Predictive Control of a New Configuration of ...

Predictive Control of a New Configuration of Bidirectional Quasi Y-Source Inverter Fed IPMSM for Electric Vehicle Applications E. G. Shehata Electrical Engineering Dept. Faculty of Engineering- Minia University El Minia, Egypt [email protected] Abstract— In this paper, a new high boosting bidirectional quasi Y-source inverter (BQYSI) is designed to overcome the problems of the traditional inverters. BQYSI has advantages of continuous input current and bidirectional power flow. The proposed inverter is controlled to drive an interior permanent magnet synchronous motor (IPMSM) for electric vehicle applications. A finite control set model predictive controller (FCS-MPC) is designed to select directly the inverter switching state based on minimum torque and flux error without modulation technique. The output voltage and current of the BQYSI are controlled to determine the shoot through duty cycle. Simulation results are analyzed to evaluate the performance of the proposed strategy under motoring and regenerating operating conditions. Index Terms— Bidirectional quasi Y-source inverter, Continuous current, IPMSM, Model predictive controller, Electric vehicles

I. INTRODUCTION Voltage/current source inverters (VSI/CSIs), dead time

compensation, miss-gating and stepping down characteristic are its main drawbacks. Dead time compensation increases the output voltage/current distortion. Stepping down characteristic limits the application of low voltage storage energy system (Battery/Supercapacitors) with high voltage traction motors of electric vehicles. To overcome this problem and for high efficiency tracking system, a bidirectional DC-DC converter is inserted between the DC source and the inverter. The bidirectional DC-DC converter operates as a boost converter during motoring operation mode to drive the traction motor and it works as a buck converter in regenerative braking mode. Depending on the storage energy system configuration, the voltage drop can be large and in turn the current is high. With storage energy system voltage variation, the traditional inverter has to be oversized to handle the full voltage and twice the current to output full power. Moreover, an extra bidirectional DC/DC stage increases the system cost and complexity and reducing reliability [1]. Recently, different types of multilevel inverters are developed, however, it suffers from complexity. A single‐stage power conversion system combines the dc‐ dc boost converter and inverter, namely, impedance source inverters. The main feature of this type is that the impedance network consists of inductors and capacitors. The impedance network is employed in the circuit to boost or buck the voltage. The impedance network is inserted between the DC source and

inverter instead of DC-DC converter. Different configurations of the impedance network are possible to improve the performance of the circuit by adding different nonlinear elements into the impedance network, e.g., diodes, switches, and/or a combination of both. Possible switch configurations range from simple-single switch topologies to very complex controlled multilevel and matrix configurations are employed [2]. Early type of impedance-source network, called a “Zsource network,” [3], [4]. A two‐port network that consists of two inductors and two capacitors connected in an X shape is employed to provide an impedance source (Z‐source). In spite of Z-source inverter overcomes the conventional inverters problems, discontinuous input current and unidirectional power flow are considered its main drawbacks. Discontinuous input current limits the applications of Z-source converter in renewable energy applications. Quasi bidirectional Zconverters is designed to ensure continuous input current while a bidirectional Z-source inverter is designed to allow bidirectional power flow [5-9]. Different configurations are designed to reduce voltage stress across its components [10]. Impedance source inverters have been employed for electric vehicle applications [11-17]. DC voltage compensation technique has been designed to overcome DC voltage variation of storage energy systems [11]. For high efficiency and minimum losses, a loss minimization algorithm has been designed for automotive applications [12]. The algorithm depends on selecting of dc-link voltage for minimum loss. PMSM fed by Z-source inverters has employed and controlled for electric vehicle applications [13-15]. A sliding mode controller has been designed to determine the shoot-through duty ratio of the bidirectional Z-source inverter feeding PMSM [16]. Field oriented control, direct torque control and predictive torque control of Z-source inverter have been studied [17-19]. Recently, a new type source impedance called Y-source converter is proposed in [20]. In this type, three winding coupled inductor is designed for deciding different gain values, which is presently not matched by related converters. For simplicity, the number of components used is kept small to allow the converter to be implemented compactly without compromising its performance. However, the conventional Ysource converter has some drawbacks such as discontinuous input current and unidirectional power operation. A quasi Y-

converter with input inductor has been designed to ensure continuous input current [21]. Quasi Y-converter networks preserves all advantages of the conventional magnetic coupling impedance source networks including a very high boost capability and flexibility in design because of the presence of multiple circuit parameters for gain tuning. In addition, magnetic core saturation, which is considered one of the magnetically coupled DC converter problems, is overcame using DC-blocking capacitors [22], [23]. However, regenerative braking to save energy cannot be applied because of unidirectional power flow of quasi Y-source inverters. In this paper, to preserve advantages of the quasi Y-source and overcome the unidirectional power flow problem, a new bidirectional quasi Y-source inverter is developed for electric vehicle applications. The proposed BQYSI feeds PMSM using Nickel-Metal Hybrid (Ni-MH) battery as an energy source/storage system. The output voltage and current of the BQYSI are controlled using two control loops. The output of the control loops are the shoot-through duty cycle. Torque and flux of the PMSM are regulated based on direct torque control principle. A finite set control- model predictive controller is designed to determine the switching state of the BQYSI, directly, based on minimization algorithm of torque and flux error. Pulse width modulation technique and transformation of the reference stator voltage are totally eliminated. Performance of the PMSM fed by BQYSI are studied under different operating condition. II. OPERATION MODES OF BQYSI Figure 1 shows he configuration of the proposed BQYSI network. The proposed inverter consists of a three-winding transformer (N1, N2, and N3), antiparallel diode/switch (D1/S7), three phase two level inverter (S1-S6), input inductor Lin, and two capacitors C1 and C2. As shown in the figure and compared to quasi Y-source inverter, the diode is replaced by a S7/D1 (switch/antiparallel diode). The possible seven operation modes of the bidirectional quasi Y-source inverter which occurs in each switching cycle are shown in Fig. 2 and explained as follows: Mode (1): Two switches of one leg of the three-phase inverter are turned on and the inverter in shoot-through state (Tst). The diode is reversed biased and the two capacitors are discharging. The capacitor voltage equation is given as:    =    (1) where

 =

 

 



,  =



  =  − 

 =  −  + 

  =  −  −  − 

 

(6)

S7

Lin

D1 C2

S1

Vin

S3

S5

N2

PMSM

S2

C1

S6

S4

Fig. 1. Connection circuit of the proposed BYSI fed IPMSM. Lin ID Lin ILin

Io

C2

ILin

Vin

C2

Io

Ic2

Vin

N2

N2

Vo

Ic1

 

 

C1

C1 Mode 1

(2)

The input inductor voltage is positive so its current increases. The capacitors charges transformer windings so the current of windings (N1, N2 and N3) increases. Mode (2): Non-shoot through state starts and the inverter during this mode in a zero switching state (T0), active state (T1) and active state (T2), respectively. The voltage equations for this case can be written as follows:    =   (3) 



(5)

From eq. (4), the input inductor voltage is negative so its current decreases. The diode is conducting and its current is decreasing. The three winding transformer current is negative and charging the capacitors (C1 and C2). Mode (3): In this mode, the inverter is still in second active state (T2). The capacitors (C1 and C2) are discharging and the input inductor and diode currents decrease. Mode (4): In this mode, the inverter is still in second active state (T2). The diode stops conducting and the inductor current decreases to zero and begins to reverse its direction. Mode (5): The inverter is in the second zero state (T7). The inductor current direction increases in the reverse direction. The capacitors (C1 and C2) are discharges. Switch S7 should be turned on in this mode when inductor current reversed. Mode (6): Input inductor current is still in the reverse direction but it begins to decrease in this mode. The capacitors (C1 and C2) charges the load and source during modes 5 and 6. Mode (7): The inductor current (input current) decreases to zero and begins to reverse. The load current (Io) is zero. For Vin=250 V, Vo=800 V, C1=470 µF, C2=150µF, LIN= 0.5 mH, the waveforms of switching signals(S1-S7), input inductor current, diode current and capacitors voltage, respectively, are given in Fig.3. The results show the variations of input inductor current, diode current and capacitors voltage under different operating modes. If switch S7 is eliminated, the input inductor current is zero (discontinuous current mode) during modes 5-7.

The input inductor voltage equation can be written as   =  +  −  − 

(4)

    

 

Lin ILin

Mode 2

Lin

ID

C2

ILin=0

Io

Ic2

C2

Vin

Vin N2

N2

Vo

Ic1

C1

C1 Mode 3

Mode 4

Lin ILin

The inverter output voltage equals  (13) *+, = BM #$  where M is the modulation index. The capacitors voltage can be expressed as:  = (1 − ) (14)  =   (15) The switching time (Ts) can be expressed as: (16) 01 = 0 + 0 + 0& The zero switching time (0& ) is divided into 0& , and 02 and 013 . Two control loops are designed to determine the shoot-through duty cycle (). Outer control loop is designed to regulate the output voltage (VO) using Proportional-Integral (PI) controller while inter control loop regulates the output current (IO) using proportional (P) controller.

IS7

IS7

Lin

Io

S7

C2

Io

S7

C2

ILin

Vin

Vin N2

N2

Vo

Vo

C1

C1

Mode 5

Mode 6 IS7

Lin ILin=0

S7

C2

Vin N2

C1

III. FCS-MPC OF BQYSI FED IPMSM

Mode 7 Fig. 2. Operation modes of the BQYSI.

Fig. 3. Switching states, inductor current, diode current, capacitors voltage waveforms, respectively.

Based on volt-sec balance of the input inductor, using (1) and (4) results in (7) and using (2) and (5) results in (8) [23]:   =  (7) 

 

 =  − 

where  represents the shoot-through duty ratio  =  = 

 

 





(8)

 and

Using (7) and (8), the capacitors voltage can be derived as: ( )#$ (9)  = where  = 

   

 =

 %  % #$  % 

(10)

Using (3-5), (9) , (10), the output voltage can be expressed as  & =  = ( (11)  % '

where ( is the boosting gain of the converter. Assuming lossless converter, the input current can be expressed as  )  =  % ' ) (12) 

In this section, FCS-MPC is designed to determine directly the switching state of the BQYSI. The concept of the FCS-MPC depends mainly on the topology of the three phase inverter. Since the BQYSI is a three phase two level voltage source inverter, there are six active, two no active and shootthrough combinations of inverter states. Using the switching state functions of the inverter, the output phase voltages can be written as 5 2 −1 −1  46 8 = 4−1 2 −18 :;7 (17)  7 −1 −1 2 where : = = ? 0 AB CℎE MLJEH IJACKℎ LB MEN A − Cℎ AI OP The output voltages in the stationary reference frame (R-β) of can be expressed in terms of the switching states as T  S V =  W :;7 (18) U Also, the d-q representation of output voltages can be expressed in terms of the switching states as (19) Vdq = C1C2SVdc where W = X

KLIY −IA Y

1  IA Y Z and W = [  KLIY 0

−



 √

−



 ] √

−  The dynamic model of the IPMSM in the synchronous reference frame (dq) can be expressed as follows: (20) x& = fx + gu + h ωe Lq   − Rs 1  0 i ,  , where x =  d  ,  f 1   Ld L Ld   g= d f = = 1 ω L − R  iq  s  0   f 2  − e d  Lq  Lq  Lq   0   V  and u =  d  h =  − ω e λ PM    Vq  

Lq



The stator flux can be described as: λd  Ld 0  id  λPM  λ  =  0 L  i  +   q  q   0   q 

(21)

λs =

λ2 + λ2 d

q

(22)

The electromagnetic torque can be expressed as

Te = 1 .5 P (λ PM iq + ( Ld − Lq )id iq )

(23)

The IPMSM time continuous model in (19) includes nonlinear terms and thus needs to be linearized. In order to linearize the IPMSG model, the rotor speed is assumed to be constant for one sample time. In addition, The FCS-MPC uses a discrete-time model for the prediction of the currents at a future sample period. For discretization, the forward Euler method with sampling time Ts is applied to the time-continuous model [26]. The predicted stator current values is used to predicate the stator flux and electromagnetic torque. A discretetime state-space model of IPMSG can be expressed as follows: bc d  `  1−   0 A; (^ + 1) A; (^) a a bc fgh  i + S V = [ bc d `  ] SA (^) V + e A_ (^ + 1) _ d 1− d

[



a

0

0

d

; (^)  ] S  (^) V _ d

(24)

where k denotes the number of sample. In this section, the FCS-MPC is designed to determine directly the switching state S of the BQYSI, thus S can be taken as the control inputs. The inverter model (19) is combined with the IPMSG model (24), and the predicted values of the stator current can be estimated for each switching state as: j(^ + 1) = k(^)j(^) + l(^) + ((^)F(^) (25) A; (^ + 1) A; (^) V , j(^) = S V, where j(^ + 1) = S A_ (^ + 1) A_ (^) q1 01 st r_ 01 p1 − w 0 r; r; v o −st xyz 01 ], k(^) = o−s r 0 , l(^) = [ q 0v r_ o t _ 1 1 − 1 1v r_ u n r_ 01 p 0w r; v ((^) oo 01 v W W { , | } F(^) = : o0 v r_ u n The predicted values of the flux and torque can be estimated using the predicted stator current values as follows: λd (k + 1) Ld 0  id (k + 1) λPM  (26) λ (k + 1) =  0 L  i (k + 1) +   q  q  q     0 

λs (k + 1) = λ (k +1) + λ (k + 1) 2

2

d

q

objective function J are calculated and denoted as J0, J1, J2, … , J7. A simple search function is used to find the minimal value of J and its associated index k. Once this index is found, the switching state at sample k to the BQYSI and the corresponding voltage are determined. However, in order to reduce unnecessary switching, if the index is found to be 0, then the previous states of the MSC are required to determine whether the index 0 or 7 should be used in the control action. The flow chart of the FCS-MPC is shown in Fig. 4. With all the variables in the objective function being updated, a minimization is performed to find the new minimal value of J and its index k+1, leading to the control signals for the inverter. The essence of the finite control set method is based on the receding horizon control principle, which uses one-step-ahead prediction and on-line optimization to solve the constrained optimal control problem. To reduce the computation time of the FCS-MPC, one horizon is assumed during each sample time. Moreover, there are no gains to be tuned. Fig. 5 shows the block diagram of the FCS-MPC. FCS-MPC strategy is simple compared to other control strategies, where axes transformation of the voltage and modulation technique are eliminated. SIMULATION RESULTS

VI.

In this section, the performance of the FSC-MPC is analyzed using simulation works conducted by Matlab/Simulink. The parameters of the PMSM, BQYSI and Ni-MH battery are given in Tables I, II and III, respectively. A PI-controller is designed to regulate the PMSM speed and generate the reference value of electromagnetic torque. The proportional and integral gains of the speed controller are 0.1 and 20, respectively. The sampling frequency of the control system is 20 kHz. For output voltage and current control of the BQYSI, the voltage controller proportional and integral gains are 1 and 151.2, respectively, while the current controller proportional gain is 0.5. Me asure men ts

Pre dictive mo de l

Fo r i=1:n

Pre dictive mo de l

C ost fun ction

(27)

i ≥ n

The electromagnetic torque can be expressed as

Te (k +1) =1.5P(λPM + (Ld − Lq )id (k +1))iq (k +1)

Sele ction of switching state

(28)

The main objective of a FCS-MPC controller is to track the desired torque and flux references. A cost function has to be developed to find the optimal control actions and can be expressed as ~ = |0t∗ (^ + 1) − 0t (^ + 1)| + |x∗1 (^ + 1) − x1 (^ + 1)| (29) For the prediction algorithm, the cost function is evaluated for each of the possible eight voltage sectors, giving seven different current predictions. For this purpose, the seven values of the

Fig. 4 Flow chart of the proposed FCS-MPC algorithm.

∑

∑

PI

∑ +

P

FCS-MPC PI

-

Fig. 5 Block diagram of the FCS-MPC controlled BQYSI fed PMSM.

Table I: IPMSM parameters [27] Rated power Rated torque Rs Ld Lq

1000 W PM flux linkage 6 N.m Pole pairs 6 ohm Inertia 0.0445 H Damping 0.1024 H Table II: BQYSI parameters.

0.337 V.s 2 0.01 kg.m2 0.001 N.m.s

Lin

18 mH

Winding factor K2

5

C1

940 µF

Transformer Turns ratio (N1 : N2 : N3 )

45:30:15

C2

150 µF

Switching frequency

20 kHz

Table III: Ni-MH battery parameters. Nominal voltage 76 V Maximum capacity Rated capacity Initial state of charge (%) Capacity at nominal voltage

6 AH 80% 5.76 AH

Full charged voltage Nominal discharge current Internal Resistance

6.42 AH 84.8 V 1.2 A

Fig. 7 performance of BQYSI controlled by FSC-MPC.

0.21 ohm

Figure 6 shows the performance of the PMSM fed by BQYSI. The reference motor speed is assumed to be increased from standstill to 1200 rpm in 0.3 second and decreased to 200 rpm in 0.15 second. The load torque is 4 N.m at starting and increased to 6 N.m at t= 1 second. It is shown that the motor speed is aligned with reference speed with small dip at load disturbance instant. The electromagnetic torque tracks the reference value and negative torque appears during fast deceleration which means that the motor operates in regenerative mode. The figure shows also the variation of stator currents during different modes, i.e., acceleration, steady state and deceleration. Figure 7 shows the waveforms of the BQYSI. The reference and actual values of the output voltage are identical with small dip and overshoot during transient instants. The capacitor voltage changes with shoot through duty ratio to preserve the output voltage at reference value. In addition, the input current is continuous which means the converter operates in continuous current mode. The capacitors voltage and inductor input current are enlarged in Fig. 8. It is shown that the two capacitors charges during inductor discharges and vice versa. The undesired modes are totally eliminated and the results are similar to Fig. 3.

Fig. 8 Enlarged waveforms of the capacitor voltages and input current.

Figure 9 shows the performance of the Ni-MH battery during different operation. The state of charge (SOC%) waveform shows that the battery discharges during motoring mode and charges during regenerating mode. Negative battery current appears during regenerative mode. In spite of DC voltage variation of the storage energy system and load current during different operation modes, the output voltage of the inverter is fixed to the reference value. The performance of the proposed inverter without switch S7 (quasi Y-source inverter) is tested during regenerative mode and the results are given in Fig. 10.The figure shows that the converter performance is normal during motoring operation, however, during regenerating mode, the recovered energy is stored in the capacitors. In turn, the capacitors voltage is increased and can damage the inverter switches. When the capacitor voltage is higher than the desired value, the shoot-through duty ratio is zero and the input current nearly zero. After braking period, the capacitors voltage decreased to a low value and the shoot-through duty ratio and input current increased then the capacitors voltage increased again to a high value and the system may become unstable.

Fig. 6 Performance of PMSM fed by BQYSI. Fig. 9. Performance of the Ni-MH battery.

[10]

[11]

[12]

[13]

[14] Fig. 10 Performance of a QYSI during regenerative mode operation.

I.

CONCLUSIONS

In this paper, BQYSI fed IPMSM is designed and controlled for electric vehicle applications. The DC output voltage and current of the Y-impedance are controlled by regulating the shootthrough duty ratio. The IPMSM torque and flux are regulated using finite set control model predictive controller. The proposed control system is simple because of absence of pulse width modulation techniques and axes transformation of stator voltage. The proposed system is tested during motoring and regenerating modes of operation. The results show that the proposed inverter has continuous input current and can operate in bidirectional power flow. In addition, the MPC has high performance where the reference and actual values are aligned under different operating conditions. Also, the converter can deal well with variable input DC voltage of storage energy units. REFERENCES [1]

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