Energy Function Based Transient Stability Assessment of Thyristor Controlled Series Capacitor

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 12, December 2014)

Energy Function Based Transient Stability Assessment of Thyristor Controlled Series Capacitor Akhilesh A. Nimje1, D. P. Kothari2 1

Associate Professor, Department of Electrical Engineering, Guru Nanak Institute of Engineering and Technology, Nagpur, India 2 Professor, Department of Electrical Engineering, Director Research, Gaikwad Patil Group of Institutions, Nagpur, India Flexible AC transmission systems (FACTS) devices are very effective in minimizing these stesses and encourages better utilization of existing network. FACTS device improve steady state and dynamic performance of the power network. The shunt FACTS controller mainly improves the voltage profile and is very effective proven damping system because in some cases, it provides negative damping. The energy function method is a powerful tool of stability assessment [2-3]. The energy function has two important components namely, kinetic energy and potential energy. The sum of these two components is called the transient energy. When a fault occurs in the system, the electrical power output of the machine reduces considerably, but the mechanical input during the period of electromechanical transient remains constant. The machine therefore tend to accelerate on account of Pa = Pm – Pe (damping effect not included) and it gains potential as well as kinetic energy. As soon as the fault is cleared, the conversion between the kinetic and potential energy takes place and this result in rotor swing about its synchronously rotating axis. However if the magnitude of disturbance is not large enough, the rotor settles down to a new stable operating point thus changing the rotor angle where the transient energy is zero. The transient energy during the fault is dissipated during the energy conversion process (K.E. into P.E. and vice versa) during the post fault period provided the system must have adequate damping. In the absence of damping, the system suffers from sustained oscillations [5]. The faster the energy dissipates, quicker the rotor settles at a new stable operating point (SEP).

Abstract— This paper presents the transient stability assessment of TCPST, UPFC and TCSC. The control laws based on few assumptions were applied and have been found to be effective for power oscillation damping for large and small signals. The bang-bang control strategy is used for IPFC in which the injected voltage magnitudes were kept constant and only one of voltage angles was varied. The results of the test data have been reported and are optimistic. Keywords— FACTS, SSSC, TCPST, UPFC, TCSC, Energy Function.

I. INTRODUCTION Flexible AC transmission system (FACTS) is the key driving force in the competitive environment to improve the effectiveness and efficiency. The transition from traditional monopolies to the increased competition among the Independent Power Producers (IPPs) has resulted in reduction in electricity tariff in few high profile cases such as Argentina, Chile and United Kingdom. The process of restructuring undergoes strictly regulated market environment to a newly deregulated and restructured environment. Power quality is a major concern when it is being delivered to high tech consumers. The reforms to achieve the set target for restructuring in power sector are taking shape closer to its perfection. FACTS devices have been found very effective in improving the power quality and stability. The transient stability assessment after the implementation of FACTS devices is an important task in order to study the reduction of fault clearing time or critical clearing (maximum allowable) time [1]. Upon the occurrence of small or large disturbance, the rotor behavior at the power plant changes, the governing system tries to bring the rotor to a new steady state torque angle after having been subjected to few numbers of oscillations of reducing amplitude. This is due to the fact that the transmission networks of the present scenario are subjected to increased stress due to continuous growth in demand. Moreover, maintaining system stability is a big threat in order to prevent blackouts.

II. BASIC STRUCTURE OF CONTROLLABLE SERIES DEVICE A static synchronous series compensator is regarded as a CSD. It represents controllable reactive impedance, or a controllable reactive voltage source phase shifted by 90o with respect to the line current.

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 12, December 2014)

Fig. 3 Transient State Representation

Fig. 1 Test System

The real power transfer during the transient state of CSC

CSC – Controllable Series Compensation, CSD – Controllable Series Device, X1, X2 – Reactance of a Longitudinal Line, G1, G2 – Generators ; V1, V2 – Voltage Magnitudes,  - transmission Angle ; SSSC – Static Synchronous Series Compensator ; I – Line Current ; P1, P2 – Active Power, XCSC – Reactance of Controllable Series Compensation device. VCSC – Controllable Injected Voltage (Inductive Mode) ; VT - Controllable Injected Voltage (Capacitive Mode) , K – Compensation Ratio The transmitted real power expressed as a function of controllable parameter (K) is:

 …………… VC1 = V1 – jX1I (2) VC2 = VC1 + VT (4) P1 = P2 = Re[V1I*] = Re[V2I*]

(8) Similarly, the real power transfer during the transient state of SSSC [

[



(9)

The following equation describes the rotor dynamics when damping is included.

(1)

VT = -j VT V2 = VC2 – jX2I

(10)

(3); (5); (6);

Where Equation (10) has two equilibrium points corresponding to maximum swing angles on two either sides of synchronously rotating axis.

Solving (2), (3), (4), (5) and (6) 

]



]

(7) *

+

*

+

(11)

The energy function is expressed as (12) The time derivative along the trajectory of the swing equation at each time considering the real power. ̇

*

(

)+

(13) Fig. 2 Phasor Diagram of SSSC in Capacitive Mode

̇

The above system is reduced to single machine infinite bus and the use of control Lyapunov function [6] CLF is implemented. The system representation during the transient conditions is shown in figure 3.

[



]

(14)

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 12, December 2014) To achieve the maximum damping and the largest transient stability enhancement, the terms within the square brackets of equation (13) and (14) must achieve maximum values over the entire range of the system parameters. The value of k is limited to kmin  kCSC  kmax . It uses the following control law for CSC. k = k max ;  . sin ‘  0and k = kmin ;  . sin ‘  0

Assumption 1) This study is based on the assumption that upon the clearing of the fault, the control parameter immediately attains their peak value and remains constant. 2) The application of energy function for stability assessment is based on the step by step numerical calculation of time derivative of energy function. 3) The critical energy is uniformly given by the amount of potential energy in the nearest unstable equilibrium points. The differential equation is evaluated analytically.

(15)

In case of SSSC [7], VT is limited to  VTmax. It uses the following control law. VT = - VTmax . sign [. sin‘]. (16) III. III. USE OF ENERGY FUNCTION FOR SERIES FACTS DEVICES

(

During the first swing of the rotor as long as the  does not change its sign, the direct methods of transient stability assessment can be used as per equation (15) and (16) which demand a constant maximum controllable parameter. Kmax or kmin for CSC and VTmax for SSSC. The energy function is constructed on the basis of (15) and (16) and is the first integral of the swing equation (10) considering (8) and (9) as ‗Pe‘.

(

( )

) )

IV. CONTROL LAWS The energy function is the measure of kinetic energy, potential energy and a constant such that at the post fault equilibrium point, the energy function is zero [5]. In order to damp the power oscillations, the total value of energy function must decrease and the FACTS device must be controlled accordingly. The time derivative of the energy function yields.

(17) ̇

The essence of this study showed that the inclusion of FACTS devices in power system results in increased potential energy which is translated into the transient stability enhancement and increasing the critical clearing time and angle. The CCT so obtained gives an optimistic result. This is because the real time application of CSD has some delay due to measurement, regulators and thyristors [7]. The energy function involving definite integrals are as follows:

[

(

)]

̇ is dependent on the derivative of voltage angle and magnitude. The first term has dominant impact on the time derivative of energy. The control strategy of series FACTS controller must satisfy: ̇

(

)

∫ Fig. 4 Injection Model for Series FACTS Controller

For the purpose of power flow and stability analysis, a thyristor controlled series capacitor is modeled as a variable reactance. The equivalent model of Unified Power Flow Controller and Thyristor Controlled Phase Shifting Transformer is valid for TCSC provided, the shunt current is set to zero, Xs is taken as transmission line reactance and K as degree of compensation.

The energy functions are regularly employed for critical clearing time estimation. Once the energy function is obtained, the critical clearing time is estimated on the fault trajectory where the total energy of the system equals the critical energy, e(‘ , ) = ecr (19)

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 12, December 2014) (29) (30) (31) C. For TCSC (32)

Xs - Effective reactance from line side of series transformer. For UPFC, Xs = Xseries For TCPST, Xs = Xseries + n2 Xshunt. bs = 1/Xs. Xseries Reactance of series transformer Xshunt Reactance of shunt transformer n depends upon phase shifting angle Vs Induced series voltage

(33) (34) .

(35)

The control laws for series connected FACTS devices are obtained by putting Psj from above set of equations and controlling the control variable such that the absolute value of time derivative of energy function becomes maximum. D. Control Laws for UPFC and TCPST (36) and from ̇ Xs - Effective reactance from line side of series transformer. For UPFC, Xs = Xseries For TCPST, Xs = Xseries + n2 Xshunt. bs = 1/Xs.

Thus

(

)

̇

(37) (

)

To attain maximum absolute value of ̇ , the term Sin(ij+) should be kept equal to ±1 depending upon the sign of ( ). The following control laws can then be achieved.

Xseries Reactance of series transformer Xshunt Reactance of shunt transformer n depends upon phase shifting angle Vs Induced series voltage Is current source. Vi‘ fictitious voltage behind the series reactance. r = Vs/Vi; 0 < r < rmax , ij = i - j.

(

If (

)

then r = rmax

) is negative, Sin(ij + (-(/2)-ij) = -1.

The overall term of equation maximum.

The various parameters such as PSi, QSi, PSj, QSj for various FACTS controller can be written as:

and  = -(/2) - ij,

̇ becomes negative

Similarly, If

A. For UPFC

(

(

)

then r = rmax

and  = (/2) - ij,

) is positive, Sin(ij + (/2-ij) = +1.

(23) (24)

The overall term of equation maximum.

(25)

E. Control Laws for TCSC

̇ becomes positive

(38)

(27) B. For TCPST ̇ (28) 464

(

)

(39)

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 12, December 2014) The transmission angle ij is used as input signals for the control strategies employed in numerous series FACTS controller. The input signals are monitored for every sampling time of 20 m-sec and the controller outputs are estimated.

Simulation Showing the Capability of SSSC to Establish Positive and Negative Power Flow No Compensation

Real Power in Per Unit

1

V. TEST DATA

Compensation for Positive Power Flow

0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1

0

0.05

0.1

0.15

5

2.5

x 10

0.3

0.35

Swing curve using when Three Phase Fault Occurs at point F

2 Delta in electrical degrees

Transmitted Power As a Parametric Fuction of Degree of Series Compensation

Ps in Per Unit

0.25

Fig. 9 Simulation Showing the Capability of SSSC to Establish Positive and Negative Power Flow

VI. RESULTS

K=0.8

5 4

NO FACTS DEVICE

1.5

1

0.5

K=0.6

3 2

K=0.4

1

K=0.2 K=0

0 0

0.2

Time in Seconds

SMIB, BASE MVA=60; Inertia Constant H=3.5 MJ/MVA; Poles P=4; Speed N=1500 rpm; Frequency f=50 Hz; voltage behind the transient reactance E=1.2 pu; Infinite bus voltage V=1 pu; Prefault Power to load Peo=60 MW; Transient Reactance X0=0.0 pu; Prefault Reactance X1=0.65 pu; During fault reactance X2=4 pu; Post Fault Reactance X3=0.9 pu; Td=0.04 sec.

6

Compensation for Negative Power Flow

0.8

20

40

60

0

80 100 120 Transmission Angle delta

140

160

0

2

4

6 Time in Seconds

8

10

12

Fig. 10 Swing Curve if a 3 Fault Occurs at Receiving End When No FACTS Device is Installed

180

Fig. 7 Transmitted Power as a Parametric Function of Degree of Series Compensation

Swing Curve if TCPST is used 100 90

Transmitted Power Pq Vs Transmission Angle As a Parametric Function of Series Compensating Voltage Vq by SSSC

2 Vq=0.8 Vq=0.6 Vq=0.4

80 Delta in Electrical Degrees

Pq in Per Unit

1.5 1 0.5

Vq=0.2 Vq=0 Vq=-0.2 Vq=-0.4 Vq=-0.6 Vq=-0.8

0 -0.5 -1 0

20

40

60

80 100 120 Transmission Angle delta

140

160

180

60.1098 Degrees in Approximately 4 Seconds 70 60 50 40

Fig. 8 Transmitted Power Pq Versus Transmission Angle delta as a Parametric Function of Series Compensating Voltage Vq Provided by SSSC

30 20

Initial Rotor Angle = 28.70 Degrees

0

2

4

6 Time in Seconds

8

10

Fig 11 Swing Curve if TCPST is Installed

465

12

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 12, December 2014) In the above fig 10 to 14,, the result so obtained showed a very high value of delta in electrical degree on account of fault existed for few cycles (2.5 x 10 5 / 360 = 694.4 cycles). Thus the simulation was carried approximately upto 14 seconds.

Swing Curve if UPFC is used 100 90

Delta in Electrical Degrees

80

Energy Function Using Multiple Series FACTS Controllers The analysis so far presented can be extended if the number of series FACTS controllers is employed in a longitudinal transmission corridor. The differentiation of energy function is expressed as :

20

1)

2) 3) 4)

Delta in Electrical Degrees

48.9471 Degrees in Approximately 3.65 Seconds

5)

55 50

6)

45

7)

40 35 Initial Rotor Angle = 28.70 Degrees

2

4

6 Time in Seconds

8

10

0

2

4

6 Time in Seconds

8

10

12

VII. ALGORITHM

65

0

Initial Rotor Angle = 28.70 Degrees

Fig. 13 Swing Curve if UPFC in Installed

70

25

50

30

Swing Curve if TCSC is used

30

58.2248 Degrees in 2.35 Seconds

60

40

∑ ̇ ( ) if the requirement of energy function is satisfied. Where m - number of series connected FACTS controller. in , jn - nodes between which FACTS controllers are employed. n - 1, 2, ………, m. The employment of multiple series FACTS controller must ensure the contribution of each device in the reduction of total energy without affecting the effectiveness of the other controllers [8]. The application of energy function for stability assessment was studied on a two distinct line incorporated with IPFC. The VT1 and VT2 are kept at their maximum values and only T1 changes. During the time interval of t, T1 is considered constant but changes when time changes from initial time to initial time plus time step.

60

70

12

Fig. 12 Swing Curve if TCSC in Installed

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The duration from the occurrence of the fault to the instant of fault clearing or critical clearing time is segmented into discrete time steps of t to assess the change in rotor angular positions. The pre-fault system parameters such as rotor angle and speed are known. The energy function at every instant is evaluated. The controllable parameters that give the largest reduction in energy function are regarded as optimal parameters. The optimal parameters do not change rapidly in a small time interval of t. However, if the optimal parameters as per step 4 are not found, the new values of controllable parameters are set and step (3) and (4) are repeated. The time domain simulation is repeated till tfinal is reached. The rotor angles are plotted on the time axis for a given series FACTS controller.

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 12, December 2014) In order to damp these oscillations, the selection of input signals for proper control to the FACTS controller is an important aspect [9-10]]. The control law depicted in this paper uses the locally measurable variables. It was seen that the selected control strategy is useful in enhancing the available transfer capacity (ATC).

injected voltage magnitudes 0.025

Vt1 = Vt2

0.02

0.015

Acknowledgement The authors are indebted to the authorities of GNIET, Nagpur and KIIT University, Bhubaneswar, for providing facilities to work.

0.01

0.005

REFERENCES 0

Natarajan Narasimhamurthi, Mohamed T. Musavi, ―A Generalized Energy Function for Transient Stability Analysis of Power System,‖ IEEE Trans. on Circuits and Systems, Vol. CAS-31, No. 1 pp 637645, July 1984. [2] Da-zong Fang, T. S. Chung, Yao Zhang, Wennan Song, ―Transient Stability Limit Conditions Analysis Using a Corrected Transient Energy Function Approach,‖ IEEE Trans. on Power Systems, Vol. 15, No. 2, pp 804-810, May 2000. [3] U. Gabrijel and R. Mihalic, ―Direct methods for transient stability assessment in power systems comprising controllable series devices,‖ IEEE Trans. Power Syst., vol. 17, no. 4, pp. 1116–1122, Nov. 2002. [4] R. Mihalic and U. Gabrijel, ―A structure-preserving energy function for a static series synchronous compensator,‖ IEEE Trans. Power Syst., vol. 19, no. 3, pp. 1501–1507, Aug. 2004. [5] Theresa Odun-Ayo, M. L. Crow, ―Structure Preserved Power System Transient Stability Using Stochastic Energy Functions,‖ IEEE Trans. on Power Systems, Vol. 27, No. 3, pp. 1450-1458, Aug 2012. [6] H.F. Hang, ―Design of SSSC damping controller to improve power system oscillation stability,‖ IEEE Transactions on Power Systems, 1999. [7] Akhilesh Arvind Nimje, C. K. Panigrahi, Ajaya Mohanty, Enhanced power transfer capability by using SSSC, Journal of Mechanical Engineering and Research, Vol. 3(2), pp. 48-56, February 2011. [8] Akhilesh Arvind Nimje, C. K. Panigrahi, Ajaya Kumar Mohanty, ―Transient Stability Analysis using Modified Euler‘s iterative technique‖, IEEE third international conference on power systems 2009. [9] C. K. Panigrahi, Akhilesh Arvind Nimje et.al ―Steady State Analysis of Interline Power Flow Controller‖ International Journal of Power System Operation and Energy Management‖ Vol. 1, Issue II, 2011, pp 12-18. [10] Akhilesh A. Nimje, C. K. Panigrahi, A. K. Mohanty, ―Energy Function Based Transient Stability Assessment of SSSC and IPFC‖, International Electrical Engineering Journal, Vol.2, (2011), No.2, pp 543 – 549. [1]

0

0.5

1

1.5

2

2.5 3 Time in Sec

3.5

4

4.5

5

Fig. 14 Injected Voltage Magnitude with Time Post fault Energy Function 0 -0.001 -0.002

Energy Function (pu)

-0.003 -0.004 -0.005 -0.006 -0.007 -0.008 -0.009 -0.01

0

1

2

3 4 Time in Sec

5

6

7

Fig. 15 Post Fault Energy Function

VIII. CONCLUSION The paper describes the improvement in power system dynamics by the use of few series connected FACTS controller. The control law has been proved satisfactory on a test system at various circumstances such as normal loading, overloading and under loading. The series reactive compensation is more effective than the shunt compensation for power oscillation damping.

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