Modified Space Vector Modulated Z Source inverters with wide modulation range and lowest switching stress.

Thangaprakash, S. ; Krishnan, A.

Introduction

Z source inverter overcomes the problems in the Traditional Voltage Source and Current Source Inverters. It employs a unique impedance network coupled with the inverter main circuit to the power source. It consists of voltage source from the rectifier supply, impedance network, three phase inverter and three phase load. The ac voltage is rectified to dc voltage by the rectifier. The output voltage of the rectifier is 1.35 times the dc input. The rectifier output dc voltage fed to the impedance network, which consist of two equal inductors ([L.sub.1] = [L.sub.2] = L) and two equal capacitors ([C.sub.1] = [C.sub.2] = C). The network inductors are connected in series arms and capacitors are connected in diagonal arms as shown in figure 1. The impedance network is used to buck or boost the input voltage depending on the boosting factor derived by applying the shoot through which is to be hidden in conventional VSIs. This network also acts as a second order filter and it should require less inductance and less capacitance. The inverter main circuit consists of six switches. These z source inverters use a unique impedance network, coupled between the power source and converter circuit, to provide both voltage buck and boost properties, which cannot be achieved with conventional voltage source and current source inverters [1]. The unique feature of the Z source inverter is that the output ac voltage can be any value between zero and infinity regardless of dc voltage. That is, the Z source inverter is a buck-boost inverter that has a wide range of voltage control [3].

Several control methods for the Z-source inverter have been developed since the Z-source inverter was proposed in 2002 [3]-[5]. In these control strategies, the capacitor voltage is controlled by the shoot-through duty ratio and the output voltage is controlled by the modulation index, respectively. Both of the two controllers are designed separately, thus the whole system stability is not guaranteed. Furthermore, it cannot make full use of the dc input voltage, which results in low control voltage margin and quite high voltage stress across the switches. The voltage boost is inversely related to the shoot through duty ratio, therefore the ripple in shoot through duty ratio will result in ripple in the current through the inductor as well as the voltage in the capacitor. When the output frequency is low, the inductor current ripple becomes significant. All the above problems are addressed by different control techniques with various control algorithms.

[FIGURE 1 OMITTED]

To address the different requirements mentioned above simultaneously, this paper presents a new voltage vector of the Z-source inverter based on space-vector PWM (SVPWM) techniques, which is composed of the traditional voltage vector and the unique boost factor of the Z-source inverter. A Modified Control algorithm for Space Vector Modulated (SVM) Z Source inverters has been proposed. Full utilization of the dc link input voltage and keeping the lowest voltage stress across the switches with variable input voltage is presented in this paper. System stability is improved since it is a single stage control method from the view point of global inverter operation.

Operation of Z Source Inverter

The operating principle and conventional control methods of the Z source inverter are discussed in [1]. The traditional three-phase voltage source inverter has six active vectors in which the dc voltage is impressed across the load and two zero vectors when the load terminals are shorted through either the lower or upper three devices, respectively. However, three phase Z source inverter bridge has one extra zero state called shoot through, when the load terminals are shorted through both the upper and lower devices of any one phase leg, any two phase legs, or all three phase legs. This shoot-through zero state is forbidden in the traditional voltage source inverter, because it would cause a shoot-through. The Z source network makes the shoot-through zero state efficiently utilized throughout the operation [5][6]. Equivalent circuit of the z source inverter could be drawn as shown in figure 2. It has three operating modes, namely traditional zero mode, shoot through mode and non-shoot through mode. Assuming that the inductors [L.sub.1] and [L.sub.2] and capacitors [C.sub.1] and [C.sub.2] have the same inductance (L) and capacitance (C) respectively,

From the symmetry of the z source network and equivalent circuit we have,

[V.sub.C1] = [V.sub.C2] = [V.sub.C]; [v.sub.L1] = [v.sub.L2] = [v.sub.L] (1)

[FIGURE 2 OMITTED]

Mode I--The inverter bridge is under shoot through state for an interval [T.sub.0], during a sampling period [T.sub.s]. The diode in the equivalent circuit will be reverse biased in this case. The voltage across the impedance elements could be related as,

[v.sub.L] = [V.sub.C]; [v.sub.d] = 2[V.sub.C]; [v.sub.i] = 0 (2)

Where [v.sub.d] is the dc voltage before the impedance network and [v.sub.i] is the dc link voltage of the inverter.

Mode--II--The circuit is in any one of the active vectors thus operating in one of the traditional vector mode. The diode in the equivalent circuit will be reverse biased in this case. From the symmetry of the z source network and equivalent circuit we have,

[v.sub.L] = [V.sub.0] - [V.sub.C] = [V.sub.0]; [v.sub.i] = [V.sub.C] - [v.sub.L] = [V.sub.C] - [V.sub.0] (3)

Where [V.sub.0] is dc supply voltage.

Mode III--The inverter bridge is in any one of the traditional zero vectors (000 or 111) thus operating in one of the traditional zero vector mode.

The peak dc link voltage across the inverter bridge is expressed in (3) and it can be written as,

[[??].sub.i] = [V.sub.C] - [v.sub.L] = 2[V.sub.C] - [V.sub.0] = 1/1 - 2[D.sub.0] [V.sub.0] = B[V.sub.0] (4)

Where B is boost factor and [D.sub.0] is shoot through duty ratio. The voltage stress Vs across the switch is equal to the peak dc-link voltage [[??].sub.i] = B[V.sub.0], therefore, to minimize the voltage stress for any given voltage gain (G = B.M), we need to minimize B and maximize M, with the restriction of that their product is the desired value. On the other hand, we should maximize B for any given modulation index M, to achieve the maximum voltage gain.

The basic idea of control is to turn traditional zero state into shoot-through zero state, while keeping the active vectors unchanged, thus we can maintain the sinusoidal output and at the same time achieve voltage boost from the shoot through of the dc link. To achieve good performance for both the dc boost and the ac output voltage in the Z-source inverter, several close-loop control methods were proposed [4]-[5]. In these control methods, the capacitor voltage is controlled by the shoot-through duty ratio [D.sub.0] and the output voltage is controlled by the modulation index M respectively. The two degree-of-freedom controllers are designed separately. It has some inherent drawbacks.

Modified Modulation Technique

Space Vector Modulation

SVPWM method is an advanced, Computation-intensive PWM method and is possibly the best among all the PWM techniques for variable speed applications. Because of its superior performance characteristics, it has been finding widespread application in recent years. All the existing PWM methods have only considered implementation on a half bridge of a three phase bridge inverter. If the load neutral is connected to the center tap of the dc supply, all three bridges operate independently, giving satisfactory PWM performance. With the machine load, the load neutral is normally isolated, which causes interaction among the phases. This interaction was not considered in other PWM techniques. SVPWM considers this interaction of the phases and optimizes the harmonic content of the three phase isolated neutral load [8][9]. There are not separate modulation signals in each of the three phases in SVPWM techniques. Instead, a voltage vector is processed as a whole. Therefore, it is very suitable to control the shoot-through time. Fig.3 shows the voltage space vectors for the traditional three-phase two-level PWM inverters. The output voltage of the inverter is determined by the different voltages between each inverter arm and the time duration in which the different voltage is maintained. Define eight voltage vectors [??], [??], [??] ........ [??] corresponding to the switching states [??] = [0 0 0], [??] = [1 0 0]........ [??] = [1 1 1] respectively. [??], [??] ......... [??] are called active vectors and [??] and [??] are called traditional zero vectors.

[FIGURE 3 OMITTED]

Fig.3. Voltage space vectors with shoot through states for Z Source inverter The length of the active vectors is unity and length of the zero vectors is zero. In one sampling interval [T.sub.s], the output voltage vector of the traditional inverter [??] is split into the two nearest adjacent voltage vectors. These two nearest active vectors and the traditional zero vectors are used to synthesize the output voltage vector. [??] and [??] (Where n = 0......6) vectors are applied at times [T.sub.1] and [T.sub.2] respectively, and zero vectors are applied at [T.sub.z] times. For example in sector I, vector [??] can be synthesized as,

[??] = [T.sub.1]/[T.sub.s] [[??].sub.1] + [T.sub.2]/[T.sub.s] [[??].sub.2] + [T.sub.z]/[T.sub.s] ([[??].sub.0] or [[??].sub.7]) (5)

Where 2n[pi] [less than or equal to] [theta] = wt [less than or equal to] 2n[pi] + [pi]/3

[T.sub.1] = 2/[square root of (3)] [absolute value of [??]] cos([theta] + [pi]/6)[T.sub.s] (6)

[T.sub.2] = 2/[square root of (3)] [absolute value of [??]] cos([theta] + 3[pi]/2)[T.sub.s] (7)

[T.sub.z] = [T.sub.s] - [T.sub.1] - [T.sub.2] = (1 - 2/[square root of (3)] [absolute value of [??]] cos([theta] + [pi]/3)[T.sub.s]) (8)

The trajectory of voltage vector [??] should be a circular while maintaining pure sinusoidal output line-to-line voltages. The boundary of the linear modulation and overmodulation is the hexagon. The time duration for the active vectors are kept constant throughout the operation and the zero vector time is conveniently placed depending upon the angle of the space vector ([T.sub.z] is decreased when voltage vector is increased). The maximum output line-to-line voltage is obtained when the voltage vector trajectory becomes the inscribed circle of the hexagon and [absolute value of [??]] becomes 2/[square root of (3)]. This limitation of the length of the active vector affects the smooth operation of loads like motor drives where overdrive is desired.

Modified Space Vector Modulation for ZSI

For a three-phase-leg two level VSI, both continuous switching (e.g., centered SVM) and discontinuous switching (e.g., 60--discontinuous PWM) are possible with each having its own unique null placement at the start and end of a switching cycle and characteristic harmonic spectrum. The same strategies with proper insertion of shoot through modes could be applied to the three-phase-leg z-source inverter with each having the same characteristic spectrum as its conventional counterpart [3]. There are fifteen switching states of a three-phase-leg z-source inverter. In addition to the six active and two null states associated with a conventional VSI, the z-source inverter has seven shoot-through states representing the short-circuiting of a phase-leg ([E.sub.1]), two phase-legs ([E.sub.2]) or all three phase-legs ([E.sub.3]). These shoot-through states again boost the dc link capacitor voltages and can partially supplement the null states within a fixed switching cycle without altering the normalized volt-sec average, since both states similarly short-circuit the inverter three-phase output terminals, producing zero voltage across the ac load. Shoot-through states can therefore be inserted to existing PWM state patterns of a conventional VSI to derive different modulation strategies for controlling a three-phase-leg z-source inverter.

The continuous centered SVM state sequence of a conventional three-phase-leg VSI, where three state transitions occur (e.g., null (000) [right arrow] active (100) [right arrow] active (110) [right arrow] null (111)) and the null states at the start and end of a switching cycle [T.sub.s] span equal time intervals to achieve optimal harmonic performance [9]-[13]. With three-state transitions, three equal-interval ([T.sub.0]/3) shoot-through states can be added immediately adjacent to the active states per switching cycle for modulating a z-source inverter where [T.sub.0] is the shoot through time period in one switching cycle. Preferably, the shoot-through states should be inserted such that equal null intervals are again maintained at the start and end of the switching cycle to achieve the same optimal harmonic performance. The middle shoot-through state is symmetrically placed about the original switching instant. The traditional switching pattern for sector-I is shown in fig.4 and modified switching pattern for sector-I is shown in fig.4.

[FIGURE 4 OMITTED]

The active states {100} and {110} are left/right shifted accordingly by ([T.sub.0]/3) with their time intervals kept constant, and the remaining two shoot-through states are lastly inserted within the null intervals, immediately adjacent to the left of the first state transition and to the right of the second transition. This way of sequencing inverter states also ensures a single device switching at all transitions, and allows the use of only shoot-through states [E.sub.1], [E.sub.2], and [E.sub.3]. The other shoot-through states cannot be used since they require the switching of at least two phase-legs at every transition. The modulating signal for the modified SVM strategy could be derived from the following equations,

[V.sub.max(sp)] = [V.sub.max] + [V.sub.off] + T (9)

[V.sub.max(sn)] = [V.sub.max] + [V.sub.off] (10)

[V.sub.mid(sp)] = [V.sub.mid] + [V.sub.off] (11)

[V.sub.mid(sn)] = [V.sub.mid] + [V.sub.off] - T (12)

[V.sub.min(sp)] = [V.sub.min] + [V.sub.off] - T (13)

[V.sub.min(sn)] = [V.sub.min] + [V.sub.off] - 2T (14)

{sp, sn} = {1,4}, {3,6}, {5,2}

Where T = [T.sub.0]/3 shoot through duty ratio.

Modified voltage vector

As aforementioned, the modulation signal produced by the conventional VSI method cannot produce voltage vector beyond [square root of (3)]/2 and z source inverters need two stage controllers separately for boost mode and non-boost mode. A modified control technique is presented in this section to overcome the above limitation and allow the voltage vector to be operated beyond [square root of (3)]/2 with single stage controller block. Normally the shoot through duty ratio is defined as follows,

[D.sub.0] = min([T.sub.z]/[T.sub.s]); for [theta] = 0 [right arrow] 2[pi]

= (1 - 2/[square root of (3)])[absolute value of [??]]sin([theta] + [pi]/3)[T.sub.s] (15)

Further [D.sub.0] could be related with the modulation index M as,

[D.sub.0] = 1 - M (16)

[absolute value of V] = [square root of (3)]/2 M; M = 2/[square root of (3)])[absolute value of V] then

[D.sub.0] = 1 - 2/[square root of (3)][absolute value of V];

B = 1/1 - 2[D.sub.0] = 1/4/[square root of (3)][absolute value of V] - 1 (17)

In boost mode of operation, shoot through periods for shoot through vector are acquired from the traditional zero vector and is calculated by (16). In non- boost mode of operation, z-source inverter operates as a traditional VSI and the boost factor (B) constantly equals one. So the new vector which is accomplished by both the operating modes non-boost as well as boost could be defined as,

[??] = B x [??] and (18)

[??] = 1/4/[square root of (3)][absolute value of V] - 1 x [??]; for boost mode (19)

[??] = [??]; for non-boost mode (20)

The length of the modified voltage vector [??] could be extended beyond [square root of (3)]/2 with proper placement of shoot through time as (9) - (14). Trajectory of the Modified space vector V' and the switching pattern for Z-Source inverter is shown in fig.3.

Modified Control Algorithm

As mentioned earlier, the operation of Z-source inverter can be divided into two modes: one is non-boost mode and the other is boost mode. In the non-boost mode, the Z-source inverter operates like the traditional three-phase V-source inverter, the output voltage vector is limited in the range of 0 ~ [square root of (3)]/2, while operation in the boost mode, with the help of shoot-through zero state (vector) to boost the voltage, the Z-source inverter can overcome the voltage limitation, any voltage vector beyond [square root of (3)]/2 can be easily implemented with proper shoot-through time given in (15).

[FIGURE 5 OMITTED]

In order to implement the modified control technique to have single stage boost and non-boost controllers the algorithm could be developed as follows,

During non-boost mode of operation (ie. If the length of the modified voltage vector [absolute value of [??]], is less than or equal to [square root of (3)]/2) the length of the voltage vector is equal to the modified voltage vector and shoot through time period is zero.

[absolute value of [??]] = [absolute value of [??]; [D.sub.0] = 0 (21)

In the other case, during boost mode, (ie. If the length of the modified voltage vector [absolute value of [??]], is beyond [square root of (3)]/2) the length of the voltage vector is as follows,

[absolute value of V] = 1/4/[square root of (3)][absolute value of V'] - 1 x [absolute value of [??]] (22)

and

[D.sub.0] = 1 - 2/3[absolute value of V] = 2[absolute value of V']/4[absolute value of V'] - [square root of (3)] (23)

The implementation of the proposed control algorithm is shown in fig. 5. It is clearly exposed that, the modified voltage vector [??] is the output of the PI controller and it determines the system operating mode and corresponding [D.sub.0] and [??] according to the algorithm.

In the Z-source inverter system with the modified control method, only the output voltage needs to be sensed, unlike the traditional control methods that use both the output voltage and the capacitor voltage. The capacitor voltage [V.sub.c] and the dc-link voltage [V.sub.i] are dynamically regulated with the input dc voltage to assure of the desired output voltage. When the dc input voltage V0 is too low to output the desired voltage [V.sub.ref] directly, the source inverter will operate in the boost mode to step up the voltage, while [V.sub.0] is high enough to produce the desired output voltage, the Z-source inverter will operate in the non-boost mode, just like the traditional three phase V-source inverter. By using the modified control method, output voltage can faithfully follow the reference voltage, and the voltage stress across the switches can maintain minimum regardless of the input voltage.

Simulation Results

The traditional modulation concepts and modified control algorithm based implementation have been verified through Matlab/Simulink simulation for three bridge-two level z-source inverters. The z-source network has been constructed using existing laboratory components of [L.sub.1] = [L.sub.2] = L = 160 mH and [C.sub.1] = [C.sub.2] = C = 1000 [micro]F with the input dc voltage of 150 V and 5 [f.sub.s] = 5kHz. The simulation results are shown in fig.7-12. Modulation signal is generated through the Modified SVPWM technique with modulation index, [m.sub.a] = 0.6; [m.sub.f] = 100 Shoot through duty ratio [D.sub.0] = 0.3 and Boost factor B = 2.5. Fig. 6 shows the modulation signal generated with the presented algorithm through SVPWM technique. Output phase voltage of the z-source inverter with symmetrical impedance source network is shown in the figure 7. Interior view of current through the impedance source inductors of the z-source inverter and boosted voltage across the impedance source capacitors are shown in fig. 8-10.

Experimental verification using a three bridge-two level z-source inverter prototype have been performed to validate the simulation results(shown in fig.13). The hardware inverter is controlled digitally using a Texas Instruments TMS320F240 digital signal processor (DSP) with composed C codes for generating the required references and a general purpose timer in the

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DSP for generating the common 5-kHz triangular carrier needed for reference comparison. The DSP generated PWM pulses were then sent out through six independent PWM channels to gate the six switches (IGBT modules) of the implemented inverter. The experimental switching line voltage and current waveform of the inverter with m = 0.6; shoot through duration Do = 0.3; boost factor B = 2.5 for the 150 [V.sub.dc] with the low pass ([??] = 1 kHz) LC filter network is shown in fig.12.

Conclusion

This paper presents an integrated algorithm to control the capacitor voltage (boost factor) of the z-source inverter to be operated beyond m = [square root of (3)]/2 with one degree of freedom. Simulations as well as experimental results are given to validate the algorithm. This presented model greatly reduces the switching stress across the power switches employed (IGBTs) and provides effective Dc link voltage utilization with lowest switching stress. It advantageously utilizes the DC link voltage effectively than the traditional SVPWM methods.

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S. Thangaprakash (1) and A. Krishnan (2)

(1) lecturer with the Department of Electrical and Electronics Engineering, Sri Shakthi Institute of Engineering & Technology, Tamil Nadu, India. Correspondence author: E-mail id: [email protected], [email protected]

(2) dean with K.S.R. College of Engineering, Tamil Nadu, India.