40 CPSS TRANSACTIONS ON POWER ELECTRONICS AND APPLICATIONS, VOL. 6, NO. 1, MARCH 2021
Brayton-Moser Passivity Based Controller for Electric Vehicle Battery Charger
Kumari SHIPRA, Rakesh MAURYA, and Shambhu N. SHARMA
Abstract—In this paper Brayton-Moser passivity-based control I0 Output current, A. (BM-PBC) methodology is developed for an on-board battery is Input source current, A. charger for plug-in electric vehicles(PHEVs). The main features of L Inductor, mH. this electric vehicle (EV) charger include improved power quality, reduced filter size and voltage stress across the switches and fast R Load resistor, Ω. dynamic response. In this paper, a dynamic model of the three-level Ri Series damping injection.
(TL) boost power factor correction (PFC) converter is developed Vd Desired output voltage, V. using the Brayton-Moser formulation. Then, the Brayton-Moser vc1,vc2,vc Capacitor voltage, V. based control technique is designed by injecting a virtual resistor vcd Desired average capacitor voltage, V. in series with the input inductor. Further, the stability analysis of V Peak value of input voltage, V. the proposed controller is also carried out using energy balance m approach. To improve the dynamic performance and reduce the V0 Output voltage, V. steady state error, a PI controller is integrated with the aforesaid vs Input voltage, V. ~ ~ controller. Therefore, the controller comprises of BM-PBC and i L , v c Error state variables. the PI controller is implemented for the TL boost PFC converter ω Angular frequency. as a battery charger and its performances are investigated under σ1 , σ2 , σ Duty ratio. various operating modes with the help of MATLAB/Simulink. P Mixed potential function. Furthermore, power quality of charger is assessed by monitoring G Content energy. source current total harmonic distortion (THD) under different operating conditions. It is also observed that the proposed system J Co-content energy. provides THD less than 5% in source current which satisfies IEC PRi Series dissipation factor.
61000-3-2 Class C standard. The performance of the aforesaid PGi Parallel dissipation factor. controller is also compared with the conventional PI controller. kp , ki Gain of PI controller. In order to validate the proposed controller, a prototype model of EL Euler-Lagrange. same specifications is tested in hardware in loop and obtained test PBC Passivity-based controller. results are also presented. BM Brayton-Moser. Index Terms—Brayton-Moser, mathematical modelling, TL Three-level. passivity-based control, three-level boost converter. EV Electric vehicle.
Nomenclature I. Introduction
C1,C2,C Capacitor, µF. LUG-in electric vehicles (PHEVs) are one of the sustaina- E(t) Rectified input voltage, V. Pble mean of transportation as compared to internal E.f Energy function. combustion engine based automobile due to various advantages Ef Derivative of Ef. such as low transportation cost, low maintenance, high
Gi Parallel damping injection. efficiency, and environmentally friendly [1], [2]. For successful
Id Desired current, A. implementation of PHEVs, the EVs charger is playing key role
iL Inductor current, A. for charging EVs battery and therefore efficient battery charger along with improved power quality features, are the main iLD Desired average inductor current, A. requirements in view of large penetration of PHEVs in electrical power grid. According to guidelines prescribed by IEEE STD 519-2014 and IEC 61000-3-2, the power factor should be more Manuscript received February 29, 2020; revised September 18, 2020; accepted December 23, 2020. Date of publication March 30, 2021; date of than 0.9 and total harmonic distortion (THD)in source current current version March 12, 2021. should be less than 5% for any single phase system [3]. In view All authors are with the Department of Electrical Engineering, Sardar of aforesaid regulation, several EVs charger as power factor Vallabhbhai National Institute of Technology, Surat 395007, India (e-mail: correction (PFC) converters are reported in literature whose [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.24295/CPSSTPEA.2021.00004 operations mainly governed by good design of power circuit K. SHIPRA et al.: BRAYTON-MOSER PASSIVITY BASED CONTROLLER FOR ELECTRIC VEHICLE BATTERY CHARGER 41 and its controller. The boost PFC converter is one of converter rate of flow of energy into the system) against disturbances. which has been extensively used as PFC in design of general The EL and the port controlled Hamiltonian based passivity purpose power supply because of simple circuit, allows low- control technique are very powerful and robust for switched distorted input currents along with unity power factor [4], [5]. electrical system[13], [24]-[27]. The passivity-based control However, it brings large switching stresses and switching losses theory is implemented to bidirectional buck-boost converter which yields low efficiency. Hence, a three-level (TL) boost for battery charging application in [28]. An adaptive passivity PFC converter topology has been proposed to reduce stress based control design technique for battery hybrid power source across the switch as well as filter size by adding additional has been proposed in [29]. A new concept of passivity-based capacitor, diode and switch in existing circuit [6], [7]. controller known as Brayton-Moser has overcome the problem Design efficient controller requires accurate mathematical of selection of damping factor unlike EL based PBC controller. modelling of the system. In the mid-seventies, the Middlebrook Additionally, the Brayton-Moser based controller requires and Ćuk was first offered a modelling of the switched controlled variables which are directly expressed in physical regulated DC-DC power converter [8]. The Euler-Lagrange measurable variables like current and voltage in switched (EL) formulation of a boost, a buck-boost and a fly-back electrical network while the EL and the Hamiltonian have converter are discussed in [9],[10]. In [11], the Lagrangian physical variables charge or flux to control current and voltage dynamics approach is used for modelling of a Ćuk, a three- of system. The concept of the Brayton-Moser based controller phase boost and a coupled-inductor Ćuk converters. The EL for switched electrical systems is reported in [30]-[32]. based modelling approach of DC-DC power converter with In this paper, a Brayton-Moser passivity-based controller has non-ideal switches including parasitic is presented in [12]. been developed for an on-board battery charger using the TL The EL modelling of the multivariable of the boost converter boost converter to achieve well-regulated voltage and current constituted by the cascaded connection is also discussed in [13]. along with nearly unity power factor operation while charging There is drawback of the EL as it is not suitable for non-ideal EV battery. The TL boost converter has an additional switch, switches, diodes, transformers, and isolation transformers etc. diode, capacitor and operation of its switches are shifted by In [13], the Hamiltonian dynamics approach are discussed for 180° out of phase. Due to these additional elements and its modelling of boost, Ćuk, fly-back for ideal switches and also interleaved operation, the switch stress as well as filter size are for non-ideal switches and diodes. A mathematical formulation reduced considerably. for switched electrical networks has been discussed by Brayton This paper is structured in the following manner. Section and Moser (1964) in [9]. In this formulation, the current and I describes the brief introduction of the TL boost converter, voltage are obtained variables, so controller can directly use obtained variables as a measured variable. This is also suitable PFC and PBCs. The mathematical modelling of the TL boost for non-ideal switches, diodes and transformers etc. converter using the Brayton-Moser formulation is carried out There are various linear and non-linear control methodologies in Section II. It also covers brief description of circuit and reported in literature which is designed to control the its operational modes under different switching states. The switched electrical system against dynamic variation [14]- Brayton-Moser equation for electrical circuit is also review [18]. Generally, linear controllers like (P, PI, PID) have been in Section II. Section III narrates the control topology of the widely used to control the converters as discussed in[14], but Brayton-Moser based PBC for the TL boost converter along these controllers have highly unpredictable tuning problem with analysis of stability. Section IV presents simulation of controller parameters. So, these controllers are not suitable study and its test results of the proposed converter for battery and user friendly. Recently, many non-linear controllers load constant current (CC) and constant voltage (CV) mode. such as sliding mode control, fuzzy logic control (FLC) etc. Concluding remarks are given in Section V. are reported in [18], [19]. Several control techniques have been proposed for controlling the switched electrical system II. Mathematical Modeling of the TL Boost PFC to charge EVs battery [20]-[22]. A conventional PI control Converter technique is highly used as it is simple to implement [20]. A schematic diagram of TL boost PFC converter with In [21], the approximate rule based FLC technique has been the Brayton-Moser passivity-based controller is depicted in implemented to achieve battery charging and discharging Fig. 1. The proposed system is employed for charging the applications. A non-linear model predictive controller for electric vehicle battery under CC and CV modes. The detailed battery charging application is discussed in [22]. mathematical analysis and operation are carried out in the Recently, power shaping based passivity-based controllers following subsections. (PBCs) have been widely used in several research areas such as robot arms, induction motors, switched power converters A. Topology etc.[23]. In order to achieve equilibrium stability, a virtual resistor is added as a damping factor in power shaping The power circuit of TL boost PFC converter along with the passivity based controller. So that the system becomes passive BM-PBC is presented in Fig. 1. It consists of a single-phase (an increase of the storage energy should be less than the diode bridge rectifier (DBR), TL boost converter, battery load 42 CPSS TRANSACTIONS ON POWER ELECTRONICS AND APPLICATIONS, VOL. 6, NO. 1, MARCH 2021
i L I0 S1 TS /2 S1 TS /2 TS TS vL ic1 D S2 S2 S1 1 vc1 v v v C1 L1 L2 L1 vL2
vs E(t) R V0 i i iL1 L2 I iL1 iL2 S c2 L1max I 2 v I L1max I C2 c2 L1min L1min iL D2 iS1 iS1 DBR v BM-PBC Three-level boost converter v S1 S1 S1 vs σ iS2 iS2 iL Td vS2 S2 vS2
iD1 iD1 Fig. 1. Schematic diagram of a TL boost PFC converter. iD2 iD2 σT and a PBC as an on-board battery charger for CC/CV charging t = 0 σT σT t(time) t = 0 s σTs t(time) s s ķ ĸ Ĺ ĺ of EV battery. The proposed TL boost converter is derived Mode ķ ĸ Ĺ ĺ Mode TS /2 TS TS /2 TS from conventional boost DC-DC converter by splitting output (a) (b) capacitor (C) into output capacitors (C1, C2), diode (D) into Fig. 2. Switching waveform of the TL boost converter over one switching diodes (D1, D2) and switch (S) into switches (S1, S2) as shown cycle for (a) and (b) . in Fig. 1. L D L D A single-phase AC supply is connected to a DBR to get iL 1 I0 iL 1 I0 + v - i + v - i rectified voltage which act as input voltage source for TL boost L c1 L c1 + S1 + S1 C v + + C vc1 + converter. The switches are operated in interleaved manner + 1 c1 1 E(t) R v E(t) R v0 0 to achieve reduced ripple contents in passive elements. A ic2 ic2 + S + S v 2 C vc2 2 C c2 BM-PBC methodology is applied to control the closed loop 2 2 i I iL I L D 0 operation of converter as shown in Fig. 1. D2 0 2 (a) (b) L D L D iL 1 I0 iL 1 I0 B. Operational Modes i ic1 c1 S + S1 + 1 v C v + + C1 c1 + + 1 c1 Prior to steady-state analysis of the proposed converter, E(t) R v0 E(t) R v0 i ic2 + few assumptions are made such as ideal passive elements and c2 + S v S2 vc2 2 C c2 C2 2 switching devices. It is also assumed that for a given sampling i i I L D I0 time (T ), supply voltage (v ) remains constant. The duty cycle L 0 2 s s (c) (d) σ(t) varies in each sample either σ(t) < 0.5 or σ(t) > 0.5 during each sampling interval as instantaneous value of rectified Fig. 3. Equivalent circuit of the TL boost converter under various operating modes: (a) mode 1, (b) mode 2, (c) mode 3 and (d) mode 4. voltage E(t), keeps on changing. For one sampling time Ts, the switch is on for σTs and off for (1-σ)Ts period as depicted in n×n m×m Fig. 2. Depending upon the switching state of switches (S1, S2), The matrices L(iL)∈R and C(vc)∈ R are the inductance four operating modes are identified which repeat several times and capacitance matrices respectively. The mixed-potential in one cycle of the line frequency (i.e., 50 Hz). The waveforms function P is: dP = dG - dJ, where G and J are content and of voltage and current of circuit elements are depicted in Fig. 2. co-content energy function respectively, dG =
dJ =
conducting and switch (S2) is off as shown in Fig. 3(a) and m where iL ∈ R″ is the input inductor currents, vc ∈ R is the correspondingly duty functions are σ1 = 1 and σ2 = 0. Hence, capacitor voltages and P: Rnxm is mixed-potential function. the MPF for switch position (1, 0) is given below: K. SHIPRA et al.: BRAYTON-MOSER PASSIVITY BASED CONTROLLER FOR ELECTRIC VEHICLE BATTERY CHARGER 43
ˈ
˄ ˅ (4)
ˈ
Mode 2: In this mode, switches are at position (0, 1), when (5) switch (S1) is off and switch (S2) is conducting and the diodes Assuming iL, vc1 and vc2 as state variables, (3)-(5) are (D1, D2) are in forward and reverse biased respectively as rearranged in the matrix-form as given below: shown in Fig. 3(b). In this case the duty functions are σ1 = 0 and σ2 = 1. Hence, MPF for switch position (0, 1) is given below:
˄ ˅
Mode 3: In this case, both the switches (S1, S2) are III. BM Passivity Based Controller conducting and diodes (D , D ) are reverse biased as shown 1 2 In this section, the BM-PBC based controller is developed in Fig. 3(c) and correspondingly duty functions are σ1 = σ2 = 1. Hence, MPF for switch position (1, 1) is given below: for the TL boost PFC converter to charge the EVs battery under CC and CV modes along with improved power factor features at AC supply side. ˄ ˅ A. BM Model of the TL Boost PFC Converter In order to control the TL boost converter, the duty ratio
of both switches (S1, S2) are same i.e., σ1 = σ2 = σ, but phase- Mode 4: In this case, both switches are non-conducting shifted by 180°. The measured and controlled variables of the proposed system is output voltage V0 which is average of vc. and diodes (D1, D2) are forward biased as shown in Fig. 3(d) So, the new average state variables can be defined as vc = vc1 + and correspondingly duty functions are σ1 = σ2 = 0 . The MPF for switch position (0, 0) is given below: vc2. Let C1 = C2 = 2C. The new equivalent state-space equation of the proposed system with new state variables (iL, vc) as derived by the Brayton-Moser formulations is given as:
˄ ˅ (6)
Now, above written MPFs for all four possible switching positions can be re-written in terms of switching functions The above average state-space equation can be written in the BM form as given below: (σ1 , σ2 ) as given below:
(2) (7) where P(σ1 , σ2 ) (i , v , v ) is the MPF for the switch position (σ , L c1 c2 1 The desired trajectories of the average state variables are σ ). From (1) and (2), partial differentiation of the above MPF 2 as follow: is done with respect to each variable and obtain following state equations:
ˈ (8)
(3) 44 CPSS TRANSACTIONS ON POWER ELECTRONICS AND APPLICATIONS, VOL. 6, NO. 1, MARCH 2021
where iLd, vcd, are the desired trajectory for the average inductor From [12], the direct control of output voltage does not current and average output voltage for one switching cycle achieve stability point. Hence an indirect control can be applied ~ respectively. The error trajectory of the state variables as iL = to achieve stability point and correspondingly achieve desired ~ iL - iLd and vc = vc - vcd, are obtained from (7) and (8). The error objective. Here, the objective of the control design is to charge dynamics are described as given below: the EV battery in CC and CV mode along with improved quality of source current with low THD. To achieve nearly unity power factor, the input inductor current should follow the rectified sinusoidal source voltage of same frequency and same phase i.e.,
(9) iLd = Id |sinωt|. Id is the desired input inductor current and Id = Vm/(1 2 - σ) R. Vm is the maximum voltage of input source voltage.
C. Controller Design A series and parallel damping dissipation factors are added to the above error dynamics equations which yields below: In PBC strategy, the energy of the system is re-shaped so that a control function can be obtained. The energy re-shaping can be done by injecting virtual damping into the system. i A virtual damping factor may be inserted in series with the input inductor or in parallel with the output capacitor. Both (10) methodologies (series and parallel) are discussed here.
i 1)Series Damping Injection
In this methodology, a virtual damping factor Ri is inserted in series with the input inductor to modify the energy of the ~2 ~2 where PR = Rii L /2 and PG = Givc /2 are the injected dissipation i i proposed system. Putting PGi = 0, in (10), then the obtained terms. Ri and Gi are the injected series damping with the closed loop dynamics is: inductor and injected parallel damping with the capacitor respectively.
B. Stability Analysis (15) Let a positive definite energy function Ef of the proposed system is created as:
(11) Subtracting (15) from (7), the closed loop dynamics could be ~ ~ From (11), Ef = 0 only when iL = 0 and vc = 0 or else Ef > 0 written as:
The derivative of Ef , is given below:
. (12) (16) ~ ~ The error dynamic (10), Li L and C vc can be represented as:
From above (16), the closed loop dynamics can be described (13) as:
Then, inserting (13) into (12), we get (14): (17)
(14)
In practical circuit, R and R > 0. Then, from (14), derivative of Hence, to control the two objectives of the system, let iLd = Id i ~ ~ Ef , is always negative unless iL = 0 and vc = 0. Hence from (11) |sinωt| and vcd = Vd. and (14), the system is stable. After solving (17), we get control law is as given below: K. SHIPRA et al.: BRAYTON-MOSER PASSIVITY BASED CONTROLLER FOR ELECTRIC VEHICLE BATTERY CHARGER 45
i V e(t) i L e(t) s vs Ld σ Ri I /V d m d L (18) dt 1 σ S1 1 1/C 1/S new i V Ld Cd T [ ] σ d V S2 V 0 1/R ref VCd Mode selector PI controller In this controller, the regulation scheme based on series CC/CV mode I SOC damping injection. So, the duty ratio is influenced due ref I0 to series damping factor as the duty ratio depends on the several state variables. From [30], for selection of series Fig. 4. Schematic block diagram of Brayton-Moser based passivity controller. damping factor Ri there should be satisfied the following condition: In this controller, the regulation scheme depends on parallel damping factor. So, the duty ratio is influenced due to parallel damping factor. From [30], for selection of parallel damping
factor Gi there should be satisfied the following condition:
For all 0 < δ <1 . i
2)Parallel Damping Injection For all 0 < δ < 1. In this methodology, to re-shape the energy of the system, In order to obtain desired objective, the controller is parallel damping factor Gi is inserted in parallel with the output designed in which damping factor is injected in series with capacitor. Putting PRi = 0 in (10), the closed loop dynamics can the input inductor and in parallel with the capacitor. But be rewritten as below: here, the series damping injected controller is implemented only because a load is already connected in parallel to the capacitor and parallel damping injected controller is not appropriate for PFC. To improve the dynamic performances of the aforesaid (19) controller, a PI controller is integrated with the conjunction to the aforesaid controller. Due to the addition of the PI controller, the steady-state errors easily eliminated, and the system quickly stabilizes. So, after adding a PI controller in parallel to the aforesaid controller a new control law is Subtracting (19) from (7), the closed loop dynamics could be obtained, i.e., written as: (23)
where kp , ki are the gain of the PI controller and e(t) = Vref - - (20) V0 , the output voltage error in CV mode and e(t) = Iref I0, the output current error in CC mode.
IV. Results and Discussions From above (20), the closed loop dynamics can be described A Simulink model of the proposed BM-PBC controller for the TL boost PFC converter, rated for 2.8 kW is developed as: using the Simulink and the Sim Power System toolbox of MATLAB. The specifications of system parameter include
AC input supply voltage (vs): 230 V, 50 Hz inductor (L): 6 (21) mH, capacitors (C1, C2): 2500 μF with switching frequency i of 5 kHz. The proposed controller is used to charge a lithium- ion battery of rated capacity 35 Ah, with nominal voltage of 345 V under CC and CV modes. In CC mode, battery starts Hence, to control the two objectives of the system, let i = Ld charging with state of charge (SOC) of 30% at 7 A current load Id |sinωt| and vcd = Vd After solving (21), we get control law i.e., C/5 rate and in CV mode, battery is charged with 70% as given below: SOC at CV of 400 V. The BM PBC control methodology is same for both modes of battery charging, but in CV mode, the output DC voltage of converter is sensed and compare with (22) constant reference voltage of 400 V and in CC mode, the load current is sensed and compare with constant reference current i of 7 A as shown in Fig. 4. Depending upon the SOC of the 46 CPSS TRANSACTIONS ON POWER ELECTRONICS AND APPLICATIONS, VOL. 6, NO. 1, MARCH 2021
200 200 (V ) S
(V ) 0
s 0 v v 200 200 20 10
(A ) 0 0 S i (A ) s i 20 10 410 420
400 (V ) 0 400 (V ) v
0 390 v 380 380 10 6 4 (A ) 0 (A ) 7 I
0 2 I 4 0 20 10 (A ) L
i 5 (A ) 10 L i 0 0 410 390
380 (V ) 400 B (V ) v
B 370 v 360 390 4 0
(A ) 2 B I (A ) 7 4 B I 6 10 30.055 70.03
SOC(%) 70.028 SOC(%) 30.05 1.8 1.82 1.84 1.86 1.88 1.9 1.92 1.94 1.96 1.98 2 2 2.02 2.04 2.06 2.08 2.1 2.12 2.14 2.16 2.18 2.2 time(s) time(s) (i) (i) 200 200 (V ) (V ) 100 sw1 sw1 100 v v 0 0 8 20 (A ) (A ) 10 4 sw1 sw1 i i 0 0 200 200 (V ) (V ) 100 100 sw2 sw2 v v 0 0 20 8 (A ) (A ) 10 4 sw2 sw2 i i 0 0 2.034 2.0345 2.035 2.0355 2.036 2.0365 2.037 2.035 2.0355 2.036 2.0365 2.037 2.0375 time(s) time(s) (ii) (ii) 100 100 10 10 Fundamental (50Hz)=17.72,THD=4.40% Fundamental (50Hz)=11.61,THD=4.68% (A ) (A )
S 0 50 S 0 50 i i 10 10 0 0 2 2.02 2.04 2.06 2.08 0 200 400 600 800 1000 2 2.02 2.04 2.06 2.08 0 200 400 600 800 1000 time (s) Mag (% of Fundume ntal) freq.(Hz) time (s) Mag (% of Fundume ntal) freq.(Hz) (iii) (iii) (a) (b)
Fig. 5. The steady state waveforms feeding battery load with the BM-PBC (i) vs, is, V0, I0, iL, VB, IB, SOC, (ii) vswl, iswl, vsw2, isw2, (iii) harmonic spectrum of supply current of converter, under (a) CC mode and (b) CV mode. battery, aforesaid modes are selected by mode selector block. charged in CC mode with 30% of SOC and after some time The steady state and dynamic performances of the aforesaid when SOC reached to,70%-80%, the converter operation is controller are investigated for battery load under both CC and shifted to CV mode. Fig. 5 depicts steady state response for CV mode and obtained results are discussed in Figs. 5 and 6. the BM-PBC of the TL boost PFC converter feeding battery load under CC and CV mode at source voltage (vs): 230 V, 50 A. Simulation Study of the TL Boost Converter Hz Fig. 5(a)(i) and (b)(i) depicts waveforms of source voltage (vs), source current (is), output voltage (Vo), load current (Io),
1)Steady State Performance input inductor current (iL), battery voltage (VB), battery current
The simulation study of the BM-PBC based controller for (IB) and SOC for CC and CV mode respectively. It has been the TL boost PFC converter employed for charging battery observed that in CC mode, the battery has been charged with (35 Ah) under CC mode or in CV mode is carried out with CC of 7 A and in CV mode, CV of 400 V with maintained MATLAB software. As conventional practice, the battery is input PF closed to unity in both modes. Fig. 5(a)(ii) and (b) K. SHIPRA et al.: BRAYTON-MOSER PASSIVITY BASED CONTROLLER FOR ELECTRIC VEHICLE BATTERY CHARGER 47
400 1 500V/ 2 50.0A/53 200V/ 4 .0A/ 344.6 100.0 / Stop 1 100V/ 2 10.0A/ 3 200V/ 4 10.0A/ 950.0 50.00 / Stop 200 1 Vo(100 V/div) 0 (V ) s 200 vs(500 V/div) v 400 2 2 Io(10 A/div) 50 T s i (50 A/div) 1 VB(200 V/div) 0 V0(200 V/div) 3 (V ) s i 50 3 4 420 I0(5 A/div) 4 IB(10 A/div) 400 T (V ) O (i) (ii) V 380 15 (a)
10 1 500V/ 2 20.0A/ 3 200V/ 4 10.0A/ 950.2 10.00 / Stop 1 500V/ 2 5.0A/ 3 200V/ 4 5.0A/ 3.082s 20.00 / Stop
(A ) 5 O 1 I 0 1 vo(500 V/div) 50 vs(500 V/div)
2 2 Io(5 A/div) (A ) T L
i is(20 A/div) VB(200 V/div) T
0 V0(200 V/div) 3 400 3 4 380
(V ) 4
B 0 IR(5 A/div) 360 I (10 A/div) V 0 (i) (ii) 5 (b) (A ) 10 B 1 200V/ 2 20.0A/ 3 200V/ 4 20.0A/ 957.7 500.0 / Stop 1 200V/ 2 10.0A/ 3 200V/ 4 10.0A/3.082s 500.0 / Stop I 15 vsw1(200 V/div) vsw1(200 V/div)
30.07 1 1 isw1(20 A/div) isw1(10 A/div)
30.05 2 2
SOC (%) 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 vsw2(200 V/div) vsw2(200 V/div) time(s) (a) 3 3 4 4 400 T isw2(20 A/div) T isw2(10 A/div) 200 (i) (ii)
(V ) 0 s v 200 (c) 400 10 0 (V )
s Fig. 7. Steady state performance of converter with battery load under (a) CC i 10 420 mode: (i) vs , is ,V0 I0 and (ii) V0 , I0 , VB and IB. (b) CV mode: (i) vs , is ,V0, I0 400
(V ) and (ii) V0 , I0 VB , IB. (c) Voltage and current of switches S1, S2: vsw1 , isw1 , vsw2, O
V 380 isw2 : (i) CC mode and (ii) CV mode. 12 3 (A )
O mode. First, the supply voltage decreased by 10% then I 6 increased by 10% from its nominal value (230 V) at t = 2s (A )
L 10 i and t = 2.5 s respectively. As observed from the simulation 0 420 study, the battery has been charged with CC (7A) in CC 400 mode and with CV (400 V) in CV mode against source (V ) B
V 380 variation. The input source current is purely sinusoidal and 6 in phase with source voltage which demonstrates the unity 3 (A ) B I 12 power factor as presented in Fig. 6. Fig. 6 also show SOC of 70.04 the battery gradually increases in both CC and CV modes.
70.025 SOC (%) 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 B. Test Results of the TL Boost Converter time(s) (b) The real-time validation of the proposed controller is implemented with TL boost converter with the similar Fig. 6. Dynamic response of converter feeding battery load under step decrease parameters as used in the simulation study and its performances in supply voltage by 10% at time t = 2 s and increase 10% from nominal are observed under battery load. The real-time simulator OP- value (230 V) at time instant t = 2.5 s under (a) CC mode and (b) CV mode. 5142 which is FPGA based XC3S5000 series processor, is used to implement Brayton-Moser based PBC controller. A 4-channel also depicts waveforms of voltage across switches (vSW1, Digital Storage Oscilloscope-DSO-X-2004A and a Fluke power vSW2) and switch currents (iSW1, iSW2) for CC and CV mode quality analyzer (43B) are used for measuring and recording the respectively. The fast Fourier transfor (FFT) analysis is also test results. The several test results are obtained while charging done and depicted in Figs. 5(a)(iii) and (b) which indicates, at the EV battery under CC and CV mode and few of them are steady state total harmonics distortion is 3.17% and 4.55% for presented in Figs. 7-9. To monitor the power quality features CC and CV mode respectively which is below 5%, according of supply current under different charging modes, are harmonic to IEEE standard. spectra of source current is recorded using Fluke power quality analyzer (43B) and its results are presented. 2)Dynamic Response Under Input Variations Fig. 6(a-b) depict dynamic performance against source 1)Steady State Response variation of the TL boost converter in CC and CV charging The test performance under steady state of the TL boost 48 CPSS TRANSACTIONS ON POWER ELECTRONICS AND APPLICATIONS, VOL. 6, NO. 1, MARCH 2021
1 500V/ 2 50.0A/53 200V/ 4 .0A/ 706.0 100.0 /Stop 1 100V/ 2 10.0A/ 3 200V/ 4 10.0A/ 654.0 100.0 /Stop 1 500V/ 2 20.0A/53 200V/ 4 .0A/ 2.468s 100.0 /Stop 1 500V/ 2 5.0A/53 200V/ 4 .0A/ 2.92s 100.0 / Stop
1 Vo(100 V/div) 1 1 Vo(500 V/div) vs(500 V/div) vs(500 V/div) o 2 2 Io(10 A/div) 2 2 I (5 A/div) T T is(20 A/div) VB(200 V/div) is(50 A/div) 1 VB(200 V/div) T V0(200 V/div) 3 3 V0(200 V/div) 3
3 4 4 3 4 I0(5 A/div) 4 4 I0(5 A/div) IB(10 A/div) IB(5 A/div)
(i) (ii) (i) (ii) 1 500V/ 2 50.0A/53 200V/ 4 .0A/ 556.0 50.00 /Stop 1 100V/ 2 10.0A/ 3 200V/ 4 10.0A/ 452.0 50.00 /Stop 1 500V/ 2 20.0A/53 200V/ 4 .0A/ 2.216s 50.00 /Stop 1 500V/ 2 5.0A/53 200V/ 4 .0A/ 2.657s 50.00 / Stop
1 Vo(100 V/div) 1 1
1 o vs(500 V/div) vs(500 V/div) V (500 V/div) 2 2 Io(10 A/div) 2 2 Io(5 A/div) T T s is(50 A/div) 1 VB(200 V/div) i (20 A/div) VB(200 V/div) T V0(200 V/div) 3 V0(200 V/div) 3
3 4 3 4 I0(5 A/div) 4 4 I0(5 A/div) IB(10 A/div) IB(5 A/div) T (iii) (iv) (iii) (iv)
1 500V/ 2 50.0A/53 200V/ 4 .0A/ 1.106s 50.00 /Stop 1 100V/ 2 10.0A/ 3 200V/ 4 10.0A/ 950.0 50.00 /Stop 1 500V/ 2 20.0A/53 200V/ 4 .0A/ 2.720s 50.00 /Stop 1 500V/ 2 5.0A/53 200V/ 4 .0A/ 3.152s 20.00 / Stop
1 Vo(100 V/div) 1
vs(500 V/div) vs(500 V/div) 1 Vo(500 V/div) o 2 2 Io(10 A/div) 2 2 I (5 A/div) T T is(50 A/div) s B 1 B i (20 A/div) V (200 V/div) V (200 V/div) T
V0(200 V/div) 3 V0(200 V/div) 3
3 4 3 4 I0(5 A/div) 4 4 0 IB(10 A/div) I (5 A/div) IB(5 A/div) T (v) (vi) (v) (vi) (a) (b)
Fig. 8. Dynamic performance of the converter with battery load under (a) CC mode and (b) CV mode. (i) Waveforms of vs , is , V0 and I0 against supply voltage variations. (ii) Waveforms of V0 , I0 , VB and IB against supply voltage variations. (iii) Waveforms of vs , is , V0 and I0 during supply voltage decrease 10%. (iv)
Waveforms of V0 , I0 , VB and IB during supply voltage decrease 10%. (v) Waveforms of vs , is , V0 and I0 during supply voltage increase 10%. (vi) Waveforms of
V0 , I0 , VB and IB during supply voltage increase 10% .
The dynamic performance against input source variation from 230 V to 207 V are displayed in Fig. 8(a)(iii) and (b)(iii) for CC and CV mode respectively and input source variation from 207 V to 253 V is shown in Fig. 8(a)(v) and (b)(v) for CC and CV
(i) (ii) (iii) (iv) mode respectively. The waveforms of the battery parameters
(a) (VB , IB) are also recorded against input variation and observed satisfactory results. Fig. 9 shows the results of Fluke power analyzer which
provides waveforms and THD of source voltage (vs) and source current (is) with their harmonic spectrums for CC and CV
(i) (ii) (iii) (iv) modes battery charger at source voltage (vs): 230 V, 50 Hz Fig. (b) 9(a)(iii) and (iv) shows the THD of 0.3% and 4.5% in source voltage and source current respectively, under CC mode Fig. 9. Power quality assessment of input supply voltage and source current of battery charger. In CV mode, when the proposed converter the system with battery load under (a) CC mode and (b) CV mode. (i) v and i , s s rated at 1.27 kW is supplied at nominal voltage (230 V), the (ii) P and Q , (iii) harmonic spectrum of i and (iv) harmonic spectrum of v . s s s s observed THD in source voltage is 0.7% and in source current PFC for the BM-PBC in CC and CV charging mode at supply is 3.4% as displayed in Fig. 9(b)(iii) and (iv). As observed from recorded data, the THD for both loads are less than 5%, which voltage (vs): 230 V, 50 Hz is presented in Fig. 7(a) and (b). Fig. 7(a) shows the battery is charging with CC (7 A) in CC mode validate the range of the IEEE standard. along with purely sinusoidal input source current and in same The comparative performance of the proposed controller phase with the input supply voltage. Similarly, EV battery is against benchmark conventional PI controller under resistive charging with CV of (400 V) in CV mode along with nearly load is depicted in Fig. 10. The efficiency curve under the unity power factor as presented in Fig. 7(b). Fig. 7(c)(i-ii) variation of input voltage and output power is presented in Fig. show the switch voltages (vSW1, vSW2) and switch currents (iSW1, 10(a) and (b) and it is observed that the efficiency of the both iSW2) for both switches, for both modes (CC and CV). controllers are lies in 96%-97%. The THD curve of the input current against input voltage and output power is also observed 2)Test Results Under Battery Load for Dynamic Response and presented in Fig. 10(c)-(d). The THD of the input current The dynamic performance of the TL boost converter with of the proposed controller is less than 10% against dynamics BM-PBC in CC and CV charging mode is depicted in Fig. 8. conditions. The comparative study of the proposed controller K. SHIPRA et al.: BRAYTON-MOSER PASSIVITY BASED CONTROLLER FOR ELECTRIC VEHICLE BATTERY CHARGER 49
100 Proposed controller 100 Proposed controller PI controller PI controller 99 99
98 98 ficiency (%) ficiency (%)
Ef 97 Ef 97
96 96 200 210 220 230 240 250 260 0.8 1.2 1.6 2 Input voltage (V) Output power (kW) (a) (b) 12 14 Proposed controller Proposed controller PI controller PI controller 10 12 ) (%) s ) (%) s i 10 8 8 THD ( 6 THD ( i 6 4 4 200 210 220 230 240 250 260 0.8 1.2 1.6 2 Input voltage (V) Output power (kW) (c) (d)
Fig. 10. Comparative performance curve: (a) efficiency vs. input voltage, (b) efficiency vs. output power, (c) source current THD vs. input voltage and (d) source current THD vs. output power.
TABLE I Comparative Study Against Input Voltage Variation
TABLE II Comparative Study Against Output Power Variation
against benchmark conventional PI controller is also done in observed that the THD is less than 10% for both modes (CC terms of control parameters like peak overshoot, rise time, and CV) against input variation. peak time and settling time against input source and output power variations as presented in Tables I and II respectively. It is observed that the proposed controller BM-PBC achieve V. Conclusion stability point faster than conventional PI controller. The In this paper, the mathematical model of the TL boost PFC performance curve of the aforesaid system with proposed converter is developed using the Brayton-Moser formulation controller is presented in Fig. 11 for both charging mode (CC and then BM-PBC based controller is established. The and CV). Fig. 11(a) and (b) shows the efficiency curve against proposed controller is based on energy modification in which input voltage variation for CC and CV mode respectively. It is its control of energy is done through suitable damping injection observed that efficiency is varying around 96%-97% against by incorporating a virtual resistor in series with the inductor large variation of input voltage in CC mode and for CV mode, or in parallel to the capacitor. The stability analysis is also it is 94%-96%. The plot of THD against input variation is carried out with the help of Lyapunov stability. To improve shown in Fig. 11(c) and (d) for both CC and CV mode. It is the dynamic performance and to reduce the steady state 50 CPSS TRANSACTIONS ON POWER ELECTRONICS AND APPLICATIONS, VOL. 6, NO. 1, MARCH 2021
100 standard and IEC 61000-3-2. It is also observed that design of 98 passivity-based control is simple and robust against dynamic 96 variations. 94 ficiency (%)
Ef 92 References 90 [1] S. S. Williamson, Energy Management Dtrategies for Electric and Plug- 180 200 220 240 260 280 In Hybrid Electric Vehicles. NewYork, NY, USA: Springer, 2013. Input voltage (V) [2] J. Larminie and J. Lowry, Electric Vehicle Technology Explained. (a) Swindon, UK.: John Wiley & Sons, 2012. 100 [3] IEEE Recommended Practices and Requirements for Harmonic Control 98 in Electrical Power Systems, IEEE standard, 519-1992. [4] J. Linares-Flores, H. Sira-Ramirez, J. Reger, and S. Hernandez-Marcial, 96 “A boost unity power factor pre-compensator, ” in 2008 IEEE Power 94 Electronics Specialists Conference, Rhodes, Greece, 2008, pp. 3623– ficiency (%) 3627. Ef 92 [5] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics 90 (2nd ed). New York, NY, USA: Springer,2007. 180 200 220 [6] X. Ruan, B. Li, Q. Chen, S.-C. Tan, and K. T. Chi,“Fundamental Input voltage (V) considerations of three-level DC–DC converters: Topologies, analyses, (b) and control,” in IEEE Transactions on Circuits and Systems I: Regular 12 Papers, vol. 55, no. 11, pp. 3733–3743, Dec. 2008. 10 [7] W.-Y. Choi and S.-J. Lee,“Three-level SEPIC with improved efficiency and balanced capacitor voltages,” in Journal of Power Electronics, vol. ) (%) s 8 16, pp. 447–454, 2016. 6 [8] R. D. Middlebrook and S. Cuk,“A general unified approach to modelling switching-converter power stages,” in 1976 IEEE Power Electronics THD ( i 4 Specialists Conference, Cleveland, OH, USA, 1976, pp. 18–34. 2 [9] D. Jeltsema, “Modeling and control of nonlinear networks: a power-based 200 210 220 230 240 250 260 perspective,” Netherlands, UK, 2005. Input voltage (V) [10] H. A. Yildiz and L. Goren-Sumer, “Lagrangian modeling of DC-DC (c) buck-boost and flyback converters,” in 2009 European Conference on 12 Circuit Theory and Design, Antalya, Turkey, 2009, pp. 245–248. [11] J. M. Scherpen, D. Jeltsema, and J. B. Klaassens, “Lagrangian modeling 10 of switching electrical networks,” in Systems & Control Letters, vol. 48, no. 5, pp. 365–374, Apr. 2003. ) (%)
s 8 [12] R. Ortega, J. A. L. Perez, P. J. Nicklasson, and H. J. Sira-Ramirez, 6 Passivity-Based Control of Euler-Lagrange Systems: Mechanical, st THD ( i 4 Electrical and Electromechanical Applications(1 edition ). UK.:Springer- Verlag London, 1998. 2 [13] G. Escobar, A. J. van der Schaft, and R. Ortega, “A Hamiltonian 200 210 220 230 240 250 260 Input voltage (V) viewpoint in the modeling of switching power converters,” in Automatica, vol. 35, no. 3, pp. 445–452, Mar. 1999. (d) [14] H. Sira-Ramirez, “Nonlinear P-I controller design for switchmode DC- to-DC power converters,” in IEEE Transactions on Circuits and Systems, Fig. 11. Performance curve: efficiency vs. input source voltage under (a) CC vol. 38, no. 4, pp. 410–417, Apr. 1991. mode and (b) CV mode. The source current THD vs. input source voltage [15] B. J. Patella, A. Prodic, A. Zirger, and D. Maksimovic, “High-frequency under and (c) CC mode and (d) CV mode. digital PWM controller IC for DC-DC converters,” in IEEE Transactions on Power Electronics, vol. 18, no. 1, pp. 438–446, Jan. 2003. [16] P. Mattavelli, L. Rossetto, G. Spiazzi, and P. Tenti, “General-purpose errors, a PI controller is integrated in conjunction with the fuzzy controller for DC-DC converters,” in IEEE Transactions on Power proposed controller. The Brayton-Moser based PBC controller Electronics, vol. 12, no. 1, pp. 79–86, Jan. 1997. for TL boost converter is simulated using Matlab software [17] W. Stefanutti, P. Mattavelli, S. Saggini, and M. Ghioni, “Autotuning of digitally controlled DC–DC converters based on relay feedback,” in IEEE and validated through hardware in loop (HIL) using FPGA Transactions on Power Electronics, vol. 22, no. 1, pp. 199–207, Jan. based XC3S5000 series processor of real-time simulator 2007. OP-5142. The proposed system is employed as an on-board [18] S. Baev, Y. Shtessel, H. Biglari, and R. Adhami, “Sliding mode control battery charger to charge the EV battery under CC and CV of a unity power factor AC-to-DC boost converter,” in 2007 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, 2007, pp. modes. It has satisfactory output response under steady-state 2005–2010. and dynamic response and it is observed that the aforesaid [19] H. S. H. Chung, E. P. W. Tam, and S. Y. R. Hui, “Development of a fuzzy passivity-based controller control strategies for the TL boost logic controller for boost rectifier with active power factor correction,” in exhibits good power qualities under different operating 30th Annual IEEE Power Electronics Specialists Conference Record (Cat. conditions. The total harmonic distortion of input source No.99CH36321), Charleston, SC, USA, 1999, pp. 149–154 vol.1. [20] M. Saleh, Y. Esa, Y. Mhandi, W. Brandauer, and A. Mohamed, “Design current is also observed for both charging mode (CC and CV) and implementation of CCNY DC microgrid testbed,” in 2016 IEEE and it is found below 5% which fulfilled the criteria of IEEE Industry Applications Society Annual Meeting, Portland, OR, USA, 2016, K. SHIPRA et al.: BRAYTON-MOSER PASSIVITY BASED CONTROLLER FOR ELECTRIC VEHICLE BATTERY CHARGER 51
pp. 1–7. Kumari Shipra received her B.S. degree in engineer- [21] T. F. Wu, C. H. Chang, and Y. H. Chen, “A fuzzy-logic-controlled single- ing in electrical engineering from the Muzaffurpur stage converter for PV-powered lighting system applications,” in IEEE Institute of Technology, Muzaffurpur, India, in Transactions on Industrial Electronics, vol. 47, no. 2, pp. 287–296, Apr. 2003, and M.E. degree in electrical engineering 2000. with a specialization in control and instrumentation [22] M. Abedi, B. Song, and R. Kim, “Nonlinear-model predictive control from the Delhi College of Engineering (now Delhi based bidirectional converter for V2G battery charger applications,” in Technological University), Delhi, India in 2012. 2011 IEEE Vehicle Power and Propulsion Conference, Chicago, IL, She is currently working toward her Ph.D. degree USA, 2011, pp. 1–6. in electrical engineering at the Sardar Vallabhbhai National Institute of Technology, Surat, India. [23] R. Ortega and M. W. Spong, “Adaptive motion control of rigid robots: a From 2008 to 2014, she was working in Inderprastha Engineering College, tutorial,” in Proceedings of the 27th IEEE Conference on Decision and Ghaziabad, India as an Assistant Professor. Her current research interests include Control, Austin, TX, USA, 1988, pp. 1575–1584, vol.2. the passivity-based controllers, high power factor AC/DC converter and battery [24] R. Ortega, A. van der Schaft, B. Maschke, and G. Escobar, “Interconnec- charger. tion and damping assignment passivity-based control of port-controlled Hamiltonian systems,” in Automatica, vol. 38, no. 4, pp. 585–596, Apr. 2002. [25] H. Sira-Ramirez and M. D. deNieto, “A Lagrangian approach to Rakesh Maurya received his B.Tech. degree average modeling of pulsewidth-modulation controlled DC-to-DC in electrical engineering from the Kamla Nehru power converters,” in IEEE Transactions on Circuits and Systems I: Institute of Technology, Sultanpur, India, in 1998, Fundamental Theory and Applications, vol. 43, no. 5, pp. 427, May 1996. M.T. degree in power electronics and electric drive [26] H. Sira-Ramirez, R. Ortega, and G. Escobar, “Lagrangian modeling of and Ph.D. degree in electrical engineering from the switch regulated DC-to-DC power converters,” in Proceedings of 35th Indian Institute of Technology Roorkee, Roorkee, IEEE Conference on Decision and Control, Kobe, Japan, 1996, pp. India, in 2002 and 2014 respectively. He is currently 4492–4497, vol.4. serving as an Associate Professor in the Department [27] J. M. Scherpen, D. Jeltsema, and J. B. Klaassens, “Lagrangian modeling of Electrical Engineering, Sardar Vallabhbhai and control of switching networks with integrated coupled magnetics,” in National Institute of Technology, Surat, India. In Proceedings of the 39th IEEE Conference on Decision and Control (Cat. last five years, he has published more than 50 research papers in journals of No. 00CH37187), Sydney, NSW, Australia, 2000, pp. 4054–4059, vol.4. international repute particularly IEEE Transactions, IETs-UK and Elsevier, [28] O. D. M. Giraldo, A. G. Ruiz, I. O. Velázquez, and G. R. E. Pérez, Taylor & Francis and many conference papers. His current research interests “Passivity-based control for battery charging/discharging applications include design of switching power converters, high power factor AC/DC by using a buck-boost DC-DC converter,” in IEEE Green Technologies converters, hybrid output converters, improved power quality converters for Conference (GreenTech), Austin, TX, 2018, pp. 89–94. battery charging applications, power quality problems, advanced electric drives [29] M. R. Mojallizadeh and M. A. Badamchizadeh, “Adaptive passivity- and applications of real-time simulator for the control of power converters. He based control of a photovoltaic/battery hybrid power source via algebraic is a member of IEEE and life member of System Society of India. parameter identification,” in IEEE Journal of Photovoltaics, vol. 6, no. 2, pp. 532–539, Mar. 2016. [30] D. Jeltsema and J. M. A. Scherpen, “Tuning of passivity-preserving controllers for switched-mode power converters,” in IEEE Transactions Shambhu N. Sharma received his B.E. degree on Automatic Control, vol. 49, no. 8, pp. 1333–1344, Aug. 2004. from the Government College of Engineering, [31] M. M. J. de Vries, M. J. Kransse, M. Liserre, V. G. Monopoli, and J. M. Rewa (M.P.), India in 1994, M.Tech. degree from A. Scherpen, “Passivity-based harmonic control through series/parallel the Banaras Hindu University (now IIT BHU), UP, damping of an H-bridge rectifier,” in2007 IEEE International Symposium India in 2000, and Ph.D. degree from the Delhi on Industrial Electronics, Vigo, Spain, 2007, pp. 3385–3390. University in 2007. Currently, he is working as a Professor in Electrical Engineering Department of [32] H. Zhou, A. M. Khambadkone, and X. Kong, “Passivity-based control the National Institute of Technology, Surat, India. for an interleaved current-fed full-bridge converter with a wide operating He specialises in the areas of stochastic systems, range using the Brayton-Moser form,” in IEEE Transactions on Power control theory, stochastic differential equations with Electronics, vol. 24, no. 9, pp. 2047–2056, Sep. 2009. applications to electrical and electronic networks. One of his works is known [33] R. K. Brayton and J. K. Moser, “A theory of nonlinear networks. I,” in as a pioneering work in stochastic systems. A stochastic system bears his name, Quarterly of Applied Mathematics, vol. 22, no. 1, pp. 1–33, Apr. 1964. the Sharma Parthasarathy stochastic two-body problems. He has published over 20 journal papers in reputed journal, which include International Journal of Control, Automatica, Royal Society Proceedings, Non-linear Dynamics, Journal of the Franklin Institute, AMC etc. He has also published about 12 papers in international conferences and symposia.