An Analysis of Transient Stability Using Center-of-Inertia: Angle and Speed

*H. Hashim, M. R. Zulkepali, Y. R. Omar, N. Ismail, I. Z. Abidin, S. Yusof Universiti Tenaga Nasional, Malaysia. Advanced Power Solution Sdn. Bhd.

{halimatun, yaakob, noraisma, izham}@uniten.edu.my. zm.ridzuwan@gmail.com, salleh@aps-my.com

Abstract - Instability in the system may cause the rotor angle of the machine to accelerate or decelerate depending on the mechanical power and electrical power; most seriously could result to tripping of the machine This paper evaluates the impact of disturbances and types of loads to system stability using Area-based COI-referred Transient Stability Indexes: COI angle and COI speed. The analysis is carried out using PSSE 32 software on IEEE 118 Bus Test System at system conditions with and without dynamic loads. The network is initially divided into significant areas based on the geographical. Keywords - Transient stability, Center-of Inertia, Dynamic load.

I. INTRODUCTION

Fault on transmission facilities, large loss of load or generation will result in transient stability causing large currents and torque experienced by the machine concerned. Any unbalanced torque acting on the rotor causes the machines to accelerate or decelerate, which may lead to loss of synchronism [5, 6] if the imbalance is too significant. Therefore, it is important to analyze the impact of these disturbances to the power network in order to maintain system stability. This paper analyzes the effect of dynamic load to power system stability upon the occurrence of fault using Area-based [3] COI-referred Transient Stability Index: COI angle and COI speed [3, 4, 5]. For this to be possible, simulation analysis was carried out on IEEE 118 Bus Test System. Apart from that, the system loads are varied by taking into account static and dynamic load conditions. II. AREA-BASED CENTRE OF INERTIA (COI)

Area-Based COI is a common transformation used in transient stability analysis. The indices as shown in equation (1) and equation (5) associate with the rotor angle and angular speed of a particular area of a power grid and are based on an equivalent inertia representing the total inertia of the generators located in that area. The indices are derived from the classical machine model by assuming that the

dynamic behavior of generators in the system [3, 4, 5]. If the indices calculated show an out of step condition after the fault is cleared, the system is considered to be in an unstable condition. In addition, if the multi-machine system is in synchronism with all the machines turning at a constant speed, the system frequency is equal to the dynamic frequency (possibly above or below the steady state speed, s) [4].

The COI reference transformation defines the COI angle as: (1) (2) ()

(3) (4)

Where N is the number of generator, M is the

moment of inertia of the machine, MT is the total system inertia, is the area equivalent rotor angle, i the individual rotor angle, while r is total number of areas in a power system.

The COI reference transformation defines the COI speed as: (5) ()

(6) Where is the area equivalent rotor speed and i is the individual rotor speed of the area.

2010 IEEE International Conference on Power and Energy (PECon2010), Nov 29 - Dec 1, 2010, Kuala Lumpur, Malaysia978-1-4244-8946-6/10/$26.00 2010 IEEE 402

III. METHODOLOGY

The index of Area-Based COI: COI angle and COI speed are used to examine the stability the IEEE 118 Bus Test System, which consists of 28 generators, 118 buses and 186 transmission lines, when subjected to fault. Figure 1 shows that the large network is organized into three areas, namely: Area 1 has 13 generators, Area 2 with 8 generators and Area 3 consists of 7 generators respectively based on geographical. Different types of power plants are modeled connected to static loads and/or dynamic loads using PSSE 32.

Figure 1: IEEE 118 Bus Test System with three electrically coherent areas.

Figure 2 represents a simplified version of the

IEEE 118 Bus Test System to highlight the interconnection between the three areas and the number of generators and inertia constant for the respective area.

Figure 2: Area Based IEEE 118 Bus Test System

Simulations are carried out on the system at base case and contingency conditions with and without dynamic loads as a comparison from different load models. Bus fault was simulated at Bus 80 and 89 with a fault clearance time of 100ms [7]. The characteristic of rotor angle for each machine in the respective area was plotted during pre-fault, fault and post-fault conditions. Data obtained from the simulation results were used to calculate the stability

indices and hence, the stability of the system could be analyzed. If the COI angle is within 180 and the COI speed is very low, the system is in stable condition; however, if the COI angle exceeds 180 and the COI speed is large, then the system is in an unstable condition [3, 4].

IV. RESULTS AND DISCUSSIONS

A. Case studies without dynamic loads

Case 1: A bus fault is created at bus 89 in Area 1. Figure 3.1 Figure 3.3 illustrate the behavior of the angle in each area: Area 1, Area 2 and Area 3. Referring to Table 1, the COI angle is lesser than 180, which means the system is in stable condition. Referring to Table 11, the individual rotor angle of each machine in all areas does not violate the stability limit of the power system. Table 2 shows that the COI speed is very low, which indicates that this multi-machine system is in synchronism with all the machines in each area turning at almost a constant speed. This indicates the system frequency is almost equal to the dynamic frequency.

Figure 3.1: Case 1 for Area 1

Figure 3.2: Case 1 for Area 2

Figure 3.3: Case 1 for Area 3

Area 3, 7- genset,

Area 1, 13- genset,

Area 2, 8- genset, 403

The total inertia of the machines of the three areas: Area 1, Area 2 and Area 3 is MT = 186.6

Table 1: Transient Stability Index: Area-Based COI

Angle Case 1

-314.102 -314.213 -314.263

COI Speed () = -314.175

0.073809 -0.03781 -0.0876

Table 2: Transient Stability Index: Area-Based COI Speed Case 1

Case 2: Figure 3.4 Figure 3.6 demonstrate the

behavior of rotor angles when fault occurs at Bus 80. After the disturbance is cleared, the individual rotor angle for each machine in particular areas goes out of step of the stability limit, which is 180 as proven in Table 3 and Table 12. In addition, the COI speed of each area in Table 4 is also high. This indicates that the machines in each area are running out of synchronism.

611.2 2133.525 2108.80

COI Angle () = 1435.294

824.094 698.231 673.506

Table 3: Transient Stability Index: Area-Based COI Angle Case 2

-366.929 -369.125 -358.628

COI Speed () = -365.404

-1.52478 -3.72024 6.776079

Table 4: Transient Stability Index: Area-Based COI Speed Case 2

B. Case studies with dynamic loads

Case 3: A bus fault is simulated at bus 89 in

Area 1. Figure 3.7 Figure 3.9 show the behavior of the rotor angle, which is decreasing due to the effect of dynamic loads connected to buses 13, 15 and 19 in Area 3. Nevertheless comparing to Case 1, the dynamic loads that are connected to the system have caused the rotor angles to be decreasing within the simulation time frame of 20 seconds.

33.5530 19.0352 40.8326 COI Angle ()

= 31.2866

2.2664 12.2514 9.5460

Figure 3.4: Case 2 for Area 1

Figure 3.5: Case 2 for Area 2

Figure 3.6: Case 2 for Area 3

Figure 3.7: Case 3 for Area 1 404

The fault does not affect the system stability

since the individual rotor angle for each machine in particular areas does not violate the stability limit of the power system as shown in Table 13. This is also proven by COI angle in Table 5. In addition, COI speed of each area in Table 6 is also low showing that the machines are turning at almost a constant speed.

3.5029 16.068 4.6827

COI Angle ()

= 4.975

1.473 11.092 9.657

Table 5: Transient Stability Index: Area-Based COI

Angle Case 3

-315.888 -315.996 -316.046 COI Speed () = -315.96

0.071775 -0.0361 -0.08592

Table 6: Transient Stability Index: Area-Based COI Speed Case 3

Case 4: Figure 3.10 Figure 3.12 show the graph of rotor angle for each generator in the three areas when a fault occurs at Bus 80 in Area 1. The system becomes unstable since the rotor angle of most of the machines exceeding the stability limit, which is 180 accept for some of the machines in Area 1 as shown in Table 14 and proven in Table 7 and Table 8 through Transient Stability Index.

650.508 2178.688 2155.869

COI Angle ()

= 1478.291

827.783 700.397 677.578

Table 7: Transient Stability Index: Area-Based COI

Angle Case 4

Figure 3.8: Case 3 for Area 2

Figure 3.9: Case 3 for Area 3

Figure 3.10: Case 4 for Area 1

Figure 3.12: Case 4 for Area 3

Figure 3.11: Case 4 for Area 2 405

-370.373 -315.996 -316.046

COI Speed () = -340.72

-29.6525 24.72438 24.67456

Table 8: Transient Stability Index: Area-Based COI Speed Case 4

Table 5 and 6 summarize the results in terms of

Transient Stability Index: COI angle and COI speed for cases with and without the dynamic loads connected to the system. The index indicates whether the system is stable or unstable. Case 1 and Case 3 demonstrate the stability of the system with the value of Transient Stability Index, COI angle not exceeding 180 and low values of COI speed. In contrast, Case 2 and Case 4 represent the unstable condition of the system with Transient Stability Index, COI angle exceeding 180 and large values of COI speed. In addition, the values of both COI angle and COI speed are higher for the system with dynamics loads compared to the system without dynamic loads.

Case 1: fault at Bus 89 Case 2: fault at Bus 80

2.2664

0.073809

824.094

-1.52478

12.2514

-0.03781

698.231

-3.72024

9.5460

-0.0876

673.506

6.776079

Case 3: fault at Bus 89 Case 4: fault at Bus 80

1.4733

0.071775

827.7827

-29.6525

11.0923

-0.0361

700.3969

24.72438

9.6569

-0.08592

677.5782

24.67456

V. CONCLUSIONS

The existence of dynamic loads in the system affects the rotor angle and speed of the machines during steady state and abnormal conditions. At transient instability condition, the system with dynamic loads receives a greater impact compared to the system without dynamic loads. Therefore, in order to ensure that the stability of a power system is preserved, it is advisable to take dynamic loads into consideration during the analysis of transient stability. Based on all the cases, if the COI angle is within 180 and the COI speed is very low, then the system is in stable condition. Furthermore, in all cases, Area-based COI-referred Transient Stability Index: COI angle and COI speed is useful in analyzing the transient stability of a system when it is subjected to disturbance.

ACKNOWLEDGMENT

The research team would like to acknowledge the Ministry of Science and Technology Malaysia for research funding (03-02-03-SF0141 and 03-02-03-SF0187), Universiti Tenaga Nasional Malaysia, Tenaga Nasional Berhad and Advanced Power Solution Sdn. Bhd. for the support given to this research.

This paper is also dedicated to the late Dr.

Sallehhudin Yusof (President, Advanced Power Solutions Sdn. Bhd.) for his tireless effort and tremendous help in making the research presented to be more meaningful. May The Al-Mighty bless him always.

REFERENCES

[1] C. W. Taylor, Power System Voltage Stability. New York: McGraw-Hill, 1994.

[2] Hadi Saadat, Power System Analysis. Second Edition, New York: McGraw-Hill, 2002.

[3] A. W. Noor Izzri, A. Mohamed, Area-Based COI-Referred Transient Stability Index for Large-Scale Power System,International Journal of Power, Energy and Artificial Intelligence, No.1, Vol. 1 (ISSN: 1985-6431), August 2008.

[4] Sauer P. W and M. A. Pai, Power System Dynamics and Stability. Prentice Hall, 1998.

[5] Kundur, P. 1994. Introduction to the Power System Stability Problem Basic Concept and Definitions, Mid-term and Long-Term Stability. Power System Stability and Control: 33-34, McGraw-Hill.

TABLE 9: TSI for system without dynamic loads

TABLE 10: TSI for system with dynamic loads 406

[6] J Machowski, J W Bialek, JR, Bumby, Power System Dynamics Stability and Control. 2nd Edition, John Wiley & Sons, 2008.

[7] TNB Transmission Division, Protection and Control Code of Practice (COP), Second Edition, September 2003.

APPENDIX

A. Rotor Angle after Fault without Dynamic Loads

M/C No

Area1

Rotor angle,

() M/C No

Area2

Rotor angle, ()

M/C No

Area3

Rotor angle, ()

69 25.5470 40 20.8900 1 39.2257 70 57.2498 42 13.8581 10 58.6341 74 43.5788 46 20.8517 12 38.5190 76 4.9322 49 20.5787 25 34.2887 80 32.0188 54 16.3275 26 41.1974 87 5.5125 55 22.0559 27 31.3702 89 21.2923 59 18.8620 31 42.5933 91 28.2124 65 18.8620

100 81.9580 103 40.9147 107 28.8721 110 32.0866

TABLE 11: Case 1: Fault at Bus 89 without Dynamic Load

M/C No

Area1

Rotor angle,

() M/C No

Area2

Rotor angle, ()

M/C No

Area3

Rotor angle, ()

69 -2149.66 40 -2133.33 1 -2111.5 70 -2126.19 42 -2140.99 10 -2090.44 74 -2152.01 46 -2130.21 12 -2109.75 76 -2139.87 49 -2132.84 25 -2114.02 80 32.815 54 -2135.03 26 -2107.33 87 102.901 55 -2133.29 27 -2120.11 89 85.8264 59 -2135.01 31 -2108.47 91 71.0956 65 -2127.5

100 72.7026 103 63.8331 107 64.0682 110 66.6714

TABLE 12: Case 2: Fault at Bus 80 without Dynamic

Load

B. Rotor Angle after Fault with Dynamic Loads

M/C No

Area1

Rotor angle,

() M/C No

Area2

Rotor angle, ()

M/C No

Area3

Rotor angle, ()

69 -28.7021 40 -15.7373 1 1.7394 70 -4.5072 42 -22.7143 10 23.7219 74 -31.1004 46 -15.103 12 2.9723 76 -17.5300 49 -15.5163 25 -1.7649 80 -9.2960 54 -19.6988 26 5.1773 87 44.4442 55 -14.1043 27 -5.4513 89 20.2945 59 -17.1486 31 6.3774 91 5.2610 65 -8.5175

100 4.2279 103 -8.0555 107 -4.5227 110 -4.3124

TABLE 13: Case 3: Fault at Bus 89 with Dynamic Load

M/C No

Area1

Rotor angle,

() M/C No

Area2

Rotor angle, ()

M/C No

Area3

Rotor angle, ()

69 -2192.30 40 -2179.43 1 -2159.90 70 -2171.83 42 -2186.71 10 -2138.78 74 -2197.39 46 -2175.47 12 -2155.58 76 -2186.75 49 -2177.85 25 -2160.48 80 30.2364 54 -2180.32 26 -2153.83 87 62.0942 55 -2178.31 27 -2167.30 89 45.0147 59 -2179.87 31 -2155.18 91 29.2325 65 -2171.54

100 32.0114 103 23.1300 107 23.7278 110 24.6400

TABLE 14: Case 4: Fault at Bus 80 with Dynamic

Load 407

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