1 Introduction
2 Modes of dc-bias in power transformers
2.1 Common mode
2.2 Differential mode
θ0 − θ1 | Dc current ratio in phase A, B and C | Ref. range [A] | ||||
---|---|---|---|---|---|---|
IA_dc | IB_dc | IC_dc | I0 | |||
DM | 0° | 1 | − 0.5 | − 0.5 | 0 | 0.4–1.6 |
60° | 0.5 | − 1 | 0.5 | |||
90° | 0 | − √3/2 | √3/2 | |||
150° | − √3/2 | 0 | √3/2 | |||
CM | / | 1 | 1 | 1 | 3 | 0.4–4.0 |
Main circuit parameters | Unit | Three-level VSC | MMC |
---|---|---|---|
Converter rating | MVA | 200 | 150 |
System frequency | Hz | 50 | 50 |
DC voltage | kV | + /− 100 | + /− 200 |
AC voltage | kV | 230 | 123 |
AC filter size | MVar | 40 | / |
Reactance of phase reactor | mH | 23.9 | 50.9 |
Converter bus voltage | kV | 100 | 123 |
Transformer rating | MVA | 200 | 150 |
Transformer leakage reactance | mH | 23.9 | 25.5 |
Reactance of smoothing reactor | mH | 8 | / |
3 Test
3.1 Test setup
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The test can be destructive due to extreme saturation condition and excessive losses.
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It is easier to manufacture, modify and assembly iron tank to investigate stray losses.
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The conclusion drawn from a scale-down lab transformer is valid for a lager transformer since the saturation phenomenon is sensitive to materials and dimension ratio, rather than absolute dimensions.
3.2 Common mode test
DC current [A] | Total losses Pt [W] | Winding loss Pw [W] | Core loss PC [W] | Stray loss Ps [W] | Reactive power Q [Var] |
---|---|---|---|---|---|
0 | 51.02 | 0.20 | 50.06 | 0.76 | 260 |
0.4 | 51.32 | 0.51 | 50.05 | 0.77 | 386 |
0.8 | 52.15 | 1.31 | 50.05 | 0.79 | 615 |
1.2 | 53.33 | 2.52 | 50.02 | 0.81 | 876.8 |
1.6 | 55.04 | 4.26 | 49.95 | 0.84 | 1140.2 |
2.0 | 57.38 | 6.58 | 49.93 | 0.87 | 1417.7 |
2.4 | 60.20 | 9.36 | 49.92 | 0.92 | 1691.6 |
2.8 | 63.57 | 12.67 | 49.85 | 1.06 | 1971.1 |
3.2 | 67.62 | 16.48 | 49.81 | 1.31 | 2245.4 |
3.6 | 72.30 | 20.93 | 49.78 | 1.60 | 2530.9 |
4.0 | 77.54 | 25.86 | 49.74 | 1.95 | 2813.4 |
3.3 Differential mode test
Configuration | Reactive power consumption [Var] | |||
---|---|---|---|---|
Phase A | Phase B | Phase C | Total | |
AC | 133.7 | 83.5 | 109.1 | 326.3 |
0° | 658.8 | 367.7 | 362.7 | 1389.2 |
60° | 415.9 | 588.5 | 408.7 | 1413.1 |
90° | 579.0 | 518.4 | 308.9 | 1406.3 |
150° | 547.3 | 304.4 | 541.9 | 1393.6 |
3.4 Influence of tank and clamping steels
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Case 1: d = 5 mm.
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Case 2: d = 20 mm.
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Case 3: Without tank.
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Case 4: Without tank and clamping plate.
Loss type | Configuration | Case number | |||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | ||
Stray loss [W] | AC | 1.9 | 1.3 | 1.2 | 0 |
0° | 32.5 | 22.8 | 7.7 | 0 | |
60° | 43.3 | 31.3 | 9.7 | 0 | |
90° | 40.4 | 28.7 | 8.4 | 0 | |
150° | 34.5 | 24.3 | 8.4 | 0 | |
Winding loss [W] | AC | 0.4 | 0.4 | 0.4 | 0.4 |
0° | 7.2 | 7.2 | 7.4 | 7.7 | |
60° | 6.9 | 6.8 | 6.9 | 7.1 | |
90° | 7.0 | 7.0 | 7.0 | 7.4 | |
150° | 6.9 | 7.0 | 7.0 | 7.3 |
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The stray loss in the tank and the clamping plates increases dramatically due to dc-bias. In case 2, for instance, it increases from 1.3 (under pure ac excitation) to 31.3 W (1.6 A dc-bias at 60°).
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Among the four configurations, the stray loss varies considerably. The variations in Case 1 (33%) and Case 2 (37%) are greater than in Case 3 (26%), largely due to the stray loss redistribution in the iron tank.
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The stray loss in the tank is sensitive to the tank height (air gap). The loss increases with more than 10 W (> 40%) when the gap distance reduces from 20 to 5 mm.
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The winding loss increases with dc-bias level. The tank and clamping structures have little impact on winding loss.
3.5 Influence of delta winding
Loss type | Configuration | Case number | ||
---|---|---|---|---|
1 | 3 | 4 | ||
Stray loss [W] | 0° | 6.3 | 5.6 | 0 |
60° | 5.9 | 6.3 | 0 | |
90° | 5.6 | 5.5 | 0 | |
150° | 6.1 | 5.8 | 0 | |
Winding loss primary side [W] | 0° | 7.7 | 7.8 | 7.9 |
60° | 7.3 | 7.3 | 7.4 | |
90° | 7.4 | 7.4 | 7.6 | |
150° | 7.3 | 7.3 | 7.4 | |
Winding loss delta [W] | 0° | 1.7 | 1.7 | 0.9 |
60° | 2.2 | 2.3 | 2.0 | |
90° | 2.0 | 2.0 | 1.5 | |
150° | 1.6 | 1.5 | 0.7 |
4 Discussion
4.1 Comparisons between DM and CM dc current
4.2 Down scaling of transformer
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Large (full-scale) transformers have sophisticated structural steels such as flitch plates close to the magnetic core which are susceptible to the leakage flux affected by saturation.
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The core material used in a grid (full-scale) transformer is often the grain-oriented (GO) steel, which has higher nominal flux density, lower specific loss and steeper magnetization curve below the knee point, compared to the lab (down-scale) transformer which is made of non-grain-oriented (NGO) steel.
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The rated current in a full-scale transformer is much larger than the lab transformer, so the winding loss generated under the same dc current in a full-scale transformer is not as problematic as the down-scaled one, since the percentage current increase (relative to nominal load current) in a full-scale transformer is much less significant.
5 Conclusions
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Three-phase, three-limb transformer can withstand much higher CM dc current, compared to DM dc current.
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Power transformers are susceptible to DM dc current regardless of their core topologies, due to low reluctance paths and higher flux density offset.
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The magnetizing current under DM dc current has higher THD level than CM and content higher-order harmonics, resulting in both higher stray loss and higher winding loss.
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The power losses caused by high-level DM dc currents depends on dc current distribution in three windings, due to the stray loss redistribution in the iron tank.
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The DM dc currents enhance the reactive power consumption and introduce an unbalanced voltage distribution in the three phases.
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Delta winding can significantly reduce the excessive stray loss (and noise) caused by the DM dc currents, as long as a proper rating is chosen for the delta winding.