A Critical Analysis of Transient Stability of Electrical Power System; A Case Study of Nigerian 330kv Power

A Critical Analysis of Transient Stability of Electrical Power System; A Case Study of Nigerian 330kv Power

Chapter One

THE OBJECTIVES OF THE STUDY

These include the following:

To determine the critical clearing angle and time of the Nigerian 330KV protection
To determine the behavior of the Nigerian power systemduring large scale disturbance and make necessary
To specify the circuit break speeds in thesystem
To determine the available transfer capability (ATC) of the Nigerian 330KV grid system during fault and make recommendation for improvement such that the system is transiently

CHAPTER TWO

CONCEPT OF ENERGY FUNCTION MODEL IN TRANSIENT STABILITYANALYSIS

In 1892, A.M Lyapunov, in his famous ph.D. dissertation, proposed that stability of the equilibrium of a non-linear dynamic system of dimension n can be ascertained without numerical integration.

According to this model, the critical clearing time of a circuit breaker can be interpreted in terms of meaningful quantities such as Maximum po.wer transfer in the pre-fault state.

x = f (x), f (0) = 0 (2.1)

He said that if there exists a scalar function V_(x) for equation (1) that is

position defini.te, for V_(x) > O around the equilibrium point “O” and the derivative V_(x) < O, then the equilibrium is asymptotically stable.. .

V(x) is obtained as Σ_i=1 ∂v xi =

∂x_i

Σi=1 ∂v fi (x) = (2.2)

Where n is the order of the system in (2.1)

Furthermore, in 1948, the application of the energy function model to power system stability actually began with the early work of Magusson and Aylett, followed by a formal application of the more general Lyapunov’s model by EL-Abad and Nagappan[19]

MODELLING ISSUES

A Power system undergoing a disturbance can be described by a set of three differential equations:-

x (t) = f¹ (x_(t)) – ∞ < t < 0 (2.3)

x (t) = f^f(x_(t) ) O < t < t_cl (2.4)

x (t) = f (x_(t) ) t_cl < t < ∞ (2.5)

x (t) is the vector of state variable of the system at time t. At t = 0, a fault occurs in the system and the dynamics change from fⁱ to f^f .

During 0<t < t_cl, called the faulted period, the system is governed by the fault – on dynamics if actually, before the fault is cleared at t = t_cl, we may have several switching in the network, each giving rise to a different f^f.

For simplicity, we have taken a single f^f, indicating that there are no structural changes between t = 0 and t = t_cl. When the fault is cleared at t = t_cl, we have the post fault system with its dynamics fⁱ (x_(t)).

However, the energy function methods have proved to be reliable after many decades of research for single machine system but for multi-machine system with complex network like that of Nigerian 330KV power system network, the value of the t_cl is not as reliable as that got with numerical integration method with digital computer. More research is still going on, on multi-machine system on this concept. [19]

NUMERICAL METHODS

Differential equations’ solution is highly restricted to the employment of numerical methods since accuracy is needed. In stability studies, non-linear highly-dimensional mathematical problems are encountered hence engineers resort to using numerical methods in their analysis. Numerical methods for the analysis of the steady state and dynamic (transient) behaviour of power system network are listed below:

STEADY STATE ANALYSIS. This is done by four methods viz:

Gauss – Elimination
Grammar’s rule.
Gauss – Jordan
Newton’s

The first three methods are suitable for linear expressions while the last two methods are suitable for linear and non-linear expressions.

DYNAMIC (TRANSIENT) STATE ANALYSIS

Nine methods are available for this analysis namely:

Euler
Improved Euler method.
Euler-Cauchy.
Adams-Bash forth fourth-order
Adams-Moulton fourth-order.
Gear’s
Finite Difference
Fourth-order Runge-Kutta
Crank-Nicolson method.

Note: Crank-Nicolson and finite difference methods are mainly used for the analysis involving partial differential equations, while the rest seven methods are very suitable for analysis involving-ordinary differential equations. [20]

CHAPTER THREE

Data Analysis and Simulation

PROJECTDESIGN

The quality of life in any country is highly dependent on a reliable electricity supply. In Nigeria, the electricity supply authority is unable in most cases to meet up with a reliable and efficient power supply to its consumers. The epileptic nature of the supply has led to low economic growth and dissatisfaction among the citizenry.

As the size and complexity of electric power system increase because of pressing economics and population, the desire to predict system behaviour more accurately will also increase. The digital computer has given the engineers the ability to predict in situations where complexity would have been two great before.

For multi-machine system like that of Nigerian power system, synchronism poses a great problem, when a machine or generator is out of synchronism within an electric power system. This affects the quality of supply to the consumers if it does not cause total collapse of such a system. These undesirable occurrences usually cause a great loss of revenue to the supplying authority and hardship to consumers because of the inability of the system to fulfill requirement of its customers. The undesirable factor of instability can be eliminated by carrying out the stability studies of the system so that the transient stability limit of the system loading can be determined.

Short circuit studies and load flow studies are carried out. These results are used in the stability analysis.

DATA SOURCES

Power holding company Plc. 330KV electrical network single Line diagram is used for this study. The generators, transmission lines and transformer parameters are taken from the most up-to-date data from National control centre, Oshogbo System Planning unit and system operations department. The subtransient reactance X¹¹ of the synchronous machines is used to give maximum fault levels at the instant of fault.

In a station where the number of machines is more than one, the machines are represented with a single unit by paralleling transient reactance and adding Inertia.

Line data for the equivalent system are used which contains a complex tap ratio.

There are two types of bus bars namely:

Load busbar
Generator busbar

At each bus bar the voltage is assumed to be (1.0 + j0.0)

CHAPTER FOUR

EXISTING 330KV NATIONAL GRID NETWORK

Chapter Five

CONCLUSION AND RECOMMENDATIONS

In this work, a suitable critical clearing time and angle has been achieved or obtained for Nigerian Power System so that our system will be able to survive any severe disturbance.

PHCN protection Engineers should endeavour to set their relay and circuit breaker operating time to clear fault at 60 milliseconds and it’s corresponding angle of 143.2⁰ or less than this time and angle. If this is done the incidence of power system collapse will be minimized to the barest minimum.

The persistent system collapse in the National grid is traceable to the inappropriate relay and circuit breakers operating time which is higher than 120 milliseconds [41],[42]. If the system is allowed to collapse, it takes time for the system to be revived and this leads to the customer’s frustrations and loss in revenue to PHCN.

RECOMMENDATION: It is very important to point out here that increasing the number of parallel lines between two points is a common means of reducing reactance. When a parallel transmission lines are used instead of a single line, some power is transferred over the remaining line even during a three – phase fault on one of the lines unless the fault occurs at a paralleling bus. Thus, the more power is transferred into the system during a fault, the lower the acceleration of the machine rotor and the greater the degree of stability, hence, a gain in critical clearing time can be achieved. Benin – Onitsha – Alaoji 330KV line is limited by a single line contingency. There is an urgent need to construct the second Benin – Onitsha 330KV circuit which had been under plan for some years past [40], [41], [42]. Also, construction of the proposed Alaoji – New Heaven – Markurdi – Jos 330KV circuit configuration should be expedited.

The results obtained from this work are used to predict the transient stability of the entire Nigerian power system since Egbin – Ikeja West is one of the heavily loaded 330KV line in the National grid.

REFERENCES

J. Stevenson, “Elements of Power System Analysis”, 4^thEdition, McGraw – Hill Inc, New York 1990

Central Station Engineers, “Electrical Transmission and Distribution References book”, Westinghouse Electric Corporation, East Rittsburgh, Pennsylvania
Gross, “A tool for the comprehensive analysis of power system dynamic stability”, IEE Transaction on power Apparatus and system Vol. 101, No. 1, pp. 226 – 234, April,1982.
A Fouad and S.E. Starton, “Transient stability of a multi- machine power system”, part 1 & 11, IEE Transaction on power systems vol. 100, No. 7, pp. 3408 – 3424, March,1981.
O. Okwu, “Power Distribution in Developing Economy; The Nigerian Perspective”, Newletter of the Nigerian Society of Engineers, Vol. No. 2, pp. 4-5 February,2007.
O.A. Awosope, C.C. Okoro & B.A.O. Ezeobi “An Assessment of the stability of the fault separated Nigerian Grid”, the Nigerian Engineer Vol. 23 No. 3, PP 75 – 91,I986.
Ernest, Pavella & D. Ruiz – Vega, “Transient stability of power system: A unified Approach to Assessment and control”, Kluwer Academic Publishers, Boston, September,2000.

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