Power SystemAnalysis and Control (EET 408) Laboratory Module

EXPERIMENT 2

Analysis the power flow with NEWTON-RAPHSON method

1. Objective:

To analyze the power flow on the power system by means of Newton-Raphson method with MiPower software

2. Equipment:

MiPower software

3. Introduction:

Power Balance Equations

1

Resolving into the real and imaginary parts:

2

We see that Eq. 2.5.6 is analogous to the nonlinear equation y = f(x), solved in Eq 2.5.2.2. We define the x, y and f vectors for the power-flow problem as

2.5.2.8

where: V, P and Q terms in per-unit

terms are in radians

For slack bus variables 1 and V1 are omitted from Eq.2.5.2.8 because they are already known. Equation 2.5.2.6 then has the following form:

2.5.2.9

where:

j = 2, 3, ……..n

if j = i -à

For load bus:

The known values are: real power demand to load at bus i = PLi

Reactive power demand to load at bus i = Qi

The known values PLi and QLi correspond to y in Eq 2.5.2.1 and also correspond to the ∆f mismatches of Eq.2.5.2.1, and by writing the power mismatches for typical load bus i:

2.5.2.10

For example system with four buses, for real power Pi, we have

2.5.2.11

The last three terms can be multiplied and divided by their respective voltage

magnitudes without altering their values, and so we obtain

2.5.2.11

Similarly, the mismatch for reactive power Qi can be written

2.5.2.13

Each non slack bus of the system has two equations like those for ∆Pi and ∆Qi.

Generally, for system with n bus collecting the mismatch equations into vector-matrix form yields

2.5.2.14

For the slack bus:

1.  Mismatches cannot include because ∆P1 and ∆Q1 are undefined when P1 and Q1 are not scheduled.

2.  All terms involving and are omit from Eq 2.5.2.14 because those corrections are both zero at the slack bus.

The partitioned form of Eq 2.5.2.14 emphasizes the four different types of partial derivatives which enter into the Jacobian J.

The solution of Eq 2.5.2.14 is found by iteration as follow;

1. Estimate values and for the state variables

2. Use the estimates to calculate:

and from Eq 2.5.2.9 , mismatch and from Eq 2.5.2.10, and the partial derivative elements of the Jacobian J.

3.  Solve Eq 2.5.2.14 for the initial estimates to obtain

2.5.2.15

4. Use the new values and as starting values for iteration 2 and continue.

In more general terms, the update formulas for the starting values of the state variables are:

2.5.2.16

The elements of the submatrix J11:

The diagonal elements :

2.5.2.17

The off-diagonal elements: 2.5.2.18

The elements of the submatrix J21:

The diagonal elements :

2.5.2.19

The off-diagonal elements: 2.5.2.20

The elements of the submatrix J12:

The diagonal elements :

2.5.2.21

The off-diagonal elements = The off-diagonal elements J21 :

2.5.2.22

The elements of the submatrix J22:

The diagonal elements:

2.5.2.23

The off-diagonal elements:

2.5.2.24

4.  procedure

Figure 2.1

Figure 2.1 shows a single line diagram of a 5 bus system with two generating units, seven lines. Per-unit transmission line series impedances and shunt susceptances are given on 100 MVA base in Table 2.1. Real power generation, real and reactive power loads in MW and MVAR are given in Table 2.2.

With Bus 1(North) is a slack bus, obtain a load flow solution by using Newton-Raphson method with tolerance of 0.01 per-unit for the real and reactive bus powers.

Bus code
From – to / Impedance
R +jX / Line Charging
B/2
1 - 2 / 0.02+j0.06 / 0.0+j0.030
1 -3 / 0.08 + j 0.24 / 0.0 + j0.025
2-3 / 0.06 + j0.18 / 0.0 + j0.02
2-4 / 0.06 + j0.18 / 0.0 + j0.02
2-5 / 0.04 + j0.12 / 0.0 + j 0.015
3-4 / 0.01 + j0.03 / 0.0 + j0.010
4-5 / 0.08 + j0.24 / 0.0 + j0.025

Table 2.1

Bus
No / Bus Voltages / Generation
MW / Generation
MVAR / Load
MW / Load
MVAR
1 / 1.06+j0.0 / 0 / 0 / 0 / 0
2 / 1.00+j0.0 / 40 / 30 / 20 / 10
3 / 1.00+j0.0 / 0 / 0 / 45 / 15
4 / 1.00+j0.0 / 0 / 0 / 40 / 5
5 / 1.00+j0.0 / 0 / 0 / 60 / 10

Figure 2.2

Element Data / Generator 1 / Generator 2
Manufacturer Ref No / 30 / 2
No of Units Parallel / 1 / 1
Specified Voltage / 220 / 220
De-rated MVA / 100 / 50
Schedule Power / 80 / 40
Real Power Min / 0 / 0
Real Power Max / 80 / 40
Reactive Power Min / 0 / 30
Reactive Power Max / 60 / 30

Table 2.3

Generator 2 Library Data
MVA Rating / 50
MW Rating / 40
kV Rating / 220
Manufacturer Name / Gen2

Table 2.4

1.  Double click the MiPower icon on your pc screen.

2.  Follow the procedure in first experiment (Introduction to MiPower) to draw and input all the data and elements.

3.  For transmission line, load and generation database, use the data from Table 2.1 and 2.2.

4.  For Generator database, use the data from Table 2.3 and 2.4.

5.  After inputting the entire database, click SolveLoad Flow Analysis in the Network Editor screen. Load Flow Analysis windows will appear. Click on Study Info. Load Flow Studies windows will appear.

6.  On Load Flow Studies popped windows, check Newton-Raphson box, and set the P and Q tolerances at 0.01.

7.  After execute, save the report in your pc and print it out.

8.  To plot the results on the single line diagram, on the Network Editor screen, click Plot Load Flow Analysis. Select Pu-Angle on the Voltage Unit dialog box and MW-Mvar option on Flow Unit dialog box.

9.  Draw the single line diagram with the power flows and losses.

10.  What are the real and reactive power flows between all the buses?

11.  What is the total reactive and real power flows in the system?

12.  What is the total real power generation and its power factor?

13.  To analyze contingency analysis, Click RMB on the element button to be opened (out of Service). For this case transmission line 1-3. Select menu

Element Status Open.

13. Select Menu option Configure Save Contingency to save the contingency in database. Following windows will appear

14.  Execute Load Flow Analysis.

15.  Are there any transmission line overloaded (exceed its thermal rating)? And which bus?

16.  What is the power flows between bus 1 and 2 and its power loss?

QUESTION

1.  For the above power system, conduct the load flow analysis by utilizing the Gauss Siedel method. Draw the single line diagram with the power flows and losses. Compare the result to Newton Raphson method. States your observations.

2.  Figure 2 below shows a single line diagram of a three-bus power system with generation at bus 1 and 2. The voltage at bus 1 is per unit. Voltage magnitude at bus 2 is fixed at 1.05 pu with a real power generation of 400MW. Load at bus 3 is 400MW and 250MW. Line admittance are marked at 100MVA base.

a) Using Newton-Raphson method, with initial estimate value

and and keeping I I = 1.05 pu, determined the value of

. Perform 3 iterations.

b)  Perform the power flow solution for above problem using MiPower. Compare your results. State of observations.

ANSWER

10.

11.

15.

16.

Conclusion

Discussion

10

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