Studying the effect of over-modulation on the output voltage of three-phase single-stage grid-connected boost inverter Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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Alexandria Engineering Journal (2013) 52, 347-358

FACULTY OF ENGINEERING ALEXANDRIA UNIVERSITY

Alexandria University Alexandria Engineering Journal

www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Studying the effect of over-modulation on the output voltage of three-phase single-stage grid-connected boost inverter

A. Abbas Elserougi *, A.S. Abdel-Khalik, A. Massoud, S. Ahmed

Faculty of Engineering, Alexandria University, Electrical Engineering Dept., Alexandria, Egypt

Received 13 December 2012; revised 11 April 2013; accepted 25 May 2013 Available online 18 June 2013

KEYWORDS

Extended gain

Over-modulation

Third harmonic injection

Abstract Voltage boosting is very essential issue in renewable-energy fed applications. The classical two-stage power conversion process is typically used to interface the renewable energy sources to the grid. For better efficiency, single-stage inverters are recommended. In this paper, the performance of single-stage three-phase grid-connected boost inverter is investigated when its gain is extended by employing over-modulation technique. Using of over-modulation is compared with the employment of third order harmonic injection. The latter method can increase the inverter gain by 15% without distorting the inverter output voltage. The performance of extended gain grid-connected boost inverter is also tested during normal operation as well as in the presence of grid side disturbances. Simulation and experimental results are satisfactory.

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University.

1. Introduction

A number of power conversion circuits have been based on extensions of the three primitive single-stage power converters, namely, the buck, boost, and buck-boost converters. The

* Corresponding author. Tel.: +20 1221268725; fax: +20 3 5921853. E-mail addresses: abbas_zone@yahoo.com, ahmed.abbas@spiretro-nic.com (A. Abbas Elserougi).

Peer review under responsibility of Faculty of Engineering, Alexandria University.

voltage source inverter can be categorized as a buck converter extension, since its output voltage is less than its input. The current source inverter can be categorized as a boost extension since it boosts the input DC voltage without an additional boosting stage. The buck-boost inverter proposed in [1] can both buck and boost the input voltage; hence, it can be classified as an extension of the primitive buck-boost converter. Applications of this topology may include the start-up and shut-down of drive systems, where the buck capability would be of use. Its buck-boost capability can be used in applications such as dynamic voltage restorers or V/F control of drive systems. The boost capability may benefit the grid connection of limited output voltage renewable energy sources. Extending the boost inverter's boost capability is the main emphasis of this work.

1110-0168 © 2013 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. http://dx.doi.org/10.1016/j.aej.2013.05.006

The voltage source inverter (VSI), current source inverter (CSI), and Z-source inverter are the prevalent converter topologies proposed for grid-connected renewable energy systems. The voltage source inverter (VSI) is the workhorse of the power converter industry. Its widespread use and versatile applications span most industrial and commercial sectors. One of the characteristics of the topology is the stepped down nature of its output voltage. If one is to consider the application of this topology in grid-connected renewable energy applications, such a characteristic emerges as an important design factor. In such applications, the low output voltage typical of renewable sources such as photovoltaic and fuel cell systems requires proper boosting in order to meet grid interface requirements. A two-stage power conversion process is thus typically used. Using an intermediate DC-DC boost converter is one means of achieving the required voltage boost. This adds significant complexity and hardware to the power conversion system [2-8]. Alternatively, a bulky low frequency output transformer to boost the inverter output voltage may be used.

A CSI boosts the input DC voltage to the AC voltage without the boost DC-DC converter stage. The converter power switches should have a reverse voltage blocking capability or series connected diodes with the switches. These semiconductor devices should be able to carry the full input DC current [8-10]. Ref. [11] provides a detailed comparative evaluation of VSIs and CSIs for grid interfaces in distributed and renewable energy systems.

The Z-source inverter is considered a combination of the VSI and the CSI. It can be employed to achieve inverting and buck/boost function in only a single stage. With a specific impedance network of capacitors and inductors, the Z-Source inverter employs the shoot-through states by gating both upper and lower switches in the same phase legs to boost the DC voltage without adding a DC-DC converter [12-15]. Buck-boost capability, intrinsic short circuit protection due to the Z-source arrangement, and improved EMI are considered advantages of the ZSI over the CSI and VSI.

Single-phase DC-AC boost converters [16-18] can also be used to connect renewable energy sources to the grid. In [16], a new single-phase voltage source inverter was described. It can generate an output AC voltage larger than the input DC voltage depending on the reference duty cycle [16,17]. Fig. 1a shows a block diagram of the single-phase boost inverter. Blocks A and B represent DC-DC converters. These converters produce a dc-biased sine wave output so that each block only produces a unipolar voltage. The modulation of each

converter is 180° out of phase with the other, which maximizes the voltage excursion across the load. The load is connected differentially across the converters. Thus, whereas a dc bias appears at each end of the load with respect to ground, the differential DC voltage across the load is zero.

A single-stage three-phase boost inverter is proposed in [18] with reference to its possible use in distributed power generation and emphasizing its impact on the overall power quality and dynamic performance. It provides both DC to three-phase conversion and voltage boost; moreover, it is comparatively lower in cost than alternative solutions, is compact, and does not need switching devices with reverse voltage blocking capability nor a power transformer [18]. The system consists of three DC to DC bi-directional boost converters with a common point as shown in Fig. 1b. These converters produce a DC-biased sine wave output. The AC component of each converter is 120° out of phase with the other. The main advantages are the use of only six IGBTs, and its low reactive element requirements to generate an output AC voltage larger than the input DC voltage.

Conventional three-phase VSIs have utilized third harmonic injection to extend the inverter gain by approximately 15% without an additional boosting stage [19-22]. In earlier work [23], employment of third harmonic injection to extend the gain of single-stage three-phase grid-connected boost inverter is proposed. Over-modulation technique may be used to extend the inverter gain as well. In this work, the effect of using over-modulation on the output voltage of the boost inverter is studied. The main contributions in this paper can be summarized in the following bullets:

• A study of the effect of modulation index on the THD of the boost inverter output voltage has been presented.

• A study on the effect of over-modulation on the inverter's output voltage has been presented.

• The performance of grid-connected inverter with extended gain is tested during normal operation as well as in the presence of grid side disturbances.

2. Boost inverter principle of operation

Each phase in the three-phase boost inverter consists of two IGBTs, one inductor, and one capacitor as shown in Fig. 1. There is a common point for the capacitors (O), which is connected to the negative terminal of the DC supply. The load is

-I Load I-

Converter V, V2 Converter

Renewable energy source

Figure 1 (a) Single-phase boost inverter block diagram and (b) three-phase boost inverter.

connected to the inverter terminals creating another common point (N), which is electrically isolated from the capacitors' common point.

The capacitor reference voltage is composed of two components:

- AC component (vaco): the AC component of each capacitor is of equal magnitude but with a mutual phase shift of 120° as shown in (1).

- DC component (VDCo): the DC component should be the same for all phases and greater than or equal to the sum of the AC component peak (Vaco) and the DC input voltage ( Vdci).

Table 1 Three-phase boost inverter parameters (MATLAB model).

Input DC voltage 100 V

Inverter inductance 1mH

Inverter capacitance 40 iF

Switching frequency 3000 Hz

vAO ref (t) 200 + 100 sin(314t) V

vBO ref (t) 200 + 100sin(314t - 120) V

vCO ref (t) 200 + 100 sin(314t + 120) V

AC load 10 X per phase

The load terminals are tapped between the capacitors connected to the upper IGBTs as shown in Fig. 1. This connection eliminates the DC component present in the voltage between the capacitors and the common point (O) from the output line voltage and consequently the output phase voltage. Eq. (2) shows the converter output line voltages with eradicated DC components.

VAo(t) = Vdco + Vaco sin(at) VBo(t) = Vdco + Vaco sin ^at - yj

vco(t) = Vdco + Vaco sin (at + y

VAß(t) = Vao (t)- Vbo (t) = V3Vaco sin (at + pj

Vßc(t) = VBo(t) - Vco(t) = Vaco sin [at - pj (2)

VcA(t) = vco(t)- VAo(t) = p3Vaco sin (at + yj

For phase A, considered as a DC-DC boost converter, the instantaneous voltage gain can be expressed as in (3), where D is the boost converter duty cycle.

VAO _ _

VDa ~ 1 - DAref(t)

Da ref(t) ~ 1 - -Vdcj-

VAO ref (t)

To get the reference voltage, vAO ref (t), across the capacitor of phase A, the instantaneous value of reference duty cycle for this phase can be obtained from (4).

The corresponding pulse width modulated (PWM) pulses can be easily generated as shown in Fig. 2, where fs is the switching frequency of the inverter. This can be carried out on phases B and C in a similar fashion.

The MATLAB/SIMULINK package was used to build a model of the basic three-phase boost inverter circuit. The parameters in Table 1 were used to carry out a simulation case study, and the corresponding simulation results are shown in Fig. 3. Fig. 3b shows that the AC component of vAO(t) is unsymmetrical, due to duty cycle variation. This is due to the fact that capacitor voltage ripples in a boost converter are linearly dependent on duty cycle. This asymmetry means that there is an even order harmonic component in the output voltage. However, the values of even order harmonics in the output voltage are within the IEEE standard values.

3. Effect of over-modulation technique on the boost inverter gain

3.1. Modulation index

The modulation index of the three-phase boost inverter is derived in terms of its primitive single-phase boost inverter representation. For the boost converter, expression (5) describes the DC gain.

1 Vdco

Gdc —

Vdco- Vd

Gdc — 1

Thus, the modulation index of the three-phase boost inverter can be defined as shown in (6).

Triangle Wave

3.2. Instantaneous AC gain

The instantaneous gain of the three-phase boost inverter is gi ven by (7).

Vo{t) Vdco + Vaco sin(rat)

gac(t) 'jr tr

vDCi V DCi

gac(t) = Gdc + M(Gdc - 1) sin(xt)]

Figure 2 PWM generation.

Substituting from (5) and (6) into (7) yields an expression for the inverter's AC gain shown in (8).

The maximum value of instantaneous AC gain is given by (9). This expression is an important design factor when considering switch rating selection.

goc = Gdc(M + 1)-M (9)

Figure 3 MATLAB/SIMULINK simulation output of the boost inverter (a) line voltages, (b) capacitor voltage (vAo), and (c) phase voltage (van).

These relations mean that if VDCi = 100 V and the DC component (VDCo) is adjusted to be 250 V (i.e., GDC = 2.5), for proper converter operation (undistorted output voltage), the AC

component peak (Vaco) can be varied from 0 to 150 V (M from 0 to 1, i.e., buck-boost capability). The output phase voltage and capacitor voltage for different values of the modulation

Figure 5 Capacitor voltage for different values of modulation index.

50-1-1-1-1-1-1-1-

0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08

Time, s

Figure 6 Capacitor voltage during over-modulation (M = 1.15).

index are shown in Figs. 4 and 5 respectively. If Vaco is adjusted to 150 V (i.e., unity modulation index), from (9), the maximum value of the instantaneous AC gain gac will be four.

3.3. Over-modulation

The amplitude of the modulating sinusoids can be increased beyond the difference between VDCo and VDCi for operation

4001-1-1-]-1-1-1-r

.400-1-1-1-1-1-1-1-

0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08

Time, s

Figure 7 Output line voltage during over voltage modulation (M = 1.15).

in the over-modulation region. Since the minimum output voltage of the boost converter is its input voltage (zero duty cycle), setting Vaco greater than VDco - VDa (i.e., greater than 150 V for our given data) will clip the capacitors' voltage at VDCi (i.e., over-modulation will occur) as shown in Fig. 6. The corresponding effect on the output line voltage is shown in Fig. 7. It should be noted that the output voltage magnitude

Figure 8 Capacitors' voltage and line voltages for (a) M = 1, (b) M = 1.5, (c) M = 2 and (d) M = 2.5.

Table 2 Effect of over-modulation.

Modulation index Flat bottom period

M 6 1 = 0

1 < M <2 <120°

M = 2 = 120°

M >2 >120°

increases during over-modulation, but due to the clipping of the capacitors' voltage, the waveform is distorted. The period in which the capacitor voltage is clipped depends on the value of modulation index. Fig. 8a-d shows the capacitors' voltage and the corresponding output line voltages for M equal to 1, 1.5, 2 and 2.5, respectively, assuming a very high switching frequency fs = 1).

It should be noted that the flat bottom portion in the capacitors' voltage will appear only when the modulation index becomes greater than unity. At this condition, the capacitors' voltage is clipped at VDCi for a certain duration depending on the value of the modulation index as shown in Table 2.

When the flat bottom period is greater than 120°, the output line voltages will become discontinuous due to overlapping between the capacitors' voltage as shown in Fig. 8d. Hence, for continuous sinusoidal line voltages, the maximum allowable duration of the flat bottom is 120° (i.e., Mmax = 2). Verification of this for the phase A case is presented in (10)-(13), assuming an infinite switching frequency.

VAo(xt) = Vdco + Vaco sin(fflt) (10)

Referred to Fig. 9,

Vao(7p/6) = Vdco + Vaco sin(7p/6) = Vdco - 0:5 Vaco (11) Also,

VAO (7p/6) = Vdc, (12)

Substituting from (11) into (12) yields,

Vdco — 0.5Vaco ~ Vdc . >

Vdco — Vdc = 0.5 Vaco ) M = 2 ( )

Practically, for VDCi =100V, L = 200iH, C = 100iF, VDCo = 250 V and a switching frequency of 3 kHz, Mmax is reduced to 1.65 as shown in Fig. 10.

3.4. Total harmonic distortion

The effect of modulation index variation and over-modulation on the THD of the output voltage is studied in this section, and

Figure 10 Capacitors' voltage at M = 1.65 and switching frequency of 3 kHz.

Table 3 Effect of modulation index variation.

Modulation index Inverter gain THD (%)

0.25 0.25 23.7

0.5 0.5 11.7

0.75 0.7479 7.72

1 0.9942 5.93

1.15 1.113 7.59

1.25 1.181 9.41

1.5 1.338 14.07

1.65 1.426 16.59

Figure 11 Modulation index versus inverter gain.

the results are tabulated in Table 3. Assuming that Vdcî = 100 V, L = 200iH, C = 100 iF, Vdco = 250 V, and switching frequency is 3 kHz. Fig. 11 shows the relation between modulation index and inverter gain. Fig. 12 shows the

Figure 12 Modulation index versus output voltage %THD.

relation between modulation index and %THD of the output voltage. From the results shown in these figures, it is clear that for a desired AC component, it is recommended to operate the three-phase boost inverter at unity modulation index to avoid high THD values. This can be done by adjusting VDCo to equal the sum of the desired Vaco and VDCi.

4. Third order harmonic injection

Operating in the over-modulation region results in distorted output. Alternatively, third harmonic injection can be used as a means to extend the inverter gain to 1.15 without adding more stress on switches or distorting the output voltage waveform. The main disadvantage of this method compared to over-modulation is its limited gain. Third harmonic injection is commonly used to extend the linear range of the conventional VSIs, producing a flat-topped modulating signal, and hence better DC-link utilization [19-21].

The most common implementation method involves the addition of a third order harmonic to the modulating signal. The addition of a one-sixth per unit third order harmonic to the modulating signal has the effect of reducing the peak by a factor of 0.866 without influencing the amplitude of the fundamental [22]. This process is illustrated in Fig. 13. It is thus possible to increase the amplitude of the modulating wave and hence better utilize the inverter DC-link as shown in Fig. 13c. Fig. 13 shows the effect of third harmonic addition to the modulating waveform. An increase of 15% in the fundamental of the phase and line voltage waveforms has been obtained. The line-to-line waveform is free of any third order harmonics due to the common mode nature of the injected harmonic.

For VDCi = 100 V and VDCo = 250 V, employing a pure sinusoidal PWM would yield a maximum voltage of 150 V.

Figure 13 Increasing fundamental output voltage by addition of third harmonic.

Figure 14 (a) Phase voltage (van) with and without adding third harmonic injection and (b) reference of capacitor voltage (phase A).

Figure 15 Block diagram of grid-connected boost inverter.

With third order harmonic injection, the output phase voltage reaches 172.5 V. The simulation results shown in Fig. 14 verify the possibility of increasing the gain of the three-phase boost inverter through third order harmonic injection into the modulating signal. Multiples of the third order harmonic can also be added to the modulating signal, which will only slightly enhance converter gain. It is obvious that the THD of the output voltage is increased from 6.3% to 8.6% when third order harmonic injection is applied.

5. Grid-connected mode

Fig. 15 shows the block diagram of the grid-connected boost inverter. Where Pref, Qref, Vg, Ig, Lg, Vgd, Igd, and Igq are reference of grid active power, reference grid reactive power, grid voltage, grid current, interface grid inductance, direct component of grid voltage, direct component of grid current, and quadrature component of grid current, respectively.

Table 4 Grid-connected boost inverter parameters.

Input DC voltage 100 V

Grid inductance 0.3 mH

Inverter inductance 1 mH

Inverter capacitance 0.04 mF

Switching frequency 3 kHz

Inverter full load current 30 A (peak)

Reference grid active and reactive powers 4 kW, zero VAR

Grid voltage (peak) 100 V (phase)

Pref and Qref are used to determine the desired current components that govern the power flow. A saturation block is used to define the limited overload capability of the inverter. The maximum allowable current is adjusted to be 1.5 times the inverter full load current as the inverter switches cannot be overloaded. A current controller is used to obtain the AC component of capacitor reference voltage. A suitable DC component is added to the AC component to obtain the inverter reference voltage. The DC component is selected to guarantee proper operation at unity modulation index (minimum THD), i.e., VDCo = Vaco + VDCi. If third order harmonic injection is used, the harmonic component is also added as shown in PWM generator for phase A in Fig. 15.

The performance of the grid-connected boost inverter during normal as well as abnormal conditions is studied in this section. The grid-connected boost inverter parameters are given in Table 4. Simulations have been carried out using MAT-LAB/SIMULINK.

• Case 1: this case studies the performance of the boost inverter during normal/healthy conditions. The simulation results are shown in Fig. 16.

Figure 17 Case 2 simulation results (grid-connected inverter during abnormal operating conditions).

• Case 2: in this case, the grid is subjected to 50% voltage sag to emulate remote fault condition. The fault starts at 0.05 s and is cleared at 0.1 s. It is expected that the fault level increases at the specified fault location but due to the limited overload capability of the inverter, the reference voltage is decreased automatically to limit the fault current to 1.5 times the full load current, and the simulation results for this case are shown in Fig. 17. It is obvious that the power is decreased from 4 kW to 3.4 kW due to current limiting capability of inverter. For any given power reference and measured grid voltages, the reference currents are calculated. If the reference current magnitudes are larger than the maximum allowable current, the reference current magnitude is reduced to be equal to the maximum current to avoid any electrical stresses on semiconductor devices; this reason makes the injected power to the grid lower than the reference value.

6. Experimental results

An experimental setup was built as shown in Fig. 18 to confirm the boosting capability. It consists of a three-phase inverter employing six IGBTs driven by a high voltage driver, three capacitors, three inductors, a resistive load, and DC supply. The gate pulses at a 3 kHz switching frequency are generated

Table 5 Experimental prototype parameters.

Figure 16 Case 1 simulation results (grid-connected inverter during normal operating conditions).

Figure 18 Three-phase boost inverter experimental setup.

from Texas Instruments DSP TMS320F28335 to obtain desired phase voltage. The system parameters are shown in Table 5. The experimental results for this system are shown in Fig. 19a and b. The over-modulation condition is tested by increasing the phase voltage magnitude by 33.3% as shown in Fig. 19c.

Inverter gain was extended by 15% using third order harmonic injection, i.e., the new AC component can be mathematically written as {30(1.15 sin (wt) + 0.19 sin (3wt)}. The corresponding experimental results are shown in Fig. 19d.

The performance of a grid-connected boost inverter during normal operating conditions was also tested experimentally. In

Figure 19 (a) Phase voltages, time base 4 ms/Div and voltage base 10 V/Div, (b) capacitors voltage, time base 4 ms/Div and voltage base 20 V/Div, (c) capacitor and line voltage during over-modulation, time base 4 ms/Div and voltage base 50 V/Div and (d) capacitor and line voltage during third harmonic injection, time base 4 ms/Div and voltage base 50 V/Div.

TekPitVu_1 J —j Noise Filtci Off

Figure 20 Capacitor voltage (20 V/Div, 20 ms/Div). TekPieVu_[ ; -i Noise Filter Off

Figure 21 Inverter output voltage (10 V/Div, 20 ms/Div).

guarantee minimum THD of the output voltage. Fig. 21 shows the inverter output voltage (30 V peak per phase) feeding a load (30 X) and coupled to the grid via an interface impedance of (1 + j3 ohm). The grid voltage is adjusted to 30 V peak per phase via an auto-transformer. The grid reference power is adjusted to 30 W resulting in the current shown in Fig. 22 (the measured current direction was from grid to inverter). The input DC current, measured using a permanent magnet moving coil instrument, was 2.6 A, i.e., the input power is 78 W. This amount of power is injected from the inverter to the load (45 W) and to the grid (30 W) in addition to the circuit losses.

7. Conclusion

This paper addresses a three-phase boost inverter suitable for a single-stage connection of renewable energy sources to the grid. The converter possesses the benefits of reduced hardware requirements and an improved gain. The main contributions of the paper can be briefly summarized in three main points as follows:

(1) The effect of modulation index variation on THD of the output voltage is studied.

(2) Employing over-modulation technique and third order harmonic injection to extend the gain of the boost inverter.

(3) The performance of the extended gain converter in normal operation as well as during disturbances was evaluated.

Simulation results supported by experimental verification show the effectiveness of the grid-connected boost inverter during normal operation well as in the presence of grid side disturbances.

Tek PieVu 1 ff H tonFMI

Grid Voltage (20V/ Div, 20ms/Div )

11 Cu rrent from grid to nvertêr (1A/Div, 2 Dms/D iv>

Figure 22 Channel 1: grid voltage, channel 2: current from grid to inverter.

this mode, the boost inverter was used to inject a certain amount of power (30 W) to the grid. The corresponding experimental results are shown in Figs. 20-22. The figures illustrate that there is an acceptable transient period during the start-up of a boost inverter circuit. The control algorithm is adjusted to select a suitable reference voltage to the boost inverter to fulfill the requirements. Fig. 20 shows the capacitor voltage, which includes two components, AC (30 V) and DC (30 V); the value of the DC component is selected via the control algorithm to

Acknowledgment

This publication was made possible by NPRP Grant NPRP 4 -250 - 2 - 080 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

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