Feeder 1 2

sv

sitv

lifi

IdealCompensator

Fig. 1. The distribution system with the installed D-STATCOM.

Steady-State Performance of D-STATCOM for Load Voltage Regulation

Kittaya Somsai and Thanatchai Kulworawanichpong* School of Electrical Engineering

Suranaree University of Technology Nakhon Ratchasima, Thailand

Somsai_kittaya@yahoo.com, thanatchai@gmail.com * Corresponding author

Nitus Voraphonpiput Department of Power System Planning

Electric Generating Authority of Thailand Bangkok, Thailand nitus.v@egat.co.th

Abstract— This paper presents the steady state performance of a D-STATCOM applied for load voltage regulation by injecting only reactive power into the system. This study begins with determining dynamic equations of the distribution system with the installed D-STATCOM. The dynamic equations are determined with reference to the synchronous rotating dq reference frame transformation theory. Then, the steady state equations are derived from the dynamic equations. The amount of apparent power of D-STATCOM for load voltage regulation in case of increased load power is considered. Additionally, the maximum load power that can regulate the load voltage magnitude without injecting any active power into the system is also determined.

Keywords; D-STATCOM, load voltage regulation, voltage sag

I. INTRODUCTION In a power distribution system, voltage sag is the most

importance power quality problems faced by many industries and utilities. It contributes more than 80% of power quality (PQ) problems that exist in power systems [1]. By definition, the voltage sag is a short time (10 ms to 1 minute) event during which a reduction in r.m.s voltage magnitude occurs. The voltage sag magnitude is ranged from 10% to 90% of nominal voltage and with duration from half a cycle to 1 min [2]. The voltage sag is caused by a fault in the utility system, a fault within the customer’s facility or a large increase of the load current, like starting a motor or transformer energizing. The voltage sag is not tolerated by sensitive equipment used in modern industrial plants such as process controllers; programmable logic controllers (PLC), adjustable speed drive (ASD) and robotics [1].

D-STATCOM is a shunt device that generates an ac voltage at fundamental frequency, which in turn causes a current injection into the system through a shunt transformer [2]. This ac voltage output controllability of D-STATCOM can control the injection of the current. The voltage at a point of a common coupling and an injected current determines the power injection of the D-STATCOM. Therefore, the D-STATCOM has been proposed for load voltage regulation [3, 5 – 7]. For lower voltage sags, the load voltage magnitude can be regulated by injecting only reactive power into the system [8]. Meanwhile, for higher voltage sags, injection of active power, in addition to reactive power, is essential to regulate the load voltage magnitude [9]. However, D-STATCOM being able to inject

the active power must install energy storage system (ESS) [10] which can cause a higher cost.

This paper investigates the steady state performance of a D-STATCOM applied for load voltage regulation by injecting only reactive power into the system. This study begins with determining dynamic equations of the distribution system with the installed D-STATCOM. The dynamic equations are determined with reference to the synchronous rotating dq reference frame transformation theory. Then, the steady state equations are derived from the dynamic equations. The amount of apparent power of D-STATCOM ( ) for load voltage regulation in case of increased load power is considered. Additionally, the maximum load power that can regulate the load voltage magnitude without injecting any active power into the system is also determined.

II. DISTRIBUTION SYSTEM MODELING The system considered here is a simplified model of a load

supplied on a distribution system. A D-STATCOM is connected in parallel with the load. The distribution system with the installed D-STATCOM and single phase equivalent circuit are shown in Fig.1 and Fig.2, respectively. The system consists of: the source modeled as an infinite bus with inductive source impedance, the load modeled by a resistance and inductance that are connected in series, the D-STATCOM modeled as a controllable current source, and coupling capacitor. The coupling capacitor is used as a harmonics filter or the fixed compensation capacitors connected in parallel load.

978-1-4577-0547-2/12/$31.00 ©2012 IEEE

It is assumed that the source, load and D-STATCOM are

balanced three phase systems. The system dynamic are described by , , , , (1) , , , , (2) , , , (3)

Here, , , , , and , are vectors consisting of the individual phase quantities denoted in Fig. 2, is the load inductance, is the load resistance, is the source inductance, is the source resistance, and is the coupling capacitor. Under the assumption that zero sequence components are not present, (1) – (3) can be transformed to an equivalent two phase x-y system by applying the following three to two phase transformation:

, ⁄ ⁄ (4)

where the complex number , . This is followed by a rotational transformation:

, , (5)

Applying the transformations, (1) - (3) can be written as (6) (7) (8) (9) (10) (11)

where is yet to be designed and may be a function of time.

III. CHOICE OF REFERENCE FRAME We choose the dq reference frame similar to that used for

field-oriented control of three phase ac machines. Thus, the angle used in (5) is tan ⁄ implying 0 0 . (12)

Defining , where is the frequency of the infinite bus phase voltages, we get , . , where is the constant magnitude of the infinite bus voltage. The relative orientation of the vectors , , , and the reference frame are shown in Fig. 3. The system equations can now be rewritten as cos (13) sin (14) (15) (16) (17) (18) (19)

where (19) is derived using (12). It should be noted that varies with time and is different from . Since 0, represents the instantaneous magnitude of the phase voltages , , while denotes the instantaneous reactive current supplied by the D-STATCOM. In addition, in the absence of negative sequence components, all the state variables in (13) – (18) are constants in steady state [11].

IV. STEADY STATE ANALYSIS The equations in the previous section are dynamic

equations. However, these equations can be transformed to the steady state equations by giving the left values of (13) – (18) as zero. The steady state equations can now be as follows: 0 cos (20) 0 sin (21) 0 (22) 0 (23) 0 (24) 0 (25)

(26)

The load voltage regulation with D-STATCOM can be done by either injecting only reactive power or injecting both active and reactive power into the system. However, the injecting only reactive power is the focal point in this paper. In this section, the for load voltage regulation by injecting only reactive power is investigated. Fig. 2 shows the

sv

αtv

θstω

Fig. 3. Orientation of reference frames.

sv fi

tV

si li

lR

sRsL

Cfi

fCtvlL

Fig. 2. Single phase equivalent circuit.

load voltage regulation with injecting only the reactive power into the system. Thus, the entire load active power ( ) must be provided by the source. The can be written as:

(27)

Since the D-STATCOM injects only the reactive power into the system, a load active current and a source active current are equal ( ). The source active current shown in (28) can be obtained by solving (20) – (21).

(28)

Substituting (27) with (28), the can be written as:

. .

(29)

If and where is an angle

of source impedance,

(30)

From (30), is an angle of the source voltage and can be expressed as:

(31)

For a feasible value of , the condition (32) must be satisfied.

1 (32)

In (32), if the load voltage magnitude is regulated at a desired value ( , .) with D-STATCOM, the load active power at the desired load voltage magnitude ( , .) and the source voltage can be rewritten as (33) and (34), respectively.

, . , . , . (33)

, . , . , . (34)

Thus, when the , . satisfies (33), the D-STATCOM can regulate the load voltage without injecting any active power into the system. Similarly, when the source voltage satisfies (34), the D-STATCOM can regulate the load voltage without injecting any active power into the system as well.

Regarding the for the load voltage regulation, the increased of , . is considered. Since losses in the D-STATCOM are ignored, the D-STATCOM active current ( ) is zero. Subsequently, the D-STATCOM reactive current ( ) can be obtained by solving (20) – (26) when the given is , .. Thus, the is as the reactive power of D-STATCOM as follows:

(35)

when , .. V. THE RESULT

Single phase equivalent circuit of Fig. 2 is used to demonstrate the steady state performance of D-STATCOM when applied to regulate load voltage with injecting only the reactive power into the system. It is considered that normal source voltage operation is 12.11kV with 10 , 1 Ω and 50 . The desired load voltage magnitude, , ., is 11kV.

From (33), the maximum load active power at the desired load voltage magnitude, , . , is calculated when 12.11 and , . 11 . Since the load active and reactive power at the desired load voltage magnitude, , . and , ., has been changed. Subsequently, the load voltage without the D-STATCOM ( and are zero), , can be obtained by solving (20) – (26) when the and are obtained by solving (36) – (37).

, . , . 0 (36)

, . , . 0 (37)

The relationship between , . and is demonstrated in Fig. 4. The solid line represents the relationship between , . and when the load reactive power at the desired load voltage magnitude ( , .) is 0 . The normal operation point is at , . 12.10 that corresponds 11.00 . As, in this point, the load voltage is as the desired load voltage magnitude, the D-STATCOM does not inject any power into the system to regulate load voltage. Form the normal operation point to , . , , . increases from 12.10 to 29.28 , this results in the decrease of the from 11.00 to 8.51 . However, the load voltage can be regulated by injecting only reactive power of the D-STATCOM until the , . is more than 29.28 .

Similarly, the dash line represents the relationship between

, . and when the load reactive power at the desired load voltage magnitude ( , .) is 3 . The normal operation point is at , . 7.10 that corresponds 11.00 . As, in this point, the load voltage is as the desired load voltage magnitude, the D-STATCOM does not inject any power into the system to regulate load voltage. Form the normal operation point to , . , , . increases from 7.10 to 29.28 , this results in the decrease of the from 11.00 to 8.21 . However, the load voltage can be regulated by injecting only reactive power of the D-STATCOM until the , . is more than 29.28 .

The for the load voltage regulation in case of the increased load power is shown in Fig. 5. Fig. 5 indicates that, for the increased load power, the increases. Although, the increase of , . does not affect , . , the increase of , . dose affect the increase of . Moreover, at the , . under the normal operation point, the is above the desired load voltage magnitude point. Therefore, the D-STATCOM regulates the load voltage by absorbing the reactive power resulting in being the negative of D-STATCOM reactive power as shown in Fig. 5.

VI. CONCLUSION This paper investigates the steady state performance of a

D-STATCOM applied for load voltage regulation by injecting only reactive power into the system in case of increased load power. For increased load power, during the , . increasing from the normal operation point to , . , the load voltage can be regulated by injecting only reactive power of the D-STATCOM until the , . is more than , . . In addition, the increase of , . does not affect , . , but it does affect the increase of

for load voltage regulation.

REFERENCES [1] R. C. Dugan, M. F. McGranaghan, and H. Wayne Beaty, Electrical

Power System Quality. NA: McGraw Hill, 1996. [2] A. Ghosh, and G. Ledwich, Power quality enhancement using custom

power devices. Massachusetts: Kluwer Academic, 2002. [3] P. S. Sensarma, K. R. Padiya, and V. Ramanarayanan, “Analysis and

Performance Evaluation of a Distribution STATCOM for Compensating Voltage Fluctuations,” IEEE Trans. Power Del., vol. 16, no. 2, pp. 259 – 264, 2001.

[4] P. Rao, M. L. Crow, and Z. Yang, “STATCOM control for power system voltage control applications,” IEEE Trans. Power Del., vol. 15, no. 4, pp. 1311 – 1317, 2000.

[5] K. R. Padiyar, and A. M. Kulkarni, “Design of reactive current and voltage controller of static condenser,” Elect. Power Energy Syst., vol. 19, no. 6, pp. 397 – 410, 1997.

[6] C. Hochgraf, and R. H. Lasseter, “Statcom controls for operation with unbalanced voltages,” IEEE Trans. Power Del., vol. 13, no. 2, pp. 538 – 544, 1998.

[7] C. Chen, and G. Joos, “Series and shunt active power conditioners for compensating distribution system faults,” Proc. Canadian Conf. Electrical Computer Engineering, 07 – 10 Mar 2000, pp. 1182 – 1186

[8] S. S. Choi, B. H. Li, and D.M. Vilathgamuwa, “Dynamic voltage restoration with minimum energy injection,” IEEE Trans. On Power Syst., vol. 15, no. 1, pp. 51 – 57, 2000.

[9] M. H. Haque, “Compensation of distribution system voltage sag by DVR and D-STATCOM,” Proc. IEEE Power Tech Conf., 10 – 13 September 2001, pp. 1 – 5.

[10] M. G. Molina, and P. E. Mercado, “Control design and simulation of DSTATCOM with energy storage for power quality improvements,” IEEE/PES Transmission & Distribution Conf. Exposition, Latin America, TDC '06, 15-18 August 2006, pp. 1 – 7.

[11] A. Jain, K. Joshi, A. Behal, and N. Mohan, “Voltage regulation with STATCOMs: modeling, control and results,” IEEE Trans. Power Deliv., vol. 21, no. 2, pp. 726 – 735, 2006. 36D STATCOMQ MVar− =

33D STATCOMQ MVar− =

, . (max) 29.28l compP MW=, . 12.10l compP MW=, . 7.10l compP MW=

, . 0l compQ MVar=

, . 3l compQ MVar=

, . ( )l compP MW Fig. 5 the for the load voltage regulation in case of the increased load power

, .(max) 29.28l compP MW=

8.5139tdV kV=

8.2069tdV kV=

11.00tdV kV= , . 0l compQ MVar=

, . 3l compQ MVar=

, . 12.10l compP MW=, . 7.10l compP MW=

, .( )l compP MW Fig. 4 The relationship between , . and