Modified Selective Harmonic Elimination Employed in Four-Leg NPC Inverters Mohammad Sharifzade1, Hani Vahedi2, Abdolreza Sheikholeslami1, Hoda Ghoreyshi1, Kamal Al-Haddad2
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[email protected] 1 Department of Computer and Electrical Engineering, Babol Noshirvani University, Iran 2 GREPCI, Ecole de Technologie Superieure (ETS), University du Quebec, Quebec, Montreal, Canada
Abstract—Three-phase four-leg neutral point clamped (NPC) inverter is more suitable in dealing with all sort of the loads especially unbalanced/nonlinear due to harmonics issues. Most control strategies applied on four-leg NPC are classified as high switching frequency lead to high power losses and low efficiency. In this paper, selective harmonic elimination pulse width amplitude modulation (SHE-PWAM) technique has been implemented on a four-leg NPC inverter to reduce the switching frequency properly. In SHE-PWAM technique, the amplitude of input voltage is considered flexible in order to eliminate one more harmonic order without increasing switching frequency. The obtained switching angles of phase legs and amplitude of input voltage are used to eliminate the non-triplen harmonics (5th,…,23th) from the output voltage. On the other hand, switching angles calculated for the fourth leg are considered to eliminate the triplen harmonics (3th,…,21th) from phase voltage. The performance of proposed technique is verified by Matlab/SPS simulations. Keywords- Four-Leg NPC inverter; SHE-PWAM; Unbalanced load
I.
INTRODUCTION
Multilevel inverters are one of the interesting research topics in high power applications due to facilitate tolerating high voltage rating and improve harmonic content and switching losses [1, 2]. Different topologies and control methods have been proposed in the literature while few ones found their way to industries and market [3-6]. In recent years the three-phase four-wire inverters have been widely employed in many power electronic applications like Uninterruptible Power Supply (UPS) [7] in order to prepare a path for neutral current [8]. The conventional three-phase three-wire inverters are designed for balanced/linear loads so they are not suited to supply unbalanced/nonlinear loads. In asymmetrical condition, zero-sequence harmonics are produced which make the output voltages imbalanced, so a neutral point connection is required to control this state. There are two main ways to provide a neutral point in three-phase four-wire inverters without using transformer which gives ability to the inverter to handle the asymmetrical loads [9]. ȱ. three-leg four-wire inverters, in which neutral point is connected directly to the midpoint of two dc-link capacitors [10, 11]. The main drawbacks of this topology are large capacitor and low utilization of dc-input voltage as well as neutral point voltage balancing issue [12]. Moreover when the load is unbalanced or nonlinear, a high voltage ripple on dclink capacitors is produced by neutral current.
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ȱȱ. four-leg four-wire inverters, in which the fourth wire is provided by the fourth leg. This structure permits to modify the neutral point voltage [13], also full utilization of the dc-link voltage and lower stress on the dc-link capacitors are possible. Therefore, regardless of the increased number of power switches of the four-leg inverter, this topology is appropriate for dealing with all kind of loads. In the three-phase four-leg inverters, if zero-sequence harmonics are appeared in the output voltage or current, the reference vector is not on the Įȕ frame; so the control strategy of four-leg inverter becomes complicated. Several schemes for the four-leg inverter topology with different control techniques have been investigated in the literature. The most efficient high frequency modulation strategies are classified as the 3-D SVM technique [14, 15], and the carrier-based PWM methods [16, 17]. The high switching frequency results in increasing power losses (switching losses) as well as reducing inverter efficiency [18]. Thus, in high power applications of four-leg inverter, the trend is to use low switching frequency modulation techniques. Different methods have been proposed to reduce the switching frequency such as a minimal switching frequency in hysteresis current PWM [19] and an efficient modulation technique in carrier-based PWM [20], but the switching frequency has not been still decreased in these methods sufficiently. Another method with desired low switching frequency is the Selective Harmonic Elimination Pulse Width Modulation (SHE-PWM) which proposed in [9, 21] to compensate asymmetrical loads with three-phase four-leg inverters. The SHE control is the most effective modulation technique to reduce the switching frequency (less than 1 kHz assuming fundamental frequency is 50 0r 60 Hz) leads to lower power losses and higher efficiency of the inverter. The SHE modulation is defined on the Fourier series expansion of the inverter branch voltage waveform. In this modulation technique, switching angles as degrees of freedom in the SHEequations are calculated accurately in order to eliminate undesirable low order harmonics from output voltage. The number of harmonics which must be eliminated is proportional to the number of switching angles. In other words, eliminating more harmonics requires more switching angles to be found; results in higher switching frequency and the related power dissipation. In selective harmonic elimination pulse width amplitude modulation (SHE-PWAM), the amplitude of dc input voltage can be considered as extra degree of freedom in addition to switching angles [22], thus, as the switching frequency
depends on the number of switching angles, selecting the amplitude of dc input voltage as a degree of freedom results in eliminating one extra harmonic order without increasing the switching frequency. In this paper, SHE-PWAM for threelevel four-leg NPC inverter considering the aforementioned extra degree of freedom is designed. In section ȱȱ the four-leg NPC inverter topology used in this paper is described. Section ȱȱȱ presents the SHE-PWAM control strategy to calculate the switching angles and also the amplitude of dc input voltage for four-leg inverter. The proposed modulation is verified by simulations in Section ȱV and finally, conclusions are summarized in section V. II.
SELECTIVE HARMONIC ELIMINATION TECHNIQUE TO CONTROL FOUR-LEG NPC INVERTER
The SHE-PWAM control strategy which is proposed in this paper is defined on the three level quarter-wave symmetry switching waveform of output voltage which is represented branch voltage of each leg in four-leg NPC inverter.
THREE-PHASE FOUR-LEG NPC INVERTER TOPOLOGY
The three-phase three-level four-leg diode-clamped inverter which is generally known as neutral point clamped (NPC) inverter is depicted in Fig. 1. The NPC inverter has been used in high power and medium voltage applications more than the two-level topology because of the main features of the NPC inverter such as low dv/dt and total harmonic distortion (THD). According to Fig. 1, four-leg NPC topology is composed of one additional leg in comparison to three-leg NPC inverter that is tied to neutral point of the load. The phase legs are denoted as A, B, C respectively and fourth leg is determined as N. Branch and phase voltages are also defined as VAg, VBg, VCg and VAn, VBn, VCn, respectively and the voltage generated by the fourth leg is VNg. This voltage is equal to common mode voltage (Vng).
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Fig. 1: Three-phase four-leg NPC inverter
Each leg is composed of four power switches and two diodes with three possible switching states, thereby four-leg NPC inverter has 81 (34) switching state. Table I gives switching states of phase leg to achieve three levels in output branch voltage. TABLE I: The possible switching state for phase leg in NPC inverter S1A 1 0 0
S2A 1 1 0
Vag +E 0 -E
In general, Fourier series for a quarter-wave symmetric can be calculated as follows: ∞
V (t ) = ¦bh sin(ωt )
(1)
n =1
Where bh is the magnitude of harmonics and h denotes the harmonic orders. Assuming three-level voltage with symmetric quarter-wave and n dependent switching angles in the first quarter-cycle according to Fig. 2, bh can be obtained as: bh =
1 (
Fig. 2: three level output voltage waveform for phase leg
4E n i +1 ¦ ( -1) cos ( hα i ) hπ i =1
∀ h = 3,5, 7,9,11, …
(2)
A. Obtaining switching angles for leg A and desired value for input voltage In the SHE equations, first harmonic must be controlled in such a way that the desirable amplitude of output voltage will be generated. At the same time some undesirable harmonic should be eliminated. In this way, non-triplen harmonic orders including 5th, 7th, 11th, 13th,... are eliminated and triplen harmonics are not considered in the SHE equations because of the fact that in three-phase system zero sequence harmonics do not appear in the line voltage. Naturally, the number of equations is proportional to the number of variables so that with assumption of n variables there are n-1 harmonics orders that can be eliminated. As usual, switching times (angles) of inverter switches are considered as variables in the equations. In this way, if more harmonics need to be removed from output voltage waveform, more switching angles are required which leads to increase in switching frequency. On the other hand, the amplitude of input voltage can be assumed as a variable in addition to switching angles in the SHE equations. In this case by considering value of input voltage as a variable
along with switching angles, there is possibility of eliminating one more harmonic without increasing the switching frequency.
Therefore, the SHE equations for the phase legs are determined by equaling first harmonic to ma×V1 (ma is the amplitude modulation index) to get the output voltage fundamental and set the amplitude of n-1 remaining harmonics equivalent to zero to eliminate from output voltage according to the following formulas:
π
E >0
2
(3)
(4)
B. Calculation switching angles for the fourth leg The fourth leg in the topology gives the ability to NPC inverter that can handle asymmetrical loads and prevent imbalanced output voltage. Furthermore this leg should act to eliminate zero-sequence harmonics from phase voltage which are produced by the other legs. To this end, the voltage that is generated by the fourth leg must contain only triplen harmonics that equals to triplen harmonics of the phase legs. Therefore, the frequency of leg N voltage waveform is triple of the frequency of the phase legs voltages. On the other hand, the number of switching angles of the fourth leg is distinct from the three other legs. The reason for this difference is the number of zero-sequence harmonics that should be eliminated from the phase voltage. The m independent switching angles for fourth leg is determined base on number of switching angles for the leg A (n) as follows:
Į Į Į
(6)
Fig. 4 amplitude of dc input voltage in SHE-PWAM technique
According to the SHE principle, switching angles for phase leg are calculated with the goal of eliminating the non-triplen voltage harmonics orders. Moreover, at the same time amplitudes of triplen harmonics of phase leg should be computed with respect to obtained switching angles and magnitude of input voltage. b3Ah
∀h = 1,3,5, …,
(7)
By equaling the harmonics amplitude of leg N (bhN) to the associated triplen harmonics (b3hA) according to the corresponding equation (8), the switching angles for leg N (ȕ1, ȕ2, …, ȕm), will be achieved so that the effect of triplen harmonics is neutralized and also constraint (9) will be satisfied too. Therefore SHE equations for leg N can be derived as: bhN = b3Ah
∀h = 1,3,5, …, 2m -1
0 < β1 < β 2 < β 3 < ... < β m
