This paper proposes a compensation PWM technique for the extension of output voltage ranges in threephase VSI applications using three shunt resistors. The proposed technique aims to solve the dead zone, which occurs in high modulation indexes. In the dead zone, two phase currents cannot be sampled correctly, so that the threephase VSI cannot be operated up to the maximum output voltage. The dead zone is analyzed in detail, and the compensation PWM algorithm is developed. The proposed algorithm is verified by numerical analysis and experimental results.
1. Introduction
In a threephase voltage source inverter (VSI) used for AC motor applications, the phase current should be precisely monitored and sensed as much as possible to ensure the stable operation of the VSI. In general, highbandwidth current sensors such as a current transducer and halleffect type current sensor are widely used to sense the phase current. However, in some cost sensitive applications, the number of sensors has been reduced and highbandwidth sensors have been replaced by low cost ones
[1
,
2]
.
One of the alternative solutions to monitoring and sensing the phase current is to use a shunt resistor, which has the advantages of low cost and small size. However, the use of shunt resistors leads to two major problems, namely, power loss and dead zone. Implementation of shunt resistors on the main power board increases the power loss. However, the power loss from a few milliohm shunt resistor is negligible in medium power applications like home appliances. Compared to the power loss, the dead zone is a much serious problem. If the output voltage is located in the dead zone, current sampling and reconstruction become limited or impossible without a proper compensation method
[3

5]
.
Two types of phase current sampling techniques using the shunt resistor has been presented in previous studies. One uses a single dclink shunt resistor connected to a negative dc bus as shown in
Fig. 1(a)
. The information of three phase currents is reconstructed in the DSP (Digital Signal Processor) by using the measured dclink current with applied pulse width modulation (PWM) switching patterns. However, in this case, when the active switching vector is not maintained for a sufficient time, a dead zone needs to be considered
[6
,
7]
. To solve this dead zone problem, which arises from the use of the single dclink shunt resistor, various strategies have been proposed: adjusted pulse width modulation method
[8
,
9]
; modified modulation method
[10]
; observer method
[11]
; and vector insertion method
[12]
. However, the single dclink shunt resistor technique is limitedly used in industrial applications since the reliability of the startup and low speed control for AC motors is not ensured. The other phase current sampling technique uses three shunt resistors, each connected between the emitter of a power switch and the dclink negative line as shown in
Fig. 1(b)
. This technique is widely used in some cost sensitive home applications and vector control drives since there is no limit on the low modulation indexes for the startup and low speed control and it can provide sufficient reliability and costeffectiveness. However, at high modulation indexes, it also induces the dead zone when the holding time of the zero switching vector is not sufficient for measurement of reliable phase current information in the DSP
[13
,
14]
.
Two types of phase current sampling techniques using shunt resistors
Phase current regulation using three shunt resistors cannot be guaranteed above about 90％ of the maximum output voltage in space vector pulse width modulation (SVPWM)
[15]
. In this problem output voltage range, the holding time of the zero switching vector is not sufficient for current sampling in the DSP. Therefore, in this paper, the advanced PWM technique for the three shunt resistors is proposed to extend the output voltage range of the threephase VSI. With the proposed technique, the threephase VSI can be controlled up to the maximum output voltage in SVPWM. Moreover, the proposed technique can be implemented simply with the lowcost DSP. The proposed technique is verified by experiments measuring the phase current under various conditions.
2. Analysis of Phase Currents Sampling Using Three Shunt Resistors
 2.1 General description of phase currents sampling
Unlike the halleffect type current sensors and current transducers, the three shunt resistors are connected between the emitters of the power switches and the dclink negative line, respectively, to share the same ground terminal, so they depend on the states of low side switches (S
_{4}
, S
_{6}
and S
_{2}
) to measure the phase currents. There are eight switching state combinations: active switching vectors (V
_{1}
~ V
_{6}
) and zero switching vectors (V
_{0}
and V
_{7}
). The sampling phase currents for each switching vector are summarized in
Table 1
. For the zero switching vector 111, no phase current can be sampled since no phase current flows through any of the shunt resistors. However, in the case of the zero switching vector 000, all phase currents can be sampled since three phase currents are freewheeled through a load and the lowside switches. For phase current regulation in the threephase VSI, information about at least two phase currents is required. The unknown phase current can be calculated assuming current symmetry, i.e., I
_{U}
+ I
_{V}
+ I
_{W}
= 0. Therefore, in the cases of vectors V
_{1}
, V
_{3}
and V
_{5}
, information about three phase currents can be obtained. However, in the case of vectors V
_{2}
, V
_{4}
and V
_{6}
, phase current regulation is impossible since only one phase current can be sampled.
Sampling phase currents according to switching vectors
Sampling phase currents according to switching vectors
In the PWM period (T
_{S}
= T
_{k}
+ T
_{k+1}
+ T
_{0}
, k = 1 ~ 5), there are two active switching vectors (V
_{k}
and V
_{k+1}
) for two active switching vector times (T
_{k}
and T
_{k+1}
) and two zero switching vectors (V
_{0}
and V
_{7}
) for a zero switching vector time (T
_{0}
). For examples, in sector 2, a reference voltage vector (V
^{*}
) is calculated as
In the PWM period T
_{S}
, at least one of the vectors V
_{2}
, V
_{4}
and V
_{6}
is included, and the switching vector time is changed according to the magnitude and angle of the reference voltage vector. Therefore, in order to obtain information about three phase currents in the DSP, regardless of the switching vectors and the reference voltage vector, the current sampling point must be synchronized with the peak of a PWM carrier since vector V
_{0}
always appears at the peak of a PWM carrier.
 2.2 Limitation of phase currents sampling
For reliable phase current sampling, the turnon times of the lowside switches should be longer than the minimum required turnon time. Based on
Fig. 2
, the minimum turnon time is determined as
Minimum required turnon time of the low side switch
T
_{MIN}
includes the IGBT turnon delay time (T
_{DEL}
), phase current rise and settling time (T
_{RS}
) and analogtodigital conversion time (T
_{AD}
). T
_{DEL}
includes the dead time, IGBT driver signal processing time and IGBT turnon delay time. T
_{AD}
is related to the extra sample and hold time, which is needed to ensure the ADC operation after the sampling has initiated. If T
_{MIN}
is not guaranteed, phase current sampling cannot be ensured.
The turnon times of the lowside switches for each phase are calculated based on the active switching vector time and the zero switching vector time as shown in
Fig. 3
. T
_{SHORT}
, T
_{MIDDLE}
and T
_{LONG}
represent the turnon times of each lowside switch. The largest phase voltage determines T
_{SHORT}
, the medium one determines T
_{MIDDLE}
and the smallest one determines T
_{LONG}
. These times vary according to the switching vectors used in each sector as shown in
Table 2
.
Relationship between the threephase PWM pattern and the lowside switches turnon time in sector 1
Limitation phase according to lowside switch turnon time
Limitation phase according to lowside switch turnon time
T
_{LONG}
is always longer than T
_{MIN}
because each phase current has a phase shift of 120 degrees. However, T
_{SHORT}
and T
_{MIDDLE}
are the limiting factors of phase current sampling since they decrease depending on the output voltage command. Accordingly, T
_{SHORT}
should satisfy the following condition to ensure measurement of three phase currents at the same time
If T
_{SHORT}
does not satisfy condition (3), the corresponding phase current cannot be sampled correctly. Then, T
_{MIDDLE}
determines whether another phase current can be sampled or not. Therefore, conditions for two phase currents sampling can be written as
In the conditions (4) and (5), the phase current corresponding to T
_{SHORT}
cannot be sampled correctly. However, the phase currents corresponding to T
_{MIDDLE}
and T
_{LONG}
can be sampled correctly. Consequently, the unknown phase current can be calculated. Nevertheless, it should be noted that if T
_{SHORT}
and T
_{MIDDLE}
are shorter than T
_{MIN}
, the use of the output voltage is limited since two phase currents cannot be sampled accurately; this condition is called the dead zone. Therefore, in the dead zone, the solving technique is strongly required to control and extend the output voltage range for the threephase VSI using three shunt resistors.
3. Proposed Compensation PWM Technique
In order to reliably use a threephase VSI using three shunt resistors up to the maximum output voltage vector, three phase currents need to be classified as a measurable phase current or an immeasurable phase current.
 3.1 Dead zone analysis
In the PWM period T
_{S}
, T
_{0}
is determined by the highest phase voltage command. As shown in
Fig. 4
, if T
_{0}
does not satisfy condition (3), the phase current corresponding to the highest voltage phase command cannot be sampled correctly. The criterion of the reference voltage vector for three phase currents sampling can be calculated as
where V
_{DC}
is the dclink voltage and the f
_{sw}
is the switching frequency in the threephase VSI. Furthermore, in this problem region, two phase currents sampling region and only one phase current sampling region exist together according to the magnitude and angle of the reference voltage vector. Especially, the only one phase current sampling region, which is the dead zone, is affected by the holding times of vectors V
_{2}
, V
_{4}
and V
_{6}
.
Problem region in sector 1 in which three phase current sampling is not possible
Fig. 5
shows the three phase PWM patterns at the maximum output voltage vector for the reference voltage vector angle of 0° and 60°. In the case of
Fig. 5(b)
, the turnon times of the lowside switches are obtained by using T
_{0}
and T
_{1}
. The highest phase voltage command does not satisfy condition (3). However, the two phase currents corresponding to T
_{MIDDLE}
and T
_{LONG}
can be sampled. In contrast, when θ approaches 60 degrees, T
_{1}
is decreased and T
_{2}
is increased. If condition (5) is not satisfied according to the increase of T
_{2}
, the information about the two phase currents corresponding to T
_{SHORT}
and T
_{MIDDLE}
cannot be sampled as shown in
Fig. 5(a)
. Therefore, a dead zone is generated when the reference voltage vector centers the marked region in
Fig. 6
, and it is also generated around V
_{4}
and V
_{6}
same as V
_{2}
.
Relationship between the angle of the reference voltage vector and the three phase PWM pattern at the maximum output voltage vector
Classification of unusable reference voltage vector due to the dead zone
 3.2 Classification of each phase
In each PWM cycle, a criterion, regardless of the magnitude and angle of the reference voltage vector, is needed to determine whether conditions (3) and (5) are satisfied or not. This criterion can be obtained from the magnitude of the phase voltage, which is compared with the PWM carrier to generate the PWM pattern. If the magnitude of the phase voltage is large, the turnon times of the lowside switches are short and if it is small, the turnon times of lowside switches are long, therefore, the magnitude of the phase voltage for T
_{MIN}
can be determined. Consequentially, after the magnitude of the phase voltage for T
_{MIN}
is determined, phase currents can be classified as either measureable or immeasurable by comparison with each phase voltage. The criterion phase voltage for T
_{MIN}
can be determined as
When all phase voltages are smaller than V
_{LIM}
, all phase currents can be sampled. However, when the largest phase voltage is greater than V
_{LIM}
, condition (3) is not satisfied as shown in
Fig. 7(a)
. In this case, the phase current can be classified as immeasurable using
Eq. (7)
. Furthermore, the dead zone is generated as shown in
Fig. 7(b)
when the magnitude of the reference voltage vector is bigger than the value of Eq. (6). If one of the three phase voltages is bigger than V
_{LIM}
, the immeasurable phase current can be calculated in the same way as in the
Fig. 7(a)
case. However, if two of the three phase voltages are bigger than V
_{LIM}
, all phase voltages need to be reconstructed to obtain a longer time than T
_{MIN}
.
Classification of each phase voltage in SVPWM
 3.3 Implementation of compensation PWM technique
The compensation PWM technique is implemented through four processes as shown in
Fig. 8
. The phase separator process compares each phase voltage with V
_{LIM}
in order to classify three phase voltages into the measurable phase current and the immeasurable phase current. The phase compensator process reconstructs all phase voltages to measure at least two phase currents when two of the three phase voltages are bigger than V
_{LIM}
. The next process is the current sampling. When all phase voltages are smaller than V
_{LIM}
, three phase current sampling is carried out. However, when one or two phase voltages are bigger than V
_{LIM}
, two phase current sampling is carried out. The current calculator process calculates the unknown phase current information at the end.
Compensation PWM technique process
Three operation modes are integrated in the compensation PWM technique. The first mode is operated when all phase currents can be sampled directly. Second mode is operated when two phase currents can be sampled. Third mode is operated in the dead zone.
 3.3.1 Mode 1
When all phase voltages are smaller than V
_{LIM}
, three phase currents can be sampled directly using the three shunt resistors. This mode is operated in the phase separator process and the current sampling process.
 3.3.2 Mode 2
When one of the three phase voltages are bigger than V
_{LIM}
, the immeasurable phase current must be calculated so that it can be classified in the phase separator. In the current calculator, the immeasurable phase current is calculated using the measurable phase current obtained from the current sampling process.
 3.3.3 Mode 3
When two of the three phase voltages are bigger than V
_{LIM}
, all voltages need the reconstruction to sample two phase currents as shown in
Fig. 9
. Two immeasurable phase currents are classified in the phase separator. In the phase compensator, first, the middle magnitude phase voltage (V
_{MIDDLE}
) between two immeasurable phases (V
_{IM_1ph}
, V
_{IM_2ph}
) is determined as follows
Modified reference voltages and switching states for two phase currents sampling in mode 3
Then, the minimum rate of voltage change to guarantee T
_{MIN}
in V
_{MIDDLE}
is calculated as
If V
_{MIDDLE}
is reduced by V
_{DIF}
, its immeasurable phase is changed to the measurable phase. Voltage reconstruction is performed as follows to guarantee T
_{MIN}
in two phases without change of the linetoline voltage
where V
_{SHORT}
is the biggest phase voltage, V
_{MIDDLE}
is medium one and V
_{LONG}
is the smallest one. Using the phase voltage reconstruction as Eqs. (11, 12) and (13), the turnon times of the lowside switches becomes longer since the reconstructed reference voltage becomes smaller than the reference voltage. V
_{SHORT}
is changed to V
_{SHORT_DIF}
, but nevertheless the phase current corresponding to V
_{SHORT_DIF}
cannot be still sampled. However, V
_{MIDDLE}
is reconstructed to V
_{MIDDLE_DIF}
which guarantees T
_{MIN}
for the phase current sampling. The phase current corresponding to V
_{LONG}
can be sampled without the voltage reconstruction since the turnon times of the lowside switches corresponding to V
_{LONG}
is always longer than T
_{MIN}
. Thus, the voltage change for phase current sampling is minimized by setting V
_{MIDDLE}
on the criterion of the voltage reconstruction. Moreover, all phase voltages are reconstructed to sample two phase currents without change of the linetoline voltage. The turnon times of the lowside switches is changed as follows during the voltage reconstruction.
where T
_{DIF}
is added to the turnon times of the lowside switches through the voltage change. Therefore, since two phase currents corresponding to V
_{MIDDLE}
and V
_{LONG}
can be sampled, the remaining phase current corresponding to V
_{SHORT}
can be calculated using these phase currents in the current calculator.
4. Experimental Results
Fig. 10
shows the entire experimental system including the proposed technique to monitor phase currents. To validate the feasibility of the proposed compensation PWM technique, a VSI using three shunt resistors based on Freescale DSP 56F803 was implemented. V23990P546A28 module of Vincotech was chosen for the inverter. The shunt resistor of 10mΩ was employed to sense the phase current. The internal variables inside the DSP were monitored through a 12bit serial digitaltoanalog converter (DAC). The other parameters used in this experiment were as follows: VDC is 310V; TMIN is 23usec; f
_{sw}
is 5kHz. An experiment was performed in V/F control with an induction motor.
Experimental testbed
Fig. 11
shows the reconstruction current waveforms without and with the proposed compensation PWM technique under no load. I
_{U_SAMP}
and I
_{U_CAL}
are DAC signals which are sampled by using the ADC in the DSP. I
_{U_SAMP}
is sampled without the compensation PWM technique and I
_{U_CAL}
is sampled with the compensation PWM technique. I
_{U}
is the U phase output current, which is measured using a current probe. Before the application of the compensation PWM technique, I
_{U_SAMP}
had an extremely distorted waveform in high MI. Especially, when θ is varied between about −60° and 60°, it could not be sampled accurately, as predicted in Sector 3. When MI is 0.66, the phase current information can be sampled correctly since the turnon times of the lowside switches is longer than T
_{MIN}
as shown in
Fig. 11(a)
. In contrast, when MI is bigger than 0.93, I
_{U_SAMP}
was extremely distorted as shown
Figs. 11(b)
and (C). When MI is higher than before, the distortion of the ADC signal is getting worse since the region where the phase voltage is bigger than V
_{LIM}
is increased. However, regardless of the MI, I
_{U_CAL}
has a nearly similar waveform as I
_{U}
.
Fig. 12
shows the reconstruction current waveform when the threephase VSI is controlled at full load. When MI is 0.66, the phase current information can be sampled correctly as shown
Fig. 12(a)
. However, same as
Figs. 11(b)
and (c), when MI is bigger than 0.93, I
_{U_SAMP}
is extremely distorted as shown
Figs. 12(b)
and (C). The difference is that the immeasurable region is shifted since a current phase angle is shifted according to load status. Nevertheless, I
_{U_CAL}
also has a nearly similar waveform as I
_{U}
regardless of MI.
Comparison of compensation PWM technique test according to MI at no load (U_{Ref}: 10V/div; I_{U}: 10A/div; I_{U_SAMP} and I_{U_CAL}: 5V/div)
Comparison of compensation PWM technique test according to MI at full load (U_{Ref}: 10V/div; I_{U}: 20A/div; I_{U_SAMP} and I_{U_CAL}: 10V/div)
5. Conclusion
A threephase VSI using three shunt resistors cannot be used until the maximum output voltage has been analyzed. From the analysis, three phase currents sampling region, two phase currents sampling region and one phase current sampling region were identified. This paper proposed the compensation PWM technique to use the whole output voltage range of the threephase VSI using three shunt resistors. The proposed technique classifies the measurable phase current and the immeasurable phase current based on a criterion phase voltage. Therefore, the minimum rate of voltage change to guarantee the minimum required turnon time of the lowside switch can be calculated. In the dead zone, voltage reconstruction is performed to guarantee T
_{MIN}
in two phases without change of the linetoline voltage. As a result, the voltage utilization of the threephase VSI can be improved from lowperformance V/F drives to highperformance vector control drives. The validity of the proposed technique has been supported by experimental results.
BIO
SeungMin Shin He received his B.S. and M.S. degrees in Electrical Engineering from Sungkyunkwan University, Suwon, Korea, in 2009 and 2011, respectively. Since 2009, he has studied for Ph.D. degree in electrical Engineering at Sungkyunkwan University. His research interests are electric vehicle drives, power electronics and advanced motor drive systems.
RaeKwan Park He received the B.S. and the M.S. degrees in Electrical Engineering from Hanyang University, Seoul, Korea, in 1992 and 1994, respectively. Since 2010, he has worked for his Ph. D. degree in Electrical Engineering at Sungkyunkwan University. His research interests include electric motor drives, electrical machines, high/low power DCDC converter for PHEV/EV and advanced motor drive systems.
ByoungKuk Lee He received the B.S. and the M.S. degrees from Hanyang University, Seoul, Korea, in 1994 and 1996, respectively and the Ph.D. degree from Texas A＆M University, College Station, TX, in 2001, all in electrical engineering. From 2003 to 2005, he has been a Senior Researcher at Power Electronics Group, Korea Electrotechnology Research Institute (KERI), Changwon, Korea. From 2006 Dr. Lee joins at School of Information and Communication Engineering, Sungkyunkwan University, Suwon, Korea. His research interests include charger for electric vehicles, hybrid renewable energy systems, dc distribution systems for home appliances, power conditioning systems for fuel cells and photovoltaic, modeling and simulation, and power electronics. Prof. Lee is a recipient of Outstanding Scientists of the 21^{st} Century from IBC and listed on 2008 Ed. of Who’s Who in America. Prof. Lee is an Associate Editor in the IEEE Transactions on Industrial Electronics and Power Electronics. He was the General Chair for IEEE Vehicular Power and Propulsion Conference (VPPC) in 2012.
Ziegler Silvio
,
Woodward Robert C.
,
Iu Herbert HoChing
,
Borle Lawrence J.
2009
“Current Sensing Techniques: A Review,”
IEEE Sensors J.
9
(4)
354 
376
DOI : 10.1109/JSEN.2009.2013914
Xiao Chucheng
,
Zhao Lingyin
,
Asada Tadashi
,
Odendaal W. G.
,
van Wyk J. D.
2003
“An Overview of Integratable Current Sensor Technologies,”
in Proc. Conf. Rec. Ind.
2
1251 
1258
Ha JungIk
2009
“Voltage Injection Method for ThreePhase Current Reconstruction in PWM Inverters Using a Single Sensor,”
IEEE Trans. Power Electron.
24
(3)
767 
775
DOI : 10.1109/TPEL.2008.2009451
Marčetić Darko P.
,
Adžić Evgenije M.
2010
“Improved ThreePhase Current Reconstruction for Induction Motor Drives With DCLink Shunt,”
IEEE Trans. Ind. Electron.
57
(7)
2454 
2462
DOI : 10.1109/TIE.2009.2035456
Metidji Brahim
,
Taib Nabil
,
Baghli Lotfi
,
Rekioua Toufik
,
Bacha Seddik
2012
“LowCost Direct Torque Control Algorithm for Induction Motor Without AC Phase Current Sensors,”
IEEE Trans. Power Electron.
27
(9)
4131 
4139
Kim Hongrae
,
Jahns Thomas M.
2006
“Current Control for AC Motor Drives Using a Single DCLink Current Sensor and Measurement Voltage Vectors,”
IEEE Trans. Ind. Appl.
42
(6)
1539 
1547
DOI : 10.1109/TIA.2006.882630
Sun Kai
,
Wei Qing
,
Huang Lipei
,
Matsuse Kouki
2009
“An Overmodulation Method for PWMInverterFed IPMSM Drive With Single Current Sensor,”
IEEE Trans. Ind. Electron.
57
(10)
4874 
4879
Blaabjerg Frede
,
Pedersen John K.
,
Jaeger Ulrik
,
Thoegersen Paul
1997
“Single Current Sensor Technique in the DC link of ThreePhase PWMVS Inverters: A Review and a Novel Solution,”
IEEE Trans. Ind. Appl.
33
1241 
1253
DOI : 10.1109/28.633802
Metidji Brahim
,
Taib Nabil
,
Baghli Lotfi
,
Rekioua Toufik
,
Bacha Seddik
1988
“Novel Current Sensor for PWM AC Drives,”
Proc Electr. Power Appl.
135
27 
32
DOI : 10.1049/ipb.1988.0005
Joo HyeongGil
,
Yoong Youn MyungJoong
,
Shin HwiBeom
2000
“Estimation of Phase Currents from a DCLink Current Sensor Using Space Vector PWM method,”
Electr. Mach. Power Syst.
28
1053 
1069
DOI : 10.1080/073135600449107
Wolbank Thomas Michael
,
Macheiner Peter Erich
2004
“CurrentControl With Single DC Link Current Measurement for InverterFed AC Machines Based on an Improved ObserverStructure,”
IEEE Trans. Power Electron.
19
(6)
1562 
1567
DOI : 10.1109/TPEL.2004.836633
Kim Hongrae
,
Jahns Thomas M.
2006
“Phase Current Reconstruction for AC Motor Drives Using a DC Link Single Current Sensor and Measurement Voltage Vectors,”
IEEE Trans. Power Electron.
21
(5)
1413 
1419
DOI : 10.1109/TPEL.2006.880262
Chi S.
,
Wang X.
,
Yuan Y.
,
Zhang Z.
,
Xu L.
2007
“A Current Reconstruction Scheme for LowCost PMSM Drives Using Shunt Resistors,”
APEC2007Twenty Second Annual IEEE
1701 
1706
Parasiliti Francesco
,
Petrella Roberto
,
Tursini Marco
1999
“Low Cost Phase Current Sensing in DSP Based AC Drives,”
in Proc. IEEE Int. Symp. Industrial Electronics (ISIE'99)
Bled, Slovenia
1284 
1289
Cho ByungGeuk
,
Ha JungIk
,
Sul SeungKi
2011
“Voltage Injection Method for Boundary Expansion of Output Voltages in ThreeShunt Sensing PWM Inverters,”
ICPE, IEEE ECCE Asia 2011
Jeju, Korea
411 
415