Page 55 - Energize September 2022

TECHNICAL

Transformer operation
Reference provides a detailed analysis of the distribution
1
transformer under forward and reverse-feed cases where the
feeder contains solar PV. The results are summarised in the
following section.
The distribution transformer may be represented as a two-
part network in which there are two impedances: short circuit and
magnetising as shown in Figure 3. The input port is connected to
the grid and output port is connected to the load/PV generation.
The magnetising branch is connected between Z1 and Z2.
Maximum power transfer is defined by terminal voltages V1 and
V2. The difference in terminal voltages V1 and V2 in terms of
magnitude and phase angle θ, represents the voltage drop in the
transformer which is derived through short circuit impedance (%Z) Figure 5: Vector representation of transformer forward and reverse power
and load currents. flow at unity power factor with similar grid voltage (V1) 1
Consider the circuit of Figure 4, drawing current or injecting
current to the grid at unity power factor (UPF). For all the three cases, positive values of P draws power from
the grid, and negative values will inject power to the grid. Constant
excitation/magnetisation necessitates an increase in injection
voltage and decrease in grid voltage. The constant load voltage
case leads to reduced excitation and grid voltage. Constant grid
voltage results in increased injection voltage (V 2) and magnetization
voltage (E). The magnetizing flux density of the core increases in
this case.
The real situation facing distribution networks is that the power
factor is not at unity, and with inverter-based power supplies and
Figure 3: Power flow representation through the transformer 1 voltage compensation equipment may be either leading or lagging.
Power transfer thus falls into four quadrants as shown in Figure 6.

• Q1: Normal load with inductive kVAR demand: The active
power flows from grid to the load with θ > 0, |E|>|V2|, and the
magnetizing current Im is drawn from the grid
• Q2: DG generation with inductive kVAR demand: The active
power flows from DG to the grid with θ < 0, |E|>|V2|, and the
magnetizing current Im is drawn from the grid

Figure 4: Forward and reverse power flow through a transformer 1

Three scenarios can be considered at unity power factor (UPF) with
currents I 2=I L (as UPF load), or I2’ = Ig (as UPF generation):
• Constant excitation/magnetisation
• Constant load voltage
• Constant grid voltage

The voltage drop across the transformer short-circuit impedance
creates phase displacement (θ) between V 1 and V 2 as shown in
Figure 5. Figure 6: Transformer operation in four quadrants 1

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