Transient Stability Analysis of the IEEE 14-Bus Test System Using Dynamic Computation for Power Systems (DCPS)

N. Hashim, N. Hamzah, M.F. Abdul Latip Faculty of Electrical Engineering

UniversitiTeknologi MARA (UiTM) 40450 Shah Alam, Selangor, Malaysia

azlan4477@salam.uitm.edu.my

A.A. Sallehhudin Advanced Power Solutions Sdn. Bhd. 40675 Shah Alam, Selangor, Malaysia

adibyss@gmail.com

Abstract –Transient Stability Analysis (TSA) is a major analysis in the operation of power systems, due to the increasing stress on power system networks. One of the main goals of this analysis is to gather critical information, such as critical clearing time (tCCT,) of the circuit breakers for faults in the system. tCCT is defined as the maximum time between the fault initiation and its clearing, such that the power system is transiently stable. This paper presents a transient stability analysis of the IEEE 14 bus test system using Dynamic Computation for Power Systems (DCPS) software package. This C++ based software package has the ability to handle systems up to 1000 buses and 250 generators, providing an alternative to expensive commercial software packages. To analyze the effect of the distance of the fault location and critical clearing time on the system stability, a three-phase fault has been applied at five different locations in the system. The stability of the system has been observed based on the simulation graphs of terminal voltage, machine’s rotor angle, machine’s speed and output electrical power. The simulation results showed that tCCT decreases as the fault location becomes closer to the main generator.

Keywords–Transient Stability Analysis; DCPS; Improved Euler Method; Critical Clearing Time

I. INTRODUCTION The two major areas in stability studies are steady-

state stability and transient stability. Steady-state stability refers to the ability of the electrical power system to regain synchronism after encountering slow and small disturbances, such as gradual power. Transient stability analysis of a power system refers to the system's ability to remain in synchronism when subjected to a large disturbance, such as a three-phase fault and the sudden outage of a transmission line or the sudden addition or removal of the loads [1, 2]. Studies regarding these types of stability are helpful in determining crucial metrics such as critical clearing time (tCCT) of the circuit breakers and the voltage level of the power system. In the study of transient stability, the critical clearing time is one significant factor for maintaining the transient stability of the power system [3]. The definition of tCCT is related to transient stability. tCCT is defined as the maximum time between the fault initiation and its clearing, such that the power system is transiently stable. The clearing time is the time duration from the instant the disturbance occurred until all three poles of the circuit breaker are completely open. The critical clearing time is obtained by increasing the fault time interval until the system loses its stability. Increasing the tCCT can reduce the protection system rating and its cost and can increase the reliability of the protection system [4].

The aim of this investigation is to analyze the transient stability of the system by analyzing the characteristics of the machine states, including machine speed, rotor angle, output electrical power and terminal voltage with respect to fault clearing time after the three-phase fault occurs in the system. Section II provides a brief overview of the Dynamic Computation for Power Systems (DCPS) software package. Section III describes the Differential Algebraic Equations (DAEs) of the power system dynamic device, including the synchronous machine, turbine-governor and exciter. Section IV describes an overview of transient stability analysis. The results of the case study using the IEEE 14-bus test system are presented in section V. Section VI concludes the paper.

II. DYNAMIC COMPUTATION FOR POWER SYSTEMS (DCPS)

The Dynamic Computation for Power Systems program was created by the late of Dr Sallehhudin Yusof, the former managing director of Advanced Power Solutions Sdn Bhd, for the purpose of research. There are three simulation programs embedded in DCPS: (i) LF for load flow, (ii) TS for transient stability and (iii) CG for coherency grouping. As a pre-requisite to transient stability analysis, the load flow program must be run to provide the steady-state operation points. There are three load flow calculation methods employed in DCPS, including (i) Gauss- Seidel, (ii) Decoupled Newton, and (iii) Fast Decoupled. Each method has its own approach to solving the non-linear algebraic equations. Although each method points to equal objectives for load flow solution, the answers obtained from each method is likely to be different. The speed of convergence of the three methods is extremely important in achieving cost effective simulations. From experience in using the DCPS, the Decoupled Newton method gives the most satisfactory results [7].

III. THE IMPROVED EULER METHOD FOR SOLVING DIFFERENTIAL ALGEBRAIC EQUATIONS (DAES)

An electrical power system consists of multiple individual dynamic devices connected together to form a large and complex dynamic system. The three most important dynamic devices are synchronous machine, exciter and turbine-governor. The relationship between these devices is illustrated in Figure 1.

2012 Third International Conference on Intelligent Systems Modelling and Simulation

978-0-7695-4668-1/12 $26.00 © 2012 IEEE

DOI 10.1109/ISMS.2012.53

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2012 Third International Conference on Intelligent Systems Modelling and Simulation

978-0-7695-4668-1/12 $26.00 © 2012 IEEE

DOI 10.1109/ISMS.2012.53

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Figure 1. Relationship Between Machine States & Controller States

Before TSA can be performed, the physical model of these devices needs to be formulated into Differential Algebraic Equations (DAEs). First-order DAEs are in the form of:

����� � ��� � (1)

where y(t) is a time-varying function subject to the initial condition: y(0) = y0. This initial value problem must be solved numerically, since there is no closed solution. The objective of solving (1) is to determine y0, y1, y2, …,yi at time t0, t1, t2, …ti. The solution must take into consideration these three aspects, including accuracy, stability, and efficiency. The solution methods for DAEs can be divided into implicit and explicit numerical integration techniques. Under the implicit technique, the Trapezoidal method is the most popular choice. Under the explicit technique, both Runge-Kutta and Euler Methods have been used extensively. In this paper, the Improved Euler Method, also known as Predictor-Corrector Method, is chosen to represent the explicit numerical integration technique that was developed in DCPS. The Improved Euler Method is depicted graphically in Figure 2. The Improved Euler Method is a Runge-Kutta based method for approximating the solution of the initial value problem [5]. In this method an initial estimate value is calculated by using the following Predictor Formula:

��� � � �� � ����� �� (2)

The time-step, h is given by (Δt = ti+1 - ti), which can be constant or variable. Using the result in (2), the final estimate value can be determined by applying the following Corrector Formula:

���� � � �� � ��������� �� � �����

� ��� �� (3)

Figure 2. Graphical Depiction of Improved Euler Method; (a) Predictor

and (b) Corrector

A. Synchronous Machine Model In DCPS, there are three synchronous machine

models that can be used for transient stability analysis, including: a) gen0 – a classical machine model. b) gen2 – a transient level machine model. c) gen5 – a detailed machine model

In this paper, only a detailed synchronous machine model (gen5) has been used in transient stability analysis. This model, also known as round rotor machine model, is shown in Figure 3. The gen5 model presumes an electric transmission network with a positive sequence source voltage where instantaneous amplitude and phase are known and current is to be determined. For clarity, the magnetic saturation and the stator resistance are excluded from the model. The stator flux is derived from stator currents and the exciter voltage [8]. The parameters of this model are shown in Appendix section. The equations which describe this model are:

����� � � � ��� (4)

����� � ��� !�" �� ��! �� ���� � �����#�����$ (5)

�%&' ��� � (�%)* �� �%&' ��� �+, �� �+,' �-,�.���/,0

' (6)

�%,' ��� � (���%,

' �� ��+& �� �+&' ��-&�.���/&0' (7)

�%&''��� � (�%&' ���%&'' ��� �+,' �� �+,

''�-,�.���/,0'' (8)

�%,''��� � (���%,

'' � %,' ���+&' ���+&''��-&�.���/&0'' (9)

Where δ is the rotor angle; ω is the angular velocity; PMECH is the input mechanical power; PE is the output

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electrical power; D is the damping constant; M is the machine inertia constant; f is the system frequency; +, is the direct-axis synchronous reactance; +,' is the direct-axis transient reactance; +,'' is the direct-axis sub-transient reactance; /,0' is the open circuit direct-axis transient time constant; /,0'' is the open circuit direct-axis sub-transient time constant; +& is the quadrature-axis synchronous reactance; +&' is the quadrature-axis transient reactance; +&'' is the quadrature-axis sub-transient reactance; /&0' is the open circuit quadrature-axis transient time constant; /&0'' is the open circuit quadrature-axis sub-transient time constant; and +� is the leakage reactance.

ι

ι

−−

XXXX

'd

''d

ι−−

XXXX

'd

''d

'd

ST1''0d

ι− XX ''d

2'd

''d

'd

)XX(XX

ι−−

'dd XX −

ST1'0d

+− +++

−−

++

dψ

dI

fdadIX

ι

ι

−−

XXXX

'q

''q

ι−−

XXXX

'q

''q

'q

ST1''0q

ι− XX ''q

2q

'q

''q

'q

)XX(XX

−−

'qq XX −

ST1'0q qψ−

qI

fdE

Figure 3. Detailed Synchronous Machine Model (Type Gen5) in DCPS

B. Turbine-Governor Model The function of a turbine-governor system is to

monitor the speed of the the rotor being driven by the turbine. The governor provides the appropriate signal to fuel valve controllers either to open or close the valve, depending on the deviation of the rotor speed with respect to the synchronous speed [7]. Figure 4 shows a simple turbine-governor control system embedded in DCPS. The input mechanical power PMECH to the generator is controlled by this turbine-governor system in order to maintain the output electrical power, PE at an acceptable level. A speed error signal �err is calculated by comparing the recorded speed at the shaft to a desired value. �err is used to determine the new gate/valve position. The speed change as an input is given by Δω = (ω0 - ω)/ω0. The equations that describe the control transfer function relating the input and output variables of the Simple Turbine-Governor are given below:

�� !�"��� � ��122 � � !�"�/ (10)

�1sT1

1+R

1

Figure 4. Turbine-Governor Model (Type Gov10) in DCPS

C. Exciter Model The exciter is a key component of a synchronous

generator control system, as it maintains the output terminal voltage at a constant level. It provides direct current to the field winding of the synchronous machine. The amount of excitation required is a function of the generator load. As the generator load increases, the amount of excitation increases. Figure 5 shows a simple excitation system used in DCPS. The differential equations relating the input and output variables of this exciter model is given as:

�3���� � �34 � 3��/5 (13)

�RsT1

1+ 1K

Figure 5. Exciter Model (Type Exc10) in DCPS

IV. TRANSIENT STABILITY ANALYSIS As a pre-requisite to TSA, load flow calculations need to be solved to determine the steady-state conditions of the network. Then, the values from these solutions will be used to calculate the initial conditions for dynamic models namely synchronous generators, turbine-governors system and exciters system. The purpose of transient stability analysis is to evaluate the ability of the power system to withstand large disturbances and to survive transition to a normal operating condition. These disturbances can include a three-phase fault on a transmission line, loss of a generator or loss of a major load [2]. In the study of transient stability, one of the most significant factors for maintaining the transient stability of the power system is the critical clearing time (tCCT). There are many methods to determine the tCCT, including the Lyapunov direct methods, transient energy function methods, equal area criterion, artificial intelligence and conventional time domain simulation. Time domain simulation can be considered as the most accurate solution, and in theory it can handle unlimited detailed models of generator, load and other system controllers. However, the solution of this simulation is very complicated, because it involves multiple nonlinear differential-algebraic equations (DAEs). In this paper, the Improved Euler Method, also known as Predictor-Corrector Method, is chosen to

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represent the explicit numerical integration technique that was developed in DCPS. /�6� 7869:;;� <97=6>>� 7��<69�79?@AB�/CD�@A�#E�C�@>�>�7FA�@A�G@BH96�I��

Figure 6. Flowchart of Transient Stability Analysis in DCPS

In this simulation, a three-phase fault has been injected to the system at t = 1s and removed from the system at the clearing time, tCT. In practice, fault clearance occurs through the removal of the affected line or branch from the power system network by protective relay action and opening of circuit breakers. After fault clearance, if the system is still stable, then the system terminal voltage is expected to recover. The generator's rotor angle would settle back to its steady state condition. To determine tCCT, tCT was increased gradually using a step time of 0.01s until the system appears to be unstable as determined by observing �69?@A:;� 87;�:B6 as a reference point. The tCCT is obtained by calculating the midpoint between the fault time when the system starts to be unstable and the time where the system was last known in a stable state. The procedure for determining the tCCT when fault occurred at bus 1 is shown in Figure 7 [7].

Figure 7. Critical Clearing Time Determination in DCPS

Figure 8. IEEE 14-Bus Test System

V. RESULTS AND DISCUSSION

The TSA was carried out on IEEE 14-bus test system as shown in Figure 8. The network data used for this work is obtained from [9]. Dynamic data for generators, turbine-governors and exciters used in this work are given in the Appendix. These data values were kept constant during the simulation. The main generator for this system is located at bus 1, and produces the largest real power of approximately 232.4 MW. To study the effect of fault distance from the main generator and critical clearing time, a three-phase fault has been applied at five difference buses namely bus 1(swing bus), bus 2, bus 3, bus 4 and bus 5. The distance of each bus from the main generator is described by the reactance value as shown in Table I.

Figure 9-12 shows the simulation graphs of terminal voltage, machine’s rotor angle, machine’s speed and output electric power in the case where a three-phase fault occurs at bus 1 when the fault clearing time is less than critical clearing time (tCT < tCCT). As can be seen, following the removal of fault from the system, the terminal voltage (Figure 9) is recovered and the machine’s rotor angle (Figure 10) is settling back to its steady state after experiencing damped transient oscillations. For this particular operating condition, the system is said to be transiently stable following a three-phase fault. When the clearing time exceeds the critical clearing time (tCT > tCCT), the machine’s rotor angle will go out of step, as can be seen in Figure 14, and in this case the system is in unstable condition. The system model is unable to sustain the fault and loses its synchronism. Based on this analysis, the critical clearing time for this case is 0.145 sec. The same analysis has been done for other buses and the summary of this analysis is shown in Table I. The results in the table clearly show that tCCT decreases as the fault location becomes closer to the main generator. The distance of the fault location from main generator was described by the values of reactance in p.u.

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Figure 9. Plots of terminal voltage for all buses (tct=0.14). (Stable)

Figure 10. Plots of machines rotor angle (tct=0.14). (Stable)

Figure 11. Plots of machines speed (tct=0.14). (Stable)

Figure 12. Plots of machines output electric power (tct=0.14). (Stable)

Figure 13. Plots of terminal voltage for all buses (tct=0.15). (Unstable)

Figure 14. Plots of machines rotor angle (tct=0.15). (Unstable)

Figure 15. Plots of machines speed (tct=0.15). (Unstable)

Figure 16. Plots of machines output electric power (tct=0.15). (Unstable)

TABLE I. SUMMARY OF ANALYSIS RESULTS Rank Faulted Bus Shortest Reactance from Bus 1 Clearing Time (s) Analysis Result Critical Clearing Time (s)

1 1 (Swing Bus) - 0.14 Stable 0.145 0.15 Unstable

2 2 0.0592 p.u 0.38 Stable 0.385 0.39 Unstable

3 5 0.2230 p.u 0.58 Stable 0.585 0.59 Unstable

4 4 0.2355 p.u 0.34 Stable 0.595 0.35 Unstable

5 3 0.2572 p.u 0.63 Stable 0.635 0.64 Unstable

Pre-fault Fault-on Post-fault

tct

Pre-fault Fault-on Post-fault

tct

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VI. CONCLUSION

In this paper, the TSA of the IEEE 14-bus test system has been successfully analyzed using DCPS software package. For the comparative analysis, five different locations of the three-phase fault was chosen to study the effect of the fault distance from the main generator and critical clearing time. As can be seen from Table I, the fastest tCCT is 0.145s when the fault occurred exactly at the main generator bus, while the longest tCCT is 0.635s when the fault occurred on bus 3, located far from the main generator. The tCCT decreases as the fault location becomes closer to the main generator. An interpretation of this finding is that faults that occur closer to the main generator must be cleared more quickly than faults that occurred some distance away. To ensure the stability of power system due to fault occurrence, proper protection system settings must be made. Information from this analysis and similar analysis based on the configuration of the target network can be used in identifying the correct settings.

ACKNOWLEDGMENT The financial assistance of the Faculty of Electrical

Engineering, Universiti Teknologi MARA is greatly appreciated. Also, special thanks to Mr Ahmad Adib Sallehhudin for permission to use DCPS software.

REFERENCES

[1] P. Kundur, Power system stability and control, New York: Mc-Graw-Hill, 1994.

[2] P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. Van Cutsem, and V. Vittal, "Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions," IEEE Transactions on Power Systems, vol. 19, no. 3, pp. 1387–1401, Aug. 2004.

[3] IEEE Committee Report, "Proposed terms and definitions for power system stability,"IEEE Transactions on Power Apparatus and Systems, vol. PAS-101, pp. 1894–1898, 1982.

[4] A. M. Hemeida, “Improvement of voltage stability and critical clearing time for multi-machine power systems using static var compensator,” ICGST-ACSE, vol. 9, no. 2, pp. 41–47, December 2009.

[5] S.C Chapra and R.P Canale, Numerical methods for engineers with software and programming applications, 4th. ed., McGraw Hill, 2002.

[6] I. Xyngi, A. Ishchenko, M. Popov, and L. van der Sluis, "Transient Stability Analysis of a Distribution Network With Distributed Generators," IEEE Transactions on Power Systems, vol. 24, no. 2, pp. 1102 - 1104, May 2009.

[7] N. Hashim, N.R. Hamzah, P. Mohd Arsad, R. Baharom, N.F. Nik Ismail, N. Aminudin, D. Johari and A.A. Sallehhudin "Modeling of Power System Dynamic Devices Incorporated in Dynamic Computation for Power Systems (DCPS) for Transient Stability Analysis," 2011 IEEE International Electric Machines & Drives Conference (IEMDC), pp. 647 - 652, May 15-18, 2011

[8] A.M Mohamad, N. Hashim, N. Hamzah, N.F. Nik Ismail, M.F. Abdul Latip "Transient stability analysis on Sarawak's Grid using Power System Simulator for Engineering (PSS/E)," 2011 IEEE Symposium on Industrial Electronics and Applications (ISIEA), pp. 521 - 526, Sept. 25-28, 2011

[9] R. Christie, UW Power System Test Case Archive, Available: http://www.ee.washington.edu/research/pstca/

APPENDIX

TABLE II. DYNAMIC DATA FOR TRANSIENT STABILITY ANALYSIS IN DCPS

Parameters Generator Turbine-Governor Exciter

M 5 - - f 50 hz - - +, 1.9 - - +,

� 0.3 - - +,

�� 0.3 - - /,0

� 4.57 - - /,0

�� 0.042 - - +& 1.6 - - +&� 0.7 - - +&�� 0.293 - - /&0� 0.5 - - /&0�� 0.3 - - +� 0.25 - - 3 JK - 1.0 - 3 LM - -1.0 - / - 30.0 - R - 0.05 -

%)* JK - - 1.0 %)* LM - - -1.0 N - - 30.0 /5 - - 0.01

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