Comparison criteria for electric traction system architectures

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available athttp://dx.doi.org/10.1109/JESTPE.2014.2298755

Comparison Criteria for Electric Traction System Using Z-source/Quasi Z-source Inverter and Conventional Architectures Alexandre BATTISTON1, Student Member, IEEE, Jean-Philippe MARTIN1, El-Hadj MILIANI2, Babak NAHIDMOBARAKEH1, Senior Member, IEEE, Serge PIERFEDERICI1, and Farid MEIBODY-TABAR1 1 GREEN Laboratory – University of Lorraine 2 avenue de la Forêt de Haye, 54500 Vandœuvre-Lès-Nancy, France [email protected] 2 IFP Energies nouvelles Abstract—This paper deals with objective criteria to

compare conventional electric traction systems composed of a DC-DC boost converter, a Voltage Source Inverter and a Permanent Magnet Synchronous Machine with alternative topologies such as Z-source or Quasi Z-source inverters. Instead of focusing only on efficiencies issues, this paper aims at dealing with other relevant criteria. The stored energy in the systems is for instance linked with their passive elements weight, size or cost. The currents rms values and the step up voltage ratio are also taken into account. A complete losses evaluation is given and validated by both simulation and experimental results. The results show that the Quasi Z-source inverter presents real advantages in terms of passive elements size since the stored energy during one operating cycle is lower than for the conventional topologies. Index Terms—Quasi Z-source inverter, Boost converter, Efficiency, Stored energy, Electric traction system.

I. INTRODUCTION

T

HE Z-source inverter (ZSI) [1] is a DC-AC converter topology that emerged about ten years ago. It is suitable for Electrical Vehicles (EV) or Hybrid Electric Vehicles (HEV) traction systems as it can boost and invert a low source voltage to any desired three-phase voltage. Indeed, if the battery voltage is not sufficient to control the electric motor, a DC-DC converter is generally required without using some field weakening techniques. For instance, in its 2011 technical report, the ORNL [2] presented the electric traction system used inside the 2010 Toyota Prius where a bidirectional DCDC allows stepping up the battery voltage (200V) to 650V [3]. Authors in [4]-[5] provides a general overview about the EV, HEV, or fuel cell traction systems. All these architectures are composed of a DC-AC or a DC-DC + DC-AC converters. This paper now focuses on those converters used to interface the source and the load (especially the electric machine). The conventional architecture (Syst1: BC+VSI) presented in Fig. 1, is composed of a Voltage Source Inverter fed by a boost converter [2]. Thus, numerous papers has proposed to compare that topology with the ZSI one [6]-[8] (Syst2: ZSI in Fig. 2). The Quasi Z-source inverter (Syst3: QZSI in Fig. 3) presents the interest of having a continuous input current 𝑖𝐿𝑞 that gives some advantages in such a field like automotive applications. The authors also investigated the way to step up the three-phase voltage using a ZSI, a QZSI [9]-[11] or other improved topologies [12]. The advantages of these systems have been widely given in other papers [1], [13]-[15]. Basically, the DC-bus voltage 𝑣𝐷𝐶 can be stepped up by means of insertion of extra short-circuit states in the PWM scheme of the inverter, also known as “shoot-through zero

states” [1], [16]. In these particular states, the two switches of a same inverter’s leg are ON and the inverter is equivalent to a short-circuit. The diode 𝐷 is open. In the second sequence, i.e. when the inverter operates at non shoot-through states (six active states and two zero states), the diode 𝐷 is ON. If 𝑡𝑠𝑡 is the shoot-through interval and 𝑡𝑛𝑠𝑡 the non-shoot through interval, the sum of these quantities corresponds to the switching period 𝑇 = 𝑡𝑠𝑡 + 𝑡𝑛𝑠𝑡 . Thus, one can define a shoot-through duty cycle 𝑑 = 𝑡𝑠𝑡 /𝑇, which will be widely used in the next parts. In [6], authors focus on a comparison between the Syst2: ZSI and the Syst1: BC+VSI taking into account losses in the power devices. They show that the semiconductors power losses in the ZSI are higher than for the BC+VSI. In [7], authors take into account motor design in an electric traction system architecture and show that ZSI-motor system efficiency is increased by 20% compare to conventional inverter. P0 Lf rf rLb Lboost rD

vs

iLb

iCf

vf

iCboost

vDC

Cf

Cboost

rK Input source and filter

DC boost converter

Inverter + PMSM

Fig. 1. (Syst1: BC+VSI) Electric traction system composed of an input source and filter, of a boost converter, a Voltage Source Inverter and a PMSM.

Lf

rf

vs

LZSI

D rD

vf

iCf Cf

iLz

P0

rL

CZSI

vC

iCZSI vC LZSI

rL

vDC

iLz

Z-source inverter

Input source and filter

PMSM

Fig. 2. (Syst2: ZSI) Electric traction system composed of an input source and filter, a ZSI and a PMSM.

vC2 i C

Qzsi

Lf

rf

vs

vf

rL

LQzsi

iCf

i Lq

Cf

Input source and filter

rD D rL

vC1

iCQzsi CQzsi

P0

LQzsi i Lq

vDC

Quasi Z-source inverter

PMSM

Fig. 3. (Syst3: QZSI) Electric traction system composed of an input source and filter, a QZSI and a PMSM.

In this paper, three electric traction system architectures presented in Fig. 1 (Syst1: BC+VSI), Fig. 2 (Syst2: ZSI) and Fig. 3 (Syst3: QZSI) are compared. It is proposed to consider the following comparison criteria: the stored energy in the

Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available athttp://dx.doi.org/10.1109/JESTPE.2014.2298755

systems, the capacitive current rms values, the voltage ratio 𝑣𝐷𝐶 /𝑣𝑓 with parasitic elements and the losses. This study aims at selecting a topology which could be a good alternative to the conventional BC+VSI without only consider efficiency results as it is proposed in numerous papers previously cited. The advantage of selecting the stored energy as comparison parameter can be explained by the relation it exists between the stored energy and the size, weight and cost of the system [17]-[20]. The three studied systems are composed of an input voltage source and its 𝐿𝑓 𝐶𝑓 filter. They feed a voltage source inverter and a Permanent Magnet Synchronous Machine (PMSM). Note that ZSI and QZSI converters are generally seen as a full part of inverter and should not be separated as it is done for the BC + VSI case. After a theoretical study in part II where all derivations are given with analytical expressions, part III focuses on the efficiency analytical results while part IV presents an experimental validation. Note that an energetic study is proposed to compare the system according to an operating cycle of the machine via a normalized speed profile. II. THEORETICAL STUDY In this second part, the three electric traction system architectures (Syst1: BC+VSI), (Syst2: ZSI) and (Syst3: QZSI) are compared according to different criteria such as the stored energy in the systems (II. A.), capacitive current rms values (II. B.), step up rate with parasitic elements (II. C.) and losses (II. D.): switching and conducting losses in the inverter (II. D. 1.), iron losses in the inductor(s) (II. D. 2.), resistive losses in passive elements (II. D. 3.). A. Stored energy in the systems In [17], the authors proposed a precise analysis on commercialized storage capacitors. The results of that study pointed out that both the volume and cost were increasing linearly with the stored energy. These results can be also found in some other papers [18] or technical reports [19]-[21]. That is why this later criteria is considered to take into account the size of the reactive components, which represents an important constraints in automotive applications. From the state models of the three considered systems that are not detailed in this paper, it is possible to express the inductance values according to given high frequency inductive current ripples Δ𝑖𝐿𝑏 , Δ𝑖𝐿𝑧 or Δ𝑖𝐿𝑞 . Generally, authors design storage capacitors according to criteria such as high frequency capacitive voltage ripples [7], voltage drop when a load step occurs [21], system stability [22], etc… In this study, the DCDC or DC-AC converters are considered well controlled, and unstable operating points are difficult to find. As regards the voltage drop in case of load step, this phenomenon can be avoided or improved by means of rapid system control with large bandwidth. The high frequency ripples are therefore considered to design the capacitors. Analytical expressions are given below for the three compared systems (1)-(6). The parameters used are detailed in Table I and are the same as used in Fig. 1, Fig. 2 or Fig. 3.

𝑣𝑓 𝑣𝑓 1 𝑑 = (1 − ) 2 𝑣𝐷𝐶 𝑣𝐷𝐶 𝑣𝐶 , 𝑣𝐶1 , 𝑣𝐶2 Δ𝑖𝐿𝑏 , Δ𝑖𝐿𝑧 , Δ𝑖𝐿𝑞 Δ𝑣𝐷𝐶 , Δ𝑣𝐶 , Δ𝑣𝐶1 , Δ𝑣𝐶2 𝐼𝑚𝑎𝑥 𝑉𝑚𝑎𝑥 𝑃0 𝑇 = 1/𝑓𝑠 𝑚 = 𝑉𝑚𝑎𝑥 /(𝑣𝐷𝐶 /√3) 𝐼𝑆𝐶

1.

𝐿𝑏𝑜𝑜𝑠𝑡 , 𝐿𝑍𝑆𝐼 , 𝐿𝑄𝑍𝑆𝐼 𝐶𝑏𝑜𝑜𝑠𝑡 , 𝐶𝑍𝑆𝐼 , 𝐶𝑄𝑧𝑠𝑖 𝐶𝑓

Description Boost converter, ZSI or QZSI inductors Boost converter, ZSI or QZSI capacitors Filter capacitor

(Syst1: BC + VSI) DC-DC boost converter and Voltage source inverter

For given current ripples Δ𝑖𝐿𝑏 , voltage ripples Δ𝑣𝐷𝐶 and filtered source voltage 𝑣𝑓 , both the electrostatic energy 𝑊𝐶𝑏𝑜𝑜𝑠𝑡 and magnetic energy 𝑊𝐿𝑏𝑜𝑜𝑠𝑡 of the BC can be expressed as follows: 1 2 𝑊𝐿𝑏𝑜𝑜𝑠𝑡 = 𝐿𝑏𝑜𝑜𝑠𝑡 𝑖𝐿𝑏 2 2 𝑣𝑓 1 𝑣𝑓 𝑃0 = ⋅ (1 − ) 𝑇⋅( ) 2 Δ𝑖𝐿 𝑣𝐷𝐶 𝑣𝑓

(1)

1 𝐶 𝑣2 2 𝑏𝑜𝑜𝑠𝑡 𝐷𝐶 𝑣𝑓 1 𝐼𝑚𝑎𝑥 2 = (1 − ) 𝑣𝐷𝐶 𝑇 2 Δ𝑣𝐷𝐶 𝑣𝐷𝐶

𝑊𝐶𝑏𝑜𝑜𝑠𝑡 =

2.

(2)

(Syst2: ZSI) Z-source inverter

In this present paper, coupled inductors are considered for both the Syst2: ZSI and Syst3: QZSI systems. Note that in order to work with symmetrical system, ZSI capacitors have the same value 𝐶𝑍𝑆𝐼 as well as ZSI inductors 𝐿𝑍𝑆𝐼 . Thus, it is possible to show that for all time, inductive currents through the two inductors are equal as well as capacitive voltages across the two capacitors. These latter are noted 𝑖𝐿𝑧 and 𝑣𝐶 respectively. It can be now expressed both the stored electrostatic and magnetic energies in the case of coupled systems with 𝐿𝑒𝑞 = 𝐿𝑍𝑆𝐼 + 𝑀𝑍𝑆𝐼 ≈ 2 𝐿𝑍𝑆𝐼 where 𝑀𝑍𝑆𝐼 represents the mutual inductance supposed to have a value close to 𝐿𝑍𝑆𝐼 . 1 𝑊𝐿𝑍𝑆𝐼 = 2 ⋅ ( ⋅ 𝐿𝑒𝑞 ⋅ 𝑖𝐿2 ) 2

2

𝑣𝑓 𝑣𝑓 1 𝑣𝐷𝐶 𝑇 𝑃0 =2⋅( ⋅( + 1) ⋅ ⋅ (1 − )⋅ )⋅( ) 8 𝑣𝑓 Δ𝑖𝐿𝑧 𝑣𝐷𝐶 4 𝑣𝑓

1 𝐶 𝑣2 2 𝑍𝑆𝐼 𝐶 2 𝑣𝑓 𝑃0 𝑇 1 𝑣𝐷𝐶 = ⋅ ⋅ (1 − )⋅ ⋅( + 1) 𝑣𝑓2 𝑣𝑓 4Δ𝑣𝐶 𝑣𝐷𝐶 4 𝑣𝑓

(3)

𝑊𝐶𝑍𝑆𝐼 = 2 ⋅

TABLE I PARAMETERS DESCRIPTION Symbol

Voltage across the filter capacitor Z-source or Quasi Z-source inverter duty cycle (2𝑑 for the DC-DC boost converter duty cycle) Inverter supply voltage Voltages across ZSI or QZSI’s capacitors Current ripples Capacitor voltage ripples Peak value of 3-phase current absorbed by the charge (PMSM) Peak value of 3-phase voltage across machine windings Absorbed power by the inverter and PMSM Switching period Modulation index, Space Vector Modulation case. Short-circuit current during extra shoot-through zero states (ZSI and QZSI case)

3.

(4)

(Syst3: QZSI) Quasi Z-source inverter

As regards the QZSI system, the same considerations as previously mentioned for the ZSI are made. The only difference concerns the capacitive voltages that are shifted by the source voltage value as follows: 𝑣𝐶1 (𝑡) = 𝑣𝐶2 (𝑡) + 𝑣𝑓 .

Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available athttp://dx.doi.org/10.1109/JESTPE.2014.2298755

TABLE II RMS CURRENT VALUES (CAPACITORS)

𝐶𝑏𝑜𝑜𝑠𝑡 Syst1: BC+VSI 𝐶𝑓

𝐶𝑍𝑆𝐼 Syst2: ZSI 𝐶𝑓

𝐶𝑄𝑍𝑆𝐼 Syst3: QZSI

2 2 𝑣𝑓2 𝑇 2 𝑣𝑓 𝑃0 𝑣𝑓 2 𝐼𝑚𝑎𝑥 𝑃0 2 √ 𝑖𝐶𝑟𝑚𝑠 = + (1 − ) ]+ 𝑚 (3 + 2 cos(2𝜙)) − 2 ( ) [( ) 2 𝐷𝐶 𝑣𝐷𝐶 𝑣𝑓 𝑣 2𝜋 𝑣 12 𝐿𝐵𝑂𝑂𝑆𝑇 𝐷𝐶 𝐷𝐶

𝑖𝐶𝑟𝑚𝑠 = 𝑓

𝑣𝑓 𝑇 2√3 𝐿𝐵𝑂𝑂𝑆𝑇

(1 −

𝑣𝑓 ) 𝑣𝐷𝐶

𝑃 2 2 2 2 8𝜋 𝑑 ( 0 ) + 2𝐼𝑚𝑎𝑥 𝑚 cos(2𝜙) + 3 𝐼𝑚𝑎𝑥 𝑚 2 𝑣 𝑑 𝑇 𝑣𝑓 4 𝑃0 2 𝑓 2 2 (𝑑 = ( ) ( − 1) + 2√3𝑚(𝑑 − 1) + 3𝑚 ) + − (𝑖𝐶𝑟𝑚𝑠 ) ( ) 𝑍𝑆𝐼 8 𝐿𝑍𝑆𝐼 (2 𝑑 − 1) 3 2𝜋 𝑣𝑓 𝑃0 2 2 2 2 8𝜋 𝑑 ( ) + 2𝐼𝑚𝑎𝑥 𝑚 cos(2𝜙) + 3 𝐼𝑚𝑎𝑥 𝑚 𝑣𝑓 𝑑 𝑇 𝑣𝑓 4 𝑃0 2 2 (𝑑 (𝑖𝐶𝑟𝑚𝑠 ) = 4 ⋅ ( ) ( − 1) + 2√3𝑚(𝑑 − 1) + 3𝑚 ) + − ( ) 𝑓 8 𝐿𝑍𝑆𝐼 (2 𝑑 − 1) 3 2𝜋 𝑣𝑓 2

2

2

2

(𝐼𝐶𝑟𝑚𝑠 ) = (𝐼𝐶𝑟𝑚𝑠 ) 𝑍𝑆𝐼 𝑄𝑧𝑠𝑖

2

𝐶𝑓

2 𝑣𝑓 𝑑 𝑇 4 (𝐼𝐶𝑟𝑚𝑠 ) =( ) ( (𝑑 − 1)2 + 2√3𝑚(𝑑 − 1) + 3𝑚2 ) 𝑄𝑧𝑠𝑖 8 𝐿𝑄𝑧𝑠𝑖 (2 𝑑 − 1) 3

Thus, capacitive voltages mean value is different for the two QZSI capacitors and stored electrostatic energy can be expressed as (6). 𝑊𝐿𝑄𝑍𝑆𝐼 = 𝑊𝐿𝑍𝑆𝐼 1 1 2 2 𝑊𝐶𝑄𝑍𝑆𝐼 = 𝐶𝑄𝑍𝑆𝐼 𝑣𝐶1 + 𝐶𝑄𝑍𝑆𝐼 𝑣𝐶2 2 2

𝑣𝑓 1 𝑃0 𝑇 1 𝑣𝐷𝐶 2 2 = ⋅ ⋅ ⋅ (1 − ) ⋅ [1 + ( ) ] 𝑣𝑓 2 𝑣𝑓 Δ𝑣𝐶2 4 𝑣𝐷𝐶 2 𝑣𝑠

(5)

(6)

Fig. 4. Stored energies in the three systems for several operating points and source voltage vs = 100V with high frequency current and voltage ripples maintained constant.

Equations (1), (3) and (5) point out that while 𝑣𝐷𝐶 /𝑣𝑓 < 7, the stored magnetic energy in both the Syst2: ZSI and Syst3: QZSI topologies are smaller than the one stored in the Syst1: BC +VSI. The stored energies are plotted against the ratio 𝑣𝐷𝐶 /𝑣𝑓 for different PMSM speeds (powers) in Fig. 4. The PMSM parameters can be found in Table III at the end of the paper. To obtain these results, the DC-bus voltage 𝑣𝐷𝐶 is adapted to the mechanical speed of the machine so that the controllability is maintained for the three systems. Thus, by varying the mechanical speed, the duty cycle 𝑑 changes so that the DC-bus voltage 𝑣𝐷𝐶 is stepped up. The results show that in terms of stored energy and thus in volume, weight and cost terms [17], both the ZSI and QZSI are competitive with

the BC, which is supposed to store more energy when the source voltage has to be stepped up (about two times in comparison with the QZSI system). B. Capacitive currents rms values Another parameter which can be considered concerns the temperature rise within the systems. This latter is influenced by the rms values of the currents through the different capacitors.

Fig. 5. Capacitive current rms values comparisons for three input voltages and different operating points.

Analytical calculations are given in Table II and simulation results are plotted in Fig. 5 against different ratio 𝑣𝐷𝐶 /𝑣𝑓 . In order to give simplified expressions, some of them are expressed in function of the duty cycle 𝑑 = 1/2(1 − 𝑣𝑓 /𝑣𝐷𝐶 ). It can be noticed that the input current of both the BC and the QZSI is continuous, which means that an input filter 𝐿𝑓 𝐶𝑓 is not necessary unlike the ZSI topology. Nevertheless, the rms value 𝑖𝐶𝑟𝑚𝑠 is the lowest for the QZSI 𝑓 topology according to calculations. The results in Fig. 5 show that the rms values of the ZSI or QZSI capacitive currents are still below those of the BC for a voltage ratio in [1, 2]. Three source voltage values 𝑣𝑠 have been tested: 60𝑉, 80𝑉 and 110𝑉.

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This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available athttp://dx.doi.org/10.1109/JESTPE.2014.2298755

C. Ideal and non-ideal voltage ratio 𝑣𝐷𝐶 /𝑣𝑓 The second criteria is based on the evaluation of the voltage ratio of the three systems. Parasitic elements are taken into account after the following ideal consideration. Neglecting losses, the ideal voltage ratios are given as follows: 𝑣𝐷𝐶 ( ) 𝑣𝑓

=

𝐵𝐶

1 1 − 𝑑𝑏𝑜𝑜𝑠𝑡

𝑣𝐷𝐶 ( ) 𝑣𝑓

=

𝑍𝑆𝐼/𝑄𝑍𝑆𝐼

(7)

1 1−2𝑑

(8)

However, in reality, parasitic elements such as serial resistor of the inductors (𝑟𝐿 , 𝑟𝐿𝑏 ) or semiconductors (𝑟𝐷 , 𝑟𝐾 ) have to be taken into account for a more realistic behavior. With the inverter and the PMSM modelled by a resistive load 𝑅𝑙𝑜𝑎𝑑 , one obtains from Fig. 1, Fig. 2 and Fig. 3: −1

𝑣𝐷𝐶 𝑟𝐿𝑏 + 𝑟𝐾 𝑑𝑏𝑜𝑜𝑠𝑡 + 𝑟𝐷 (1 − 𝑑𝑏𝑜𝑜𝑠𝑡 ) ( ) = (1 − 𝑑𝑏𝑜𝑜𝑠𝑡 + ) (1 − 𝑑𝑏𝑜𝑜𝑠𝑡 ) 𝑅𝑙𝑜𝑎𝑑 𝑣𝑓 𝐵𝐶

𝑣𝐷𝐶 ( ) = 𝑣𝑓 𝑍𝑆𝐼

𝑣𝐷𝐶 ( ) 𝑣𝑓

𝑄𝑍𝑆𝐼

1−2𝑑+

(9)

−1

2 𝑟𝐿 1 − 𝑑 ⋅ + 𝑅𝑙𝑜𝑎𝑑 1 − 2 𝑑

(10)

2 𝑟 𝑑 𝑟𝐷 3 𝐾 + (1 𝑅 − 𝑑) ⋅ (1 − 2 𝑑) 𝑅𝑙𝑜𝑎𝑑 (1 − 2 𝑑)) ( 𝑙𝑜𝑎𝑑

(11)

Functions (9), (10) and (11) are plotted against the duty cycle 𝑑 (𝑑𝑏𝑜𝑜𝑠𝑡 = 2𝑑) for different load powers 𝑃0 (Fig. 6). Results show that the voltage ratios are quite similar for the three systems. A slight advantage is however given to both the ZSI and the QZSI topologies for 𝑑 ∈ [0.4; 0.5](𝑑𝐵𝑂𝑂𝑆𝑇 ∈ [0.8; 1]). 18 BOOST converter 16 P 0 =80 W

(Syst1: BC+VSI) Conduction losses in a voltage source inverter without legs short-circuits (BC case) For the BC+VSI case, no short-circuits are added in the space vector modulation scheme of the voltage source inverter and expression of the losses can be given as follows: 𝐶𝑜𝑛𝑑 𝑃𝐼𝐺𝐵𝑇 = 𝑣𝑘0 ⋅

P 0 =290 W

8

As mentioned above, three short-circuit strategies are investigated according to the number of short-circuited legs of the inverter. One obtains three expressions detailed in (13)(15) with 𝑑 = 1/2(1 − 𝑣𝑓 /𝑣𝐷𝐶 ). 𝑐𝑜𝑛𝑑 𝑃𝐼𝐺𝐵𝑇 = 𝑣𝑘0 ⋅ 𝐴1 + 𝑟𝑘0 ⋅ 𝐴2 1𝑙𝑒𝑔

(13)

𝑐𝑜𝑛𝑑 𝑃𝐼𝐺𝐵𝑇 = 𝑣𝑘0 ⋅ 𝐵1 + 𝑟𝑘0 ⋅ 𝐵2 2𝑙𝑒𝑔𝑠

(14)

𝑐𝑜𝑛𝑑 𝑃𝐼𝐺𝐵𝑇 = 𝑣𝑘0 ⋅ 𝐶1 + 𝑟𝑘0 ⋅ 𝐶2 3𝑙𝑒𝑔𝑠

(15)

P 0 =1100 W

+

4

𝐵1 = (

2

0.41

0.42

0.43

0.8

0.82

0.84

0.86 0.88 0.90 0.92 0.94 duty cycle 𝑑𝐵𝑂𝑂𝑆𝑇 (boost converter)

0.44 0.45 0.46 0.47 duty cycle 𝑑 (ZSI/QZSI)

0.48

0.49

0.5

0.96

0.98

1

Fig. 6. Non-ideal gain 𝑣𝐷𝐶 /𝑣𝑓 plotted against the duty cycle 𝑑.

D. Losses and efficiency In order to analytically express the efficiency of the three systems, losses taken into account are detailed below. 1.

(12)

(Syst2-3: ZSI and QZSI) Conduction losses in the Z-source or Quasi Z-source inverters

6

0 0.4

2 𝐼𝑚𝑎𝑥 𝑚𝜋 2 𝐼𝑚𝑎𝑥 ⋅ (1 + ⋅ ⋅ 𝑐𝑜𝑠(𝜙)) + 𝑟𝑘0 ⋅ 2𝜋 4 √3 2𝜋

𝐼𝑚𝑎𝑥 𝐼𝑠𝑐 √3 √3 𝐴1 = ( 𝑑+ 𝑚 𝜋 cos(𝜙)] + 𝑑) [1 − 2𝜋 2 6 3 2 𝐼𝑚𝑎𝑥 𝐴2 = ( [3√3𝑑 + 6𝜋 + 4𝑑𝜋 + 2(8√3 − 5)𝑚 cos(𝜙)] 48𝜋

12

𝑣𝐷𝐶 𝑣𝑓

where 𝑖̅𝑇 represents the mean value of the current through an IGBT and 𝑖 𝑇𝑟𝑚𝑠 its rms values.

with:

14

10

𝐼𝐺𝐵𝑇 2 𝑃𝐶𝑜𝑛𝑑 = 𝑣𝑘0 ⋅ 𝑖̅𝑇 + 𝑟𝑘0 ⋅ 𝑖 𝑇𝑟𝑚𝑠

𝜋 8√3 − 5 ⋅( + ⋅ 𝑚 ⋅ 𝑐𝑜𝑠(𝜙)) 4 12

−1 4 (𝑟𝐾 𝑑) 3 1−2𝑑+ + (1 − 2 𝑑)𝑅𝑙𝑜𝑎𝑑 = 2 𝑟𝐷 (1 − 𝑑) 2 𝑟𝐿 (1 − 𝑑) + (𝑅𝑙𝑜𝑎𝑑 (1 − 2 𝑑) (1 − 2 𝑑)𝑅𝑙𝑜𝑎𝑑 )

Z-source or Quasi Z-source inverter

semiconductors and discrete switches of the DC-side network. Since both the ZSI and QZSI are controlled by means of inserting extra inverter’s legs short-circuits, three methods are considered according to the number of shortcircuited leg(s) during the shoot-through states (1, 2 or 3 legs). Since the short-circuit current 𝐼𝑆𝐶 (for the ZSI and QZSI) is conducted by the IGBTs, the conduction losses of the inverters’ diodes are supposed to be the same for the three converters and will not be discussed in this part. However, they will be taken into account for final result. Thus, IGBTs conduction losses are estimated according to the following equation [23]:

Conduction and switching losses in the semiconductors Classical formulas [6] are used to estimate both the conduction and the switching losses of the inverters’

𝐼𝑠𝑐 𝑑(16𝜋𝐼𝑠𝑐 − 24√3𝐼𝑚𝑎𝑥 )) 48𝜋

𝐼𝑚𝑎𝑥 𝐼𝑠𝑐 √3 𝑚 𝜋 cos(𝜙)] + 𝑑) [1 − 𝑑 + 2𝜋 6 3

𝐵2 = (

2 𝐼𝑚𝑎𝑥 9√3 3 1 𝑑 + (2 + 𝑑)𝜋 + (8√3 − 5)𝑚 cos(𝜙)] [ 12𝜋 16 4 2

+

𝐼𝑠𝑐 𝑑(2𝜋𝐼𝑠𝑐 − 3√3𝐼𝑚𝑎𝑥 )) 12𝜋

𝐼𝑚𝑎𝑥 𝐼𝑠𝑐 √3 𝐶1 = ( 𝑚 𝜋 cos(𝜙)] + 𝑑) [1 − 𝑑 + 2𝜋 6 3 2 2 𝐼𝑚𝑎𝑥 3𝜋 1 𝐼𝑠𝑐 𝑑 𝐶2 = ( [ + (8√3 − 5)𝑚 cos(𝜙)] + ) 12𝜋 2 2 9𝜋

Note that 𝐼𝑆𝐶 represents the current absorbed by the inverter during a short-circuit and its expression is given by 𝐼𝑆𝐶 = 2 𝑃0 /𝑣𝑓 with 𝑃0 the absorbed power by the inverter and the PMSM. To derive the IGBTs switching losses, simplified

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formulas are used and expressed as follows [6] according to switching energies values given in datasheets and detailed in Table III. (Syst1: BC+VSI) Switching losses in a voltage source inverter 𝑆𝑊 𝑃𝐼𝐺𝐵𝑇 =

1 𝑣𝐷𝐶 𝐼𝑚𝑎𝑥 ⋅ 𝑓𝑠 ⋅ ⋅ ⋅ (𝐸𝑜𝑛 + 𝐸𝑜𝑓𝑓 ) 𝜋 𝑉𝑟𝑒𝑓 𝐼𝑟𝑒𝑓

(16)

𝑢

Short-circuit Short-circuit

Short-circuit

𝐵

𝐵𝑚𝑎𝑥 𝐵𝑖𝑛 𝑡1 𝐵𝑖𝑛 𝑡2

𝐵𝑚𝑖𝑛

0

dT  dh  dT   4 2 4

(Syst2-3: ZSI and QZSI) Switching losses in either the Zsource or the Quasi Z-source inverters 𝑆𝑊 𝑃𝐼𝐺𝐵𝑇,1−2−3−𝑙𝑒𝑔𝑠 =

1 𝑣𝐷𝐶 ⋅ 𝑓𝑠 ⋅ (𝐸𝑜𝑛 + 𝐸𝑜𝑓𝑓 ) ⋅ 𝜋 𝑉𝑟𝑒𝑓 1 2 ⋅ ((1 − √3)𝐼𝑚𝑎𝑥 + 𝐼𝑠𝑐 𝜋) 𝐼𝑟𝑒𝑓 3

(17)

Iron losses (hysteretic and Eddy’s) are estimated using an improved Steinmetz formula [24]-[27] given by (18). 1 𝑥−1 ̂ 𝑦 𝑃𝑖𝑟𝑜𝑛 = ⋅ 𝑉𝑜𝑙 ⋅ 𝐶𝑚 ⋅ 𝑓𝑒𝑞 ⋅𝐵 (18) 𝑇 ⋅ (𝑐𝑡2 𝑇𝑝2 − 𝑐𝑡1 𝑇𝑝 + 𝑐𝑡 ) where 𝐶𝑚 , 𝑥, 𝑦, 𝑐𝑡 , 𝑐𝑡1 , 𝑐𝑡2 are coefficients available in the datasheet, 𝑉𝑜𝑙 the magnetic circuit volume (𝑚3 ), 𝑓𝑒𝑞 is an equivalent frequency (Hz), 𝑇 the switching period (Hz), 𝑇𝑝 the temperature (°C) and 𝐵̂ the peak value (T) of the induction (sinus case). Original Steinmetz equation (𝑃 = 𝐶𝑚 𝑉𝑜𝑙 𝑓 𝑥 𝐵̂ 𝑦 ) is widely used for losses evaluation of AC low frequency transformers. However, in power electronics applications, the induction waveforms are not sinus and have DC bias components [26], [28] as it can be seen for induction waveforms of the considered converters in Fig. 7 and Fig. 8. The improved form (18) therefore has to be used to take into account this specificity. The equivalence is realised by calculating an equivalent frequency as follows: (19)

(Syst1: BC+VSI) DC-DC boost converter For the BC, this latter equivalent frequency (19) can be calculated according to the induction waveform plotted in Fig. 7. One has for the two sequences: 𝑡 ∈ [0, 𝑑𝑏𝑜𝑜𝑠𝑡 𝑇] 𝑡 ∈ [𝑑𝑏𝑜𝑜𝑠𝑡 𝑇, 𝑇] 𝑣𝑓 𝑑𝐵 𝑑𝐵 𝑣𝑓 − 𝑣𝐷𝐶 = = 𝑑𝑡 𝑁 ⋅ 𝑆 𝑑𝑡 𝑁⋅𝑆 Note that 𝑁 is the turns number, 𝑆 the effective magnetic cross section and 𝑙𝑧 the effective magnetic path length. The equivalent frequency is thus equals to: 2 1 1 ⋅( + ) 𝜋 2 𝑑𝑏𝑜𝑜𝑠𝑡 𝑇 (1 − 𝑑𝑏𝑜𝑜𝑠𝑡 )𝑇 2 1 = 2 ⋅ 𝑓𝑠 ⋅ 𝑣 𝑣𝑓 𝑓 𝜋 ⋅ (1 − ) 𝑣𝐷𝐶 𝑣𝐷𝐶 𝑣𝑓 1 1 𝑣𝑓 𝐵̂ = ⋅ Δ𝐵 = ⋅ ⋅ (1 − )𝑇 2 2 𝑁⋅𝑆 𝑣𝐷𝐶 𝐵𝐶 = 𝑓𝑒𝑞

𝑥−1 2 1 𝐵𝐶 𝑃𝑖𝑟𝑜𝑛 = 𝑓𝑠 ⋅ 𝑙𝑧 ⋅ 𝑆 ⋅ 𝐶𝑚 ⋅ ( 2 ⋅ 𝑓𝑠 ⋅ ) 𝜋 𝑑 ⋅ (1 − 𝑑) 𝑦 1 𝑣𝑓 ⋅( ⋅ ⋅ 𝑑𝑇) ⋅ (𝑐𝑡2 𝑇𝑝2 − 𝑐𝑡1 𝑇𝑝 + 𝑐𝑡) 2 𝑁⋅𝑆

(21)

(Syst2-3: ZSI and QZSI) Z-source or Quasi Z-source inverters For the ZSI or QZSI, the induction waveforms are quite different from the latter because of the way to insert shortcircuits in the PWM inverter’s scheme. One can refer to Fig. 8 for illustration. Note that the duration 𝑑ℎ represents the available time in the space vector modulation scheme to insert short-circuits. It corresponds to the states when the load is short-circuited (zero states) and can be expressed in the worst case as: 𝑑ℎ = 𝑇 ⋅ (1 − √3/2 𝑚). 𝑑𝑇 ] 4

𝑑𝐵 𝑣𝐶 = 𝑑𝑡 𝑁 ⋅ 𝑆

𝐵

(20)

Finally, iron losses in the inductor of the DC-DC BC are finally expressed as follows:

𝑡 ∈ [0,

𝑢

T 2

T 2

Iron losses in the inductors

𝑑𝐵 2 2 𝑇 ( 𝑑𝑡 ) 𝑓𝑒𝑞 = 2 ∫ 𝑑𝑡 𝜋 0 Δ𝐵

dh 2

Fig. 8. Induction waveform in a Z-source or Quasi Z-source inverter inductors.

where 𝑉𝑟𝑒𝑓 , 𝐼𝑟𝑒𝑓 , are reference data given in datasheets as well as energies 𝐸𝑂𝑁 and 𝐸𝑂𝐹𝐹 . Note that 𝑓𝑠 represents the switching frequency. All the given expressions have been validated using blocks from the SimPowerSystems Simulink library. An important result is that IGBTs switching losses remain the same regardless of the switching strategies to insert short-circuits in either ZSI or QZSI systems. The experimental results are presented in the last section. Losses in the switches of the DC-side as well as diodes losses are not detailed in this paper but will be taken into account for the final result in parts III and IV. 2.

Short-circuit

𝑑𝑇 𝑑ℎ 𝑑𝑇 𝑡∈[ , − ] 4 2 4

𝑑ℎ 𝑑𝑇 𝑑ℎ 𝑡∈[ − , ] 2 4 2

𝑑ℎ 𝑇 𝑡∈[ , ] 2 2

𝑑𝐵 𝑣𝑓 − 𝑣𝐶 = 𝑑𝑡 𝑁⋅𝑆

𝑑𝐵 𝑣𝐶 = 𝑑𝑡 𝑁 ⋅ 𝑆

𝑑𝐵 𝑣𝑓 − 𝑣𝐶 = 𝑑𝑡 𝑁⋅𝑆

One obtains (22) according to (19):

𝐵𝑚𝑎𝑥

2

𝑍𝑆𝐼/𝑄𝑍𝑆𝐼

𝐵𝑚𝑖𝑛

𝑓𝑒𝑞

𝑑𝑏𝑜𝑜𝑠𝑡 𝑇

0

𝑇

𝑇 Fig. 7. Induction waveform in a DC-DC boost converter inductor.

√3 (1 − 𝑑 − 𝑚) 2 2 8𝑑 4 = 2 ⋅ 𝑓𝑠 ⋅ + 16 ⋅ + 2 2 𝜋 3𝑚 3 𝑚 (2 − 𝑑 − √3 𝑚) √3 𝑚 (

𝐵̂ =

)

(22)

1 √3 𝑚 ⋅ |𝐵𝑚𝑖𝑛 − 𝐵𝑚𝑎𝑥 | = |𝑣 − 𝑣𝐶 | 2 8 ⋅ 𝑁 ⋅ 𝑆 ⋅ 𝑓𝑠 𝑓

Iron losses in the ZSI or QZSI can finally be expressed as (23).

Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available athttp://dx.doi.org/10.1109/JESTPE.2014.2298755

𝑍𝑆𝐼/𝑄𝑍𝑆𝐼

𝑃𝑖𝑟𝑜𝑛

=

√3 (1 − 𝑑 − 2 𝑚)

𝑦

2 2 8𝑑 4 ⋅ 𝑙 ⋅ 𝑆 ⋅ 𝐶𝑚 ⋅ ⋅𝑓 ⋅ + 16 ⋅ + 𝑇 𝑧 𝜋2 𝑠 3𝑚2 3𝑚2 (2 − 𝑑 − √3𝑚) √3𝑚 (

3.

𝑥−1

2

(

√3𝑚 ⋅( |𝑣 − 𝑣𝐶 |) ⋅ (𝑐𝑡2 𝑇 2 − 𝑐𝑡1 𝑇 + 𝑐𝑡) 8 ⋅ 𝑁 ⋅ 𝑆 ⋅ 𝑓𝑠 𝑓

(23)

))

Resistive losses in the passive elements (DC-side networks)

Resistive losses in the passive elements are deduced from the expression of the different currents rms values. For instance, thanks to the waveforms presented in Fig. 7 and Fig. 8, it can be deduced the rms values of the inductive currents. The losses are expressed for the three considered systems as (24) and (25).

when the source voltage is high enough to control the machine, the QZSI efficiency is higher than the BC+VSI one. On the other hand, the BC+VSI efficiency becomes higher when short-circuits are inserted in the PWM scheme of the ZSI or QZSI systems. Instead of considering the efficiency for different operating points, it is suitable to compare the systems according to a speed profile on one operating cycle.

(Syst1: BC+VSI) DC-DC boost converter 𝑃𝐿𝐵𝑂𝑂𝑆𝑇

𝑣𝑓 2 2 2 𝑣𝑓2 (1 − ) 𝑇 𝑃0 𝑣𝐷𝐶 = 𝑟𝐿𝑏 ⋅ (( ) + ) 𝑣𝑓 12 𝐿2𝑏𝑜𝑜𝑠𝑡

(24)

(Syst2-3: ZSI and QZSI) Z-source or Quasi Z-source inverters 𝑍𝑆𝐼/𝑄𝑍𝑆𝐼

𝑃𝐿

2

2

𝑣𝑓 ⋅ 𝑑 ⋅ 𝑇 𝑃0 = 2 ⋅ 𝑟𝐿 ⋅ [( ) + ( ) 𝑣𝑓 8 ⋅ 𝐿𝑍𝑆𝐼/𝑄𝑍𝑆𝐼 ⋅ (2𝑑 − 1)

4 ⋅ ( (𝑑 − 1)2 + 2√3 ⋅ 𝑚 (𝑑 − 1) + 3𝑚2)] 3

(25)

Since the inductance value in the BC case is higher than that of ZSI or QZSI system, serial resistor 𝑟𝐿𝑏 is taken higher than 𝑟𝐿 according to turn’s number ratio between the systems. III. ANALYTICAL RESULTS, EFFICIENCY STUDIES All the analytical results are given according to the parameters detailed in Table III. These parameters are close to the real one (experimental test bench). Efficiency analytical results are plotted in Fig. 9 for different source voltage and operating points by varying the mechanical speed of a synchronous machine.

Fig. 10. Energetic comparison on a normalized speed profile between a BC+VSI and a QZSI.

Fig. 9. Efficiency plotted against mechanical speeds and for different source voltages.

Note that a viscous load torque has been taken into account. Its expression is given by 𝑇𝑠 = 𝑓𝑅 Ω. This corresponds to the experimental case where a generator and a 3-phase resistor is used to emulate the shaft torque (𝑓𝑅 is experimentally estimated to 0.0055 Nm s). Two surfaces are superimposed. The light gray one represents the BC+VSI efficiency whereas the dark gray one the ZSI/QZSI efficiencies. On the one hand,

In Fig. 10 are presented energetic consumption of two systems (BC+VSI and QZSI) according to the speed cycle in Fig. 10(d). This speed cycle is close to the New European Driving Cycle with urban driving and extra-urban driving steps. It has to be simulated for 1200s and with four urban driving cycles. However, for adaptation to the experiment test bench, it has been slightly modified. Fig. 10(a) presents the energy provided by the source during the cycle. This latter is evaluated to 6010 J and 6046 J for the BC+VSI and the QZSI respectively. The difference of consumption is thus about 0.6% higher for the QZSI system. As regards the stored energy in the systems, the results presented in Fig. 10(b) confirm that the BC has to store more energy, especially when the source voltage has to be stepped up. Concerning the efficiency calculated for one cycle, they are estimated to 90.3% and 90.8% for the QZSI and BC+VSI respectively. Thus, for a realistic use of the converters where the source voltage elevation is only used in case of machine overspeed, the converters are almost equivalent in efficiency terms. By focusing on QZSI, Fig. 11 presents details of the provided and

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consumed energies during one cycle. The difference between these latter curves represents losses. They are estimated to 580 J. This figure will be compared to the experimental results of the next part.

running simultaneously. The switching frequency and the sampling frequency has been fixed to 10 kHz. A stabilized DC-source is used to replace the voltage source. Besides, the load is a 3-phase resistor fed by a synchronous generator coupled with the machine used.

Computer

Scope

dSpace 1005

QZSI

DC-source

𝑃𝑀𝑆𝑀 3-phase resistor Fig. 11. Provided energy and consumed energy of the QZSI system for one speed cycle.

Fig. 12 presents now both the QZSI and the BC stored energies when the source voltage is reduced to 60V. Thus, this latter has to be stepped up earlier than the previous case and more energy has to be stored when the duty cycle is different from zero. Results point out that the stored energy in the QZSI passive elements (two capacitors and coupled inductors) is lower than in the BC one. From a design point of view, BC passive elements will have to be sized for the maximum stored energy and their volume and cost will be larger than those of the QZSI. Note that when the stored energy is doubled, both the cost and the volume are almost doubled according to the analysis made in [17].

𝐶𝑄𝑍𝑆𝐼

inverter

𝐿𝑄𝑍𝑆𝐼

𝐶𝑓

generator

Fig. 13. Experimental test bench with the Quasi Z-source inverter. Top: overview of the experimental test bench. Bottom: zoom on the QZSI system

Experimental results presented in Fig. 14 are in accordance with this latter property because the three surfaces are actually almost equivalent. However, the 3-leg method will be chosen in order to reduce current stress on switches. In Fig. 15, the ZSI experimental efficiency and analytical efficiency are superimposed. This validate the analytical losses estimation presented above.

Fig. 12. Stored energies for 𝑣𝑠 = 60𝑉 for the same operating cycle as presented in Fig. 10(d).

IV. EXPERIMENTAL RESULTS ON THE QZSI In order to experimentally validate all these efficiency results, a PMSM supplied with a QZSI or ZSI is realized and tested. The experimental test bench is presented in Fig. 13. Global control is implemented on a dSPACE DS1005 processor programmable from Simulink. In addition, a DS5203 FPGA board is used to generate both the sampling interruptions and the modified SVM reference functions to insert the shortcircuits according to the 1-leg, 2-legs or 3-legs strategies. This FPGA board is programmed via the RTI FPGA Programming Blockset from dSPACE and Xilinx System Generator. Applications for the processor board and the FPGA board are

Fig. 14. Experimental result comparing the three methods to insert short circuit in the Z-source or Quasi Z-source inverters topologies.

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TABLE III EXPERIMENTAL/SIMULATION SYSTEMS PARAMETERS

Fig. 15. Validation of the analytical expressions given here for the Z-source inverter.

As in simulation, an experimental energetic study is led in response to a normalized speed profile. In Fig. 16, the speed profile, the energies and efficiency are plotted against real time. Provided energy during this cycle is noted 𝐸𝑆 while consumed energy is noted 𝐸𝐿 . These results have to be compared with the one obtain above in simulation with the same parameters as in experimental case (see Fig. 11). Thus, energetic losses during one cycle are equal to 500 J. They had been overestimated to 580 J in simulation for the same test. This allows validating energetic study and confirms that the Syst3: QZSI stores less energy than the Syst1: BC+VSI.

(20% /div) (1400 J/div)

Description

𝑙𝑑 = 𝑙𝑞

5 mH

Stator inductance

𝑟𝑠

1.5 Ω

Stator resistance

𝜙𝑓

0.068 Wb

Magnet flux linkage

𝑝

4

Number of pole pairs

Ω

0 – 2500 rpm

Mechanical speed

𝑇𝑠

0.0055 Nm

Shaft torque

𝑓

0.01 Nm s

Friction coeffcient

𝐽

500 10−7 kg m²

Inertia coefficient

𝐶𝑄𝑍𝑆𝐼

680 µF

QZSI capacitors

𝐿𝑄𝑍𝑆𝐼

500 µH

QZSI inductors

𝑟𝐿

0.3 Ω

QZSI inductors serial resistors

𝑁

26

Turns number (inductors)

𝑆

10.70 𝑐𝑚

𝑙𝑧

29.4 𝑐𝑚

2

Effective magnetic cross section Effective magnetic path length

3

𝑉𝑜𝑙

157 𝑐𝑚

𝑟𝑘0

35 𝑚Ω

IGBT resistor

𝑣𝑘0

1.1 V

IGBT threshold voltage

Effective magnetic volume

𝐸𝑂𝑁

0.34 mJ

IGBT switch ON energy

𝐸𝑂𝐹𝐹

0.63 mJ

IGBT switch OFF energy

𝐸𝑟𝑒𝑐

0.5 mJ

Diode recovery energy

[1]

F. Z. Peng, “Z-source inverter,” IEEE Trans. Ind. Appl., vol.39, no.2, pp. 504- 510, Mar/Apr 2003.

[2]

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Fig. 16. Experimental energetic study for a Quasi Z-source inverter in response to a normalized speed profile.

This paper has presented a way to compare electric traction systems with objective criteria taking into account the stored energy, the rms capacitive currents values, the voltage ratios and the losses. According to these results, the Quasi Zsource inverter seems to be a good alternative to the conventional topology using a BC+VSI association. Energetic studies show that for a given speed profile, the efficiency between the systems is about the same but the stored energy is smaller for the QZSI than for the BC+VSI. This leads to the conclusion that the Quasi Z-source inverter has smaller passive elements, which represents a good advantage in automotive applications. As regards the converters cost, the QZSI has one switch less in comparison to BC+VSI topology.

Value

REFERENCES

(420 rpm/div)

V. CONCLUSION

Symbol

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This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication. The final version of record is available athttp://dx.doi.org/10.1109/JESTPE.2014.2298755

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