The short-circuit impedance of a transformer, also known as impedance voltage, is defined in the transformer industry as follows: when the secondary winding of the transformer is short-circuited (steady state), the voltage applied to the primary winding while the rated current flows is called impedance voltage Uz. Typically, Uz is expressed as a percentage of the rated voltage, i.e., uz=(Uz/U1n)*100%.

When the transformer is operating at full load, the level of short-circuit impedance has a certain impact on the output voltage on the secondary side. A small short-circuit impedance results in a small voltage drop, while a large short-circuit impedance results in a large voltage drop. When a short circuit occurs in the transformer load, a small short-circuit impedance leads to a large short-circuit current, and the electromagnetic force borne by the transformer is large. Conversely, a large short-circuit impedance results in a small short-circuit current, and the electromagnetic force borne by the transformer is small.

(1) Parallel operation of transformers with different voltage ratios:

Since the principles of three-phase transformers and single-phase transformers are the same, for ease of analysis, we will analyze the parallel operation of two single-phase transformers. Since the primary voltages of the two transformers are equal but the voltage ratios are not, the induced potentials in the secondary windings are also unequal, resulting in a potential difference △E. Under the influence of △E, a circulating current IC appears in the secondary winding. When the rated capacities of the two transformers are equal, i.e., SNI=SNII, the circulating current is:

IC=△E/(ZdI＋ZdII)

Where ZdI represents the internal impedance of the first transformer.

ZdII represents the internal impedance of the second transformer.

If Zd is expressed as impedance voltage UZK, then

Zd=UZK*UN/100IN

Where UN represents the rated voltage (V), IN represents the rated current (A).

When the rated capacities of the two transformers are not equal, i.e., SNI≠SNII, the circulating current IC is:

IC=á＊II/[UZKI＋(UZKII/â)]

Where: UZKI represents the impedance voltage of the first transformer.

UZKII represents the impedance voltage of the second transformer.

INI＜INII

á represents the secondary voltage difference expressed as a percentage.

II is the load current of the secondary side of transformer I.

From the above analysis, it can be seen that under load conditions, due to the presence of circulating current Ic, the current in the winding of the transformer with a smaller voltage ratio increases, while the current in the winding of the transformer with a larger voltage ratio decreases. This causes the parallel operation of transformers to not share the load in proportion to their capacities. For example, if the total load current of the bus is I (I=INI＋INII), if transformer I is operating at full load, then transformer II is underloaded; if transformer II is operating at full load, then transformer I is overloaded. Thus, when transformers with unequal voltage ratios operate in parallel, the presence of circulating current Ic prevents the transformers from carrying full load, resulting in the total capacity not being fully utilized.

Moreover, since the circulating current of the transformer is not the load current, it occupies the capacity of the transformer, thereby reducing the output power and increasing losses. When the voltage ratios differ significantly, it may disrupt the normal operation of the transformer and even cause damage to the transformer. To avoid excessive circulating current Ic due to a large difference in voltage ratios affecting the normal operation of parallel transformers, it is stipulated that the difference in voltage ratios should not exceed 0.5%.

(2) Parallel operation of transformers with unequal impedance voltages:

Because the load distribution between transformers is proportional to their rated capacities and inversely proportional to the impedance voltages. In other words, when transformers operate in parallel, if the impedance voltages are different, their loads are not distributed in proportion to their rated capacities. The current carried by the parallel transformers is inversely proportional to the impedance voltages, i.e., II/III=UZKII/UZKI or UZKIIII=UZKIIIII. Let the two transformers operate in parallel with capacities SNI and SNII, and impedance voltages UZI and UZII, then the loads of each transformer can be calculated using the following formulas:

SI=[(SNI+SNII)/(SNI/UZKI+SNII/UZKII)]＊(SNI/UZKI)

SII=[(SNI+SNII)/(SNI/UZKI+SNII/UZKII)]＊(SNII/UZKII)

That is, S△I/SII=(SNI＊UZKII)/(SNII＊UZKI)

From the above analysis, it can be seen that when two transformers with unequal impedance voltages operate in parallel, the transformer with a larger impedance voltage has a smaller load distribution. When this transformer is at full load, the other transformer with a smaller impedance voltage will be overloaded. Long-term operation of transformers at overload is not allowed; therefore, only the transformer with a larger impedance voltage can operate underloaded, which limits the total output power, increases energy losses, and cannot ensure the economical operation of the transformer. Therefore, to avoid severe load current distribution imbalance due to excessive differences in impedance voltages, which affects the full utilization of transformer capacity, it is stipulated that the difference in impedance voltages should not exceed 10%.

(3) Parallel operation of transformers with different connection groups:

The connection group of a transformer reflects the corresponding relationship between high and low side voltages, generally represented using clock notation. When parallel transformers have equal voltage ratios and equal impedance voltages, but different connection groups, it means that there is a phase angle difference á and a voltage difference △U in the secondary voltages of the two transformers. Under the influence of the voltage difference, circulating current Ic is generated:

Ic=△E/(ZdI+ZdII)

If the angle á represents the angle between the line voltages of transformers with different winding groups, and Zd is expressed as UZK, the circulating current can be expressed as follows:

Ic=2U1sin(á/2)/(ZdI+ZdII)=200sin(á/2)/[UZK1/In1+UZK2/In2]

If In1=In2=In, UZK1=UZK2=UZK, then the above formula becomes

Ic=100sin(á/2)/UZK

Where In and UZK can be any rated current and impedance voltage of a transformer.

Assuming two transformers have equal transformation ratios and equal impedance voltages, with their connection groups being Y/Y0-12 and Y/△-11 respectively, it can be inferred from the connection groups that when á = 360° - 330° = 30°, UZK% = (5～6)% Ic = 100sin(á/2)/UZK leads to IC = (4～5)In, which means the circulating current is 4 to 5 times the rated current during circulating current analysis. It can be seen that when two transformers with different connection groups operate in parallel, the circulating current can sometimes be comparable to the rated current, but their differential protection and current instantaneous protection cannot act to trip, and when the overcurrent protection cannot act in time to trip, it will cause the transformer windings to overheat and even burn out.

From the above analysis, it can be seen that if the voltage ratios (transformation ratios) are not the same, the parallel operation of two transformers will generate circulating currents, affecting the output of the transformers. If the percentage impedances are not equal, the load carried by the transformers cannot be proportionally distributed according to the capacity of the transformers; the transformer with smaller impedance carries a larger load, while the transformer with larger impedance carries a smaller load, which also affects the output of the transformers. The parallel operation of transformers often encounters situations where the voltage ratios (transformation ratios) and percentage impedances are not completely the same. The method of changing the transformer tap connections can be used to adjust the impedance values of the transformers. If the third condition is not met, it will cause circulating currents equivalent to a short circuit, potentially burning out the transformer; therefore, transformers with different connection groups cannot operate in parallel. Generally, if it is necessary to operate transformers with different connection groups in parallel, methods such as exchanging the names of each phase and swapping the starting and ending points should be adopted according to the differences in connection groups, so that the connections of the transformers can be made the same to operate in parallel.

According to operational experience, the capacity ratio of two transformers in parallel should not exceed 3:1. This is because transformers with different capacities have relatively large impedance values, leading to extremely unbalanced load distribution; at the same time, from an operational perspective, when the operating mode changes, during maintenance, or in the event of a power outage, the smaller capacity transformer will not serve as a backup.