6
International Review on Modelling and Simulations (I.RE.MO.S.), Vol. 3, N. 5 October 2010 Manuscript received and revised September 2010, accepted October 2010 �op�rig�t � 2010 �raise �ort�ri�e S.r.l. - All rig�ts reserved 753 Neutral Point Balancing for Three Phase Three Level Voltage Source Converter (Case Study: STATCOM) M. S. Javadi, M. Joorabian, S. Gh. Seifossadat, B. Noshad Abstract T�e neutral point unbalance is a problem w�ic� results in t�ree-level inverter w�en t�e neutral point is connected to c�arging current for longer periods t�an to disc�arging currents (or vice-versa). Alt�oug� t�e dc voltage regulator works properl�, t�e inequalit� between c�arging and disc�arging neutral point current results in an unbalance between t�e dc voltage across t�e upper and lower capacitors. T�is is an undesirable c�aracteristic since even if t�e converter is properl� modulated t�e resulting output waveform becomes as�mmetric about t�e x- axis and consequentl�, similar distortion results in t�e line currents. In t�is case, t�e neutral point connection time is controlled since t�e modified-�M sc�eme is easil� modified and t�e concept is relativel� straig�tforward. �� K��w: STAT�OM, T�ree Level Inverter, Voltage Source �onverter, Neutral �oint Balancing I. Introduction The use of Voltage-Source Inverter/Converter (VSI/VSC) has been widely accepted as the next generation of flexible reactive power compensation to replace other conventional VAR compensation, such as the thyristor-switched capacitor (TSC) and thyristor controlled reactor (TCR). Switched capacitors and inductors have been replaced by static var compensators (SVCs) and recently, due to the advent of high power, self-commutated switches, STATic COMpensators (STATCOM) are showing great promise and could be a favorable alternative to SVCs of similar rating. The basic STATCOM model consists of a step-down transformer with leakage reactance XT, a three-phase switch, such as GTO, IGBT�VSI, and a dc side capacitor [1]. The ac voltage difference across this transformer leakage reactance produces reactive power exchange between the STATCOM and the power system at the point of interface. The voltage can be regulated to improve the voltage profile of the interconnected power system, which is the primary duty of the STATCOM [2]. A secondary damping function can be added to the STATCOM for enhancing power system dynamic stability. The STATCOM�s main function is to regulate key bus voltage magnitude by dynamically absorbing or generating reactive power to the ac grid network, like a thyristor static compensator. This reactive power transfer is done through the leakage reactance of the coupling transformer by using a secondary transformer voltage in phase with the primary voltage (network side). This voltage is provided by a voltage-source PWM inverter [2]-[3]. Many complicated modulation schemes for three level VSCs, exist. A modified PWM scheme was implemented in this paper for its simplicity. The algorithm follows from conventional SPWM and although it is more simplified by nature, its performance does not differ significantly from more in depth schemes. II. Theoretical Considerations Seen from the STATCOM converter, the power system is represented as an equivalent Thevenin voltage Vs with the equivalent Thevenin reactance Xs. All load changes in the power system can simply be viewed as change in data of Vs and Xs [4]. The simplified three-phase version of the STATCOM circuit is shown in Fig. 1. Fig. 1. Simplified three-phase STATCOM model The Thevenin voltages are denoted by [v s ]=[v sa , v sb , v sc ] T , and the injected currents from STATCOM are denoted by [i t ]=[i ta , i tb , i tc ] T . The equivalent Thevenin impedance is denoted by R s and L s ; the reactance of coupling transformer is denoted by L t ; where the resistance R represents the switching and other losses of the STATCOM.

Neutral Point Balancing for Three Phase Three Level ...rms.scu.ac.ir/Files/Articles/Journals/Abstract/IREMOS1.pdf...... T ree Level Inverter, Voltage Source onverter, ... A Space Vector

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International Review on Modelling and Simulations (I.RE.MO.S.), Vol. 3, N. 5 October 2010

Manuscript received and revised September 2010, accepted October 2010 �op�rig�t � 2010 �raise �ort�� �ri�e S.r.l. - All rig�ts reserved

753

Neutral Point Balancing for Three Phase Three Level Voltage Source Converter (Case Study: STATCOM)

M. S. Javadi, M. Joorabian, S. Gh. Seifossadat, B. Noshad

Abstract � T�e neutral point unbalance is a problem w�ic� results in t�ree-level inverter w�en t�e neutral point is connected to c�arging current for longer periods t�an to disc�arging currents (or vice-versa). Alt�oug� t�e dc voltage regulator works properl�, t�e inequalit� between c�arging and disc�arging neutral point current results in an unbalance between t�e dc voltage across t�e upper and lower capacitors. T�is is an undesirable c�aracteristic since even if t�e converter is properl� modulated t�e resulting output waveform becomes as�mmetric about t�e x-axis and consequentl�, similar distortion results in t�e line currents. In t�is case, t�e neutral point connection time is controlled since t�e modified-��M sc�eme is easil� modified and t�e concept is relativel� straig�tforward.�������������������������������������������������������������������

K��w����: STAT�OM, T�ree Level Inverter, Voltage Source �onverter, Neutral �oint Balancing

I. Introduction The use of Voltage-Source Inverter/Converter

(VSI/VSC) has been widely accepted as the next generation of flexible reactive power compensation to replace other conventional VAR compensation, such as the thyristor-switched capacitor (TSC) and thyristor controlled reactor (TCR).

Switched capacitors and inductors have been replaced by static var compensators (SVCs) and recently, due to the advent of high power, self-commutated switches, STATic COMpensators (STATCOM) are showing great promise and could be a favorable alternative to SVCs of similar rating.

The basic STATCOM model consists of a step-down transformer with leakage reactance XT, a three-phase switch, such as GTO, IGBT�VSI, and a dc side capacitor [1]. The ac voltage difference across this transformer leakage reactance produces reactive power exchange between the STATCOM and the power system at the point of interface. The voltage can be regulated to improve the voltage profile of the interconnected power system, which is the primary duty of the STATCOM [2]. A secondary damping function can be added to the STATCOM for enhancing power system dynamic stability. The STATCOM�s main function is to regulate key bus voltage magnitude by dynamically absorbing or generating reactive power to the ac grid network, like a thyristor static compensator. This reactive power transfer is done through the leakage reactance of the coupling transformer by using a secondary transformer voltage in phase with the primary voltage (network side). This voltage is provided by a voltage-source PWM inverter [2]-[3].

Many complicated modulation schemes for three level

VSCs, exist. A modified PWM scheme was implemented in this paper for its simplicity. The algorithm follows from conventional SPWM and although it is more simplified by nature, its performance does not differ significantly from more in depth schemes.

II. Theoretical Considerations Seen from the STATCOM converter, the power

system is represented as an equivalent Thevenin voltage Vs with the equivalent Thevenin reactance Xs.

All load changes in the power system can simply be viewed as change in data of Vs and Xs [4].

The simplified three-phase version of the STATCOM circuit is shown in Fig. 1.

Fig. 1. Simplified three-phase STATCOM model The Thevenin voltages are denoted by [vs] = [vsa, vsb,

vsc]T, and the injected currents from STATCOM are denoted by [it] = [ita, itb, itc]T.

The equivalent Thevenin impedance is denoted by Rsand Ls; the reactance of coupling transformer is denoted by Lt; where the resistance R represents the switching and other losses of the STATCOM.

� �����6����������6�� ��������7'�����/��������5����'���

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754

The loop equation for the circuit is:

� � �� � � � � � � � � � �

��� � � � 4

��(1)

The voltage and current are decomposed into d-q

coordinates to analyze the reactive/active power flows [5].

Considering the synchronous characteristic of the transmission line voltage ��, we analyze the circuit with the synchronous rotating reference frame.

In the synchronous rotating reference frame, �-axis is defined to coincide with the instantaneous voltage vector of transmission line voltage ��, while the 1-axis is in quadrature with it.

The injected current it is decomposed into ��� and ��1 which represent the instantaneous active current and instantaneous reactive current components [5].

Fig. 2. Phasor diagram of STATCOM circuit The transformation matrix 8 of the synchronous

rotating reference frame is eq. (2):

23

2 23 3

2 23 3

1 2 1 2 1 2

8

�� � �� � �� �

��� � ��� � ��� �

where:

0. .

�� �1 �� � ��� � 8 � � � (3)

0. .

�� �1 �� � ��� � 8 � � � (4)

0. .

�� �1 �� � ��� � 8 � � � (5)

In eq. (4), �� �� � , 0�1� . The phasor diagram is shown in Fig. 2.

���1� ���l�/��.A.C���

With the transformation of 8, eq. (1) is transformed into:

00

0

��

�� ��� �

�1 �1�1

�� �

�1

��� �4��� 4� ��� 4

��� ��

(6)

Using the Laplace transformation:

� �� � �� �1 �� �� � �4 � 4� � � (7)

� �1 � �1 �� �1� � �4 � 4� � (8)

From eq. (7), we get:

�� ��� �1

� � � �

� � 4� �� �4 � �4

(9)

Placing eq. (9) into eq. (8), give:

2 2� � � �

� �1 �� �1� �

� �4 4 � �4� � � �

4 4(10)

Eq. (10) is the transfer function of the STATCOM

model.

���2� ���l�/��'����C�

From the AC side, a hysteresis current controlled VSC can be viewed as a controllable current source.

The output current of the VSC is regulated by the reference current.

The input reference current is usually a sine wave at utility frequency, while the output current tracks it within the limits of the tolerance band.

Neglecting the small harmonic components at comparatively high frequencies, the output current can be viewed to be the same as the reference current.

With this assumption, it is possible to analyze the power flow behavior of the VSC [6].

Seen from the transmission line, the input active power of the VSC at the AC side can be calculated from:

32�� � � � ��P � � � � (11)

The active power of the VSC on the DC side is:

2� �

�� �� ��

P � C� ��

(12)

M. S. Javadi, M. Joorabian, ���7'�����/��������5����'���

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755

Assuming no switching or other power losses within the converter: �� ��P P (13)

To analyze the small signal disturbance response, V� is assumed as regulated stable.

Using ��� and �� to represent the small signal disturbances, eq. (13) is transformed into:

23

2� � �

� �� �� � � �� � � C� ��

(14)

After using Laplace transformation, eq. (14) is transformed into:

3 2

2� �

�� � �

� � �� � � � �C�

(15)

Hence, Eq. (15) is the transfer function of the VSC

model.

III. STATCOM Modeling This section details the modeling of a three-level

based inverter in EMTP-RV. A three-level inverter is modeled which enables an

effective doubling of the switching frequency compared with a two-level design.

This allows for a reduction of one-half of the switching frequency while maintaining the same harmonic content.

����1� .'����4���l����������

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756

The PWM signals are produced using two triangular signals: starting from a conventional triangular carrier, two different offsets of opposite sign are added to the triangular waveform to give the required carriers.

Then, the two new carrier signals are compared with the reference voltage waveform and the output as well as its inverse is used for the various gating signals. In order to deduce which outputs correspond to which gating signals one simply refers to Table I.

The figures of the reference voltage, the triangular carrier and the desired output voltages are given below.

Figs. 4. (a) Reference voltage with triangular carriers (b) three level output line to ground voltage and (c) line to line voltage

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IV. Simulation Results "���������������������)��)������������)�����������

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757

Fig. 6. Gate Control signals

Fig. 7. STATCOM output phase voltage

Fig. 8. STATCOM output line voltage (filtered by capacitor) It can be seen that the harmonics of the STATCOM

output voltage appear as side-bands centered on the frequency of /� (990 Hz).

Therefore, the STATCOM output voltage has very high equivalent switching frequency, which simplifies the design and implementation of the filter. The filtered output also presented strictly subsequent.

Fig. 9. Frequency spectrum of STATCOM output voltage

V. Conclusion In order to counteract a neutral point potential

unbalance; the neutral point connection of the phase which will contribute further to the imbalance is omitted. This is done by utilizing traditional two-level modulation for that phase only. Since neutral point unbalance does not occur with large frequency for a 1% tolerance band and due to the fact that only one phase is modulated using two-level PWM, there is not a significant reduction in the effective switching frequency. To summarize, the redefined modulation scheme, taking into account neutral point balancing consists of the following: a) Identify whether neutral point unbalance exist by

comparing the upper and lower capacitor voltages. b) If not, modulate according to three level theory

presented above. c) If unbalance exists, first identify the phase current

which will contribute further to the unbalance. d) Modulate that phase using two-level modulation, the

other two are modulated using the three level theory. This is method is realized continuously, therefore if

the unbalance is eliminated or if the phase current which contributes to the unbalance changes, the control responds accordingly.

References[1] Gyugyi L., Power Electronics in Electric Utilities: Static Var

Compensators, P�����������l��:;�����<, April 1988. [2] Miller T. E. J., ed.: ��������� p ��� /����� ��p�������, John

Wiley, New York, 1985. [3] Gyugyi L., Reactive power generation and control by thyristor

circuits, ����� .������ �������y� Appl��������� 1=:=�� 1��� ���, pp. 521-532.

[4] Gyugyi L., Dynamic compensation of AC transmission lines by solid-state synchronous voltage sources, ����� .������ P ���9�l����y��1==<��=���2�, pp. 904-911.

[5] Dong Shen, Lehn P. W., Modeling, analysis, and control of a current source inverter-based STATCOM, I����.�������������P ���9�l����y��2002��1:�1�3 pp. 248-253.

[6] D. Krug, S. Bernet, S. Dieckerhoff, Comparison of state-of-the-art voltage source converter topologies for medium voltage applications, P��������������Appl��������l��1, pp. 168�175, Oct. 2003.

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[7] M. Saeedifard, H. Nikkhajoei, Reza Iravani, A Space Vector Modulated STATCOM Based on a Three-Level Neutral Point Clamped Converter,������.������P ���9�l����y���l��22�����2,April 2007, pp. 1029,1039.

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