Novel Carrier PWM Technique with Extension Range For 4-Switch Inverter Nguyen Van Nho1, To Huu Phuc2, Nguyen Xuan Bac3 1,2,3 HCMC University Of Technology Department of Electrical Engineering 268 LyThuongKiet, District 10, HCM City, Vietnam Email:
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Abstract— Three-phase 4-switch voltage source inverters are advantageous for reduced number of power switches. For these topologies, space vector Pulse Width Modulation (SVM) methods have been commonly used for controlling the circuit. This paper presents a novel carrier based PWM method for 4-switch inverters, which is simple and flexible. Linear overmodulation will be also investigated. The proposed method will be mathematically analyzed and demonstrated by simulation and experimental results.
I.
INTRODUCTION
Three-phase Four switch inverter has been known as a possible hardware solution for reduced cost in some electric drive applications. One of the drawbacks is reduction of available maximum output voltage [1]. To supply motor of higher rated voltage, the inverter requires a high AC voltage source or to be deployed with a PWM rectifier, these however will give rise to voltage stress on switching devices. Another problem of this unsymetric inverter is the unbalance between two dc voltage cells, which deforms the space vector diagram and further confines the load voltage range. Voltage ripples for definite capacitors further reduces the inverter performance [2],[3]. The level of unbalance between two dc cells varies depending on output frequency and load currents. Therefore, a good control of overmodulation can contribute to improving of inverter performance. As a result, properly utilising the dc voltages for overmodulation range can help to improve the voltage control range. In the paper, a novel carrier based PWM method for 4-switch inverter on condition of unbalanced dc sources will be proposed. The method bases on the modifying of modulating signals, depending on the dc source variation [4]. Two-mode overmodulation using the principle control between two limit trajectories will be presented [5]. II.
PROPOSED PWM TECHNIQUE
A particular characteristics of PWM control in 4-switch inverter is that offset control is not available since voltage level of the first phase is fixed as shown in Fig.1. a) Define the voltages on dc sources and their total value as
Vc1 ,Vc 2 and Vd = Vc1 + Vc 2 .
Figure 1: Four switch inverter. Circuit diagram a), voltage space vector diagram for unbalanced dc sources b) and proposed circuit model c).
b) Analysis of circuit [2] Phase-leg voltages can be described in a general form as:
V x 0 = V x12 + V0 ; x=a,b,c
(1)
From Fig.1, it can be seen that:
Va0 = Va12 + V0 = Vc1 Vb0 = Vb12 + V0 = Vc1 + (Vb12 − Va12 ) = Vc1 + Vba12 (2) Vc0 = Vc12 + V0 = Vc1 + (Vc12 − Va12 ) = Vc1 + Vca12 The phase leg voltage is confined by the total dc voltage as:
0 ≤ V x 0 ≤ Vd
(3)
For generating the control signals, it is enough to measure the dc source as Vc1, and to determine two active line-line voltage components Vba12 and Vca12 . For undermodulation range, the reference voltages can be deduced as:
Vba12,1 = V L12 m cos(θ − 5π / 6)
(4)
Vca12,1 = V L12 m cos(θ − 7π / 6)
In the fundamental period, let’s define the parameter d as
d = Min(Vc1 , Vc 2 ) = Min(Vc1Min , Vc 2 Min ) .
(5)
where the condition for the line-voltage amplitude is: VL12 m ≤ d (6) Linear overmodulation: From (6), overmodulation happens if V L12 m > d . Because of the unbalance and oscilation of dc voltage sources, the boundaries between under- and over-modulation values will continuously change. To simplify the algorithm for determining the reference voltages on the condition of variable dc sources, some nominal voltages will be performed first, and the reference voltage on condition of unbalance will be deduced. The principle control between two limit trajectories will be applied [5]. For two-mode overmodulation, three limit modulation indexes are considered as
m1N = 0.5 , m2 N = 0.52645 and m3 N = 0.55125 ,
(7)
The standard modulating signals described below are produced for the balanced condition of dc sources :
Vc1 = Vc 2 = VCN / 2 .
(8)
For case of m1 N = 0.5 :
For case of m2 N = 0.52645
0.5VCN(θ − 2π 3) −0.5V (θ −5π 3) CN Vca12,2N = 0.5VCN −0.5VCN
(10)
for 0 ≤ θ < 2π / 3 for π ≤ θ < 5π / 3 for 2π / 3 ≤ θ < π for
(11)
−0.5VCN for (0 ≤θ
