Calculating losses in distribution transformers is essential for assessing their efficiency and performance. Two main types of losses occur in distribution transformers: core (iron) losses and copper losses. By quantifying these losses, engineers can determine the transformer’s total loss and make informed decisions regarding transformer selection, maintenance, and optimization.

Core (Iron) Losses

Core losses, also known as iron losses, occur in the transformer’s core due to the alternating magnetic field. These losses are independent of the load current and are present whenever the transformer is energized. The two components of core losses are hysteresis losses and eddy current losses. Hysteresis losses result from the energy required to continuously magnetize and demagnetize the core material, while eddy current losses are caused by circulating currents induced in the core by the changing magnetic field.

To calculate the iron loss power in kilowatt-hours (kWh), multiply the no-load loss (in kilowatts) by the power supply time (in hours). The no-load loss is determined by measuring the power consumed by the transformer when it is energized but not connected to a load. This value can be obtained from the transformer’s manufacturer or through testing. The power supply time is the duration for which the transformer is energized.

Iron loss power (kWh) = no-load loss (kW) × power supply time (hours)

For example, if a transformer has a no-load loss of 0.5 kW and is energized for 720 hours (30 days), the iron loss power would be:

Iron loss power = 0.5 kW × 720 hours = 360 kWh

Copper Losses

Copper losses occur in the transformer’s windings due to the resistance of the conductor material. Unlike core losses, copper losses are load-dependent and increase with the square of the load current. The primary factors affecting copper losses are the resistance of the winding conductor, the load current, and the operating temperature.

The copper loss calculation depends on the transformer’s load factor, which is the ratio of the average load to the rated load over a given period. For transformers with a load factor less than or equal to 40%, the copper loss is estimated as 2% of the monthly power consumption. For load factors greater than 40%, the copper loss is approximated as 3% of the monthly power consumption.

For load factor ≤ 40%: Copper loss = monthly power consumption × 2%
For load factor > 40%: Copper loss = monthly power consumption × 3%

To illustrate, consider a transformer with a monthly power consumption of 10,000 kWh and a load factor of 35%. The copper loss would be:

Copper loss = 10,000 kWh × 2% = 200 kWh

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Distribution Transformer Losses Calculation

Introduction

Distribution transformers are a critical component in electrical power distribution systems, stepping down high voltage power from the grid to levels suitable for end users. However, no transformer is 100% efficient – a portion of the energy passing through the transformer is lost as heat due to various factors. Accurately calculating these losses is essential for utilities to optimize their systems, select appropriately sized transformers, and estimate operating costs.

This article will provide a detailed guide on how to calculate the total losses in a distribution transformer and determine the transformer’s load factor, a key metric that impacts its efficiency. We’ll break down the relevant formulas step-by-step so electrical engineers and technicians can confidently perform these important calculations.

Total Loss Calculation

The total losses in a transformer consist of two main components: no-load losses (also known as core losses or iron losses) and load losses (also called copper losses or winding losses). No-load losses are present whenever the transformer is energized, even if there is no load connected to the secondary winding. They are caused by hysteresis and eddy currents in the transformer core. Load losses, on the other hand, occur when current flows through the transformer windings to supply a load. They are primarily due to the resistance of the winding conductors.

To calculate the total losses (P_TL) in a transformer in watts, we use the following formula:

P_TL = P_NL + P_LL

Where:

• P_NL = No-load losses in watts
• P_LL = Load losses in watts

The no-load loss value can be obtained from the transformer manufacturer’s datasheet or by performing an open-circuit test on the transformer. In this test, rated voltage is applied to the transformer primary with the secondary open-circuited (no load). The small current that flows is measured and multiplied by the applied voltage to give the no-load losses.

Load losses are usually quoted on the datasheet at full rated load. However, the actual load losses vary with the square of the load current:

P_LL = I₂R

Where:

• I = RMS load current
• R = Effective resistance of transformer windings

So for example, if a 100 kVA transformer has quoted load losses of 2000 W at full load, but is only supplying a 60 kVA load, the actual load losses would be:

P_LL = (60/100)² x 2000 = 720 W

The total losses at 60% loading would then be:

P_TL = P_NL + 720

Load Factor Determination

The load factor (LF) of a transformer is the ratio of its actual average load over a given period to its rated full load capacity. It’s an important metric because transformers achieve their highest efficiency when operating near their rated load – at light loads, the fixed no-load losses make up a larger proportion of the total losses. Transformers are therefore often intentionally slightly undersized to keep the load factor high.

Load factor can be calculated as follows:

LF = kWh / (P_FL x t)

Where:

• kWh = Energy consumed by load in kilowatt-hours over time period t
• P_FL = Rated full load capacity of transformer in kilowatts
• t = Number of hours in the time period

For example, consider a 150 kVA transformer supplying a load that consumes 8100 kWh over a 30-day month. The load factor would be:

LF = 8100 / (150 x 24 x 30) = 0.75 or 75%

A load factor of 0.75 means the transformer is on average loaded to 75% of its full capacity.

In some cases, a transformer’s historical load profile may not be known. The load factor can then be estimated based on the type of load it serves: