### 1 Distribution Transformer Loading September 14 , 2011

The following method allows a quick and accurate way of determining the average loading

on distribution transformer s. It can be broken into five stages.

**•** kWhr sales through distribution transformers

**•** Installed kVA base of distribution transformers

**•** Estimation of power factor

**•** Average loading calculation

**•** Average losses calculation

kWhr Sales

Utilities know the kWh rs of power they sell to their customers. The figure is usually know n by class of customer, so primary voltage customers and transmission voltage customer

sales , etc. can be excluded and only kWhr s of electricity sold through distribution

transformers included. This can be turned into an average kW demand. Accuracy of this number should be hig h.

At Xcel Energy Colorado area the sales are as follows:

Voltage Level kWhr Sales

Total Xcel Energy Sales 28,188,827,436

Transmission Voltage Sales (2,376,767,267)

Primary Voltage Sales (3,254,979,074)

Sales Through Distribution

Transformers 22,557,0 81,095

Hours per year 8760

Average kW demand 2,575,009

Transformer Installed Base Many utilities have a GIS system that has all the kVA of distribution transformer installed on their distribution system. If this is lacking then the kVA of distribution transformers may be available through plant accounting records . Care needs to be taken to exclude primary voltage to primary voltage step

- down transformer or other non

- customer transformers. Accuracy should be high as long as utility records are good.

At Xcel Energy Colorado area the kVA installed base is as follows:

Type kVA

Overhead Transformers 3,199,869

Padmounted transformers 10,572,436

kVA of Distribution Transformers 13,772,304

Power Factor Estimates and studies vary on the average power factor. Most range around .9

, but .85 is

used to be conservative. (The range has some dependency on if correcting power factor is built into your rates.)

Average kW demand 2,575,009

Estimated Power Factor .85

Average kVA demand 3,029,423

### 2 Average Loadin g Calculation The average loading on distribution transformer s can then be calculated by simple

division.

Average kW demand 2,575,009

kVA of Distribution Transformers 13,772,304

Average Loading 22%

Losses vary as the square of the load so accounting for the sum of the squares being greater than the square of the sum is appropriate. Stated without example, an estimation of loading variation of all transformers on the system could give losses running about 5 0% higher than simply squaring the average l oad.

A common misconception is that transformer start out lightly loaded but the load increase s over the life of the transformer, so over the life of the transformer the average load is 50%. A total distribution system loaded at 22% cannot yield a model where over the life of the

transformer i t could be loaded to 50% on the average. (Extremely rapid growth of the

installed base would not be sufficient. This number has changed little since I first did this calculation over 25 years ago )

If transformer s are divided into categories such as overhead, single phase pad mounted and three phase pad mounted or by kVA

, the average load calculation can still be used as a base line. If one category is loaded above the average then the other categories must

loaded less than the average.

Average Losses Calculation

Transformer
50kVA, 14.4/24.94
– 240/120

No Load Losses – 108 W

Load Losses 55 o C
– 476 W (Can be corrected for a calculated average temperature)

Transformer loaded 22%. 108W + (476W * .22^ 2 * 1. 5 ) = 1 4 3W average loss over life of transformer (35 W of load losses) If the transformer is assumed to be loaded 50% the answer is quite different. 108W + (476W * .50^ 2 * 1.5 ) = 2 86 W average loss over life of transformer (1 78 W of load losses)

C onclusions Calculating the average load from a utility average gives an appropriate baseline for calculating energy saving. Accuracy using this method should be good. It is also appropriated as a baseline for a calculation of the ratio of no load to load losses.

At 25% loading the ratio should be around 8 to 1, but will vary with the loading and with the cost of capacity and energy. If the ratio is wrong, you will be specifying a transformer that is more efficient than necessary and may not be reducin g losses appropriately.

Manufacturers tell us a $4.00/W no load and $1.00/W load roughly gives DOE efficiency.

If loss costs are $ 4.00 /W no load and $0.5 0 /W load, instead, the n any increase in the efficiency standards will not have a payback over a 30 year life.

David Flaten, Xcel Energy