2011 International Conference on Electrical Engineering and Informatics 17-19 July 2011, Bandung, Indonesia

A Modular Multilevel Inverter Using Single DC Voltage Source for Static Var Compensators

Firman Sasongko1, Hadyan Nur Buwana2, Riko Iswara3, and Pekik Argo Dahono4 School of Electrical Engineering and Informatics, Institute of Technology Bandung

Jl. Ganesha 10, Bandung 40132, Indonesia 1firman@konversi.ee.itb.ac.id 2hadyan-nur.buwana@total.com

3r_iswara@yahoo.com 4pekik@konversi.ee.itb.ac.id

Abstract— Multilevel inverter has emerged as a new solution of power converter for high power applications. Many efforts have been done to obtain the best performance of multilevel inverter to provide the need of power converter for high-power medium-voltage applications. Multilevel inverter using modular-cascaded topology with single dc voltage source is presented in this manuscript. Inverter topology, features and control method will be discussed. Simulation results for static var compensator application are included to verify the effectiveness of the proposed method. Keywords— Multilevel inverter, modular cascade inverter, static var compensator.

I. INTRODUCTION Reactive power compensation has become an indispensable

requirement to provide a better power system performance [1], [2]. Var compensator system has three major roles: improving the transient stability, damping the power oscillation, and supporting the grid voltage to prevent voltage instability. In recent years, static var compensators are preferable to their traditional counterpart of using rotating synchronous condenser and mechanically switched capacitors or inductors [3], [4]. Static var compensator provides faster time response to absorb or generate the reactive power. The advances of power electronic devices, analytical tools, and micro-computer technologies has create the more sophisticated power converter to be used for static var compensator and other high-power applications.

Multilevel system is especially important in high-power applications such as Flexible AC Transmission System (FACTS). At present, most of FACTS controllers that have been installed worldwide are using conventional two-level inverter modules that are interconnected by using a special design multipulse transformer [5], [6]. In order to reduce the switching losses, the inverter switching devices are switched at the fundamental frequency. The transformer is configured in such a way so that certain low-frequency harmonics are eliminated. The output voltage is controlled by adjusting the dc voltage of the inverter with the consequence of slow control response. Thus, a multilevel inverter may become an

alternative solution to achieve a simple structure converter with a fast control response for high-power applications.

The concept of multilevel converters has been introduced since 1975. Since then, various multilevel converter topologies were proposed [7], [8]. These converters are suitable for high-power medium-voltage applications. The main advantage of multilevel converter is that high output voltage can be obtained without series connection of switching devices. Moreover, better output waveforms can be obtained without the need of high switching frequency operation with the associated high switching losses.

In this paper, a new modular multilevel inverter topology based on cascaded H-bridge cells is proposed. Neither complicated transformer nor separate dc sources are required. A single dc source is used for the whole single-phase H-bridge cells. High output voltage is accomplished by the use of identical single-phase transformer connected in series at the ac side. Each cell output voltage can be controlled using phase difference between each leg. The output voltage harmonics are minimized by controlling the phase differences of H-bridge cells. By using fundamental switching frequency, all H-bridge cells have identical device rating and utilization factor. The use of identical power cells leads to a modular structure, which is an effective means for cost reduction. The proposed inverter topology and also control scheme for static var compensator are presented. Simulated results show the effectiveness of the proposed multilevel inverter for static var compensator application.

II. PROPOSED TOPOLOGY Multilevel inverter can be considered as a series connection

of several ac voltage sources as shown in Fig. 1. In most applications, the resultant of the voltage must be adjustable in magnitude and low in harmonic contents. In high-power applications, PWM switching operation is avoided because of switching losses problem. Thus, the inverter switching devices must be operated at fundamental frequency. To comply with these constraints, the following methods can be chosen:

i) Controlling the dc voltage and using a special connection transformer to reduce the harmonics.

E2 - 1

978-1-4577-0752-0/11/$26.00 ©2011 IEEE

ii) Controlling the devices gating signals to produce a

staircase waveform which control the output voltage and reduce harmonic contents.

The first method is simple but the response is slow because of large time constant of dc circuit. Moreover, a special transformer connection is necessary. The second method is more promising because of faster control response by using controlled switching of inverter legs. Separate dc sources are necessary if no galvanic isolation provided in the ac side. Using many large dc electrolytic capacitors is prone to failure. Therefore, using single dc capacitors with galvanic isolated system is preferable here.

Several choices are available to use transformer as a galvanic means. A special connected transformer can be used to reduce the harmonics, which however, different transformers have to be used if the number of levels is changed. Thus, modularity of the system cannot be achieved.

V1

V2

V3

V4

V5

Vout Vout

V1

V2

V3

V4

V5

V1

V5

V2

V3

V4

Fig. 1. Series connection and phasor diagram of several voltage sources.

The preferred system is the one without custom-made transformer. An ordinary transformer can be used to reduce the harmonic contents by controlling the gating signals of the inverters. Reference [8] proposes the gating pattern by controlling switching angle for each level which produced a staircase waveform. However, utilization factor of each level is different and so does the losses of each level and cooling system requirements.

A. Circuit Arrangement Fig. 2 shows the topology of the proposed modular

multilevel inverter discussed in this paper. All single-phase H-bridge inverter and transformer are identical, therefore, can be considered as one module for each level. A single large dc capacitor is connected in parallel on dc side. IGCTs or IGBTs can be used as the switching devices. In practice, a small LCL filter is usually connected on the ac side to reduce high-order harmonics. As the output voltage levels increase, the filter may be omitted.

The proposed method produces a staircase waveform by controlling the phase angle differences among inverter levels. In general, for N H-bridge cells, the optimum phase angle difference is 60o/N which associated with the order of harmonic contents of 6 1 (1)

B. Output Voltage Control Inverter cell output voltage of the proposed multilevel

inverter is determined by phase difference of each leg. Each single-phase H-bridge inverter is operated under quasi square-wave mode as shown in Fig. 3, ensuring the same utilization factors of each level. The effective output voltage is controlled by adjusting the β angle. The effective fundamental voltage of each cell can be defined as 2√2 2 (2)

For N H-bridge cells, the general expression of phase output voltage can be obtained as

1 4 cos 2 cos~

3 1 (3)

where h is odd harmonic number only. For N = 5, using transformer ratio of 1 : r, the phase-to-phase effective fundamental output voltage is 7.45 cos 2 (4)

It can be seen from (2) and (4) that the output voltage varies linearly to cosines of β⁄2. This feature has the advantage to generate a simple switching control scheme.

Fig. 2. Modular cascaded multilevel inverter and its waveform.

Fig. 3. Signal waveform of each inverter leg in each cell.

C. Comparative Evaluation In order to clarify the performance of the proposed modular

multilevel inverter system, a conceptual design of static var compensator with 10 MVAR rating is used. It is assumed that the static var compensator is designed to operate on medium-voltage of distribution system (20 kV). The proposed multilevel inverter design is then compared to the ones using quad-series [6] and cascaded [8] inverter systems. Using the most advanced power switching devices with rating up to 6kV/6kA, the dc source voltage can be as high as 3.1 kV. Table I shows performance comparison among the three types of static var compensator.

III. CONTROL METHOD A static var compensator can be considered as voltage

source converter which connected in parallel to the power grid through series inductance as shown in Fig. 4. The line resistance is usually very small and can be neglected. The objective of multilevel inverter control system is to ensure dc voltage and reactive power flow at a desired command. When the inverter voltage vi is higher than grid voltage vg, inverter current will lead the voltage by 90o (reactive power injection). On the contrary if the inverter voltage vi is smaller than grid voltage vg, then inverter current will lag the voltage by 90o

(reactive power absorption). Thus, controlling the inverter voltage magnitude means controlling the reactive power flow.

Although theoretically var compensator does not exchange active power to the grid, the inverter internal losses will cause the capacitor voltage to deviate from its nominal value. By adjusting the phase angle α between inverter and grid voltages, the active current will flow in/out to keep the dc voltage constant.

The circuit equation for three-phase system as in Fig. 4 can be written as

C (5)

In d–q synchronous reference frame, this equation can be written as follows:

C CC C (6)

where ω is system frequency; the subscript ‘d’ and ‘q’ are d-axis and q-axis voltage/current component respectively. Because the grid voltage vector is always aligned with d-axis voltage component vgd, the q-axis component of grid voltage vgq is always zero. The instantaneous active and reactive power in d–q synchronous reference frame can be expressed as

(7)

TABLE I COMPARISON SUMMARY

Aspects Inverter Topology Quad-series Cascade Proposed

Voltage level 11 21 21 Capacitor 1 15 1

DC voltage ±3100 V ±3100 V ±3100 V

Transformer

Complex configuration

-

15 single phase

ΔS – ΔP = 1:2 ΔS – YP = √3:2 1:1

Converter construction

Identical but not modular

Identical and modular

Identical and modular

Utilization factor equal unequal equal

Power switch 24 60 60 Control

strategies α angle α angle and MI

α and β angle

DC unbalance problem

No Yes No

Response time Medium Fast Fast

THD 8.7% 6.6 – 7.2% 3.6 – 7.6%

Fig. 4. Static var compensator model and its operation modes.

From (7), the active and reactive power control can directly

be determined by active and reactive current provided a constant grid voltage. Therefore, controlling the reactive current iiq alone is sufficient to control reactive power to the grid. Moreover, to keep a constant dc voltage by controlling active power flow, only the active current iid need to be controlled. Thus, a fast current controller is desirable in this method to achieve the system with fast dynamic time response.

A. Static Var Compensator with Proposed Multilevel Inverter The complete control system and block diagram of the

proposed static var compensator is shown in Fig. 5. There are two reference values in this system, which are the dc voltage reference and q-axis current reference which proportional to reactive power q. The control system will then produce α* and β* commands, which will control the active and reactive power respectively. The α*and β* angle can be obtained from d- and q-axis voltage references as

2cos (8)

tan (9)

where K is a topology characteristic constant and r is the transformer ratio. The K value will be unique for each cell numbers as in (3) with h = 1. For N = 5, K is equal to 7.45, while for N = 3, K is equal to 4.49.

The inverter output voltage must be synchronized to the power grid voltage. For this purpose, a phase locked loop (PLL) circuit is used to obtain the grid voltage angle θ. This angle will be used for all d–q transformation process.

The dc voltage reference is compared to the actual dc capacitor voltage which then will be processed by a PI controller to generate the d-axis current reference . The actual d- and q-axis currents, which obtained from inverter currents using d–q transformation, are then compared to the reference values and the PI current controllers will

compensate the errors. The output of the current controllers is the desired d-axis and q-axis inverter output voltages. By using a look up table, the required β and α angle can be determined.

B. Decoupled Current Control The plant block diagram as shown in Fig. 5 implies that the

d- and q-axis currents cannot be controlled independently. To solve the coupling problem, a feed-forward technique as shown in current controller block diagram of Fig. 5 is used. The actual output currents Iid and Iiq are multiplied by the line reactance ωLC to produce additional signals to cancel out the coupling effects. By using this method, the d-axis currents can be controlled independently as shown in Fig. 6. The control method for q-axis current has the same approach. The inverter is assumed to have a unity gain, so the inverter output voltage Vid is equal to the voltage reference Vid*.

From Fig. 6, the transfer function of d-axis current can be determined as CC C CCCC CC C (10)

The damping ratio ζC and undamped natural frequency ωnC can be obtained as follows:

ζC 1 2 C CC (11)

C CC C (12)

By using critically damped control response, the damping ratio is ζC = 1 and the current control gain KC and time constant TC can be determined as

C 4000 CV/A with C 1 ms (13)

Fig. 5. Proposed static var compensator system and its control block diagram.

Fig. 6. Decoupled current control block diagram.

C. DC Capacitor Voltage Control Single dc capacitor is used in the proposed system. A

simple control system is required to maintain dc voltage level. By avoiding the resonance condition between dc capacitor and line reactor, reduction of the dc voltage fluctuation can be achieved. A simple right-hand rule can be used to determine the required capacitance for single capacitor circuit with nominal reactive power of QVAR [8] as follows: 2 VAR (14)

The dc capacitor voltage may deviate from its nominal value because of overall losses in the inverter. The regulation factor of dc voltage ε is defined as

2 (15)

This factor may range from 5-20% practically. Using the regulation factor ε of 10% in the 10 MVAR of static var compensator system connected to 20 kV of distribution system, the required capacitance C is 8.28 mF for 3.1 kV nominal dc voltage.

If the total system losses can be expressed as D, then the inverter active power flow can be defined as

(16)

The instantaneous dc capacitor voltage can be written as Δ (17)

Δ 1 (18)

where Vdc is the average dc voltage and Δvdc is the dc voltage ripple. From Fig. 5, (16) and (18), the block diagram for dc voltage control can be depicted as in Fig. 7 assuming an ideal current control with unity gain.

Fig. 7. DC capacitor voltage control block diagram.

From Fig. 7, the transfer function can be obtained as Δ (19)

The damping ratio ζdc and undamped natural frequency ωndc are given by

ζ 1 2 (20)

(21)

By using critically damped control response, the damping ratio is ζdc =1, leading to control system parameters as follows: 800 A/V with 5 ms (22)

IV. SIMULATION RESULTS To verify the proposed multilevel inverter topology as

static var compensator, the simulation using 7-level inverter was carried out. The system configuration and system parameters are shown in Fig. 5 and Table II. The system is connected to low-voltage distribution system of 380 V and controlling a 5 kvar of reactive power flow. The utility voltage is assumed to be balanced three-phase system with constant magnitude and frequency.

The simulation results of the proposed static var compensator can be seen from Figs. 8–9. The system has the capability to inject/absorb 5 kvar of reactive power. Fig. 8 shows the phase voltage and current of the proposed multilevel inverter when the reactive power is change from 2 kvar leading to 5 kvar leading and finally to 5 kvar lagging. The inverter voltage reacts instantaneously whenever the reactive power reference is changed suddenly. Although the reactive power reference changes from injecting to absorbing mode, the inverter voltage can adapt the reactive power demand with fast time response.

TABLE II SIMULATION PARAMETERS

System Voltage VG 380 V 50 Hz Var Rating QVAR ±5 kvar DC Voltage Vdc ±97.7V

Interface Inductance LC 12% (11 mH) Source Impedance LS 2% (1.8 mH)

Cell Number N 3 DC Capacitor C 8.337 mF

Regulation Factor ε 5% Transformer Turn Ratio r 1:1

q

via

iia

Fig. 8. Simulated results when the reactive powe

q

vdc

Fig. 9. Simulated result of DC capacitor voltage whestep changed.

The dc voltage can be kept constant at aV and only a small distortion occurs when is changed, as can be seen from Fig. 9.regulation factor ε will affect the distortiovoltage.

V. EXPERIMENTAL SYSTEM

To further validate the proposed systestrategy as a static var compensator, a protomodular inverter is being built and wexperiment based on Table II parameters. Twill be implemented in dSPACE (DS110has MPC8240 250 MHz core procTMS320F240 as slave. The controller can psystem for floating point numbers calculatio

For real time evaluation of the control sUser Interface (GUI) will be designed Simulink and dSPACE platform as can be spreviously explained control scheme will

er is step changed.

en the reactive power is

approximately 97.7 the reactive power

. The selection of on in the capacitor

M em and its control otype of seven-level will carry out the The control system 4) platform which essor with DSP provide a powerful on. ystem, a Graphical using MATLAB/

seen in Fig. 10. The l be automatically

processed and run in DS1104platform will provide the inpupower and capacitor voltage resystem parameters continuousinverter voltage and current, ppower and dc capacitor voltage.

Fig. 10. Experimen

VI. CONC

This paper has proposed a inverter. Inverter topology, swsystem for static var compendetail. The simulation resultmultilevel inverter has a inject/absorb reactive power tproposed control system schemadjusted as desired. Moreovmaintained at a constant level un

In general, the proposed topomodularity, equal utilization fand simple control procedure. Aneither unbalance problem nor cThus, the proposed modular mufeatures with which very appliapplications.

REFERE[1] L. Gyugyi, “Power electroni

compensators,” in Proc. IEEE, vo[2] J. Dixon, L. Moran, J. Rodrigu

compensation technologies: state93, no. 12, pp. 2144-2164, Dec. 2

[3] E. Larsen, et.al., “Benefits of Gelectric utility applications,” IEE2064, Oct. 1992.

[4] A. E. Hammad, “Comparing the and future var compensating tIEEE Trans. Power Del., vol. 11

[5] C. Schauder, et al., “Developmenvoltage control of transmission sy10, pp. 1486-1496, July 1995.

[6] H. Fujita, S. Tominaga, and Hadvanced static var compensatinverters,” IEEE Trans. Ind. App1996.

[7] J. Rodriguez, J. S. Lai, and F. Z.of topologies, controls, and appli49, pp. 724-738, Aug. 2002.

[8] F. Z. Peng, et al., “A multileveldc sources for static var generat32, pp. 1130-1138, Sept. /Oct. 19

via PCI card slot. The GUI ut references such as reactive eferences, and also shows the sly, e.g. the system voltage, phase angle, injected reactive

ntal control system.

CLUSION modular cascaded multilevel

witching pattern and control sator have been presented in ts show that the proposed fast dynamic response to

to/from the system. With the me, the control response can be ver, the dc voltage can be nder dynamic condition. ology has the advantages of its factors among inverter blocks As a single dc capacitor is used, complex controllers are existed. ultilevel inverter provides some icable to low-cost high-power

ENCES ics in electric utilities: static var ol. 76, no. 4, pp. 483-494, Apr. 1988. uez and R. Domke, “Reactive power e-of-the-art review,” in Proc. IEEE, vol. 2005. GTO-based compensation systems for EE Trans. Power Del., vol. 7, pp. 2056-

voltage control capabilities of present techniques in transmission systems,” , pp. 475-484, Jan. 1996. nt of a ± 100 Mvar static condenser for ystems,” IEEE Trans. Power Del., vol.

H. Akagi, “Analysis and design of an tor using quad-series voltage-source plicat., vol. 32, pp. 970-978, July/Aug.

. Peng, “Multilevel inverters: A survey ications,” IEEE Trans. Ind. Electr., vol.

l voltage-source inverter with separate tion,” IEEE Trans. Ind. Applicat., vol. 996.