Title: EE341 Energy Conversion Ali Keyhani Transformer Lecture
1 EE341 Energy Conversion Ali KeyhaniTransformer Lecture 2 3-Phase Transformer 2 3-phase Transformers
1.Three single-phase transformers connected in a three-phase bank.
2. Three sets of windings wrapped on a common core.
Three-single phase transformers are connected grounded Y-Y to two three phase loads connected in and Y
a)Draw single-line diagram.
b)The single-phase equivalent circuit with transformer referred to HV side.
c)P.U equivalent circuit
4 (No Transcript) 5 a)
6 b) 7 c) 2. Y- 3. -Y 4. - 1. Y-Y Y-Y 8 (No Transcript) 9 The voltage ratio of each phase The line voltage ratio From the above 10
Y-. The secondary voltage is shifted 30 relative to the primary voltage.
Because of the phase shift. transformers can not be connected in parallel unless they have proper phase sequence. (ie. They are in phase with each other).
Y Y parallel Y- NO
Y- parallel Y- Yes. However you must identify the correct phase sequence.
12 -Y From above we have 13
For -Y connection the secondary Voltage Lags the primary Voltage by 30
- - for 14 Problem 2
Three identical single-phase transformers each rated 12.7kv/196.3kv 333.33 MVA 14short circuit leakage reactance are connected at (a) Y-Y (b) -Y. IF transformer banks (ie. Y-Y or -Y) are fully loaded at utility power factor and loads are connected to HV windings compute the required voltage to be supplied to LV windings.
15 Solution pf1.0 pf1.0 16 -Y 17 Problem 1
Three single-phase transformers each rated at 4.4 kVA 220 volts(primary) to 440 volts (secondary) 60cps gave the following test results on open and short circuits tests. When the rated voltage was applied to the primary side .77 amp and 73 watts were measured at the primary winding with the secondary winding open-circuited. When 3.41 of the rated secondary voltage was applied to the secondary winding with the primary winding short-circuited 10 amp and 60 watts were measured at the primary winding. Transformers are connected as a tree phase Y-Y. Determine
a) Estimate the parameters(ie. RmXmRs and Xs) draw the one phase equivalent circuit. and p.u Eq. circuit
b) Determine the required primary voltage when the 3 Y-Y transformer is supplying full load at a power factor of .6 lagging and rated voltage.( Ignore Xm and Rm ). You must use per unit analysis.
18 Solution 19 (No Transcript) 20 (No Transcript) 21 (No Transcript) 22 P.U. equivalent circuit 23 Open Delta 24 (No Transcript) 25 (No Transcript) 26 For open delta 27 The output of the open-delta bank is only 57.7 percent of the original banks rating. What happens to the rest of the open-delta banks rating To find out examine the Q of the open delta bank. Trans 1 Trans 2 28 Thus one transformer is producing reactive power which the other one is consuming. It is this power exchange of energy back and forth between the two transformers that limits the power output to 57.5 percent of the original banks rating instead of the otherwise expected 66.7 percent. 29 Per-Unit Circuit One-phase circuits Where 30 (No Transcript) 31 Three-phase circuits 32 The Zb is defined for one-phase circuits 33 (No Transcript) 34 Example Three single-phase 2SkVA 34500/277 Volts transformers are connected in -Y. Test measure----/---- on high voltage side with the low voltage side short circuited gives the following data. Determine the P.U. Equivalent circuits 35 Method1 Using -Y 36 Method 2 Using Y-equivalent 37 (No Transcript) 38 j j j j 39 j 40 Example 41 j RsjXs jXM 42 (No Transcript) 43 jXM 44 jXM jXs 45 Example 2
An electric lamp is rated 120 volts and 500 watts. If the voltage applied across the lamp is twice the rated value compute the per-unit current that flows through the lamp. Use the per-unit method.
46 jXs 47 RsjXsZs 48 (No Transcript) 49 Voltage Regulations a)VPRI/VSEC
Vfl Desired load voltage at full load. It may be equal to rated voltage above or below the rated voltage.
Vnl is the no-load rated voltage(ie. When the pri. voltage has the desired value in order the sec. voltage be at its desired value at full load)
A single-phase transformer rated 200kVA 200/400V and 10 short circuit reactance. Compute
a) The VR when the transformer is fully loaded at unity power factor and rated voltage of 400V.
b)same except the load voltage is ten percent above its rated value.
51 j0.10 j0.10 52 (No Transcript) 53 (No Transcript) 54
Problem 1 Three identical single-phase transformers rated each 12.7kV/196.3kV 333.33MVA 14 short circuit leakage reactance are connected at (a) Y-Y (b) -Y. If transformer banks (ie. Y-Y or - -Y) are fully loaded at unity power factor and loads are connected to HV windings compute the required voltage to be supplied to LV windings.
Problem 2. Three single-phase transformers each rated at 4.4 kVA 220 volts (primary) to 440 volts (secondary) 60 cps gave the following test results on open and short circuit tests. When the rated voltage was applied to the primary side .77 amp and 73 watts were measured at the primary winding with the secondary winding open-circuited. When 3.41 of the rated secondary voltage was applied to the secondary side 10 amps and 60 watts were measured at the secondary winding with the primary winding short-circuited. Transformers are connected as a three phase Y-Y. Determine
(20 points) a) Estimate the parameters(ie. Rm Xm Rs and Xs) draw the one phase equivalent circuit and p.u Eq.CKT
(20 points) b) Determine the required primary voltage when the 3 Y-Y transformer is supplying full load at a power factor of .6 lagging and rated voltage. (Ignore Xm and Rm). You must use per unit analysis.
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