2012 I EEE 7th I nternational Power Electronics and Motion Control Conference - ECCE Asia June 2-5, 2012, Harbin, China

Control Strategy Study of STAT COM Based on

Cascaded PWM H-bridge Converter With Delta

Configuration

Sixing Du, Jinjun Liu, Jiliang Lin, Yingjie He

School of Electrical Engineering and State Key Lab of Electric Insulation and Power Equipment Xi'an Jiaotong University

Xi'an, China dusixing@163.com

Abstract-this paper describes a transformerless static

synchronous compensator (STATCOM) system based on

cascaded pulse-width-modulation (PWM) H-Bridge converter

with delta configuration. It is intend for dynamically

compensating reactive power and negative-sequence load current,

as well as for improving power quality and reliability of power

distribution system. In this paper, attention is paid to reactive­

power control, negative-sequence current compensation, along

with voltage-balancing control consisting of clustered balancing

control and individual balancing control. Clustered balancing

control that keeps the dc voltage of each cluster equal to the dc

mean value of all the three clusters is achieved by introducing a

zero-sequence current flowing through the loop of the three

delta-connected clusters in three phases. The aim of this control

scheme is to fully extend power-quality- improving capability of

STATCOM system. A 100-V 3-kVA down scaled laboratory

system is designed, constructed and tested, using large-capacity

electrolytic capacitors as dc-voltage sources. Experimental results

obtained from the laboratory system verify the viability of this

cascaded multilevel PWM STATCOM system.

Keywords- Cascade nmlti/evel converter, STATCOM, voltage

balancing control, reactive power, compensating unbalanced load

T. INTRODUCTION

At present, the cascaded H-bridge topology is suitable for high-power STATCOM system, because the single-phase H­bridge modular design brings great convenience to the construction, repairs and maintains. When it is applied to medium-voltage STATCOM, each of the H-bridge converter cells should be equipped with a large-capacity electrolytic capacitor.

To solve the problem of unequal DC voltage across each floating capacitor, power electronics researchers have carried out research works in both staircase modulation and PWM modulation and the resultant papers have been published in literature[ 1 ]-[ 11]. On the condition of compensating reactive power, DC voltage balancing control has been focused in these papers which also present the designing process, detail algorithm and accurate control block. Some of the ideas proposed in the literatures have been applied in medium­voltage cascade STATCOM [1] [2] [6]. Seldom papers in the

This paper and its related research are supported by the National Key Basic Research Development Program of China (973 Program) (No. 2009CB219705).

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literatures, however, has mentioned about the performance of cascade STATCOM when it is required to compensating negative-sequence current produced by seriously unbalanced three-phase load. Literatures [4] [12] have mentioned the idea of introducing zero-sequence current to balance three-phase DC voltages when the negative-sequence current is required to compensated, but the close-loop based algorithm for zero­sequence current control has not been sufficiently discussed. Nothing has been published on a practical algorithm being capable of not only maintaining equal DC capacitor voltage but also making the command reactive power and negative­sequence current accurately followed without any pollution to the power grid.

The aim of this paper is to figure out the influence of DC capacitor voltage coming from the negative-sequence and zero­sequence current flowing in the cascaded H-bridge topology. The analysis is implemented by mathematic method. Then, layered control algorithm consisting of overall control, clustered-balance control and individual-balance control, is proposed in this paper not only for meeting the demand of accurate reactive power control and negative-sequence current control, but also for keeping the voltage of each floating capacitor dynamically equal. Overall control gives out small active current command which is determined by the sum of all the floating capacitor's voltages and used for compensation of switch loss and capacitors equivalent power consumption. Clustered-balance control introduces a zero-sequence current floating through the loop of three phase clusters with delta connection to solve the problem of unequal DC voltages between three phase caused by negative-sequence current and different converter loss. Individual balance control, as the last layer, maintains the equal DC capacitor voltages. The reactive current command and negative-sequence current command are obtained by sampling and calculating load current.

IT. DOWNSCALED EXPERIMENTAL SYSTEM

Fig 1 shows the configuration of a three-phase ST A TCOM rated at 100-Y and 3-kY A, which is based on cascade single­phase H-bridge converter cell. It's scaled down from the medium-voltage high-power STATCOM system to verifY the availability of the medium-voltage STATCOM system, as well

978-1-4577-2088-8/11/$26.00 ©20121EEE

as the capability of the control strategy to compensating the seriously unbalance load while balancing the DC capacitor voltage. Design parameters are summarized in table I for the 100-V3-KVA STATCOM.

L,

O~~ __________ J~ ________ ~ ~ MCl~ MCI

MC2 R MC2

Fig.I. lOO-V 3-kVA downscaled STATCOM

Table I. Circuit parameters in fig I

Rated reactive power 3kVA Nominalline-to-line rms voltage 100V

AC inductor 6mH Starting resistor 51 n

DC capacitor voltage reference SOV DC capacitor capacitance 9600 f.1F

Carrier frequency for PWM 2.5kHz

Fig.2. Fully digital control system for lOO-V 3-kVA STATCOM

The cascade number of N = 2 is assigned to the 100-V 3-kVA STATCOM system because of the restriction of the author's laboratory condition. Therefore, the 100-V 3-KV A STATCOM consists of six converter cells with the same current and voltage rating. As a result, five-level voltage waveform could be produced for cascade ac voltage. This design is reasonable to verifY the capability of the medium-voltage high-power STATCOM system because the control

method has no restriction on the cascade number of the converter cells.

Each converter cell is equipped with an isolating electrolytic capacitor with a capacitance of 9600 JL F. External circuit or DC voltage source are not required to install on the DC side of converter cell. The equal and constant DC voltage is achieved by the control of voltage-balance algorithm. An interface inductor is also installed in each cluster to support the difference between the line-to-line ac grid and five-level PWM voltage from the cluster. It also makes contribution in filtering out switch current ripples caused by fast-speed switching.

The on-off state of each switch device configured in converter cells is determined by the PWM modulation based on the so-called phase-shifted unipolar sinusoidal PWM technique. As a result, an equivalent carrier frequency of 10-kHz is produced. It matches the 10-kHz sample frequency well.

The experimental system adopts a fully digital controller using a fast speed digital signal processor (DSP) and field-programmable gate arrays (FPGA). Most of the calculation is implemented on the floating-support DSP chip and all the PWM signal are generated and sent out by the FPGA chip. The whole control system is shown in fig.2.

m. MATHEMATIC ANALYSIS OF POWER FLOW THROGUGH CASCADED H-BRIDGE TOPOLOGY

The three-phase line-to-line grid voltage is assumed as follows:

Usah = U psah + Unsah = .[iu p sin OJt + .[iun sine OJt + f/Jvn)

U,"bc = U psbc + Um"be = .[iu p sin(OJt - 27r / 3) + .[iun sin(OJt + f/J,,, + 27r / 3)

U'W = U psca + Unsca = .[iu p sine OJt + 27r / 3) + .[iu n sine OJt + f/Jvn - 27r / 3)

(1)

Then, the three-phase currents input the three clusters are given by:

= fil I' sin(rot + (jIil' - 27r /3) + filn sine rot + (jIin + 27r /3) + fil n sin(rot + (jIin)

= fil p sin(rot + (jIip + 27r /3) + fil n sin(OJt + (jIin - 27r /3) + fil u sin(rot + (jIio)

(2)

The power provided by the grid can be calculated from equation (1) and (2):

P sab = U psabicpu + U psabicnll + U psabio +

Unsabicpll + Unsabicnll + Unsabio

Psbc =Upsbcicpv +Upsbcicnv +Upsbcio +

Unsbcicpv + Unsbcicnv + Unsbcio

P sca = U pscaicpw + U pscaicnw + U pscaio +

unscaicpw + unscaicnw + unscaio

(3)

Substituting equations (1) and (2) into equation (3), the following vectors can be obtained:

lu psabicpll j l V pI p cos rpip - V pI p cos(2mt + rpip ) j P pp = U pSbc�epv = V pI p cos rpip = V pI p cos(2mt + rpip : 2n / � )

U psealepw V pI p cos rpip V pI p cos(2mt + rpip 2n / .) ) (4)

lu psabienu j l V pIn cos rpin - V / n cos(2mt + rpin ) j P pn = U pSbc�cnv = V pI n cos( rpin - 2n / 3) = V pI n cos(2mt + rpin)

U pscalenll' V / n cos( rpin + 2n / 3) V pI n cos(2mt + rpin) (5)

[UPsabiO ) [ Vplo COSrpio -Uplocos(2mt+rpio) 1 Ppo = UpSbC�O = UploCOS(rpio:2n/3) =UploCOS(2mt+rpio-2n/3)

Upsca10 Uplocos(rpio 2n/3) Uplocos(2mt+rpio+2n/3)

(7)

[UlISahiel/u l l Vl/il/coS(tp"l/-tpil/)-Vl/il/cos(2aJl+tp"l/+tpil/) • PI/I/= UI/she/elll' = VI/II/COS(tp"l/ = tpil/) = V'/I/COS(2aJl+tp"I/+tpil/-27r/ �)

UI/sea/el/II' V,,! n COS(tp,'n tpin) V nl n cos(2aJl + tp,'n + tpin + 27r I -')

(8)

(9)

Each element of the vectors from (4) to (9) consists a term fluctuating at twice of the line frequency. Those terms just result in the DC voltage fluctuation and have no influence on the mean value of DC capacitors.

Therefore, conclusions can be gotten as follows: the power components of P po and Pno result in the redistribution of

active power between the three clusters while keep the overall power constant. P po and Pno result from the zero-sequence

current which flows through the loop of the three delta­connection clusters and is not injected into grid. When the cascade STATCOM is required to compensate reactive current

and negative-sequence current, the power flow of P pn and

Pnp will not be zero and then the imbalance DC voltage

between the three clusters may happens. Tn order to balance the DC voltages, the zero-sequence current must be introduced. Then the power flows of P po and Pno will cancel the effect of

P pn and Pnp . At last, the imbalance phenomenon could be

cancelled.

As the clustered-balance problem could be solved according to the above analysis, the solution of individual

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imbalance problem relays on the individual analysis. Taking the first converter in U -phase cluster for example, the power

absorbed by this converter is referenced as Piul .AC voltage of

first module is assumed as follow:

N

Uilll = .J2Vililsin(mt+rpilll)+ I.J2Vj sin(jmt+rp) (10)

j�2

Based on equation (2), the current input the converters can be rewritten as:

icu = .J2I p sine mt + rpip) + .J2I n si n( mt + rpin) +

.J2Josin(mt+rpio) (11)

= .J2Iu sin(mt + rpzJ

According to equation (10) and (11), the power Pill I could

be calculated by:

Piul = U iul . icu = V iu lI U

cos(rp iul - rpu )

N+I

+ IVkIucos(kwt+rpk) k=1

(12)

The mean value of Pilll during one line period is given by:

(13)

Equation (13) indicates that individual DC capacitor voltage is determined by the two factors of Villi and rpilll . If the

DC voltage value need to be adjusted, the two factors,

Villi and rpilll , can be trimmed respectively or both.

iell icv iew

IV. CONTROL STRATEGY

io *

U ill Uilll *

Ui1l2 U Indi vidual bala ncing Uivl

• control Uiv2 U lliwl Uiw2

Fig.3. Block diagram of the total control scheme for IOO-V 3-kVA STATCOM.

Fig.3 shows the block diagram of the control algorithm

proposed in this paper. The whole control algorithm is mainly

divided into three parts: decoupled current control based on d - q transformations, command current generating algorithm,

voltage balance control for the six converter cells. The block diagram of decoupled current control is shown in figA and the command current generating algorithm is designed according to instantaneous power theory [13].

Moreover, the voltage balance control ,which will be described in detail in section V, could also be classified into three parts, namely, overall voltage control, clustered balancing control, individual balancing control. This control algorithm is characterized by easy expansion to high cascaded number of STATCOM system.

U Inverse

d-q •

U Transform

-ation • U

Fig.4. Block diagram of decoupled control

V. VOLTAGE-BALANCING CONTROL

Based on the analysis in section III, a layered voltage­balancing control algorithm is described in this paper. It consists of overall voltage control, clustered balancing control and individual voltage control.

A. Overall voltage control

The sum of the three elements in power vector P pp is the

total active power absorbed by all the three clusters of converter cells, which equals to a term of p = usd . idcre/ + usq . iqcre/' Here, idcre/ is the only factor for

overall dc voltage control because of usq = 0 . The control

diagram is shown in figS.

U . d""� �f

_ kvp + kVi / S

udcsum

Fig.5. Block diagram of overall voltage control.

B. Clustered balancing control

Fig 6 shows the diagram of clustered balancing control by introducing a zero-sequence current. The aim of this control is to keep the dc voltage of each cluster equals to the dc mean voltage of the three clusters. The clustered balancing control considers a cluster of cascaded-connection converters as one single-phase H-bridge PWM converter with a dc capacitor of C / n . Here, n is the cascade number of cascaded-

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connection converters in one cluster. Note that a resistance nRc is introduced to represent the converter loss.

Based on the power vector p po' the mean values of power

caused by zero-sequence current can be calculated as:

- I f+1;"" Poca = - Pocad! = U pI 0 cos(lp;o - 2" /3) �ine

(14)

Due to linear correlation of the three equations In (14), solving the first two equations in (14) leads to:

J a cos (jJio = P oab / Up (15)

losin(jJ;o =-(Poab +2Pobc)/Up

Assum ing lo cos (jJio = I'1loab and 10 cos( (jJio + 2Jr /3) = I'1lobc , the command zero-sequence current can be rewritten as:

iore/ = Ji.! a sinew! + lpiO) (16) = Ji. sin(w!)· I'll oab - Ji. COS(WI)· (1'11 oab + 2M abc)

In order to improving the stability, an inner current loop for the clustered balancing control is introduced. The diagram of clustered balancing control is shown in fig.6.

Fig.6 . Clustered balancing control between the three clusters by introducing a

zero-sequence current, where each of the three clusters is considered as a

single-phase H-bridge converters

C. Individual voltage control

Fig.7 shows the block diagram of the individual balancing control. The aim is to keep each dc voltage of the converters in one cluster equals to the dc mean value of the corresponding cluster.

Fig. 7. Individual balancing control between the converters in one cluster, taking U -phase cluster for example.

VI. EXPERIMENT RESULTS

Fig. 8. Experiment waveforms in a transient state from inductive to capacitive

operation at 3kYA with ucul =80Y.

Fig 8 shows the experiment waveforms in a transient state

from inductive to capacitive operation from q * =3kV A to -

3kVA with a sharp change. The U -phase cluster voltage is a

five-level voltage waveforms in both state. Compared with the

grid voltage Usab , the current input the U -phase cluster iCli

leads by 90 degrees in capacitive operation, and the current

iCli in inductive operation is out of phase by 90 degree as

expected.

• .r 1 0.00 v

Fig. 9. Experiment waveforms confirming the effectiveness of the clustered balancing control when the ST A TeOM was operated in capacitive state at 4kYA with capacitor voltage of 80Y. Both of the overall voltage control and the individual balancing control remain active in this experiment

Fig .9 shows the experiment waveforms respectively of the

line-to-neutral grid voltage Usa ' A -phase line current ica and

the dc capacitor voltages, to verify the effectiveness of

clustered balancing control. The clustered-balancing control is

intentionally disabled for 20s, and then, it was enable again.

During the period of experiment, the overall voltage control

and individual balancing control are constantly active. After

the clustered balancing control became disabled, the diverse of

the six capacitor voltages occurred. As soon as the clustered

balancing control recovered, the six dc mean value started to

converge at its average value.

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Te 11

Fig. 10. Experiment waveforms confirming the effectiveness of the individual balancing control when the ST A TeOM was operated in inductive state at

3kYA with capacitor voltage of 80Y. Both of the overall voltage control and the clustered balancing control remain active in this experiment.

The experiment waveforms in fig 10 confirm the

effectiveness of the individual balancing control. As the

individual balancing control is intentionally disabled for 20s,

the overall voltage control and clustered balancing control still

keep active. After the individual balancing control was

enabled again, the capacitor voltage traces merged into one

waveform as shown in fig 10. Th�--------------------t---------------------.

Fig. II. Experiment waveforms when the ST A TeOM is required to compensate balanced three-phase reactive load with capacitor voltage of 80Y. All of the overall voltage control, the clustered balancing control and individual balancing control are active in this experiment

Fig.11 confirms the effectiveness of compensation when the three-phase load is balanced. During the compensating process, the dc mean voltage of capacitors stays balance and the total dc voltages are the same with the reference value.

After compensation, grid side current keeps in phase with grid voltage.

·llI�_...,....._....,...._-===;::;=:=lf=====;::�--, __ .,......_.,

20.0ms .

...... .. - 2tlOm't j

-4.00nW

Fig.12. Experiment waveforms when the ST A TCOM is required to compensate serious unbalance three-phase load with capacitor voltage of 80V. All of the overall voltage control, the clustered balancing control and individual balancing control are active in this experiment

Fig.12 confirms the effectiveness of compensation when the

three-phase load is seriously unbalanced. As is shown in fig 12,

a great difference exists in the three magnitudes of the output

current. Tn order to compensate imbalance load, the

STATCOM injects unbalanced line current to grid while a

zero-order current is produced by the clustered balancing

control to keep the equal of the three cluster voltages. During

the compensating process, the dc mean voltage of capacitors

stays balance and the total dc voltages are the same with the

reference value. After compensation, the three-phase grid

currents with the same magnitude are in phase with the grid

voltages. The power quality is greatly improved with the

350

power factor being unit.

VIT. CONCLUSION

This paper has addressed a transformer less ST A TCOM system based on cascaded H-Bridge with delta configuration. The control scheme proposed in this paper is characterized by the suitable application for compensating serious unbalance load. This control strategy has no limitation on the cascade number of the single-phase H-bridge converters and can also be easily expanded to a higher number of voltage levels. Experimental results obtained from a 100-V 3-kVA laboratory downscaled model have verified the viability of the control scheme.

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