can be obtained as follows t v 1 = k1p (Iodref − Iod ) + k1i (Iodref − Iod )dt 0 (27) t (Ioqref − Ioq )dt v 2 = k2p (Ioqref − Ioq ) + k2i
0 −10
• Step 3: Formulation of partial feedback linearizing control laws Since the internal dynamic of the V2G system with an LCL filter does not have any affect, the original control law in dq-frame (Md and Mq ) can be obtained from equation (20) as γ 1 v1 + αIid − βIiq + γvCd + ηIoq − Md = Ed D L2 (26) 1 γ v2 + βIid + αIiq + γvCq − ηIod − Eq Mq = D L2
533
30
Current (A)
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0.205
0.21
0.215
0.22
0.225 Time (s)
0.23
0.235
0.24
0.245
0.25
Fig. 3. Grid current at unity power factor for V2G system with LCL filter grid voltage is 220 V, the output current will be 22.72 A. Though the output current with the designed controller does not contain any harmonic as shown in Fig. 3 but the current with the same controller for the V2G system without an LCL filter as presented in (Mahmud et al., 2014a) contains some harmonics which can be seen in Fig. 2. The designed controller will perform in a similar way for all other operating conditions as it is designed in a manner that the linearization of the V2G system with an LCL filter is independent of operating conditions. 6. CONCLUSIONS A partial feedback linearizing controller has been designed for a V2G system with an output LCL filter where the dynamical model has also been developed for similar structures. The partial feedback linearizability of the whole V2G system determines the applicability of the proposed control scheme. Simulation results clearly indicate the superiority of the designed scheme over the existing one where the system model was mainly developed without any filter. Simulation results also reflect the harmonic rejection capability of the proposed V2G system structure along with the designed control scheme. The designed controller enhances the power quality in a much better way as compared to the existing controller. Since feedback linearization is sensitive to the variations in system parameters, future works will consider these parameter variations into the controller design. REFERENCES Ceraolo, M. (2000). New dynamical models of lead-acid batteries. IEEE Trans. on Power Systems, 15(4), 1184– 1190.
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Das, R., Thirugnanam, K., Kumar, P., Lavudiya, R., and Singh, M. (2014). Mathematical modeling for economic evaluation of electric vehicle to smart grid interaction. IEEE Transactions on Smart Grid, 5(2), 712–721. Datta, M. (2014). Fuzzy logic based frequency control by V2G aggregators. In 2014 IEEE 5th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 1–8. Datta, M. and Senjyu, T. (2012). Fuzzy control of distributed PV inverters/energy storage systems/electric vehicles for frequency regulation in a large power system. IEEE Transactions on Smart Grid, 4(1), 479–488. Fernandez, L.P., Roman, T.G.S., Cossent, R., Domingo, C.M., and Frias, P. (2011). Assessment of the impact of plug-in electric vehicles on distribution networks. IEEE Transactions on Power Systems, 26(1), 206–213. Galus, M.D., Zima, M., and Andersson, G. (2010). On integration of plug-in hybrid electric vehicles into existing power system structures. Energy Policy, 38(11), 6736–6745. Kaushal, A. and Verma, N. (2014). Implementation of vehicle to grid concept using ANN and ANFIS controller. In 2014 IEEE 9th Conference on Industrial Electronics and Applications (ICIEA), 960–965. Khayyam, H., Ranjbarzadeh, H., and Marano, V. (2012). Intelligent control of vehicle to grid power. Journal of Power Sources, 201, 1–9. Liu, F., Zhou, Y., Duan, S., Yin, J., Liu, B., and Liu, F. (2009). Parameter design of a two-current-loop controller used in a grid-connected inverter system with LCL filter. IEEE Transactions on Industrial Electronics, 56(11), 4483–4491. Lu, Q., Sun, Y., and Mei, S. (2001). Nonlinear Control Systems and Power System Dynamics. Kluwer Academic Publishers, Boston. Madawala, U. and Thrimawithana, D. (2011). A bidirectional inductive power interface for electric vehicles in v2g systems. IEEE Transactions on Industrial Electronics, 58(10), 4789–4796. Mahmud, M.A., Hossain, M.J., and Pota, H.R. (2013). Voltage variation on distribution networks with distributed generation: Worst case scenario. IEEE Systems Journal, In Press, 1–8. Mahmud, M.A., Hossain, M.J., Pota, H.R., and Roy, N.K. (2014a). Implementation of vehicle to grid concept using ANN and ANFIS controller. In 2014 IFAC World Congress, 7659–7664. Mahmud, M.A., Hossain, M.J., Pota, H.R., and Roy, N.K. (2014b). Robust nonlinear controller design for three-phase grid-connected photovoltaic systems under structured uncertainties. IEEE Transactions on Power Delivery, 29(3), 1221–1230. Mahmud, M.A., Pota, H.R., and Hossain, M. (2012). Dynamic stability of three-phase grid-connected photovoltaic system using zero dynamic design approach. IEEE Journal of Photovoltaics, 2(4), 564–571. Papadopoulos, P., Skarvelis-Kazakos, S., Grau, I., Cipcigan, L.M., and Jenkins, N. (2012). Electric vehicles’ impact on British distribution networks. IET Electrical Systems in Transportation, 2(3), 91–102. Shen, G., Zhu, X., Zhang, J., and Xu, D. (2010). A new feedback method for PR current control of LCL-filterbased grid-connected inverter. IEEE Transactions on 534
Industrial Electronics, 57(6), 2033–2041. Singhand, M., Kumar, P., and Kar, I. (2012). Implementation of vehicle to grid infrastructure using fuzzy logic controller. IEEE Transactions on Smart Grid, 3(1), 565–577. Thirugnanam, K., Joy, T.P.E.R., Singh, M., and Kumar, P. (2014). Modeling and control of contactless based smart charging station in V2G scenario. IEEE Transactions on Smart Grid, 5(1), 337–348. Appendix A. SYSTEM PARAMETERS Battery Parameters: R1 =0.4 mΩ, τ1 =7200 s, R0 =2 mΩ Grid Parameters: Grid voltage (rms)=220 V, Frequency=50 Hz, R=0.1 Ω, L=10 mH