01․ A transmission line has a surge impedance of 400 Ω is connected with the cable having surge impedance of 40 Ω, a surge magnitude of 100 kV is travelling from the transmission line towards the cable. Find the reflected voltage?
Transmitted voltage V" = V + V'
Transmitted current I" = I + I'
Transmission or reflection coefficient of voltage Tv = V"/V
Transmission or reflection coefficient of current Ti = I"/I
I" = V"/Zl, I = V/Zs, I' = -V'/Zs
V"/Zl = V/Zs - V'/Zs
V' = V" - V
Therefore, Tv = V"/V = 2Zl/(Zl + Zs)
Reflection coefficient of voltage is Rv= V'/V = Tv - 1
Rv = V'/V = (Zl - Zs)/(Zs + Zl)
02․ Surge impedance loading of a line is increased by which of the following compensation methods?
Surge impedance Zs = √(L/C)
Surge impedance loading SIL = Vl² *√(C/L)
Shunt capacitor compensation:
After shunt capacitor compensation new surge impedance Zn = √(L/C(1 + Kcsh))
Where Kcsh = Degree of shunt capacitance = Csh/C
Therefore, new surge impedance Zn = Zs/√(1 + Kcsh)
New surge impedance loading SILn = SIL*√(1 + Kcsh)
Series capacitor compensation:
New surge impedance Zn = Zs*√(1 - Kse)
New surge impedance loading SILn = SIL/√(1 - Kse)
Shunt reactor compensation:
New surge impedance Zn = Zs/√(1 - Kcsh)
New surge impedance loading SILn = SIL*√(1 - Kcsh)
Therefore, surge impedance loading of a line increases by shunt capacitor compensation and series capacitor compensation and surge impedance loading decreases with shunt reactor compensation.
03․ A transmission line has surge impedance of 400 Ω, operating at Vs = Vr = 400 kV line is compensated with a shunt capacitance of 30%. Find the surge impedance loading with compensation?
Surge impedance loading with out compensation
SIL = Vl²/Zs = (400*10³)²/400 = 400 MW
Surge impedance loading with shunt capacitance compensation
Shunt capacitor compensation:
After shunt capacitor compensation new surge impedance Zn = √(L/C(1 + Kcsh))
Where Kcsh = Degree of shunt capacitance = Csh/C
Therefore, new surge impedance Zn = Zs/√(1 + Kcsh)
New surge impedance loading SILn = SIL*√(1 + Kcsh)
SILn = 400*√(1+0.3) =456 MW
04․ A transmission line has surge impedance of 400 Ω, operating at Vs = Vr = 400 kV line is compensated with a shunt capacitance of 30%. The line is connected to a generator delivering 200 MW. Find the load angle with out and with compensation respectively?
With out compensation:
With compensation:
With compensation:
05․ If the load is short circuited, then reflection coefficient of voltage is
Transmission or reflection coefficient of voltage Tv = V"/V
Transmission or reflection coefficient of current Ti = I"/I
I" = V"/Zl, I = V/Zs, I' = -V'/Zs
V"/Zl = V/Zs - V'/Zs
V' = V" - V
Therefore, Tv = V"/V = 2Zl/(Zl + Zs)
Reflection coefficient of voltage is Rv = Tv - 1
Rv = (Zl - Zs)/(Zs + Zl)
When load is short circuited, V" = 0
Therefore, Tv = 0 and Rv = -1
06․ The Y bus matrix of a 100 bus interconnected system is 90% sparse. Then find the number of non zero elements in the Y bus matrix?
Sparsity of Y bus matrix = Number of zero elements/ Total number of elements
Total number of elements for 100 bus = 100*100 = 10000
Number of zero elements = 0.9 * 10000 =9000
Therefore, number of non zero elements = 1000
07․ At slack bus, which one of the following combinations of variables is not specified?
Load bus:
Known quantities - P and Q
Unknown quantities - V and δ
Generator bus:
Known quantities - P and V
Unknown quantities - Q and δ
Slack or reference bus:
Known quantities - V and δ
Unknown quantities - P and Q
08․ Which of the following statements are true?
Y bus matrix is a sparse matrix, containing more number of zero elements. So that faster calculation is possible. The Y bus matrix is used for the load flow studies.
Z bus algorithm or matrix is used for the fault analysis. Inverse of Y bus matrix gives the Z bus matrix, But Z matrix is a full matrix even though Y bus is a sparse matrix. More time is required for inverse of Z bus matrix if the size of the matrix is more than three.
But a practical system network has large number of buses and hence Z bus matrix is not uses for the load flow analysis, Y bus is preferred.
09․ Which of the following statements is/are true?
The elements of each row of a Y bus matrix for load flow studies in power system add up to zero
Properties of Y bus matrix:
1. Y bus is a square matrix.
2. For n bus power system size of Y bus matrix is n*n
3. Value of diagonal element corresponding to bus i, then
Yii = Sum of the admittances connected to bus i.
4. The value of off diagonal elements Yij = Yji , which is connected between bus i and bus j and which is represented with negative sign.
5. Sum of the elements of row i equal to shunt admittances connected to bus i. If this summation is zero, indicates there is no shunt admittance and mutual coupling between the transmission lines.
10․ In a Gauss Seidel load flow method, the number of iterations may be reduced if the correction in voltage at each bus is multiplied by
Advantages of gauss siedel method:
1. It is a simple algebraical equation, so that calculation time for each iteration is less.
2. More suitable for small size networks.
Disadvantages of gauss siedel method:
1. More number of iterations are required, so that it has slow convergence.
2. Initial approximate guessing value is required for convergence.
3. It required accelerating factor for convergence.
4. The choice of slack bus affects the convergence.
5. It is not applicable for the large power system networks.
Accelerating factor is used for reducing number of iterations using Gauss Seidel method.
The value of accelerating factor is around 1.6 to 1.8 .
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