**Transformer Performance & Electrical Parameters Calculation**

Table of Contents

**Rated Power of Transformer**

**Rated Power** is the **amount of power that a transformer can handle **and it is limited by the size of the winding conductors, and by the corresponding amount of heat they will product when current is applied.

This heat is caused by **losses**, which results in a difference between the input and output power. Because of these losses, transformers are rated **not ***in terms of kW or MW *(*active power*), but in *terms of ***kVA **or **MVA **(*apparent power*).

** Rated Power **is noted as “

**S**”.

If a transformer as **two cooling systems ***Rated Power* of the transformer **depends of the cooling method that is in use in a certain moment**, and so at the *name plate* of the transformer **two ***Rated Powers* are indicated.

Considering a transformer with an **ONAN / ONAF **(*Oil Natural Air Natural/Oil Natural Air Forced*) **cooling system**, *Rated Power* of this transformer is, for example **30/40 MVA**, **30 MVA corresponding to ONAN and 40 MVA corresponding to ONAF**.

- Related Article: Power Transformer Protection & Faults

**Rated Voltages, Ratio & Rated Frequency of Transformer**

**Rated Voltages** of a transformer are the *service voltage of the primary and of the secondary*, **V _{1}** and

**V**, respectively.

_{2}The **ratio** of a transformer is the *relation between the number of turns of primary winding and the number of turns of the secondary windings*, and is noted as “*a*”.

Considering a transformer with **N _{1} turns** in the

*primary winding*,

**N**in the

_{2}turns*secondary winding*,

**V**and

_{1}**V**the

_{2}*primary and the secondary voltages*, and

**I**and

_{1}**I**the

_{2}*primary and the secondary currents*, the

*ratio*can expressed by the following equation:

**a = N _{1 }/ N_{2} = V_{1 }/ V_{2} = I_{2 }/ I_{1}**

The **rated frequencies** are usually **50 Hz and 60 Hz**.

**Losses & Efficiency in Transformer**

Transformers are subject to **two types of losses**:

**P**: resistive losses (_{Cu }**W**)**P**: iron losses or core losses (_{0 }**W**)

The **resistive losses**, due to *Joule effect* on the windings, depends on the **current that goes through the turns of the windings**, which results from the loads connected to the transformer.

The **iron losses**, are the **sum of hysteresis losses and eddy current losses**, which happens **even** when the transformer has **no load** (due to this fact *iron losses* are also known as **no-load losses**).

Both *resistive losses and iron losses* are indicated by the transformer’s manufacturer.

It is common that transformers that are not in service permanently (example: public lighting transformers) are required to have *reduced iron losses*.

Also Read: Maintenance of Transformer – Power Transformers Maintenance, Diagnostic & Monitoring

**Total losses **(**P _{t}**) are given by the equation:

**P _{t} = P_{0} + P_{Cu} (W)**

Iron losses are determined from open circuit test and resistive losses from short circuit test.

Efficiency of a transformer (noted “**η**” and expressed in “**%**”) is defined as the **ratio between the input and the output active power**.

Considering a transformer with the following parameters:

*Input*:**P**_{1 }; V_{1}, I_{1}*Output*:**P**_{2 }; V_{2}, I_{2}*Load power factor*:**Cos Φ**

Efficiency is then calculated according to the following equation:

Hence at any volt-ampere load, the efficiency depends on power factor; at unity power factor efficiency has its maximum value.

**Impedance Voltage Drop in T/F**

**Impedance voltage drop **of a transformer represents the **internal resistance** of the transformer, and is usually noted as “**u _{k}**” and indicated in “

**%**”.

The *equivalent impedances* of the transformer are calculated by the equations:

__Primary side__

**Z _{T }= u_{k}(%) x U_{1}^{2 }/ 100 x Sn**

__Secondary side__

**Z _{T} = u_{k}(%) x U_{2}^{2} / 100 x Sn**

The values of the equivalent resistance and reactance of the transformer are given by the following equations:

**R _{T }= P_{Cu} / 3xI_{n}^{2}**

** ^{}**Related Post: What is the normal or average life expectancy of a Transformer ?

**Vector Group of Transformers**

**Vector group** of three-phase transformers indicate the **phase shift between primary and secondary voltages** and the **way the windings are connected**.

Three-phase windings transformers can have “**star**” (**Y/y**), “**delta**” (**D/d**) [ In *delta connection*, windings are connected in **triangl e**, so it is usual to represent this connections by

**Δ**] and “

**interconnected star**” / “

**zigzag**” (

**Z/z**) connections, being the

**most common**

*star*and

*delta*.

If the transformer has *tertiary windings*, usually for **harmonic compensations**, (mainly *3rd harmonic*) these windings have a “*delta*” connection.

**Capital letters refer always to highest voltage and lower-case letters to lowest voltage.**

When *neutral point* is accessible letter “**N**” or “**n**” is added to the symbol.

Table 1 shows the most common vector groups.

Table 1 – Common vector groups

Most common connections are **Y-Δ, Δ-Y, Δ-Δ and Y-Y**; *star-star* is common in **EHV and HV**, although it presents **imbalance and 3rd harmonic problems**, being *necessary the third winding* above referred.

*Star-Delta* (**Y-Δ**) is frequently used as *step down* (**EHV/HV**); *delta-delta* (**Δ-Δ**) is commonly used for *medium voltage* (**MV/MV** transformers); *delta-star* (**Δ-Y**) is used in *step-up* transformer in a *generation station* and in **MV/LV** transformers.[**EHV**: Extra High Voltage (**V ≥ 150 kV**). **HV**: High Voltage (**60 kV ≤ V < 150 kV**). **MV**: Medium Voltage (**1 kV < V < 60 kV**). **LV**: Low Voltage (**V ≤ 1 kV**)]

Common groups in *MV/LV* power transformers are **Dyn5 and Dyn11**; for *HV/MV* power transformers is usual to have a vector group **YNd11**, and for *HV/HV* transformers is common to have **YNyn0 and Ynyn1**.

**Voltage Regulation of Transformer**

*Electrical networks* may have **voltage fluctuations**, due to *load changing, network configuration and level of energy production*.

For that reason is necessary to proceed to **voltage regulation**; Transformer regulation is done *usually at the highest voltage windings of power transformers (because the current is lower)*.

Those *windings* must be provided with **taps, voltage regulators and tap-changers**.

At **MV** installations transformers have usually **5 taps** (*central point that corresponds to rated voltage and***± 2×2.5 %***taps*) and **off-load tap changer**. The *ratio of the voltages* of the transformer is so defined as:

**33 ± 2×2.5 % / 6.6 kV**

At *HV* installations transformers have **several taps**, including the *central point* and **on-load tap changer **(*OLTC*) that can me manually and locally or remote operated or automatic operated through the *Control and Monitoring System*.

The *ratio of the voltages* of the transformer, taking into account the **number of taps and their range**, may be defined as:

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