This document discusses power system analysis and focuses on generalized circuit constants. It provides an overview of topics covered in the course including generalized circuit constants, representation of power systems, symmetrical faults, symmetrical components, and power system stability. It then discusses generalized circuit equations and how the input voltage and current of a transmission line can be expressed in terms of output voltage and current using circuit constants A, B, C, and D. Finally, it shows how to determine the circuit constants for simple series and parallel circuits and combined networks using nominal T, nominal pi, and rigorous methods.

1. Power System Analysis
Presented By: Engr. FAZAL UR REHMAN
Lecturer Electrical KPTEVTA
Visiting Lecturer COMWAVE INSTITUTE ISLAMABAD

2. Course Objectives
 This course is focused on
 Generalized Circuit Constants
 Representation of Power System
 Symmetrical Three Phase Faults
 Symmetrical Components
 Unsymmetrical Faults and
 Power System Stability.

3. Today's Topics
Generalized Circuit Constants
 General Circuit Equation
 Generalized Constants of simple network
 Constants of combined network

4. General Circuit Equation
 In any four terminal network, the input voltage and
input current can be expressed in terms of output
voltage and output current.
 Incidentally, a Circuit Constants of a Transmission
Line is a 4-terminal network ; two input terminals
where power enters the network and two output
terminals where power leaves the network.
 Therefore, the input voltage (VS) and input current (IS)
of a 3-phase Circuit Constants of a Transmission Line
can be expressed as :

6.  A,B,C and D (generally complex numbers) are the
constants, known as Generalised Circuit
Constants of the transmission line.
 The values of these constants depend upon the
particular method adopted for solving a Circuit
Constants of a Transmission Line.
 Once the values of these constants are known,
performance calculations of the line can be easily
worked out.

7.  The constants A,B,C and D are generally complex
numbers.
 The constants A and D are dimensionless whereas
the dimensions of B and C are ohms and Siemens
respectively.
 For a given transmission line,
 For a given transmission line,

8. Generalized Constants of simple
network
 As stated previously, the sending end voltage (VS) and
sending end current (IS) of a transmission line can be
expressed as :
 The values of these constants A, B, C and D can be found
for simple networks as follows;

9.  Simple Series
Impedance Circuit
 Comparing with standard equations we get;

10. Experimental Determination

12.  Simple Parallel Admittance Circuit
Vs = Vr + 0 * Ir
And
Is = Yp Vr + Ir
Comparing with equation 1 and 2. we get;
A = 1, B= 0, C= Yp and D= 1

13. Constants of combined network

16.  Medium lines — Nominal T method. In this
method, the whole line to neutral capacitance is
assumed to be concentrated at the middle point of the
line and half the line resistance and reactance are
lumped on either side as shown in Fig. 10.24.

18.  Substituting the value of V1 in eq. (v), we get,
 Substituting the value of IS, we get,

19.  Comparing eqs. (vii) and (vi) with those of (i) and (ii),
we have,

20.  Medium lines—Nominal π method. In this
method, line-to-neutral capacitance is divided into
two halves ; one half being concentrated at
the load end and the other half at the sending end as
shown in Fig. 10.25.

22.  Putting the value of VS from eq. (x), we get,

23.  Comparing equations (x) and (xi) with those of (i) and
(ii), we get,

24.  Long lines—Rigorous method. By rigorous method,
the sending end voltage and current of a long Circuit
Constants of a Transmission Line are given by :
 Comparing these equations with those of (i) and (ii),
we get,