Improvement of Transient Stability Margin

13th International conference on Sciences and Techniques of Automatic control & computer engineering December 17-19, 2012, Monastir, Tunisia

Improvement of Transient Stability Margin in Power Systems with Integrated Wind Generation Using the SVC M. Amroune1, A. Bourzami1, and T. Bouktir 1 1

Department of Electrical Engineering, University of Setif 1, Algeria

[email protected],[email protected],[email protected]

Abstract. Wind energy, is one of the most prominent renewable energy sources, is gaining increasing significance throughout the world. Wind turbines used with fixed speed induction generators provide a cost effective solution for wind power generation and are still the most commonly used type of wind turbine. However, this type of generator always consumes reactive power. While shunt capacitors are typically used to fully compensate for this reactive power consumption but these devices exhibit rather poor performance during transient events. Therefore, controllable reactive power supporters, such as Flexible Alternating Current Transmission Systems (FACTS) are necessary in these cases. In the present paper the improvement of transient stability margin in power systems with integrated wind generation using the Static Var Compensator (SVC) is investigated. The wind generators considered are the squirrel cage induction generators (SCIG), which is a fixed speed. Case studies are carried out on the IEEE-30 bus test system. Simulation results show that the SCIG with SVC devices significantly improve the performance of the power network during transient disturbances.

Keywords. Transient stability; Critical Clearing Time; Static Var Compensator; squirrel cage induction generator.

1. Introduction There has been a growing interest in distributed generation by renewable green energy resources. Wind energy, as one of the most prominent renewable energy sources, is gaining increasing significance throughout the world. Worldwide there are now many thousands of wind turbines operating. In the year 2011, the worldwide wind capacity reached 237 016 Megawatt, after 196 630 Megawatt in 2010 and 159 050 MW in 2009. So far it is the most developed technology among various renewable energy STA'2012-5(&-, pages - Academic Publication Center of Tunis, Tunisia

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STA′2012 – Topics …, pages 1 to X

technologies. Between 2005 and 2011 the average annual growth in new installations was 27.6 percent [1]. Wind turbines used with fixed speed induction generators provide a cost effective solution for wind power generation and are still the most commonly used type of wind turbine. However, a notable characteristic of the fixed speed induction generators is that this type of generator always consumes reactive power. While shunt capacitors are typically used to fully compensate for this reactive power consumption during steady state operation, these devices exhibit rather poor performance during transient events [2]. Therefore, controllable reactive power (VAR) supporters, such as Flexible Alternating Current Transmission Systems (FACTS) are in some cases necessary to provide dynamic voltage support with their actively controllable VAR injection, especially under voltage depression. With FACTS, a number of valuable benefits can be attained in power systems [3]: • Dynamic voltage control, to enable limiting of over-voltages over long, lightly loaded lines and cable systems, as well as prevent voltage depressions or even collapses in heavily loaded or faulty systems. • Increased power transmission capability and stability, without any need to build new lines. This is a highly attractive option, costing less than new lines, with less time expenditure or environmental impact. • Facilitating integration of renewable power by maintaining grid stability and fulfilling grid codes, as well as making room for this additional power in existing grids. The Static Var Compensator (SVC) is a shunt device of the Flexible AC Transmission Systems (FACTS) family using power electronics to control power flow and improve transient stability on power grids. The SVC regulates voltage at its terminals by controlling the amount of reactive power injected into or absorbed from the power system. When system voltage is low, the SVC generates reactive power (SVC capacitive). When system voltage is high, it absorbs reactive power (SVC inductive). In a wind power application, the SVC has up to several of the following tasks to fulfill at the PCC [3]: • Steady-state and dynamic voltage stabilization • Continuous power factor control • Aiding fault ride-through of the wind farm • Power quality control by mitigation of flicker (caused by tower shadow effect, fluctuating wind, and/or starts and stops of WTGs); also harmonic reduction and reduction of phase imbalance. This paper presents results from the investigation into the impact in power system transient stability of installing a Stic Var Compensator at an existing wind farm.

2.

Power System Model

The power system model consists of synchronous generator, transmission network and static load models, which are presented below. The machine classical electromechanical model is represented by the following differential equations [4]:

Paper title 3

d δi = ωi − ωs dt d 2δ i π f = ( Pmi − Pei − PDi ) Hi dt 2

(1)

dδ dt D is the generator damping coefficient; H is the inertia constant of machine expected on the common MVA base; Pm is the mechanical input power and Pe is the electrical output. The transmission network model is described by the steady-state matrix equation: (2) I bus = YbusVbus Where: PD = D

Where Ibus is the injections current vector to the network, Vbus is the nodal voltages vector and Ybus is the nodal matrix admittance. The electrical power of the ith generator is given by [5]: ng

Pei = Ei2 Gii + ∑ Cij cos θ ij − δ i + δ j 

(3)

j =1

Where i = 1, 2, 3…ng is the number of generators. Cij = |Ei||Ej||Yij| is the power transferred at bus ij; E is the magnitude of the internal voltage; Yij are the internal elements of matrix Ybus; Gii are the real values of the diagonal elements of Ybus. The static model of load is represented by load admittance YL defined by [5]:  P - jQ  YLi =  i 2 i   Vi 

(4)

3. Wind Generator Model The fixed-speed, squirrel cage induction generator (SCIG) is connected directly to the distribution grid through a transformer. There is a gear box which maces the generator’s speed to the frequency of the grid. During high wind speeds, the power extracted from the wind is limited by the stall effect of the generator. This prevents the mechanical power extracted from the wind from becoming too large. In most cases, a capacitor bank is connected to the fixed speed wind generator for reactive power compensation purposes. The capacitor bank minimizes the amount of reactive power that the generator draws from the grid [6] (see f gure 1).

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Fig. 1. Representation of the fixed speed induction generator The model for the fixed speed synchronous generator is shown in Fig.2. Where Rs represents the stator resistance, Xs represents the stator reactance; Xm is the magnetizing reactance, while Rr and Xr represent the rotor resistance and reactance, respectively.

Fig. 2. Asynchronous machine equivalent circuit model

A standard detailed two-axis induction machine model is used to represent the induction generator. The relationship between the stator voltage, rotor voltage, the currents and the fluxes are given by the following equations [7]:

d  vds = -Rs × ids - ωs × λqs + dt λds  v = -R × i + ω × λ + d λ s qs s ds qs  qs dt d  vdr = 0 = Rr × idr - g × ωs × λqr + dt λdr  v = 0 = R × i + g× ω × λ + d λ r qr s dr qr  qr dt

(5)

(6)

Where Vs is the stator voltage while Vr represents the rotor voltage, λs and λr are the stator and rotor flux respectively, while ωs is the synchronous speed. The rotor voltage is zero because the rotor has been short-circuited in the single cage induction generator. The model is completed by the mechanical equation as given below: dωr 1 = ×(Tm - Te ) dt 2H

(7)

H is the inertia constant; Tm is the mechanical torque; Te is the electrical torque and ωr is the generator speed.

Paper title 5

4. SVC Model Static VAR Compensator (SVC) is a shunt connected FACTS controller whose main functionality is to regulate the voltage at a given bus by controlling its equivalent reactance. Basically it consists of a fixed capacitor (FC) and a thyristor controlled reactor (TCR). A TCR consists of a fixed shunt reactor in series with a bi-directional thyristor valve (see Fig. 3). Generally they are two configurations of the SVC: •

SVC total susceptance model. A changing susceptance BSVC represents the fundamental frequency equivalent susceptance of all shunt modules making up the SVC as shown in Fig. 3 (a). • SVC firing angle model. The equivalent reactance XSVC, which is function of a changing firing angle α, is made up of the parallel combination of a thyristor controlled reactor (TCR) equivalent admittance and a fixed capacitive reactance as shown in Fig. 3 (b). SVC total susceptance model is implemented in this paper. The primary objective of the control system is to determine the SVC susceptance needed in the point of connection to the power system, in order to keep the system voltage close to the desired value. VK

VK α

α

Xc c

bSVC XL

(a)

(b)

Fig. 3. SVC schemes: (a) f ring angle model and (b) equivalent susceptance model

The simplif ed control scheme is depicted in Fig. 4 and undergoes the following differential equation [8]: •

bSVC = (K R (ωref - ωi ) - bSVC ) / Tr

(8)

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STA′2012 – Topics …, pages 1 to X bSVC max

ωi

Kr 1 + Trs

ωréf

bSVC

bSVC min

Fig. 4. SVC control diagram

Where: bSVCmax: Maximum Susceptance; bSVCmin: Minimum Susceptance; Kr: Regulator gain; Tr: Regulator time constant; ωréf : Reference generator speed. The regulator has an anti-windup limiter, i.e., the reactance bSVC is locked if one of its limits is reached. Table 1 reports data and control parameters for the SVC. Table 1. Data and control parameters for the SVC Kr

200

Tr [s]

0.05

bSVCmin

bSVCmin

[MVAr]

[MVAr]

-200

200

5. Simulation Results Simulation studies are carried out in this section to demonstrate the transient performance of the power system with wind power generation using the Stati Var Compensator. The Critical Clearing Time (CCT) is used as indices to evaluated transient stability and the IEEE 30-bus test system shown in Fig. 5 is employed to conduct the transient stability simulation. Detailed parameters of this system can be found in [9]. A wind farm based on Fixed Speed Induction Generator (FSIG) is used and the FSIG parameters are outlined in the Appendix. A SVC is to be installed at the Point of Common Coupling (PCC), where the wind farm is integrated with the utility system.

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Fig. 5. Single line diagram of the IEEE 30-bus system

The test system is analyzed using optimal power flow (OPF). A standard OPF problem can be formulated as follows [10, 11]: ng

F ( x ) = ∑ (ai + bi Pgi − c i Pgi2 )

(9)

Pi (V , θ ) + Pdi − Pgi = 0

(10)

Q i (V , θ ) + Q di − Q gi = 0

(11)

Pgimin ≤ Pgi ≤ Pgimax ;i=1,...ng

(12)

Q gimin ≤ Q gi ≤ Q gimax ;i=1,...ng

(13)

i =1

Where F(x) is a cost function; ai, bi, ci are cost coefficients shown in the Appendix; Pgi and Qgi are the active and reactive power generations at ith bus; Pdi and Qdi are the active and reactive power demands at ith bus; Pi and Qi are the active and reactive power injections at ith bus.

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4.1. Case 1: Single FSIG wind farm In this case the FSIG wind farm of 20 MW has been connected to bus 10. The Optimal Power Flow results obtained with used of the Differential Evolution Algorithm (DEA) [12, 13] with and without of wind farm is listed in Table 2. According to this table integration the wind farm in the system will be a better option in terms reduction in the total costs and power losses. Table 2. OPF Results with DEA

BUS №

PG (MW) Without Wind Farm

1 2 5 8 11 13

PG (MW) With Wind Farm at bus 10

176.8141 48.8318 21.4853 21.6837 12.1033 12.0000 9.51813 802.333

Ploss Total cost ($/h)

167.0748 46.4729 20.7535 15.9062 10.0000 12.0000 8.80743 741.518

A disturbance in the form of a three phase to ground fault is occurs at t = 1 second at bus 1, cleared by opening the line connecting the nodes 1–2. The Figures 6 and 7 show the dynamic responses of all machines for Fault Clearing Time (FCT) equal to 220 ms. 250

δ1-δ2 δ1-δ3 δ1-δ4 δ1-δ5 δ1-δ6

Angle rotorique relatif, degree

200

150

100

50

0

0

1

2

3

4 t, sec

5

6

7

Fig. 6. Rotor angle differences without of SVC (FCT = 220 ms)

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Paper title 9 250

δ1-δ2 δ1-δ3 δ1-δ4 δ1-δ5 δ1-δ6

Angle rotorique relatif, degree

200

150

100

50

0

0

1

2

3

4 t, sec

5

6

7

8

Fig. 7. Rotor angle differences with SVC (FCT = 220 ms)

These Figures show that the Critical Clearing Time (CCT) increased after the introduction of the Static Var Compensator. For FCT = 220 ms, the system with SVC at bus 10 (Point of Common Coupling: PCC) remains stable and can return to steady state finally. However, the system without SVC is unstable. Another’s simulations have been performed for different fault locations in IEEE-30 bus system, in order to know the effect of wind farm with SVC on transient stability. The results from the cases study are presented in Table 3 and Figure 8. The comparative results have shown that the insertion of an SVC with wind farm increases the transient stability and the location of wind farms has an effect in power system transient stability.

Table 3. CCT with and without of SVC

Faulted bus 1 1 2 2 2 2 4 4 6 6

Open line 1-2 1-3 1-2 2-4 2-5 2-6 2-4 4-6 2-6 4-6

CCT without of SVC (ms) 216 261 296 357 370 357 624 637 834 854

CCT with SVC (ms) 220 267 300 363 377 364 635 647 866 885

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Fig. 8. CCT with and without of SVC

To know the impact of SVC with wind penetration level on the power system Critical Clearing Time, the analysis has been carried out on 10%, 20%, 30% and 35% wind penetration levels based on the total power required (283.4 MW). The optimal active powers generated by all generators when FSIG wind farm is connected to bus 10 are shown in Fig. 9. The variation of CCT for the fault at bus 1 with opening the line 1–2 is shown in Fig. 10. From these Figure, it can be seen that the power system transient stability can be improved by the Static Var Compensator with improving penetration level of FSIG wind turbines.

Fig. 9. Power generation with FSIG wind farm at bus 10

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Fig. 10. CCT variation with and without SVC for a fault at bus 1

4.2. Case 2: Two FSIG wind farms In this case the two FSIG wind farms have been connected to bus 10 and bus 24 simultaneously, both farms generate 30 MW. Table 4 shown the total cost obtained with three penetration level scenarios. According to this table the total cost is low when the penetration level of wind farm is high at bus 10 and low at bus 24 (scenario 3). This scenario is considered, for this scenario two Static Var Compensators are connected to Point of Common Coupling. The Table 5 shows the CCT with and without of SVCs when a three-phase short circuit is acquired at bus 1 and 2 respectively. The CCT is more improved when the SVCs are connected with wind farms. Table 4. OPF Results with DEA

G10

G24

Total cost ($/h)

Scenario 1

15%

15%

562.244

Scenario 2

10%

20%

664.419

Scenario 3

20%

10%

561.28

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Fig. 11. Power generation for deferent scenarios Table 5. CCT With and Without of SVC for Scenario 3

Faulted

CCT Without of

CCT With

bus

SVCs

SVCs

1

445

454

2

586

597

6. Conclusion Increasing usage of wind power worldwide requires a new insight into stability issues of power system. Herein, the transient stability improvement of an existing wind farm through the addition of a Static Var Compensator have been illustrated and discussed. The wind generators considered are the squirrel cage induction generators (SCIG), which is a fixed speed. A Static Var Compensator is placed at Point of Common Coupling (PCC) in a 30-bus multi-machine power system with a large wind farm. From the obtained results using the SVC not only improves load-ability parameter and voltage profile of power system but also helps the improving transient stability by improving critical clearing time.

References 1. World Wind Energy Association (WWEA 2011), 10th World Wind Energy Conference & Renewable Energy Exhibition, April 2011.

Paper title 13 2. L. Qi, J. Langston, M. Steurer, " Applying a STATCOM for Stability Improvement to an Existing Wind Farm with Fixed-Speed Induction Generators," in Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 2008 IEEE. Center for Adv. Power Syst., Florida State Univ, 2024 July 2008, pp. 1-6. 3. Rolf Grünbaum, "FACTS for Grid Integration of Wind Power," Innovative Smart Grid Technologies Conference Europe (ISGT Europe), 2010 IEEE PES.11-13 Oct. 2010, pp. 1-8 4. Reza Ebrahimpour, Easa Kazemi Abharian, Ali Akbar Motie Birjandi and Seyed Zeinolabedin Moussavi, "Transient Stability Assessment of a Power System with a UPFC by Mixture of Experts," International Journal of Computer and Electrical Engineering, Vol. 2, No. 4, August, 2010, pp. 643-648 5. P. Kundur, Power System Stability and Control 1994 . New York: Mc Graw-Hill, 1994. 6. K. Folly, "Impact of Fixed and Variable Speed Wind Generators on the Transient Stability of a Power System Network," in IEEE/PES Power Systems Conference and Exposition, 2009. PSCE '09. , Univ. of Cape Town, Cape Town , 15-18 March 2009, pp. 1-7. 7. L. Holdsworth, "Comparison of fixed speed and doubly-fed induction wind turbines during power system disturbances ," IEE Proceedings-Generation, Transmission and Distribution, vol. 150, no. 3, pp. 343-352, 2003. 8. F. Milano, Power System Modelling and Scripting. London: Springer, 2010. 9. M. Iannone and F. Torelli, "Acoherency-basedmethod to increase dynamic security in power systems," Electric Power Systems Research, vol. 78, no. 8, p. 1425–1436, Aug. 2008. 10. T. Bouktir, L. Slimani, and M. Belkacemi, "A Genetic Algorithm for Solving the Optimal Power Flow Problem ," Leonardo Journal of Sciences, no. 4, pp. 44-58, Jan. 2004. 11. P. Somasundaram and N. Muthuselvan, "a modified particle swarm optimization technique for solving transient stability constrained optimal power flow," Journal of Theoretical and Applied Information Technology, pp. 154-164, 2010. 12. R. Storn, "Differential Evolution – A Simple and Eff cient Heuristic for Global Optimization over Continuous Spaces," Journal of Global Optimization, p. 341– 359, 1997. 13. T. Bouktir and L. Slimani, "Optimal Power Flow Solution of the Algerian Electrical Network using Differential Evolution Algorithml," TELKOMNIKA, vol. 9, no. 1, pp. 1-8, Apr. 2011.

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Appendix: A. Power generation limits and cost coefficients BUS Cost Coefficients PGMIN № (MW) a b c 1 0 2 0.00375 50 2 0 1.75 0.0175 20 5 0 1 0.0625 15 8 0 3.25 0.0083 10 11 0 3 0.025 10 13 0 3 0.025 12

PGMAX (MW) 200 80 50 35 30 40

B. Induction wind turbine model parameters Stator resistance (Rs): 0.1015 pu Rotor resistance (Rr): 0.0880 pu Stator reactance (Xs): 3.5547 pu Rotor reactance (Xr) : 3.5859 pu Magnetizing reactance (Xm): 3.5092 pu Inertia constant (H): 4 s