Laboratory 1 – Power System Representation and Equations

LABORATORY 1 POWER SYSTEM REPRESENTATION AND EQUATIONS

Student Name: Sanzhar Askaruly

Student ID: 201100549

Student Group: Session 1

Laboratory 1 – Power System Representation and Equations

INTRODUCTION

The purpose of this experiment is to investigate one-line diagrams, the power system representation in per-phase, per-unit equivalent circuits as well as node equations for these equivalent circuits. The experimental circuit is then constructed in PowerWorld simulator.

THEORY

Almost all modern power systems are three-phase systems, with similar phases equal in amplitude and shifted in phase from each other by 120 degrees. Because the three phases are all similar, it is customary to sketch power systems in a simple form with a single line representing all three phases of the real power system. When combined with a standard set of symbols for electrical components, these one-line diagrams provide a compact way to represent a great deal of information. Some of the standard symbols used in one-line diagrams are shown in figure 1.

Figure 1. Symbols used in power system one-line diagrams

Figure 2 shows a one-line diagram of a simple power system. This system contains of two synchronous machines, two loads, two busses, two transformers, plus a transmission line to connect two busses together.

Figure 2. A one-line diagram of a simple power system

Once the per-phase, per-unit equivalent circuit of a power system is created, it can be used to find the voltages, currents and powers present at various points in a power system. The most common technique used to solve such circuits is nodal analysis. We use Kirchhoff’s current law to determine the voltages at each node (each bus) in the power system, and then use the resulting voltages to calculate the currents and power flows at various points in the system.

Laboratory 1 – Power System Representation and Equations

RESULTS

Figure 3 shows a one-line diagram of a three-phase power system. The ratings of the various components in the system are:

Synchronous Generator 1: 40 MVA, 13.8 kV, R = 3%, XS = 80%

Synchronous Motor 2: 20 MVA, 13.8 kV, R = 3%, XS = 80%

Synchronous Motor 3: 10 MVA, 13.2 kV, R = 3%, XS = 100%

Y-∆ Transformers: 20 MVA, 13.8/138 kV, R = 2%, X = 10%

Line1: R = 10 Ω, X = 50 Ω

Line2: R = 5 Ω, X = 30 Ω

Line3: R = 5 Ω, X = 30 Ω

The per-unit system base for this power system is 40 MVA, 128 kV in transmission line 1. First, to find out admittance matrix and impedance matrix, analytical solution is developed.

SOLUTION

Figure 3. One-line diagram of the power system

Laboratory 1 – Power System Representation and Equations

Laboratory 1 – Power System Representation and Equations

Due to the fact that base quantities are the same for all transformer impedance, these are:

The admittance of the circuit is calculated from:

Laboratory 1 – Power System Representation and Equations

Obtained results of admittances and impedances are collected into the Figure 5 and Figure 7, presented below

Figure 4. Circuit shown in the form of admittances

Figure 5. Analytical solution of admittances matrix

Figure 6. Empirical result of admittances matrix obtained from simulation

In fact, It can be noted that some degree of error is still present between analytical solution and the one which was obtained with PowerWorld. This is due to the fact that analytical solution is not exact, whilst software program tries to approximate until some small degree of error. In general, values obtained can be used in educational purpose. However, if the real power system is to be analyzed, more proper approach such as software is to be used.

Laboratory 1 – Power System Representation and Equations

The bus impedance matrix Z!"#equals to

Figure 5. Analytical solution of Z bus matrix

The diagram, which was simulated in PowerWorld software is presented below.

CONCLUSION

As it was mentioned in the beginning, The purpose of this experiment is to investigate one-line diagrams, the power system representation in per-phase, per-unit equivalent circuits as well as node equations for these equivalent circuits. The experimental circuit was then constructed in PowerWorld simulator. Moreover, Ybus and Zbus results were calculated analytically, and then Ybus results were compared to the empirical values of admittances, taken from PowerWorld simulator. In conclusion, we were introduced to PowerWorld simulator, tried to build simulate real power diagram, obtained the results and compared to analytical solution. Hence, it can be considered that the goals were achieved.