Abstract: This paper presents an efficient nine-level inverter controlled by selective harmonic elimination pulse width modulation (SHE-PWM) method.
Single-phase Nine-level SHE-PWM Inverter with Single DC Source suitable for Renewable Energy Systems Mohamed S. A. Dahidah1, Senior Member IEEE, Georgios S. Konstantinou2, Student Member IEEE, and Vassilios G. Agelidis2, Senior Member IEEE 1
Department of Electrical and Electronic Engineering, The University of Nottingham, Malaysia Campus Jalan Broga, 43500, Semenyim, Selangor, Malaysia 2
School of Electrical and Telecommunications Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia Abstract: This paper presents an efficient nine-level inverter controlled by selective harmonic elimination pulse width modulation (SHE-PWM) method. The proposed inverter circuit is supplied with a single DC voltage source which makes it a very attractive for renewable energy systems e.g. inverter-based PV systems and fuel cell. The proposed method employs a single multi-winding transformer with two-winding of different turn numbers at the primary side and one-winding at the secondary side to synthesis the multilevel waveform. The device-account is considerably reduced when compared with conventional multilevel inverters for the same number of output voltage levels. The quality of the output voltage is enhanced using the SHE-PWM technique which guarantees the elimination of the low order harmonics and the magnetizing inductance of the transformer will get rid of high order of harmonics. The effectiveness of the proposed inverter is validated with different cases using simulation studies.
Keywords: SHE-PWM; multilevel inverter; DC/AC inverterbased PV systems; renewable energies conditioning I. INTRODUCTION Traditional power generation resources are decreasing fast and in addition causes greenhouse gases emission; however the demand for electric power is increasing. Therefore, renewable energy resources have attracted more and more attention over the last decades. Renewable power sources are difficult to be directly connected to the power grid due to their variable and intermittent nature [1]. Power-electronic converters technology plays an important role in integrating and utilizing these alternative energy sources into the electricity grid, and it is widely used and rapidly expanding as these applications become more integrated with the gridbased systems [2]. Multilevel converter topologies have drawn a large research interest over the last two decades due to their inherent merits compared with their conventional counterpart especially for medium or high-power applications. They synthesize the ac output voltage from several levels of voltage, hence generate low distortion voltage and current
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waveforms and reduced amplitude of harmonics in the output [3]-[5]. On the other hand, for low-power systems (< 10 kW), multilevel converters have been also competing with highfrequency pulse width-modulation converters in applications where high efficiency is of major importance. Moreover, the lower prices and rapid growth of power switches and new semiconductor technologies, as well as the current demand on high-performance inverters required by renewable energy systems have extended the applications of multilevel converters [6]. Various multilevel inverters structures are reported in the literature, such as: diode-clamp multilevel inverters, flying capacitor multilevel inverters, and cascaded H-bridge with separate dc-link sources. The later appears to be superior to other multilevel inverters in applications at high power rating due to its modular nature, ease of control, flexibility of application and robustness. However, the need for independent dc-link sources is a major limitation of this type of inverters [3]-[5]. Alternatively, a combination (i.e. hybrid structure) of the former multilevel inverters have been also developed to improve the quality of the output voltage waveform or/and to reduce the device-account and hence the cost and the complexity of the system [7]. Transformer-based multilevel inverters with either multiple transformers or multi-winding transformer have been also developed and commercially available [6], [8]-[10]. Furthermore, it has been shown that the efficiency of the multi-winding transformer based inverter is outperform the multiple transformer topologies as it uses only one transformer, therefore it is recommended for high performance battery inverters [6]. A key issue in designing an effective multilevel inverter is to ensure that the total harmonic distortion (THD) in the voltage output waveform is low enough. Therefore selective harmonic elimination pulse width modulation (SHE-PWM) has been intensively concerned recently and documented in several works in order to achieve low THD [11] and [12]. The common characteristic of the SHE-PWM method is that the
waveform analysis is performed using Fourier theory [13]. The main challenge associated with SHE-PWM techniques is to obtain the analytical solution of the system of non-linear transcendental equations that contain trigonometric terms which in turn provide multiple sets of solutions [14] and [15]. A number of approaches have been proposed for attaining the solutions. These include optimization methods [14] and [15], genetic algorithms [16] and [17], Walsh functions [18], theory of resultants [11] and modulation based methods [19]. The main objective of this paper is to present an efficient single-phase nine-level SHE-PWM inverter fed from a single dc-link source. A single multi-winding transformer with twowinding at the primary side and one-winding at the secondary side is used to synthesize the nine-level waveform. The essential different aspect of the proposed inverter compared to the conventional multilevel methods, in the synthesis of the multilevel output waveform is the utilization of the accumulated voltages of the multi-winding transformer rather than the accumulation of dc-link voltage sources. Therefore, the proposed technique resolves the issue of multiple independent dc-link sources requirement, where only one dclink source is used to generate a nine-level output voltage waveform, hence significantly reduces the size, the cost and the complexity of the inverter compared with the conventional counterpart. This makes the inverter very promising technology for renewable energy sources applications such as PV and fuel cell. The paper is organized as follows. Section II presents the circuit configuration and operation of the proposed inverter. The nine-level SHE-PWM waveform formulation is illustrated in Section III. Selected results are discussed in Section IV. Finally conclusions are summarized in Section V.
waveform. Therefore, the associated switching states are presented in Table I. The proposed work is aimed at voltage source converter (VSC) multilevel systems in applications where the converter output frequency is fixed to the utility's grid frequency. Therefore, the modulation index range does not significantly change and remains within a region between 0.7p.u. to 1p.u.. Hence, there is no problem when using the low frequency transformers [6] and [9], which are usually used in the conventional multilevel inverter for grid-connected applications. In the proposed inverter, the transformer is used to synthesize the output voltage by accumulating the twoprimary voltages with their associated turn ratios and at the same time provides a galvanic isolation.
II. CIRCUIT CONFIGURATION AND OPERATION Fig. 1 shows the proposed inverter circuit which consists of two H-bridge cells supplied from a single DC voltage source, such as photovoltaic panel or fuel cell. The output voltage of each individual H-bridge inverter is connected to a transformer with two windings at the primary side and one winding the secondary side. The turn ratios of these windings are chosen so that a maximum of nine-level waveform can be generated with a selected set of switching states. Let x1 be the turn ratio between the primary winding which is connected to H-bridge 1 and the secondary winding of the transformer. Similarly, let x2 be the turn ratio between the second primary winding and the secondary winding of the transformer. Therefore, in order to generate a nine-level output waveform; x1 and x2 should be 1:2 and 1/3:2, respectively. By selecting a proper switching sequence of the eight power switches, the nine-level waveform can be synthesized at the secondary side of the transformer. Apparently, there are a number of switching redundancies which could produce different output voltage waveforms from the same inverter circuit. However, the aim of this work is to only investigate and generate a nine-level PWM
Fig.1. Proposed single-phase nine-level inverter
Considering the same number of the output voltage levels (L) to be generated by the conventional multilevel inverters (i.e. for a single-phase system), we can find that a diodeclamped multilevel inverter needs 2 × (L − 2) clamping diodes to generate L-level outputs. In the case of a flying capacitor, it requires (L + 1) clamping capacitors for the generation of L-level outputs. On the other hand, a cascaded H-bridge inverter needs [(L − 1)/2] × 4 power switches and [(L − 1)/2] number of independent dc sources [3]. However, the required number of switches for the proposed topology is only [(L − 1)/2] with a single dc source and no clamping diodes or capacitors. From Table II, it is clear that the advantage of the proposed multilevel inverter is the significant reduction in the number of switching devices.
TABLE I SWITCHING STATES FOR THE PROPOSED NINE-LEVEL INVERTER S21
S22
S23
S24
0
0
1
1
1
0
0
1
1
1
0
0
V4
0
1
1
0
V5
0
0
1
1
0
Vdc
V6
1
0
0
1
Vdc
4Vdc
1
1
0
0
0
Vdc
V8
0
1
1
0
-Vdc
-2Vdc
V9
0
0
1
1
0
0
1
0
0
1
Vdc
3Vdc
1
1
0
0
0
0 -3Vdc
S11
S12
S13
S14
V1 V2 V3
V7
V10 V11
0
1
1
0
0
1
1
1
0
1
0
0
+Vdc
0
Vout = VH1 + 3VH2
0
0
Vdc
3Vdc
0
0
-Vdc
-3Vdc
0
1
1
0
-Vdc
V13
0
0
1
1
0
-Vdc
V14
1
0
0
1
Vdc
2Vdc
1
1
0
0
0
1
1
0
0
1
1
0
V16
TABLE II COMPONENT-BASED COMPARISON BETWEEN CONVENTIONAL NINE-LEVEL AND THE PROPOSED INVERTERS
Power switch
0
VH-2
V12
V15
Device
VH-1
DiodeClamped
CapacitorCamped
Cascaded H-Bridge
Proposed Inverter
16
16
16
8
Diode
16
16
16
8
Clamping diode
14
NA
NA
NA
DC-link capacitor/supply
8
7
4
1
Balancing capacitor
NA
10
NA
NA
Gate drivers
16
16
16
8
III. THE PROPOSED NINE-LEVEL SHE-PWM : KEY WAVEFORMS AND EQUATIONS The proposed multilevel SHE-PWM strategy is defined according to the waveform shown in Fig. 2. The number of levels of the waveform in this paper is assumed to be nine, i.e., 1p.u., 2p.u., 3p.u., 4p.u, 0p.u., -1p.u., -2p.u., -3p.u. and 4p.u. Let N be the total number of switching angles per-quarter period of the output voltage waveform, which could be odd or even number. Let Pj the number of switching angles in every level, where j = 1, 2, 3, and 4 in the case of nine-level
-Vdc
0
-Vdc
-Vdc
-4Vdc
waveform. The equation that describes the Fourier analysis of the nine-level waveform is then defined as: hn =
4 nπ
K3
+
( ∑ (−1) K1
i =1
i +1
cos nα i +
∑ (−1) i cos nα i +
i = K 2 +1
K2
∑ (−1) i cos nα i
i = K1 +1
N
∑ (−1) i cos nα i
i = K 3 +1
)
(1)
where, n = 1, 3,…, 2 N − 1 , K1 = P1, K2 = K1 + P2, and K3 = K2 + P3, α i is the i th switching angle. Equation (1) possesses N unknown variables (i.e. , α N ) and a set of solutions is obtainable by equating N − 1 harmonics to zero and assigning a specific value for the fundamental. Therefore, an objective function describing a measure of effectiveness of eliminating selected order of harmonics while controlling the fundamental is defined by
α1 , α 2 ,
f ( α ) = (h1 − M ) 2 +
2 N −1
∑ hn2
(2)
n=2
where, M is the normalized fundamental component. The optimal switching angles are obtained by minimizing (2) when it is subject to the constraint of (3).
( 0 < α 1
