Implement phasor model of three-phase OLTC phase-shifting transformer using delta hexagonal connection

FACTS/Transformers

This block is used to model a phase-shifting transformer using on-load tap changers (OLTC) for introducing a phase shift between three-phase voltages at two buses in a transmission system. Controlling phase-shift on a transmission system affects primarily flow of active power. Although the phase-shifting transformer does not provide as much flexibility and speed as power-electronics based FACTS, it can be considered as a basic power flow controller. This is why it has been included in the facts library. The dynamic performance of the phase-shifting transformer can be enhanced by using a thyristor-based tap changer instead of a mechanical tap changer. As this model is a phasor model which does not implement the details of current transfer from one tap to the next tap, you can use it to model a thyristor-based phase-shifter. You can also use this block together with the Three-phase OLTC Regulating Transformer (Phasor Type) block for building phasor models of more complex transformer-based FACTS topologies.

The delta hexagonal connection consists of three pairs of windings interconnected in a hexagonal configuration as shown on the figure below.

**Delta-Hexagonal Phase-Shifting Transformer
Connections**

$$\psi =2\times \mathrm{arctan}(-k/\sqrt{3})$$

Symbol | Range |
---|---|

ψ = phase shift of abc output voltages with
respect to ABC input voltages | –60° ≤ ψ ≤ +60° |

N = tap position | –N_{tap} ≤ N ≤
+N_{tap} |

k = relative tap position = N/N_{tap} | –1 ≤ k ≤
+1 |

Each phase consists of two coupled windings drawn in parallel on the figure: one tapped winding with two OLTCs and one winding without taps. All windings have the same number of turns. The two OLTCs vary phase shift by moving transformer input terminals (A, B, C) and outputs terminals (a, b, c) symmetrically with respect to center tap 0. This delta hexagonal connection has the advantage of keeping a 1:1voltage ratio while the phase shift is varied.

When the two OLTCs move taps from the center position (0) to the winding end (position Ntap), the phase shift between inputs (ABC) and outputs (abc) varies from 0 degrees to 60 degrees. When ABC are at position −Ntap and abc are at position +Ntap, the output voltages abc are lagging input voltages ABC by 60 degrees. On the other end, when ABC are at position +Ntap and abc are at position −Ntap, the output voltages abc are leading input voltages ABC by 60 degrees. For intermediate positions, the phase shift ψ is given by the equation on the figure. This equation assumes that all tap are evenly spaced.

For example, if each half tapped winding consists of 10 taps (total of 21 taps/ winding including center tap 0) and if ABC and abc terminals are respectively at tap −7 and tap +7, then, k=7/10 =0.7.

Therefore, abc voltages are lagging ABC voltages by 44 degrees.

The phase angle varies almost linearly as function of tap position as shown on the figure below.

**Variation of Phase Shift as Function of
Tap Position**

You control tap positions, and therefore phase shift, by sending pulses to one of the two block inputs labeled Up and Down. Applying a pulse to the Up (or Down) input moves the tap position upward (or downward) when the signal is changing from 0 to 1.

Mechanical tap changers are relatively slow devices. The time required to move from one tap position to the next one is comprised between 3 and 10 seconds. You specify this mechanical time delay in the block menu.

OLTCs use additional switches and resistors (or inductors) to
transfer current from the outgoing tap to the ongoing tap without
interrupting load current. During the transfer, taps are temporarily
short circuited through resistors or inductors. The transfer time
(typically from 40 ms to 60 ms) is fast as compared to the tap selection
process (3 s to 10 s). As this block implements a phasor model for
study of transient stability of power systems in the range of seconds
to minutes, the tap transfer process is not modelled and an instantaneous
tap transfer is assumed. A detailed delta-hexagonal phase-shifting
transformer model is provided in the `power_PSTdeltahex`

example.

**Nominal parameters [Vnom Pnom Fnom]**The nominal line to line voltage, in volts rms, the three-phase nominal power, in VA and the nominal frequency, in hertz. Default is

`[120e3 300e6 60]`

.**Resistance and leakage reactance at max. tap [R X]**The transformer short circuit impedance due to winding resistances and leakage reactances, at maximum phase shift (input and output taps at −Ntap and +Ntap positions). Specify resistance and reactance, in pu. Default is

`[0.15/30 0.15]`

.The transformer positive-sequence impedance

*Z*_{1}, in pu, and zero-sequence*Z*_{0}, in pu, vary with relative tap position*k*as follows:$$\begin{array}{c}{Z}_{1}=\left(R+jX\right)\frac{\left|k\right|\left(-3{k}^{2}+2\left|k\right|+9\right)}{2\left({k}^{2}+3\right)}\\ {Z}_{0}={k}^{2}\frac{{R}_{m}j{X}_{m}}{{R}_{m}+j{X}_{m}},\end{array}$$

where:*R*,*X*are the transformer resistance and reactance defined in the parameter**Resistance and leakage reactance at max. tap**(*k*=1 or*k*=–1) and**R**m**, X**m**are the transformer magnetizing**resistance and reactance defined in the**Magnetizing branch**parameter described below.Note that these impedances keep the same value for positive and negative values of

*k*. For*k*=0, impedances are zero because the transformer input terminals are short-circuited with output terminals.**Magnetizing branch [Rm Xm]**The resistance, in pu, and the reactance, in pu of the parallel

*R*,_{m}*X*branch modelling respectively iron losses and reactive magnetizing currents. Saturation is not modelled. Default is_{m}`[500 500]`

.**Number of taps per half winding (Ntap)**The number of taps per half winding. The total number of taps per winding, including center tap 0, is therefore 2*Ntap+1. Default is

`10`

.**Initial tap**Specify an integer (Tapinit) corresponding the initial tap position of output terminals abc. The initial tap position of input terminals ABC is therefore –Tapinit. Default is

`0`

.**Tap selection time**The mechanical time delay, in seconds, required for the OLTCs to move the taps by one position. Typical values are in the 3s-10s range. Default is

`2.9`

.**Initial pos. seq. output currents [Mag Phase]**The initial value of the positive-sequence current phasor (Magnitude in pu and Phase in degrees) flowing out of terminals abc. If you know the initial value of currents you may specify it in order to start simulation in steady state. If you don't know these values, you can leave

`[0 0]`

(default). The system will reach steady-state after a short transient.

`A B C`

The three transformer input terminals

`a b c`

The three transformer output terminals

`Up`

Simulink

^{®}input for controlling tap position. Applying a pulse to this input will initiate upward tap changing when the pulse is changing from 0 to 1.`Down`

Simulink input for controlling tap position. Applying a pulse to this input will initiate downward tap changing when the pulse is changing from 0 to 1.

`m`

Simulink output vector containing 17 internal signals. These signals are either complex signals (voltage phasors, current phasors or impedances) or control signals. They can be individually accessed by using the Bus Selector block. They are, in order:

Signal

Signal Group

Signal Names

Definition

1-3

VABC (cmplx)

VA (pu)

VB (pu)

VC (pu)Phasor voltages (phase to ground) at the transformer input terminals A, B, C (pu)

4-6

Vabc (cmplx)

Va (pu)

Vb (pu)

Vc (pu)Phasor voltages (phase to ground) at the transformer output terminals a, b, c (pu)

7-9

IABC (cmplx)

IA (pu)

IB (pu)

IC (pu)Phasor currents flowing into the input terminals A, B, C

10-12

Iabc (cmplx)

Ia (pu)

Ib (pu)

Ic (pu)Phasor currents flowing out of the output terminals a, b, c

13-14

Z (cmplx)

Z1 (pu)

Z0 (pu)Positive- and zero-sequence complex impedances (R+jX)

15

Psi

(degrees)Psi

(degrees)Phase shift of abc output voltages with respect to ABC input voltages

16

Tap

Tap

Tap position

17

Ready

Ready

Logical signal generated by the tap changer controller. The Ready signal becomes (1) after the tap selection has been completed, thus enabling a new tap change. The Up and Down pulses to the OLTC are blocked as long as the Ready signal is (0).

See the `power_PSTdeltahex`

example, which
illustrates the use of the Three-Phase OLTC Phase Shifting Transformer
Delta-Hexagonal (Phasor Type) block to control power transfer between
two equivalent sources in a 120-kV transmission. The phasor model
is compared with a detailed model of phase shifting transformer. Look
under the masked blocks to see how both models are implemented. The
detailed model uses switches and three Multi-Winding Transformer blocks,
whereas the phasor model uses current sources.

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