Star-Star and Star-Delta Transformers | What Is 3-Phase Power?, Part 3 - MATLAB & Simulink
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    Star-Star and Star-Delta Transformers | What Is 3-Phase Power?, Part 3

    From the series: What Is 3-Phase Power?

    In 3-phase electrical power systems, transformers are used to change both voltage magnitude and voltage phase. Common configurations include Star and Delta windings. Understanding how these connection options affect voltage and current is fundamentally important for AC electrical system analysis and operation.

    You will learn:

    1. How a transformer can change voltage level between primary and secondary connections
    2. The impact that Star and Delta connections have on voltage magnitude and phase
    3. The difference between D1 and D11 Delta connections
    4. Some practical considerations for a certain connection choice

    Published: 19 May 2022

    Hello, everyone. My name is Graham Dudgeon, and welcome to the third in a series of videos on three-phase power. The aim of the video series will be to build up our engineering knowledge on the design, analysis, and operation of three-phase electrical power systems. Today we will explore star-star and star-delta transformers. Note that star is also referred to as y.

    We'll begin by considering what a transformer actually is, and use single-phase to set the context before we move to three-phase. Here you can see a representation of a coiled wire, otherwise known as an inductor, that has an AC voltage across its terminals. The AC voltage creates a magnetic field within the coil. You can see the flux lines growing and collapsing as a function of the instantaneous voltage level.

    If we place a second coil close to the first coil, you will see that the magnetic flux lines intersect the second coil. Because we have a moving magnetic field cutting through the second coil, a voltage is induced in the second coil, as described by Faraday's law of electromagnetic induction. We'll not cover the mathematics of Faraday's law here, but numerous sources are available in the literature.

    Notice that not all the magnetic flux lines are cutting into the second coil. This means the transfer of energy is not efficient. To make the system more efficient, we need a way to direct more of the magnetic flux lines to cut through the second coil.

    The way we do this is to wind the coils around an iron core. An iron core has much higher permeability than air, meaning the magnetic flux lines favor traveling through iron rather than air. You can see in this case that the magnetic field is contained in the iron core. We are seeing an ideal situation here. In reality, there will be some magnetic flux lines that are not fully contained within the core. When this happens, we say there is flux leakage.

    In addition to flux leakage, there are other sources of loss in a transformer which we'll not cover today. Today we'll focus on ideal lossless transformers.

    Now let's orient ourselves around this system. We call the supply side of the transformer the primary side. The load side is called the secondary side. We have voltage V1 at the primary side and V2 at the secondary side, current I1 at the primary side and I2 at the secondary side. And the primary coil has N1 turns, and the secondary coil has N2 terms.

    We now have all the information we need to write the equations for an ideal transformer. V2 is equal to V1 times the number of coils in the secondary, N2, divided by the number of coils in the primary, N1. I2 is equal to I1 times the ratio of the number of coils in the primary, N1, divided by the number of coils in the secondary, N2. The ideal transformer equations allow perfect transfer of power from the primary side to the secondary side.

    If we increase the turns ratio N2 over N1, then we see a corresponding increase in the secondary voltage magnitude relative to the primary voltage magnitude. In this case, the upper configuration is N2 over N1 equal to 1, and the lower configuration is N2 over N1 equal to 2. The lower secondary voltage is twice the magnitude of the lower primary voltage. Note that the lower secondary current will be half the magnitude of the primary current in this case.

    I wanted to show you these different visual representations of coil windings. On both representations, I draw the voltage vector across the coil. On the representation on the right, note that the two voltage vectors point towards each other, but they are in fact in phase. This will be important for subsequent discussion.

    For a three-phase transformer, a common core construction is so-called three-limb, which we can see here. In this case, the winding configuration is star-star. And note that the primary and secondary windings for each phase is wound on the same limb. Recall that the vectors pointing towards each other in this representation mean the voltages are in phase. I've used the notation p for primary and s for secondary.

    Here I have a dynamic representation of primary and secondary voltages, and of the magnetic flux permeating through the core. I have more windings on the secondary side, and so we have a step-up transformer. The representation of the flux here is highly stylized, and I've included it to give an indication of how the magnetic fields grow and collapse and overlap during three-phase operation.

    I like to emphasize the role of simulation in helping build our understanding of power systems concepts. Simulation is a tremendous tool for us to give insights and confirm that we are seeing expected operation. Also, all the animations that I show in these tutorials I've generated using MATLAB graphics. I personally find the combination of animation driven by simulation to be a powerful learning tool.

    What you see here is Simscape Electrical. I put this together to generate the vector data that supports this tutorial. You'll notice I have two different star-delta configurations, so-called D1 and D11 configurations. Let's explore this further.

    Here we see a circuit diagram of a star-delta transformer with the delta configured as D1. So what does that mean? Well, if we look at the voltage across AB on the primary and the voltage across AB on the secondary, and bring those vectors together like hands of a clock face, and assume that the primary line voltage points to 12, then the secondary line voltage points to 1. Hence, D1.

    With the orientation shown, the system frequency rotates anti-clockwise. And so with D1, secondary line voltage lags primary line voltage by 30 degrees. I'll make one more observation here-- line voltage V AB on the secondary is in phase with phase voltage V AN on the primary.

    To understand this better, let's revisit the diagram of the three-limb core. What you can see from this diagram is that because the line-to-line coils in the secondary are wound on the same limb as the line-to-neutral coils in the primary, then the corresponding voltages are in phase. Phase voltage V AN on the primary is in phase with line voltage V AB on the secondary, and so on. I've also shown a vector representation of this configuration on the right.

    Here is a D11 configuration. If we look at the voltage across AB on the primary and the voltage across AB on the secondary and form the clock face, then the secondary line voltage points to-- you've guessed it-- 11. Hence, D11. With the orientation shown, the system frequency rotates anti-clockwise, and so with D11, secondary line voltage leads primary line voltage by 30 degrees.

    Like the D1, I'll make one more observation here-- line voltage V CA on the secondary is in antiphase with phase voltage V AN on the primary. To understand this better, let's look at the winding configuration on our three-limb core diagram.

    What you see here is that because we flipped the coil orientation on the line-to-line coils in the secondary, then the corresponding voltages are in antiphase. Phase voltage V AN on the primary is in antiphase with line voltage V CA on the secondary, and so on. I've also shown a vector representation for this configuration on the right.

    There are a number of factors that influence the choice of transformer configuration. Some factors include star connections offer a neutral point, which can be grounded to increase safety and provide line-to-neutral connections for distribution systems. For a given power level, delta connections reduce current, and so I-squared R losses are reduced. Delta is common in high-voltage transmission. Delta windings can contain third harmonics, and so third harmonics will not transfer to the other side of the transformer. We'll cover this aspect in more detail in a future tutorial. And phase-shifted transformers allow correct operation of parallel connected power converters. We'll cover this in more detail in a future tutorial.

    So in summary, transformers are used to change both voltage magnitude and voltage phase in three-phase electrical systems. Transformers can either step up or step down voltage. If voltage steps up, then current will step down, and vice versa. The voltage magnitude ratio between primary and secondary sides is primarily dictated by the ratio of the number of turns in the coils. Transformer coils can be connected in star and delta configurations, and there are a number of variations possible. In a D1 delta connection, secondary line voltage lags primarily line voltage by 30 degrees. In a D11 delta connection, secondary line voltage leads primarily line voltage by 30 degrees.

    I hope you found this information useful. Thank you for listening.