Power Electronics Specialists Conference, 20

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Consequence of Unbalance Supplying Condition on a Distribution Static Compensator

M. Tavakoli Bina University of K. N. Toosi Email: [email protected]

Absfrad-A Static Compensator (STATCOM) is composed of an addc converter connected to a power system through a transformer to regulate voltage or compensate load reactive power. The applied unbalanced voltages from a distribution feeder would affect the behavior of the converter, both the harmonic performance and converter efficiency. Here we present different practical results, taken from an installed i250 kVA STATCOM, showing the quick variations of the capacitor voltage at twice the synchronous frequency. In fact, this is an energy oscillation between the de and ac sides, making waveforms distorted hy introducing low order harmonics to the inverter output voltages and currents. This work, initially, analyzes the unbalance issue, while experimental results demonstrate the validity of the performed analysis. Then, a possible solution is suggested to eliminate the energy oscillation of STATCOM, confirming it hy presenting satisfactory practical resul!~.

I. INTRODUCTION

The use of acldc power converters in ac power systems can be basically considered for a wide range of applications including voltage regulation, active filtering and inactive power compensation. The static compensator (STATCOM) is employed as a parallel device in ac power systems, generating balanced three-phase sinusoidal voltages at fundamental frequency. The amplitude and angle of these voltages should be rapidly controllable. Different voltage-sourced inverters topologies could be implemented using GTOs and IGBTs for high power utility applications. The analysis of STATCOM is presented in [1]-[3].

A. STATCOM Operating Principles

Fig. l(a) shows a three-phase STATCOM, comprising a voltage-sourced inverter connected through an inductance in series with a transformer to a power system. The contactor C I connects the power electronic device to the power system.

The contactor C2 in parallel with a current limiting resistor is used for starting process. During the normal operation of STATCOM both contactors are closed. Now suppose both the ac system voltage v and the converter-composed voltage v' are in phase. When v'

>

^v,STATCOM delivers reactive power to the power system. When v' = v, reactive power is zero. When

v'

<

v, STATCOM absorbs reactive power from the power

system. Thus, by varying v', reactive power can be controlled to emulate a certain application such as voltage regulation.

M. D. Eskandari ACECR Research Center Email: [email protected]

However, for stable operation of STATCOM, the converter output has a small phase difference with the ac system voltage (8). In other words, the converter ac currents contain both reactive and active components. In fact, changing 8 will vary the d c voltage VC. and consequently the converter output v'. In [1]-[3], the explained mode of operation is modeled by transforming the system to a synchronous frame. Then, the resulting state space model is analyzed, showing a stable system with oscillatory dynamic response for STATCOM.

When B is negative, STATCOM works in capacitive mode, and positive B corresponds to inductive mode. A typical steady state operation of STATCOM as a function of 8 is depicted in Fig. I(b).

11. U N B A L A N C E ISSUE

Figure I(a) shows principal circuit of a STATCOM. Each phase of the converter is controlled using a separate PWM scheme. A control signal w?..,(t) (reference) is compared with a repetitive switching frequency triangular waveform (carrier) to generate switching signals for the specified control objec- tives. The frequency of the carrier establishes the switching frequency fa, which its ratio over the reference frequency is fixed. However, the reference has a desired fundamental frequency f l . recognizing that it may contain both positive and negative sequence components along with voltage harmonics.

The device works perfectly as long as the applied voltages are balanced. Nevertheless, unbalance condition on a distribution feeder is unavoidable due to uneven allocation of single- phase loads for the three phases. This would cause consider- able practical issues for the STATCOM [ 5 4 . A reciprocative active power is oscillated between the dc-side and ac-side, causing ripples on the capacitor dc voltage. These oscillations are dominantly at twice the synchronous frequency. Practical results show that the converter output waveforms are also distorted because of the dc voltage oscillation. To analyze a general unbalance case, let the applied voltages v,(t), U b ( t ) ,

v,(t) be given as follows:

U&) =

v,,

cos(wt)

?&(t) =

v h

cos(wt - a b )

& ( t ) =

v,,

cos(wt

+

^a,) ⁽¹⁾

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2004 35th Annual IEEE Power Electronics Specialists Conference Aachen, Germany. 2004

PCC

qr

^"I

1. a

Fig. 1. (a) Single-line diagram of STATCOM; (b) equivalent reactive currenL active current, and capacitor voltage as a function of 8.

Where V,,, V,,, and V,, are the applied voltages amplitudes, and a b . U, are the relative angles of phases b and c with respect to phase a. Ignoring the high frequency ripples, the converter voltages can be derived as:

e.(t) =

+

^cos(wt

⁺

^9,)

eb(t) = COs(wt - a b + e h ) ( 2 ) e.(t) = cos(wt

+

^a,

+

9,)

Where e.(t), eh(t). e J t ) are the converter fundamental voltages (.50/60 Hz), m,, ^mb,m, are three PWM modulation indexes for three phases, O,, Ob. & are the phase shifts between the converter output and the applied voltages, and V,, is the converter dc-side voltage. The STATCOM needs to absorb

~

active power from the power system due to its switching losses as well as unavoidable resistive losses. This instantaneous active power pc(t) can be obtained as:

PC(t) = % ( t ) i C a ( t )

+

ub(t)iCb(t)

+

v c ( t ) i C c ( t ) (3) Where ic,(t), icb(t). ic,(t) are the compensator currents.

These currents are calculated by three KVLs in three input loops on Fig. l(a). By substituting both the supplying unbalanced voltages and the converter fundamental voltages from ( I ) and (2) in (3). the resulting absorbed active power are obtained and simplified as follows:

Where

pc

is the average power, and fizc(t), fi~c(t) introduce oscillating powers. These three components form the instantaneous active power absorbed by STATCOM. The first term,

pc.

is the active power absorbed by the converter to compensate the losses (capacitor voltage drop) and is expressed by:

FC = ,,w[Va,m,sin(9,)

v,, +

V,,mbsin(Ob)

+

V,,m,sin(9,)]

(5) Since

e,,

ob, and 8, are small (typically less than 1.5"),

pc

should be as low as the needed parasitic losses of STATCOM.

The second term, p z c ( t ) , shows the oscillating power at twice the fundamental frequency between the ac power system and the dc-side of the converter. This also is given by:

fizc(t) = &[[v,m, sin(2wt

+

^8,^+a,)+

&mmh sin(2wt

+

^9,^-^{a b )}

+

V,,m, sin(2wt

+

^Sa)]

-&[V,, sin(2wt)

+

V& sin(2wt - ab) +V:, sin(2wt - ac)]

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This oscillating power affects the shape of the dc-side capacitor voltage of converter, forcing it to fluctuate at twice the fundamental frequency. Note that when the power system supplies balanced voltages, then fizc(t) = 0 because V,, = Vmb = V,,, three modulation indexes are the same, and three relative phase differences 9,. 96. and 9, are equal. In other words, fizc(t) is nonzero as long as the supplying condition is unbalanced. The third component, plc(t), introduces fun- damenral frequency oscillating power as follows:

The term Blc(t) also imposes energy exchange at fundamental frequency between the converter and the power system. This

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Fig. 2. Exprimon1 m u l e concerned wiul h e unbalance issue. a) the installed STATCI before application of suggerted canUol mhd. and d) a typical dirt& waveform of b

also changes the capacitor voltage shape. Again, under balanced supply voltages, the resulting fundamental frequency oscillating power is zero Qlc(t) = 0). However, plc(t) is small even under unbalanced supplying condition because the factors sin(0.). sin(&), and sin(&) in (7) are very small.

Thus, the dominant oscillating power would occur at twice the synchronous frequency. As a result of these chnnges on the dc voltage shape, the unbalance supplying condition also affects the converter output voltages and currents. Possible low order harmonic currents are produced by STATCOM as a consequence of available second harmonic on the converter voltage, worsening the harmonic performance.

A. Experimental results

A f250 kVA STATCOM was installed at a 1.6 MVA distribution power system. The device performs two main tasks, voltage regulation and load balancing. Under balanced condition, capacitive and inductive modes of operation are managed by the converter, providing the needed reactive power

to regulate the network voltage. Details of balanced operation of the installed STATCOM were presented in [4].

A power transformer (20 kV/400 V, 1.6 MVA) supplies eight distribution feeders, capable of delivering 5000 A short circuit current. A picture of the installed device is illustrated by Fig. 2(a). A typical light load condition is shown by Fig.

2(b) in which three applied phase voltages on 400 V side are unbalanced. Fig. Z(c) depicts the capacitor voltage, confirming the presence of two harmonic voltages including a dominant 100 Hz ripple along with a negligible 50 Hz ripple on top of the average dc voltage. Furthermore, Fig. 2(c) shows that the STATCOM current (together with the same phase supplying voltage) is distorted, including third harmonic current as an unbalance issue. This was also analytically predicted by (6) and (7) corresponding to fizc and

PE,

respectively.

Moreover, the applied voltages may also contain harmonic voltages. These harmonics would impose more harmonic voltages to the converter, affecting directly the compensator

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2004 35th Annual IEEE Power Electronics Specialistr Conference Aachen, Germany, 2004

current spectral. Hence, the available harmonic voltages should also he prevented from generating oscillating active powers.

Controlling the unbalance issues is addressed by the next section.

111. SOLUTION TO THE PROBLEM

Consider a control strategy is established for STATCOM based on specific aims, leading to a reference current vector to he followed by the converter. At the same time, even for a small degree of power system voltage unbalance, this reference should be used to generate a converter voltage reference vector such that no oscillating power is exchanged under unbalanced condition. To find a solution for the unbalance issue, concentrating on two points is helpful. First, to avoid the 100 Hz ripples, we should reshape the reference voltage of the PWM scheme in a way that the mentioned reference current vector still remains unchanged. Also, the voltage- sourced converter needs to distinguish between balanced and unbalanced modes of operation. This is necessary because the instantaneous active power is constant under balanced supplying condition. In other words, oscillating active power corresponds to unbalanced condition, according to (6) and (7).

extendible to other harmonic frequencies as well.

Second, on the one hand, when the converter voltages are in phase with the applied voltages, no active power i s neither absorbed nor delivered. On the other hand, however, exchang- ing active power needs a small phase difference between the power system and the converter output. Nevertheless, inactive power is generated in both cases, recognizing that this is the main objective of STATCOM.

Considering the above two points, Fig. 3 suggests a general control diagram to remedy the unbalance issue. In brief, the

Fig. 3. The Suggested conuol algorithm to deal wiul &e unbilance iswe

load terminal voltages and currents together with the STAT- COM currents are monitored and digitized by an analogue to digital ( A D ) card. These samples are then used by a digital signal processing (DSP, TMS320VC5416) unit to program the control strategy. A positive sequence detector detects V + as well as

If-

from the supply voltage V. At the same time, the load instantaneous inactive power along with the STATCOM instantaneous active power are calculated as follows [7-81:

These instantaneous powers are then passed through two low-pass filters (LF) to get the averaged quantities of the load inactive power a(t) and the STATCOM power losses

&,.

Hence, two equations can be managed for STATCOM

to produce q ( t ) while absorbing the power losses Additionally, two other equations are provided to neutralize the oscillating powers expressed by (6) and (7). Not that these four equations are stated in terms of converter output positive and negative sequence components (V> and V;). Then, the Newton-Raphson method is used to find the two converter output references.

Simultaneously, a zero voltage detector (ZVD) detects zero- crossing of the supply voltage, and sends a reset signal for an electronic board responsible for generating three reference waveforms for three phases. The ZVD output is also fed to a phase locked loop (PLL). Thus, the mains supply frequency is multiplied by N, and is used as a clock for the reference generator. This clock is also employed for creating the carrier waveform. These are all arranged with a separate electronic card out of the DSP, providing carrier and reference waveforms

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(b)

Fig. 4. Rdctical remlts under lhe controlled conditions. a) Lhe & vollagc afier applying

me suggested contml m e l d . b) a typical irnpmved STATCOM c m n l .

for the PWM scheme.

Meanwhile, it should be noted that the power losses ob-

A. Practical results

The above control strategy was applied to the described f 2 5 0 kVA STATCOM. Fig. 4(a) shows the resulting capacitor voltage for a transient condition in which the device is transited from an inductive to a capacitive mode. Comparing this figure with that of uncontrolled case in Fig. 2(c), it can be seen the effectiveness of the control algorithm to tackle the unbalance supplying condition. Moreover, Fig. 4(b) illustrates the STATCOM current along with its corresponding supplying voltage. This waveform in comparison with that of Fig. 2(c) introduces less third harmonic component, showing that the harmonic performance is improved under the employed control strategy. Note that second harmonic component on converter output imposes third harmonic component on the STATCOM current.

IV. CONCLUSION

Unbalance condition of the power supply affects the converter performance of STATCOM, causing additional distor- tion of waveforms. The presence of dominant oscillations at twice the synchronous frequency is analytically shown for a PWM-controlled STATCOM. Furthermore, insignificant synchronous frequency oscillations can also be observed.

Experimental results taken from an installed f250 kVA STAT- COM illustrate these issues. A control method is suggested to remedy the problem, which decomposes the applied voltages into their positive and all other remaining components. Then, corresponding reference voltages are established for’the converter to implement. The control strategy is effective as it is shown by practical work.

REFERENCES

[ I ] P, Ran. M. L. Crow. and 2. Yang, “STATCOM Control for Power System Voltage Control Application”. Applied Power Electronics Con& vol. 15, No. 4, pp. 131 1-1317. Oclober 2000

[21 L. Gyugy, “Dynamic Compensation of AC Transmission Lines by Solid- State Synchronous Voltage SourceT’, IEEE Transarriom on Power De- livery, vol. 9. No. 2. pp. 904-911, June 1994

[31 L. Gyugy, N. G . Hingorani, and P. R. Nannery, “Advanced Static VAr Compensator using gate turn-off thyristors for Utility Application”, CIGRE, 1990 Session, PP. 23-27, 1990

141 C. Schauder and H. Mehta. “Vector analysis and control of advanced static var compensators”. IEE PmrwdingrC. vol. 14. No. 4, pp. 266272.

b i n d by (8) does not necessarily show the exact losses of STATCOM. In other words, the capacitor dc voltage may drop Or increase to the needed active power Of

STATCOM. To balance the STATCOM exact losses (including

active power

Ross,

the dc voltage V d , is controlled. Here the switching, snukrs, dc and ac side losses) with the absorbed

Julv 1w3,

. .

by a gain K~~ (depending on the modulation index) to get a Unbalanced Voltages”, IEEE Transartions on Power Delivery, vol. 13.

No. 2, pp. 266-212. April 1998.

[6] P. Pillary and M. Manyage. “Definitions of voltage unbalance”. IEEE

reference dc voltage Vderef. This reference is then compared

with the actual dc voltage, and using a PI controller the power ~ ~~ ~“01. ~ 5, pp. i 50.51. M ~ Y i~ ~2001. ~ . ~ ~ ~ i ~ ~

resultant error will provide the required Wwer loss A-Pi,,, ~~~ ^[7]^F.^Z.Peng and J. S . hi. “Generalized Instantaneous Reactive Power

of STATCOM, ~h~ average power

pi,,,

along with this ^Theory^forThree-phase Power Systems”, IEEE Tramsortions m t I n . r t r - nrenration and Meorurentenl, vol. 45, No. I , pp. 293-297. Februaly 1996.

power A-pkvs be the total corrected power losses Of 181 C. A. Quinn, N. Mahan. and H. MehIa, “A four-wire current-controlled STATCOM. The Newton RaDhson method can now work ^~~ ^~~ converter movides Harmonic Neutralization in three-ohase. four wire Out new references which improve the power balance of the ^SYStem”.IEEE Applied Power EIectmni~.s Confere,rce (APEC.93). pp.

841-M. 1993 device.