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stritchick

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## Homework Statement

The objectives of this exercise is to develop a load flow algorithm based on Gauss Seidel method and then investigate the phenomena of transport of active and reactive power over transmission networks.

**Background**

A remote load centre is supplied by a remote hydro generating station over a 210 km long transmission circuits that operates at 275kV and local fossil fuel generator, as shown below in Figure 1.

The analysis required will be performed using a Gauss Seidel Power Flow that you are required develop in Matlab. Convergence criteria should be 0.1% power mismatch.

**System Data**

Transmission Lines

Construction: 2 x 0.4 square inches Steel Cored Aluminium (SCA duplex) per phase, per circuit.

Zline = 0.067 + j 0.32 ohm/km/circuit

Length = 210 km, switched at 70 km intervals

Rating: 275 kV, 450 MVA

Transformers

Step-up transformer:

275/18 kV, 450 MVA

9% reactance (on rating)

± 10% taps on the 275 kV windings

Step-down transformer:

275/66 kV, 450 MVA

11.57% reactance (on rating)

± 10% taps on the 275 kV windings

Local generator transformer:

66/11 kV, 400 MVA

5.7% reactance (on rating)

± 10% taps on the 66 kV windings

Generators

Hydro generator: 450 MVA at 0.8 p.f. lagging, 18kV. XS = 1.2 p.u., RS = 0.003 p.u.

Local generator: 400 MVA at 0.8. p.f. lagging, 11kV, XS = 2.0 p.u., RS = 0.004 p.u.

Note that all parameters given in p.u. are calculated on the basis of the equipment rating.

## Homework Equations

Power System Analysis

4.1 Performance at the unity power factor

Run power flow calculations for loads of 50, 100, 150, 200 and 350 MW with both line circuits connected (with the local generator disconnected). Record and present load and generator active and reactive powers, losses in transformers and overhead lines, voltage magnitudes and phases at all buses, as well as the number of interactions required for the load flow to converge. All your results that are presented in tables need to be explained. Observe trends and discuss your results.

4.2 Performance at 0.9 p.f. lagging

Change the load power factor to 0.9 lagging by introducing an appropriate MVAr component. Repeat the calculations of section 4.1. You will notice that for larger load values, the voltage at the load bus becomes unacceptably low and that for some values of load the power flow may not converge. Observe trends and discuss your results.

4.3 Performance with reactive power compensation

A way to correct the voltage problem is to connect a source of reactive power near the load bus. We will use the local generator to represent a synchronous condenser (a synchronous machine which is operated as a motor with no load and whose excitation is adjusted so that it produces reactive power). This synchronous condenser can be operated as a reactive power source or as a voltage control source. When it is operated as a reactive power source, the amount of VARs it produces is kept constant. On the other hand, when it is operated as a voltage source, its reactive output is adjusted to keep its terminal voltage constant.

Repeat the computations of section 4.2 for the following conditions:

The reactive output of the condenser set at 50 MVAr.

The voltage at the terminals of the condenser set a 1.0 p.u.

Observe trends and discuss your results.

4.4 Performance with local generation

Due to an economic boom unanticipated by the planners, the demand has grown up to 500 MW at 0.9 p.f. lagging. What is the minimum of active power that the local generator should produce (assuming it operates in voltage control mode) to avoid overloading the transmission system, in case when one of the lines is on outage?

5. Reporting

Present your results in a short report that should include the following sections: Introduction, Gauss Seidel Load Flow formulation, Algorithm and Implementation, Case studies (covering the analysis in 4.1 – 4.4, with discussion), Conclusions and an Appending with your code.

## The Attempt at a Solution

I have tried but I am still stuck. Would really appreciate some help!

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