3W Transformer Test Report Impedance Calculator Equations. Use these Equations for: Primary Secondary Primary Tertiary Secondary - Tertiary
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1 W ransformer est Report Impedance Calculator Equations Loss = est Report Load Losses ot otal Losses Base = est Report MVA %Z = est Report rimary econdary %Impedance VHigh est = est Report rimary Voltage VLow est = est Report econdary Voltage VHigh = ominal ystem rimary Voltage VLow = ominal ystem econdary Voltage Loss Base %Z 100 R pu Change to 100MVA Base: R pu@100 = R pu 100 Base X pu@100 = X pu 100 Base if est Voltage ominal ystem Voltage: Voltage Base Change is Required if VLow est VLow: R pu X pu VLow est VLow VLow est VLow if VHigh est VHigh AD VLow est = VLow: R pu X pu VHigh est VHigh VHigh est VHigh Use these Equations for: rimary econdary rimary ertiary econdary - ertiary
2 IEEE hree Winding ransformer Zero equence Impedance esting rocedure and Equations IEEE requires three () separate test procedures. First test is used to determine a quantity known as Z1no. ame phase Voltage source is applied between the three rimary and eutral terminals. econdaries are left open. hase Voltage is increased until current reaches some arbitrary amount that prevents overloading the ertiary he applied Voltage, resulting total current and phase power are recorded. econd test is used to determine a quantity known as Z1ns. ame phase Voltage source is applied between the three rimary and eutral terminals. econdaries are shorted to eutral. hase Voltage is increased until current reaches some arbitrary amount that prevents overloading the econdary he applied Voltage, resulting total current and phase power are recorded. hird test is used to determine a quantity known as Zno. ame phase Voltage source is applied between the three econdary and eutral terminals. rimaries are left open. hase Voltage is increased until current reaches some arbitrary amount that prevents overloading the ertiary he applied Voltage, resulting total current and phase power are recorded. I est Other hases est Other hases I est est V measured V Ф V Ф V measured
3 he measured data is then mathematically corrected to determine the Z, R, and X for each test. First Consider the Impedance magnitudes Z for each test Recall or realize that the per-unit Impedance magnitude is the ratio of the test voltage required to produce rated phase current divided by the rated test voltage. However, the test voltage applied was not enough to produce the required current herefore, a correction is needed. Z1no test: I ri (rated) = Base (test) V LL ri (rated) V ri (rated) = V LL ri (rated) I ri (rated) V (corrected) = V (test) = V (corrected) Z pu Z pu = V ri (rated) V (test) V LL ri (rated) I ri (rated) Z1ns test: I ri (rated) = Base (test) V LL ri (rated) V ri (rated) = V LL ri (rated) I ri (rated) V (corrected) = V (test) = V (corrected) Z pu Z pu = V ri (rated) V (test) V LL ri (rated) I ri (rated) Zno test: I ec (rated) = Base (test) V LL ec (rated) V ec (rated) = V LL ec (rated) I ec (rated) V (corrected) = V (test) = V (corrected) Z pu Z pu = V ec (rated) V (test) V LL ec (rated) I ec (rated) ote: Z1no, Z1ns, Zno are different measurements and calculations.
4 ext Consider the real power measurements. Real power delivered (losses) is used to determine Resistance. However, losses under full load are needed to determine the Resistance. o the loss measurements are scaled up to reflect full load conditions Z1no test: loss = test loss = 9 test I ri (rated) I ri (rated) Z1ns test: loss = test loss = 9 test I ri (rated) I ri (rated) Zno test: loss = test loss = 9 test I ec (rated) I ec (rated) Calculate Resistance: loss Base (test) loss Base (test) loss Base (test) Calculate Reactance: Z pu Rpu Z pu Rpu Z pu Rpu Reactance does not change with emperature. Done with this part... Z1no = R pu + jx pu Z1ns = R pu + jx pu Z1no = R pu + jx pu
5 But Wait a second, if you are really particular I R losses are emperature dependent. Resistance of the copper windings increase with emperature. IEEE requires that the test temperature of the transformer oil be recorded test used for this example. Losses under full load and maximum operating temperature are needed to rate the ransformer Resistances. Maximum transformer operating temperature is typically 65 C above accepted lab temperature of 0 C or 85 C. o, the losses are again mathematically corrected for maximum operating temperature. Use: 5.0 for aluminum windings Z1no test: max loss = loss test loss Base (test) Z pu = R pu + jx pu Z1ns test: max loss = loss test loss Base (test) Z pu = R pu + jx pu Zno test: max loss = loss test loss Base (test) Z pu = R pu + jx pu Done with this part... Z1no = R pu + jx pu Z1ns = R pu + jx pu Z1no = R pu + jx pu
6 What does Z1no, Z1ns, Zno represent? Z 1no = Z p + Z t Z 1ns = Z p + Z t Z s Z 1no = Z s + Z t
7 ow olve for,, and. Keep in mind that these are complex numbers. Z 1no = Z p + Z t Z no = Z s + Z t Z 1ns = Z p + Z tz s Z t + Z s solving equations and unknowns: Z t = ± Z no Z 1no Z 1ns Z t = + Z no Z 1no Z 1ns assumed Z p = Z 1no Z t Z s = Z no Z t You now have the ransformer - Model he Δ Model can be calculated: R p jx p R s jx s R t R pt R ps jx t jx pt jx ps R st jx st Z ps = Z p + Z s Z pt = Z p + Z t Z st = Z s + Z t
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