Transformer winding connection, clock number and vector group
This article explains the winding connections, clock number and vector group of phase-shifting transformers used to supply variable frequency drives (VFD).
Motivation
Some of the most common keywords that bring the readers to our webpage are associated with multi-winding transformers, their connection diagrams and vector groups [1, 2] . Recently we have registered search terms such as:
“vfd isolation multipulse transformer”, “yd11y0 transformer harmonic cancellation“, “transformer loosely coupled”, “12-pulse phase shifting transformer”, “transformer with two secondary windings”, “three winding phase shifting transformer”, “transformer winding configuration”, “extended delta transformer” etc.
We have recognized that connection groups of multi-winding VFD transformers and corresponding vector groups create some confusion. It was an impulse for us to write one more article that might shed little more light on this topic.
Winding connections
A brief description of winding connections had already been provided in [2]. Three-phase power and distribution transformers typically use two basic connections:
Star (Wye)
– Star or wye is denoted as ‘Y’ or ‘y’. The windings are connected phase to neutral.
Delta
– Delta connected windings are denoted as ‘D’ or ‘d’. The windings are connected phase to phase.
Capital letter indicates the winding(s) with higher voltage (often referred to as ‘HV’) and small letter is used for winding(s) with lower voltage (referred to as ‘LV’). With these conventional winding connections a phase shift of 30° (degree) or its multiple can be achieved. For details refer to clock number further below.
In phase shifting transformers a 30 degree phase displacement between the secondary windings is used to achieve a 12-pulse configuration. For higher pulse number a smaller phase displacement is required: less than 30 degree, i.e. less than one hour in clock number notation [3]. For such purpose modified winding connections are used:
Zig-Zag
– Zig-Zag (zigzag) is denoted as ‘Z’ or ‘z’. It is modified star connection with each phase consisting of two magnetically connected phases. Sometimes it is called “interconnected star”.
Extended delta
– Extended delta, together with polygon delta, are common winding configurations to achieve phase displacement less than 30 degree. Notation is usually same as delta and the phase displacement is added in brackets, e.g. d(-15°).
Polygon delta
– Polygon windings are characterized by hexagonal form of voltage vectors.The notation is usually same as extended delta, i.e. ‘d’ with displacement angle in brackets.
Simplified winding connection diagrams are shown below. The figures are principal. Real phase displacement is smaller.
Phase shifting VFD transformers use the described winding connections to achieve the required phase shifts. Main reason is elimination of specific current harmonic orders and minimize the impact of the VFD on the supplying grid.
Clock number and vector group
Clock number notation as per IEC definition [3] is widely used to describe the winding connection and transformer vector group. It is a visual aid to easily imagine the phase displacement between the windings. Yet, people get confused sometimes. Let’s try to explain it in a simple way. Imagine a nice Swiss watch or astronomical clock at Old Town square in Prague…
Principles of clock number notation
1. As in normal watch face the circle is divided into 12 equal sections = 12 hours. The full angle is 360 degree and one hour corresponds to 1/12 of the full angle, i.e. 30 degree.
2. Same as in a clock system, each hour is divided into 60 minutes.
3. Reference point is 12 o’clock (noon).
4. The positive sense of rotation is counter-clockwise (often forgotten).
Summary: 1 hour = 60 minutes, 1 hour = 30 degree (30°), rotation is counter-clockwise
Multi-winding phase shifting transformers for pulse number higher than 12 require phase displacement less than 30 degree, i.e. less than 1 hour in clock number notation. Phase displacement of 20 degree can be written as 0.67 hour or 0 hour 40 minutes (0:40).
Transformer vector group
Combining what we have already learned – winding connections and clock number notation – we shall be able to read transformer vector group. Winding with highest voltage is denoted as HV and capital letters are used (Y, D, Z). Winding(s) with lower voltage is (are) marked as LV. It does not necessarily mean that it is “low voltage”. For medium voltage VFD applications the input transformers are almost always step-down transformers. Therefore, the converter side windings are called LV windings (although the nominal voltage us normally above 1’000 V).
The notation defined by IEC is always HV-LV.
Let’s start with simple example before jumping into more complex phase-shifting units.
Example 1: Yd11
Two-winding transformer has vector group Yd11. It means that primary winding (HV) is star connected and secondary winding (LV) is delta connected. The secondary winding is 30 degree leading with reference to primary. Remember that the positive sense of rotation is counter-clockwise (11 o’clock is one hour ahead of 12 o’clock).
Example 2 is a typical transformer for 12-pulse rectifier.
Example 2: Yy0d1
Three-winding transformer has vector group Yy0d1. Primary HV winding is again star (wye) connected. One secondary winding is star connected without any phase displacement towards primary. Other secondary winding is delta connected and 30 degree lagging with respect to primary Y. The two secondary winding have 30 degree relative phase displacement. Such configuration is typically used for 12-pulse rectifiers. Alternative vector group is Yy0d11. In this case delta connected secondary is 30 degree leading. From VFD perspective both vector groups can be used. Both of them help to achieve 12-pulse reaction towards the grid.
Next case is transformer for VFD with 18-pulse rectifier.
Example 3: Dd11d11:40d0:20
Four-winding transformer designed to supply an 18-pulse rectifier has vector group Dd11d11:40d0:20. Primary winding is connected in delta. One secondary winding (d11) is delta connected and 30° leading with respect to primary delta. Secondary d11:40 is extended delta and is 10° leading. Secondary d0:20 is extended delta and is 10° lagging. The secondary windings have 20° relative phase displacement.
For simplicity the vector group from example 3 could also be written as Dd(+30°)d(+10°)d(-10°). Such system does not follow the clock number notation from IEC, but is easy to understand and therefore usually accepted.
Now we are already on master level and jump to 24-pulse configuration.
Example 4: Dd(+15°)d(0°)d(-15°)y(-30°)
This is a phase shifting transformer for 24-pulse rectifier. We have just used the alternative method of vector group notation. There are four secondary windings: one LV is star connected (30° lag), one LV is delta connected (no phase displacement, i.e. 0°) and other two LV windings are of extended delta type with +15° and -15° phase displacement.
Remark 1: The phase displacement less than 30°, i.e. less than one hour in clock number system, is not so strictly defined. Different users use slightly different notation. For example, extended delta secondary winding that is 15° leading with respect to primary star connected winding can be written as:
– Yd11:30 –> 11 hours and 30 minutes
– Yd11.5 –> 11 1/2 hour
– Yd(+15°)
Remark 2: The two methods of stating a vector group, i.e. with clock number or with phase displacement in brackets, shall preferably not be mixed to avoid confusion.
Summary: clock number and vector group
Multi-pulse phase shifting transformers in VFD applications use, apart from standard star and delta connections, also zig-zag, extended delta or polygon delta winding configurations. These are particularly necessary when phase displacement less than 30° (1 clock) shall be achieved. The clock notation uses the same principle as in power and distribution transformers. The little unusual thing is the use of fractions of clock.
References
[1] VFD transformers: Introduction, https://mb-drive-services.com/vfd-transformers-introduction/
[2] VFD transformers: Multi-winding design, https://mb-drive-services.com/vfd_transformer_design/
[3] IEC 60076-1 Power transformers – Part 1: General
[4] Bin Wu, High-Power Converters and AC Drives, IEEE Press/John Wiley & Sons, Inc., ISBN-13 978-0-471-73171-9
[5] X. Liang, W. Jackson, R. Laughy, “Transformer winding connections for practical industrial applications”, PCIC 2007
[6] Variable speed drive (VSD) transformers, https://new.abb.com/products/transformers/special-application/variable-speed-drive-(vsd)-transformers
[7] Trasfor – Engineered dry type transformers, http://www.trasfor.com/products
