#### Transcript Today’s Topics - Department of Electrical Engineering

Today’s Topics 1- The per unit system 2-Transformer Voltage Regulation 3- Transformer Efficiency 4- Transformer Taps 5- Transformer Rating and Related Problems The Per Unit System In power systems there are so many different elements such as Motors, Generators and Transformers with very different sizes and nominal values. To be able to compare the performances of a big and a small element, per unit system is used. In per unit system, each electric quantity is measured as a decimal fraction of some base level Per Unit Value = Actual value Base value e.g. in a synchronous generator with 13.8 Kv as its nominal voltage, Instead of saying the voltage is 12.42 Kv, we say the voltage is 0.9 p.u. How Are the Base Values Defined For an electric element, we have : Power, Voltage, Current and Impedance Usually, the nominal apparent power (S) and nominal voltage (V) are taken as the base values for power and voltage The base values for the current and impedance can be calculated Sbase ,Vbase I base Sbase Vbase Z base Vbase V 2base I base Sbase Example 1: A load takes 20 A at a power factor 0.9 lead when connected to a 600 Voltage. If the base voltage and apparent power are 600 and 6000 VA, determine the variables and impedance in per unit system 600 Z 30 20 Sbase 6000,Vbase 600 I base Sbase 10 Vbase V 1 .0 Z base Vbase 60 I base Z 0 .5 I 2 .0 Ideal Transformers in Per Unit Values vp vs Np Ns ip Ns 1 is N p S p Vp .I p Vs .I s Ss S Sbase V p . I p Vs . I s V p ,base Vs ,base vp vs 1 ip is 1 Ignore the transformer Example: Given the transformer in the previous example rated at 20 kVA, 8000/240, calculate the equivalent circuit, with per unit values Sbase 20000 I p ,base Sbase 2 .5 V p ,base Z p ,base V 2 p ,base 3200 Sbase V p ,base 8000 Vs ,base 240 I s ,base Z p ,base Sbase 83.33 V p ,base V 2 p ,base 2.88 Sbase The equivalent circuit in per unit values Referred to the primary or secondary Transformer Voltage Regulation Fact: As the load current is increased, the voltage (usually) drops. Transformer voltage regulation is defined as: VR Vs ,nl Vs , fl Vs , fl Other useful formulas VR VP / a Vs , fl Vs , fl VR Vs ,nl Vs , fl VR Vs , fl VP Vs , fl Vs , fl Prefer small VR For an ideal transformer : VR=0 Note: If there were only resistive loads, the VR would not be much large in real transformers, but because loads normally have different power factors, VR may be considerably large in real transformers. VR in real transformers VR VP / a Vs , fl Vs , fl V P / a V s Req.I s jX eq.I s V P / a V s Req.I s jX eq.I s At unity power factor Resistive load At lagging power factor Inductive load At leading power factor Capacitive load Transformer Efficiency Pout Pin Pout Pout Ploss Pout PCu Pcore Pout Vs . I s . cos PCu Pcore Vs . I s . cos Is 2 PCu ReqP .( ) a 2 ReqP . I P Pcore 2 P V Rc PCu ReqS . I Pcore 2 P V Rc 2 S Transformer Taps The voltage in a distribution line is not constant. It may be 1.05 p.u. at generator terminal and 0.95 at the load side. Depending on the place the transformer is used, we may need to adjust the transformer ratio to get similar load voltage. That’s why we need Tap In Tap Changing Under Load (TCUL) transformer, the tap changes automatically to keep the output voltage constant Transformer Rating and Related Problems Transformers have three major ratings: Voltage, Apparent power (current) and frequency The parameters of equivalent circuit are given in p.u. As long as a transformer is working under rated conditions, there should be (is) no problem What should we consider if we want to use a transformer under de-rating conditions? Voltage rating The insulation has been designed to stand up to a particular voltage 10% increase in voltage in the linear part of B-H curve would result in 10% increase in magnetization current, but in the saturation part, the magnetization current may be unacceptable Frequency rating Exactly the same problem. If a 60 Hz transformer is going to be used in a 50 Hz system, the applied voltage should be reduced by a factor 5/6. Vm e Vm . cos t . sin t N . Apparent power (current) rating Each coil has limit for current magnitude and also the higher current results in higher power loss (which is converted to heat) and may damage the insulation. This has a dramatic effect on transformer life. If the voltage rating has been reduced, the apparent power should be reduced by the same factor. Current Inrush If a transformer is switched to a system, there may be some current with large magnitude (Current Inrush), in the first few milliseconds after the switch is closed. The reason behind the current inrush is transient Transients Transient in electrical systems is the severe changes in current and voltage after a switch is closed or opened Vm e Vm . cos t . sin t N .