Modeling of Three-phase or Bank of Three Single Phase Three Winding Transformers Zero-phase-sequence Leakage Impedance in PSS E Short Circuit Module

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1 Siemens Industry, Inc. Power Technology Issue 125 Modeling of Three-phase or Bank of Three Single Phase Three Winding Transformers Zero-phase-sequence Leakage Impedance in PSS E Short Circuit Module Carlos Grande-Moran, Ph.D. Principal Consultant carlos.grande@siemens.com The zero-phase-sequence impedance characteristics of three phase three winding transformers or a bank of three single phase three winding transformers depend on the winding connections and sometimes on their core construction. Presence of a delta winding connection introduces a path from the winding terminals to the reference of the zero-phase-sequence (ZPS) network. Two winding connections are presented in this newsletter because of their extensive use in 2x1 combined cycle plants and transmission substations. One is the connection Dyn0d and the other is the connection YN0yn0d with conventional 3 winding transformers or YNa0d with three-phase three-winding autotransformers. The Dyn0d connection is often used in 2x1 combined cycle plants to connect the two GTG units to the D connected windings and the wye grounded winding (HV) connects these 2 generating units to the transmission system. The connection YN0yn0d or YNa0d is often used in transmission substations connecting EHV and HV networks. Figures 1 and 2 below show the ZPS representation of these winding connections. Note that N0 is the reference (i.e., ground) for the ZPS network and 3ZG represents the grounding impedance that can be connected between the neutral point of wye connected windings and ground. If the wye connected windings are solidly grounded then ZG=0 and thus a zero impedance jumper is required in the model to connect the physical winding terminal and the terminal associated with the winding in the T equivalent network used for modeling 3 winding transformers. When the neutral of the wye connected windings is ungrounded the value for ZG is and thus an open circuit is used in the model to connect the physical winding terminal and the terminal associated with the winding in the T equivalent network. P Z01 R Z02 Z03 3ZG2 S t N0 Figure 1 - ZPS Equivalent Network for the Dyn0d Connection

2 P 3ZG1 Z01 R Z02 Z03 3ZG2 S t N0 Figure 2 - ZPS Equivalent Network for the or YN0yn0d or YNa0d Connection The ZPS data provided by the equipment manufacturer for the Dyn0d connected windings will be an equivalent zero sequence impedance between the terminals of the wye grounded winding and N0, Z0 in per unit on a three-phase MVA rating of the wye connected windings and the winding phase-phase base voltage. Now, since there is only one known impedance value and three unknowns (Z01, Z02 and Z03) then there are two degrees of freedoms when choosing the values of two of three unknown impedances. If, we select Z02 = Z0/2 then Z01=Z03=Z0 which is as good of a choice as any other for this winding connection. The user can select any other combination as long as it satisfies Eqn. 1 below, Z0 = Z01* Z03 Z02 Z01 Z03 Eqn. 1 Regarding the YN0yn0d or YNa0d winding connection, the equipment manufacturer provides the ZPS leakage impedances Z01, Z02 and Z03 in per unit on a winding common three-phase MVA base and phase-phase winding voltages. Occasionally, the equipment manufacturer provides the impedance voltage test report where the following tests are shown (assumption - winding 1 and winding 2 are wye connected with externally available neutral and winding 3 is delta connected) [1] : 1. Test 1: with phases A, B and C terminals of winding 1 short circuited apply a single phase voltage (Vph) between the shorted terminals and its neutral. All other windings are open circuited. The ratio Vph/Itest = Z013 = Z01 Z03 from Figure Test 2: with phases A, B and C terminals of winding 2 short circuited apply a single phase voltage (Vph) between the shorted terminals and its neutral. All other windings are open circuited. The ratio Vph/Itest = Z023 = Z02 Z03 from Figure Test 3: with phases A, B and C terminals of winding 1 short circuited apply a single phase voltage (Vph) between the shorted terminals and its neutral. Short the terminals A, B and C of winding 2. All other windings may be open-circuited or shorted. The ratio Vph/Itest =Z1NS = Z01 Z02//Z03. From Test 3 results, the impedance Z03 can be obtained using Eqn. 2 below, Page 2 Z03 = Z023 * (Z013 - Z1NS) Eqn. 2 Now, using the result from Eqn.2 one can compute the leakage impedances Z10 and Z20 from the results obtained in Tests 1 and 2 as follows, Z013 - Z03 Z01= Eq. 3 Z02 = Z023 - Z03 Eqn. 4

3 It is important to note transformer units with a 5 leg core type and shell type design have a zero-phase sequence leakage impedance that is equal to its positive-phase sequence leakage impedance and thus zero sequence voltage impedance tests are generally not needed. In the event that a test is performed then the 3 tests listed above should be carried out. The ZPS leakage impedance data required by the short circuit module in PSS E for three winding transformers of the type presented in this newsletter are as follows, 1. Dyn0d: a. CC=3 ; Z01, Z20 and Z30 b. CC=13 ; Z012 = Z01 Z02, Z023 = Z02 Z03 and Z031 = Z013 = Z01 Z03 c. If the neutral of the wye winding is grounded then enter ZG2 Note that the wye connected winding can be assigned to any of the 3 windings of the three-phase three winding transformer. Using the User Code option with the connection code (CC) flag, one can specify CC=133 and ZG1 for the YN0dd winding connection and CC=331 and ZG3 for the Ddyn0. Also it is important to note that the indices used in Eqn.1 ought to be changed accordingly to account for the location of the wye connected winding. 2. YN0yn0d or YNa0d: a. CC=2 ; Z01, Z02 and Z03 (for conventional 3 winding transformers) b. CC=12 ; Z012 = Z01 Z02, Z023 = Z02 Z03 and Z031 = Z013 = Z01 Z03 (for conventional 3 winding transformers) c. CC=17 ; Z012 = Z01 Z02, Z023 = Z02 Z03 and Z031 = Z013 = Z01 Z03 (for 3 winding autotransformers) d. If the neutral of the wye windings for conventional transformers are grounded then enter ZG1 for winding 1 and ZG2 for winding 2 e. If the neutral of the wye connected windings of the three winding autotransformer is grounded then enter ZG2 The delta winding connection can be assigned to any of the 3 windings in conventional three winding transformers. What is needed is to use the connection code flag CC with the option User Code. For example, if the delta winding is assigned to winding 1, the connection code will be CC=311 and grounding impedances ZG2 and ZG3 in the events the neutral of the wye connected windings is grounded through and impedance, and if the delta winding is assigned to winding 2 then CC=131 and the grounding impedances will be ZG1 and ZG3. Note that for the case CC=311, first the impedance Z10 (winding 1 is connected delta) is determined from Eqn. 2 replacing 3 with 1 and performing Test 1 to obtain the impedance Z021, Test 2 to obtain the impedance Z031 and Test 3 to obtain the impedance Z2NS = Z02 Z03// Z01. Then using Eqns. 3 and 4 the impedances Z02 and Z03 are determined replacing 1 with 3. Numerical Example The following original equipment manufacturer (OEM) test data is provided: Three-phase, three-winding autotransformer connected YNa0d solidly grounded HV circuit rated voltage 230 kv, MV circuit rated 115 kv and tertiary LV circuit rated 14.4 kv Impedance values are in percent on common MVA base of 168 MVA and 230/115/14.4 kv voltage base. Where NOMV1 = 230, NOMV2 = 115 and NOMV3 = Test 1: HV energized with single-phase voltage applied to A, B, C short circuited phase terminals. MV and LV open circuited. Z0HV-LV = Z0HV Z0LV = 0.778% j % 2. Test 2: MV energized with single-phase voltage applied to A, B, C short circuited phase terminals. HV and LV open circuited. Z0MV-LV = Z0MV Z0LV = 0.285% j 7.413% 3. Test 3: HV energized with single-phase voltage applied to A, B, C short circuited phase terminals. MV phase terminals short circuited and LV open or short circuited. Z1NS = Z0HV Z0MV //Z0LV = 0.291% j 5.364%. Page 3

4 Below is the test data provided by the OEM: From Test 3 and Eqn. 2, the zero-phase sequence impedance Z0LV is obtained: Z0LV = (Z0MV - LV) * (Z0HV - LV - Z1NS) = ( j ) * ( j ) Z0LV = = = j pu on 168MVA,230/115/14.4 kv base From Eqns. 3 and 4, Z0HV = Z0HV-LV Z0LV = j per unit on 168 MVA, 230/115/14.4 kv base Z0MV = Z0MV-LV Z0LV = j per unit on 168 MVA, 230/115/14.4 kv base Choosing W1 connected to a 230 kv bus (BASKV=230), W2 to a 115 kv bus (BASKV=115), W3 to a 13.8 kv bus (BASKV=13.8), CZ=CZ0=2, CZG=1, connection code CC=17 and vector group YNa0d1. The zero-phase impedance data is entered as follows: R01 j X01 = Z0HV-LV = Z120 = j pu on 168 MVA, 230/115/14.4 kv base R02 j X02 = Z0MV-LV = Z230 = j on 168 MVA, 230/115/14.4 kv base R03 j X03 = Z0HV-LV = Z310 = j on 168 MVA, 230/115/14.4 kv base ZG2 = 0.0 j 0.0 (solidly grounded) Page 4

5 Figures 3 and 4 below show the zero-phase sequence data record for the 3W autotransformer connected YNa0d Figure 3-3W Autotransformer Vector Group, Connection Code and Z0HV-LV Impedance Figure 4-3W Autotransformer Z0MV-LV and Z0HV-LV Impedances Figure 5 shows the GUI in PSS E that displays the connection and vector group for a three-phase, three winding autotransformer connected YNa0d Note that a phase shift of 11 (30 ), 1 (-30 ), 7 (150 ) and 5 (-150 ) can be chosen for the delta connected windings. Figure 5 - Vector Group and Connection Code for 3W Autotransformer Connected YNa0d1 Reference: [1] IEEE Std C , IEEE Standard Test Code for Liquid-Immersed Distribution, Power, and Regulating Transformers, Sections 9.5.1, 9.5.2, and Page 5