Selective Harmonic Elimination for a SinglePhase 13level TCHB Based Cascaded Multilevel Inverter Using FPGA
Wahidah Abd. Halim†,**,*** Nasrudin Abd. Rahim** and Maaspaliza Azri*,**,***
**
Fac. of Electrical Eng., Universiti Teknikal Malaysia Melaka, Melaka, Malaysia UM Power Energy Dedicated Advanced Centre (UMPEDAC), University of Malaya, Kuala Lumpur, Malaysia *** Dept. of Electrical Eng., Fac. of Eng., University of Malaya, Kuala Lumpur, Malaysia
†*
Abstract
This paper presents an implem
Selective Harmonic Elimination for a SinglePhase 13level TCHB Based Cascaded Multilevel Inverter Using FPGA
Wahidah Abd. Halim
†,**,***
Nasrudin Abd. Rahim
**
and Maaspaliza Azri
*,**,***
†
*
Fac. of Electrical Eng., Universiti Teknikal Malaysia Melaka, Melaka, Malaysia
**
UM Power Energy Dedicated Advanced Centre (UMPEDAC), University of Malaya, Kuala Lumpur, Malaysia
***
Dept. of Electrical Eng., Fac. of Eng., University of Malaya, Kuala Lumpur, Malaysia
Abstract
This paper presents an implementation of selective harmonic elimination (SHE) modulation for a singlephase 13level transistorclamped Hbridge (TCHB) based cascaded multilevel inverter. To determine the optimum switching angle of the SHE equations, NewtonRaphson method is used in solving the transcendental equation describing the fundamental and harmonic components. The proposed SHE scheme used relationship between the angles and a sinusoidal reference waveform based on voltageangle equal criteria. The proposed SHE scheme is evaluated through simulation and experimental results. The digital modulator basedSHE scheme using fieldprogrammable gate array (FPGA) is described and has been implemented on Altera DE2 board. The proposed SHE is efficient in eliminating the 3
rd
, 5
th
, 7
th
, 9
th
and 11
th
order harmonics, validating the analytical results. From the results, the adopted 13level inverter produce higher quality with better harmonic profile and sinusoidal shape of stepped output waveform.
Key words:
Pulsewidth modulation, multilevel inverter, total harmonic distortion (THD), fieldprogrammable gate array (FPGA)
I.
I
NTRODUCTION
Multilevel inverter technology has drawn tremendous interest among researchers from industry and academia in recent years due to their superior performance. In contrast to conventional twolevel inverter, they are more efficient and more suited for applications requiring high power and high voltage level. Among various types of multilevel inverter topologies, cascaded Hbridge (CHB) has attracted special attention due to its modular structure, which provides high reliability and better fault tolerance. Increasing the number of levels is also easier with minimum modification in hardware and control algorithm. Therefore, CHB multilevel inverter has become popular in renewable energy (solar/wind power inverters), reactive power compensation (STATCOM) and motordrive applications up to MegaWatt (MW) power levels [16]. For these applications, the converter’s output voltage must fulfill the requirement for maximum voltage and current THD as specified in IEEE Std.5191992 [7]. It is essential to produce an effective power converter from the perspective of cost, efficiency and output quality. These factors have leads for emerging a new family of multilevel inverter known as transistorclamped converter (TCC) [5, 8]. By adding additional devices (such as power switch, power diode and capacitor) to an existing Hbridge topology, it is possible to increase the number of output voltage levels and produce a better sinusoidal output waveform. The TCC has reduced number of dc power supplies and switches compared to that of conventional CHB topology designed for the same number of voltage level. Modulation strategy has a profound impact on the performance of multilevel inverters, as it determines the switching losses as well as the voltage and current harmonics. Generally, the multilevel modulation strategies can be classified according to the switching frequency, into two categories: highfrequency switching and lowfrequency (fundamental frequency) switching methods. The most popular modulation schemes discussed in the literature for multilevel inverter are multireference/multicarrierbased PWM [4, 5, 9, 10], multilevel spacevector PWM (SVM) [11, 12] and multilevel selective harmonic elimination (SHE) [7, 13]. Multilevel carrierbased PWM and SVM techniques are considered highswitching frequency schemes, whereas SHE falls within the lowswitching frequency group. Each solution has its unique advantages and drawbacks, hence the choice of modulation technique usually depends on the inverter topology and its application. Among the many modulation strategies, SHE is commonly adopted in high power applications where switching frequency has to be low enough to minimize switching losses. Since the
effectiveness of SHE method depends heavily on the switching angle, various algorithms have been developed for determining the optimum switching angles [14, 15]. Usually, this is done offline, using optimization technique such as NewtonRaphson (NR) method [1417]. More complex techniques such as the genetic algorithm (GA) [15, 1820] and particle swarm optimization (PSO) [15, 21, 22] have also been demonstrated. Although these new techniques are fast in solving the optimized angle, the solutions only minimize the harmonics rather than eliminating them. Moreover, as prerequisite, the engineers need to understand advance control and mathematics algorithms [6]. More recently, online methods have been proposed where realtime calculations of the switching angles are made possible using high speed processor. In [23], mathematical
calculation based on trigonometric function was proposed to obtain the switching angles. In [24], a simple and improved realtime algorithm for calculating the switching angle has been introduced and then proven by mathematical derivation. In [6], the authors have proposed fourequations method based on harmonic injection and equal area criteria, regardless of the number of inverter output level. An artificial neural network (ANN) was used for obtaining the optimal switching angles for multilevel inverter in solar application in [3]. However, due to the simplification used, the online methods cannot fully eliminate the harmonics. Hence, they generally yield significantly higher THD are inferior to the offline methods. SHE analysis for 5level up to 13level CHB inverter with unequal dc sources considering for minimum THD with or without elimination of the lowest order harmonics are discussed in [25]. However, the real implementation results are discontinued for 11 and 13level cases. For 13level case, only simulation studies have been reported so far [26]. Here in this paper, real implementation of SHE method on 13level inverter is demonstrated. Normally, digital implementation of SHE modulation involves two steps. First, the switching angles are calculated offline through solving a set of nonlinear and transcendental equations. Then, the switching angles are stored in lookup table (LUT) for realtime applications [27]. In order to implement realtime control system in power electronics applications, the system designers have many choices. Microcontrollers, microprocessors and DSPs are softwarebased devices, which come with efficient software compilers and the program is usually written in C or assembly language. Although these technologies are matured and usually have dedicated PWM generation blocks, they have limited sampling rate and limited speed due to its natural sequence based operation (the program is executed line by line, not simultaneously). This limitation can be resolved with fieldprogrammable gate array (FPGA) as an alternative to programmable logic device (PLD) and application specific integrated circuit (ASIC) technologies. FPGAs are digital hardwarebased devices and now an increasingly popular technology in digital prototyping for multilevel inverter [15, 28] due to their speed and flexibility. In this paper, SHE modulation is suggested for a 13level transistorclamped Hbridge (TCHB) inverter based cascaded multilevel inverter topology. NewtonRaphson method is used to calculate the switching angles with the capability to eliminate the lowest order harmonics while maintaining the fundamental component. In order to generate an optimum stepped output waveform, a simple SHE modulation is defined according the voltageangle equal criteria. Real implementation of SHE modulation for the TCHB inverter using FPGA is presented. The analytical results are validated using both simulation and experimental results.
II.
T
HE
P
OWER
C
IRCUIT
Fig. 1 shows the studied inverter configuration based on 5level transistorclamped Hbridge (TCHB) multilevel inverter. The 5level TCHB is modified by adding one bidirectional switch to the Hbridge module. A very attractive feature of the bidirectional switch is that it allows bidirectional current flow and enables five output voltage levels of 0, ±½
V
DC
and ±
V
DC
. Even though such topology has been discussed in [9], SHE modulation method is used instead of multicarrier modulation method. The inverter is supplied by three independent dc sources, three Hbridge modules and three bidirectional switches to produce a 13level output. Multiple dc sources at the input of the inverter may be obtained from constant dc supplies,
LoadV
DC
V
DC
V
DC
C
1
C
2
C
3
C
4
C
5
C
6
S
11
S
12
S
13
S
14
S
15
S
21
S
22
S
23
S
24
S
25
S
31
S
32
S
33
S
34
S
35
LR+Vinv+VoIo+V
L1
+V
L2
+V
L3

Fig. 1. The 13level TCHB based cascaded multilevel inverter topology.
batteries, super capacitors, pv or fuel cells. Generally, the number of output levels for the inverter is given by 4
i
+ 1, where
i
is the number of TCHB cells. Through combinations of the on state of the switches (
S
i
1

S
i
5
), the cell output voltage
V
i
can be expressed as
{ }
43215
2124
)(
iiiiiii DC i
S S S S S S S V V
−⋅−+−=
(1)
The modes of operation, the switches to be turned on and the corresponding output voltage levels are summarized in Table I. The 13level TCHB inverter’s operation involves 14 switching states, and all the operating states are illustrated in Fig. 2. In order to justify the use of the TCHB inverter, performance comparisons are made against the conventional CHB inverter with the same 13level voltage outputs. In general, the output voltage quality for both inverters is the same. The most obvious advantage of the adopted inverter has fewer component count compared to the CHB inverter with the same number of output level. This will result in lower total power losses produced by the TCHB inverter as compared to the CHB inverter [5]. Since CHB inverter requires two series connected cells to produce 5 voltage levels, a total of 24 switches are needed to generate 13level voltage. In contrary, the TCHB inverter requires only 15 switches to produce the same number of voltage levels. Moreover, the provision of isolated sources is the main disadvantage of the CHB topology. In this case, a total of six isolated dc sources is needed for CHB, whereas the TCHB inverter requires three isolated dc sources. Owing to a bidirectional switch connected at the midpoint of the dc link to the TCHB inverter output, both topologies required six capacitors. However, a larger value of capacitance is required in the TCHB inverter to prevent the capacitor voltage imbalance [5], [9]. A few practical approaches to balance the capacitor voltages are by replacing capacitors with isolated dc sources, applying backtoback intertie system [29] or use of auxiliary dcdc converter circuits [30]. It is expected that the overall cost of the TCHB inverter will be lower than that of the conventional CHB inverter due to the reduced switch count and lower number of isolated dc sources required.
III.
B
ACKGROUND AND
S
OLUTION FOR
SHE
M
ODULATION
A. Harmonic elimination technique
In general, the inverter output voltage
V
inv
waveform (see Fig. 3) can be expressed in Fourier series as
TABLE
I S
WITCHING
S
TATES AND
V
OLTAGE
L
EVELS OF THE
13L
EVEL
TCHB
I
NVERTER
States
S
11
S
12
S
13
S
14
S
15
S
21
S
22
S
23
S
24
S
25
S
31
S
32
S
33
S
34
S
35
V
inv
1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 3
V
DC
2 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 2½
V
DC
3 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 2
V
DC
4 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1½
V
DC
5 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0
V
DC
6 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 ½
V
DC
7 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 8 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 9 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 ½
V
DC
10 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0
 V
DC
11 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1½
V
DC
12 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1

2
V
DC
13 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 2 ½
V
DC
14 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 3
V
DC