Power Flow Modeling of Wireless Power Transfer for EVs Charging and Discharging in V2G Applications A. A. S. Mohamed, Alberto Berzoy and Osama Mohammed Energy Systems Research Laboratory, Department of Electrical and Computer Engineering Florida International University, Miami, Florida, USA
[email protected]. Abstract— Despite, the large scale introduction of Electric Vehicles (EVs) presents large challenges for the power grid, they can provide services to the power grid which is known as vehicle-to-grid (V2G) applications. A flexible, automatic, and bidirectional charging and discharging system, is essential for the best interaction between EVs and grid. Thus, this paper presents a steady-state harmonic mathematical model for the bidirectional inductive wireless power transfer system for charging and discharging EVs in V2G applications. The proposed model provides an accurate estimation for the system variables under different conditions. A 1.5kW bidirectional wireless system is simulated in MatLab Simulink, and its results are compared with the proposed theoretical model for validation purposes. Keywords— Bidirectional; Electric Vehicle (EV); Power Flow; Steady-state Model; Vehicle-to-grid (V2G); Wireless Power Transfer (WPT).
I.
INTRODUCTION
Over the past decade, several efforts are done to improve conversion and utilization of energy to reduce the dependence on fossil fuel in the field of transportation electrification and electric energy generation. Thus, the future will see increased introduction of renewable energy in power generation and EV in transportation [1]. However, installing the renewable energy sources (RES), especially wind and solar systems, causes stability and power quality issues for the main grid, due to the stochastic nature of the environmental conditions. Also, the large scale introduction of EVs (hybrid or pure battery based) presents large challenges for the power grid [2]. Involving Renewable Energy Sources (RES) for compensating the required demand of EVs is an ideal solution for the power grid [1]. Moreover, the RES with EVs can be used for enhancing the power grid stability and improving its power quality, which is known nowadays by V2G applications. This kind of integration between RES, EVs and grid requires flexible, automatic, simple, safe and reliable charging and discharging system for EVs. Consequently, techniques for charging and discharging of EVs, with emphasis on simplicity, low cost, high efficiency, and flexibility are the main focus of current research. The bidirectional power flow between EVs and grid can be achieved either by wired or wireless connection. Several studies have been conducted which show comparative analysis for the percentage of EV interactivity between the wired and wireless connection [2]–[4]. The studies conclude that the wired connection guarantees about 10% of EV to
interact successfully, while the wireless connection provides about 65% [2]. In the past, many contactless inductive power transfer (IPT) systems with various circuit topologies, compensation strategies and control have been proposed for EV applications [5]. However, these systems cannot be used in V2G applications, which require bidirectional power transfer system to charge and discharge EVs. According to literature, the bidirectional IPT (BD-IPT) systems have been proposed in [6]–[8]. These systems have been developed for aircraft applications and would not be appropriate for V2G applications. A current sourced BD-IPT system for EVs applications has been presented in [9]–[11]. Then, a generalized mathematical model for the same system was presented in [12], [13], and a dynamic multivariable statespace model was presented in [14]. These models shows good results, but still complex and have too much calculations. Different from the presented models, this paper presents a steady-state mathematical model for the energy flow between power grid and EVs. The model is based on the Tmodel representation of the mutual coupling between the circuits. The proposed model shows the effect of the applied control to manage the power transfer. The proposed model is analyzed and compared by means of simulation for verification. I. SYSTEM DESCRIBTION AND INTERACTION. The integration among RES (such as Photovoltaic array), power grid and EVs depends on the point at which all feeding or consuming components are located. This point can be the public grid, as shown in Fig. 1. In this configuration, the Photovoltaic (PV) panel side and the EV side should have a DC-AC unit to be linked with the grid. In consequences, the system shows high cost and low efficiency. However, these disadvantages can be eliminated using the DC bus-connection, as shown in Fig. 2. In this configuration all components are integrated through DC bus and the power flow can be easily and efficiently controlled. Thus, this configuration is considered in this paper.
Fig. 1: Block diagram of system connection with AC bus.
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between the primary and secondary inverter voltages (Vpi and Vsi), and ωr is the angular resonance frequency for both the primary and secondary circuit, which is related to the circuit parameters as given in (2). (2)
Fig. 2: Block diagram of system connection with DC bus.
The PV array is coupled with the DC bus through unidirectional DC-DC converter for providing maximum power point tracking (MPPT) control [16], [17]. The DC bus voltage level is regulated by controlling the bidirectional grid-tie inverter. During the charging mode, the power flows from the PV panel and/or the power grid to the EVs. DC power is converted to high frequency AC power by the primary inverter of the wireless system to supply the primary (track) circuit. The high frequency primary power transfers by induction to the secondary (pick-up) circuit, through a large air-gap. Then, the secondary power is converted to DC by high frequency converter to supply the EV battery. The compensation circuit is essential in the IPT system to provide VAr compensation and unity power factor operation in the primary and secondary side, to minimize the required VA form the supply and maximize the system efficiency [18]. In the discharging mode, the power transfer from the EV and the PV panel to the grid, through the same path.
Fig. 3: The BD-IPT power electronic circuit diagram
II.
where, Lpi and Lsi are the filter inductances of primary and secondary inverters, respectively, Lpc and Lsc are the primary and secondary coils inductances, respectively, and Cp and Cs are the primary and secondary compensating capacitances, respectively. The mutual inductance between the primary and the secondary coils is calculated in terms of the circuit . parameters and the coupling factor (k) as, Due to the linear magnetization characteristics of the air gap, the mutual effect between the coupler circuits can be modeled by the T-model as indicated in Fig. 4. The figure shows the steady state equivalent circuit of parallel-parallel BD-IPT system including the RL filters of the two converters and the resistive losses of the coils.
Fig. 4: BD-IPT equivalent circuit using T-model coupling.
By applying star/delta transformation and simplifying the circuit, the π-model of the system can be obtained, as shown in Fig. 5, where Zp, Zs and Zm are given in (3).
Fig. 5: π-Model equivalent circuit of the BD-IPT.
. .
MATHEMATICAL MODELING OF BD-WPT SYSTEM.
The grid inverter is able to keep the DC bus voltage level constant and to manage the power flow from and to the grid. Thus, for simplicity the grid and the PV side can be represented as DC source (Vdc) and the EV battery as a second DC source (Vb), as shown in Fig. 3. Both the primary and secondary inverter generate periodic square wave voltage (Vpi and Vsi) which can be described using Fourier series analysis as given in (1). ∑ , ,… cos . . sin (1) ∑ , ,… cos . . sin where, n is the number of harmonics, α and β are the phase shift between the switching of the two legs of the primary and secondary converters respectively, δ is the phase shift
. . . .
. where, . .
1 1 . .
. (3)
.
. . .
. .
. .
. . . .
Thus the primary and secondary inverter currents (Ipi and Isi) can be expressed in terms of the voltages Vpi and Vsi using the admittance-model of the equivalent circuit as shown in (4).
.
(4) .
Formulas for calculating the primary and the secondary coil currents (Ipc and Isc) can be obtained by applying KVL on the loops L1 and L2 in Fig. 4 and substituting by (4). Thus the coil currents in terms of Vpi and Vsi and the π-model parameters are described in (5). 1 1
achieve the unity power factor operation as given by (10), while its sign is used to control the power flow direction to charge or discharge the EV as shown in Fig. 7. When Vpi leads Vsi (δ is negative) and the power flows from the primary to the secondary for charging the EV. However, when Vpi lags Vsi (δ is positive) and the power flows from the secondary to the primary for supplying the grid. Thus, for controlling the magnitude of the power flow the angle β is adjusted between 0:180o by the secondary controller (see Fig. 3 and 7).
;
1 1
(5)
where;
, , and
, .
Based on the presented steady state model, the primary and secondary active and reactive power can be calculated as in (6). Also, the charging and discharging efficiency and power factor can be obtained as in (7) and (8), respectively. . (6) . , (7) ,
(8)
| |
In the resonance inductive wireless power transfer system, the power transfer from one side to the other by induction at the resonance condition given in (2). Thus, to get a mathematical formula for the fundamental power flow, the resonance condition given in (2) needs to be applied. Also, the effect of Vpi on Ipi and Vsi on Isi appears only in the higher order harmonics components, thus, for simplification it can be neglected while calculating the fundamental power. Based on these assumptions, a simple formulas for the fundamental component of Ipi (Ipi_1) is given in (7). . _ (9) _ where, Vsi_1 is the fundamental component of Vsi. The active and reactive primary fundamental power model is obtained by substituting by (1), (9) into (6), which is described in (10). . .
. .
.
.
.
. sin
. sin
. sin δ
.
. sin
. sin
. cos
(10)
where, γ is a real number which is very close to unity and is given by (11) (γ equal unity for neglected resistive losses). . (11) Based in (10) the maximum active power transfer occurs when δ = ±90o and α = β =180o. Normally in these system, especially for multiple secondary, the angle α is controlled by the primary controller to keep the primary coil current constant as shown in Fig. 3. The magnitude of δ is kept constant at 90o to cancel the reactive power component and
Fig. 7: Active and reactive power vs. δ at different β.
III.
SIMULATION RESULTS
To verify the proposed theoretical model for BD-IPT system operation, the model is simulated in MatLab script and compared with a simulink model which performed in SimPowerSystems/Simulink MatLab for 1.5 kW BD-IPT system. The system is designed to resonate at 40 kHz and the air-gap length between the primary and secondary coils is 500 mm, which is the case of EV situation. The design parameters of the system under study are indicated in table I. The results from the proposed theoretical model and the comparison are presented and discussed in this section. TABLE I. SYSTEM DESIGN PARAMETERS Parameter Value Parameter Value Lp 20 µH Ls 20 µH Cp 47.22 µF Cs 47.22 µF Rp 20 mΩ Rs 20 mΩ Lpf 20 µH Lsf 20 µH Rpf 20 mΩ Rsf 20 mΩ k 0.25 f 40 kHz
A. For Fundamental Supply Voltages. In this case the harmonics effect are neglected and sinusoidal inverter voltages (Vpi and Vsi) are assumed. This supply condition is applied on both simulation and theoretical model and the system performance is described and compared in this subsection. As mentioned before the direction of power flow is controlled by adjusting the sign of δ while the magnitude is controlled by adjusting α and/or β. Fig. 8 indicates the system performance under full power charging operation (power flow from primary and secondary). This operation is achieved by setting (α = β =180o and δ = -90o). The output of primary and secondary inverters
49.8 49.81 49.82 49.83 49.84 49.85 50
Theo. Ipc
0
Sim. Isc
-50 49.8
Theo. Isc 49.81 49.82 49.83 49.84 49.85 Time (msec) Fig. 8: System performance under full sinusoidal supplies for charging operation (α = β =180o, δ = -90o) (a) primary inverter variables, (b) secondary inverter variables, (c) coils currents.
V , 10*I
pi
200
Sim. V
49.81 49.82 49.83 49.84 49.85
200
pi si
V , 10*I
Sim. I
-200
si
Sim. I 49.81 49.82 49.83 49.84 49.85
I ,I
pc sc
50
pi
si
pi si si
-200
Sim. I
si
si
Theo. I Sim. I
si
pc
Theo. I
0
pc
Sim. I
The primary, secondary power and system efficiency are calculated in each case from the proposed model and compared in table II. The negative sign in the table refers to the power direction. For the charging cases the primary power is positive and the secondary power is negative, and this situation is reversed in the discharging operation. The system efficiency slightly increased in the reduced power model due to current and losses reduction. Also, for the same supply condition the system has the same efficiency under charging and discharging operation. TABLE II. FUNDAMENTAL POWER RESULTS
pc pc
sc
Theo. I
si
sc -50 Theo. I 49.8 49.81 49.82 49.83 49.84 49.85 sc Time (msec) Fig. 10: System performance under reduced sinusoidal supplies for discharging operation (α= β =120o, δ = 90o) (a) primary inverter variables, (b) secondary inverter variables, (c) coils currents.
cases
si
Theo. I
49.81 49.82 49.83 49.84 49.85 Time (msec)
si
50
si
Theo. I Sim. I
0 -50 49.8
Theo. I
Theo. V
-200
pi
pi
Sim. V
0
49.8
pi
Theo. V
0
Sim. I
49.8 49.81 49.82 49.83 49.84 49.85
Sim. Ipc
pi
Theo. V
0
Theo. Isi
pi
pi
Theo. I Sim. V
200
Sim. Isi
-200
49.8
V , 10*I
Theo. V si
0
Ipc, Isc
Theo. Ipi Sim. V si
200
Sim. I
49.8 49.81 49.82 49.83 49.84 49.85
pc sc
V si, 10*Isi
49.8 49.81 49.82 49.83 49.84 49.85
pi
Theo. V
-200
Sim. Ipi
-200
Sim. V
200 0
pi
Theo. V pi
0
V , 10*I
Sim. V pi
200
the system currents are reduced and in consequence the power. On the other hand, the discharging operation is described in Fig. 10. As it can be noticed, the secondary voltage lead the primary voltage by 90o, which make the power to flow from the EV to the grid. In this case, Vpi and Ipi are anti phase and Vsi and Isi are in phase, which means that the system still working at unity power factor but with the reverse power flow direction.
I ,I
V pi, 10*Ipi
are shown n Fig. 8-a and 8-b respectively. The coupler currents (Ipc and Isc) are indicated in Fig. 8-c. As it can be noticed in Fig 8-a that Vpi and Ipi are in phase, and Vsi and Isi are anti phase which means that both the primary and secondary circuits are working at unity power factor. It can be noticed also that Vsi lags Vpi by 90o, which allows the power flow from the grid to charge the EV. Moreover, both the inverter (Ipi and Isi) and the coils (Ipc and Isc) currents are pure sinusoidal. The figure shows the perfect match between the simulation and theoretical model.
sc
Fig. 9: System performance under reduced sinusoidal supplies for charging operation (α= β =120o, δ = -90o) (a) primary inverter variables, (b) secondary inverter variables, (c) coils currents.
Fig. 9. shows how to control the magnitude of the power flow by adjusting α and β. In this figure α and β are reduces to 120o, and system is analyzed using both the simulated and theoretical model. As discussed before only the magnitude of
1 2 3
Pp (kw)
Ps (kw)
%η
o
o
1.587
-1.5358
96.77
o
o
1.1902
-1.1519
96.78
o
o
-1.1519
1.1902
96.78
β = α = 180 , δ = -90 β = α = 120 , δ = -90 β = α = 120 , δ = 90
B. For Real Supply Voltages. By applying the real system, in which the primary and secondary circuits are supplied from a full bridge converter with four switches (MOSFETs) and DC supply as discussed in section I. In this case the converters output voltages are periodic square waves, with amplitude equal to the DC supply voltage. In this situation, the power flow direction is still controlled by the angle (δ), and the magnitude is controlled by (α) or secondary (β) converter switches. These
Theo. I
49.8 49.81 49.82 49.83 49.84 50
pi pi
Sim. I
pc
Theo. I
0
pc
Sim. I
sc
-50 Theo. I 49.8 49.81 49.82 49.83 49.84 sc Time (msec) Fig. 11: System performance under full real supplies for charging operation (α = β =180o, δ = -90o) (a) primary inverter variables, (b) secondary inverter variables, (c) coils currents. 6
pc
Theo. I
0
pc
Sim. I
si
sc -50 Theo. I 49.8 49.81 49.82 49.83 49.84 sc Time (msec) Fig. 13: System performance under reduced real supplies for charging operation (α = β =120o, δ = -90o) (a) primary inverter variables, (b) secondary inverter variables, (c) coils currents.
6 THD = 3.372%
5 |FFT| of Ipi
pi
|FFT| of I
si
Sim. I
THD = 28.42 %
5 4 3 2
4 3 2 1
1 0 0
si
Theo. I
50
si
si
Sim. I
49.8 49.81 49.82 49.83 49.84
si
si
Theo. V
-200
Sim. I
-200
Sim. V
0
si
si
V , 10*I
Theo. V
0
si
si
pi
200
pc sc
pi si
V , 10*I
Sim. V
pi
Theo. I
49.8 49.81 49.82 49.83 49.84
pi
pi
Sim. I
-200
pi
Theo. I
200
pc sc
pi
pi
Theo. V
0
Sim. I
-200 49.8 49.81 49.82 49.83 49.84
I ,I
pi
Theo. V
0
Sim. V
200
I ,I
pi
V , 10*I
Sim. V
200
harmonic distortion (THD) as percentage of the fundamental component.
V , 10*I
angles (α and β) can vary from 0 to 180o, to change Vpi and Vsi form 0 to maximum, respectively. The system is simulated and compared with the proposed theoretical model for the first 13 harmonics.
0 0
50
100 150 200 Frequency (kHz)
250
300
100 150 200 Frequency (kHz)
250
300
Fig. 14: Magnitude of FFT analysis for Ipi at α = β =120o, δ = -90o).
Fig. 12: Magnitude of FFT analysis for Ipi at (α = β =180o, δ = -90o).
Fig. 11 presents the system performance under charging mode operation and the converters supplying the maximum voltage. It can be noticed that, Vpi and Vsi are full square waves with 90o phase shift in between. Vpi and Ipi are in phase while, Vsi and Isi are anti phase to charge the EV. As noticed also, the inverter currents (Ipi and Isi) are not pure sinusoidal, but the coils currents (Ipc and Isc) are almost pure sinusoidal due to the filtering effect of the circuit impedance. The system efficiency is slightly reduced by 0.06 % and the power factor is deviated from the unity in both the primary and secondary circuit as indicated in table III. This effect due to the large harmonics level in the system which causes higher losses and drawing more reactive power from the supply. The harmonic contents of Ipi up to the 7th harmonics are shown in Fig. 12. It is clear the odd harmonics in the current with 28.42 % total
50
TABLE III. REAL SYSTEM POWER RESULTS
cases
Pp (kw)
Ps (kw)
Qp = Qs
%η
PFp
PFs
1
1.586
-1.534
352
96.71
0.976
-0.974
2
1.190
-1.152
59
96.76
0.998
-0.998
3
-1.152
1.190
59
96.76
-0.998
0.998
To indicate the power level control, the system is analyzed at α = β = 120o, and the results are shown in Fig. 13. As can be noticed, Vpi and Vsi waves exhibit the level zero which causes the reduction of the transferred power and also the decrease the harmonics level in the supply currents. Due to these effects, the system efficiency and power factor are increased as shown in table III. The harmonics contents of Ipi are shown in Fig. 14. It can be noticed that the third harmonic is completely disappear and the THD is significantly reduced to 3.372%. The discharging mode under the low power level is also indicated in Fig. 15 and
table III. Generally speaking reducing the harmonics level in the current leads to higher efficiency and PF as well as increase the ability of the system to transfer more active power as indicated in table III. pi
V , 10*I
Sim. V
200
pi
Sim. I
-200 49.8 49.81 49.82 49.83 49.84
si
V , 10*I
si
Sim. I
49.8 49.81 49.82 49.83 49.84 50 pc sc
Theo. I
[7] si si
si
pc
Theo. I
IV.
sc
Theo. I
CONCLUSION
REFERENCES
[4]
[11]
sc
This paper presents a steady-state harmonics mathematical model for bidirectional inductive wireless power transfer system for charging and discharging EVs in V2G applications. From the proposed model all the system variable (voltage, current and power) at steady-state can be analyzed. Also, it provides an accurate calculation for the system efficiency and power factor. Moreover, it can be used to study the effect of the control parameters on the steady-state system performance and power flow. Moreover, the proposed model presents a clear sight for the harmonics contents in the system. For validation purpose, a 1.5 kW BD-IPT system is built in SimPowerSystems/Simulink MatLab and its results are compared with the theoretical model results. The results shows a good correspondence between the theoretical and the simulation model.
[3]
[10]
Sim. I
Fig. 15: System performance under reduced real supplies for discharging operation (α = β =120o, δ = 90o) (a) primary inverter variables, (b) secondary inverter variables, (c) coils currents.
[2]
[9]
pc
-50 49.8 49.81 49.82 49.83 49.84 Time (msec)
[1]
[8]
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0
[6]
pi
Theo. V
-200
pi
pi
Sim. V
200 0
I ,I
pi
Theo. V
0
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