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S3: Power System Calculations
24 EEE8044: Fundamentals
Section 3
Power System Calculations
Introduction
In this section we will perform line voltage, power and reactive power 数学建摸论文calculation based onthe line models developed earlier. We will also introduce the per unit method of analysis sowidely used by power engineers and then use this method to carry out some relatively
simple load flow and fault level calculations.Learning Outcomes
On completion of this section you will be able to:
􀂃 Apply the per unit method of analysis to perform power system calculations.
􀂃 Calculate system fault levels for balanced three-phase fault conditions.
􀂃 Perform simple 2 busbar load flow calculations.
Time
You will need about 3 to 4 hour for this section.
Resources
Calculator, pen and paper.
S3: Power System Calculations
25 EEE8044: Fundamentals
3.1 Transfer of Impedance
Power system calculations often involve transformers and circuits at many differentvoltage levels. The values of effective transformer resistance and reactance depend onwhether the circuit being studied is at the high voltage side or the low voltage side of thetransformer.
Similarly, the impedances of generators, lines and other circuit elements must betransformed to the values appropriate to the voltage level under consideration beforecarrying out circuit calculations.
Fig. 3.1 shows a simple equivalent circuit of a single-phase transformer supplying a loadwith impedance ZL. Z1, Z2 are the series impedances of the primary and secondarywindings, respectively.
To study the system on the primary side of the transformer (side 1), the impedances on thesecondary side (side 2) must be multiplied by the factor (V1 ⁄ V2)2. Similarly, if we wish toperform the calculations on side 2, then the series impedance Z1 must be multiplied by (V2 ⁄
V1)2.
Z1 Z2
ZL
V1 V2
I1 I2
1 : N
Fig. 3.1 Transfer of impedance.
S3: Power System Calculations
26 EEE8044: Fundamentals
3.2 The Per Unit System
In analysing power networks, electrical engineers often prefer to use per unit (p.u.) orpercentage (%) values of system variables instead of using the actual values of voltages,impedances, etc.
The per unit value of any quantity is a fraction defined by
base valueper unit value = actual value (3.1)
The use of this method generally give a better relative sense of the variables underconsideration allowing apparatus of widely varying sizes and ratings to be compared witheach other in terms of losses, voltage drops, etc. The use of per unit values can also be usedto avoid problems of transforming impedances across different voltage levels in complexnetworks involving a large number of voltage steps.
Of the four major quantities (voltage, current, impedance and voltamperes), two basevalues may be chosen independently. Common practice is to define a 3-phase VA base anda line voltage base, corresponding to the rated values of the equipment being used. The
base values of the other two quantities (current and impedance) are then fixed.
In the following sections we will look at how base values are usually selected for threephase
p.u. calculations.
3.2.1 Base Voltage
The base voltage is usually the nominal line-to-line voltage in a three-phase system.
Vbase = VL = √3 Vp (3.2)
where VL is the rms line voltage and Vp is the rms phase voltage.
3.2.2 Base Power