Transformer Loadings and Efficiency

DOE Distribution Transformer Negotiating Subcommittee Memo

November 28, 2011 

The efficiency of a transformer is defined as the ratio of load to load plus losses, calculated as

. 

Where:

Eff = the efficiency;

kVA = the transformer capacity; 

RMS = the root-mean-square average load relative to the transformer capacity; 

NL = the no-load loss rate; 

LL = the load loss rate; 

The efficiency is a non-linear function of the RMS load. It can be shown that maximum 

efficiency for a given transformer occurs for a value of the RMS load such that the load and noload losses are equal; this optimal value is given by the formula 

RMSopt = (NL/LL) 1/2. 

The test procedure efficiency (EffTP) is defined for a specific RMS load, equal to 50% for 

medium-voltage transformers. If the actual RMS loading in the field is not 50%, the actual 

efficiency will be different from EffTP, with the value of the difference dependent on the details 

of the transformer design. This property is illustrated in Figure 1, which shows the efficiency at 

the test procedure load vs. the efficiency at 35% RMS load for the designs include in the 

engineering analysis for Design Line 1 (DL1). The diagonal is shown as a heavy black line. 

While some designs are more efficient at 35% RMS than at 50%, for many of these designs the 

efficiency is lower at the lower loading.
Figure 1 Comparison of the efficiency at RMS=35% to the efficiency at 

RMS=50% for DL01 units 

The Department’s engineering analysis provides a sample of possible transformer designs which 

are used to quantify the change in price induced by a change in efficiency across a range of 

design options. Efficiency targets can be met by varying both the load (coil) loss and the no-load 

(core) loss rates. Generally, units that are more efficient at lower loads are those which minimize 

core losses. In Figure 1, the lowest core losses are for amorphous core designs, which make up 

the small cloud of points in the upper right of the chart. 

The standard places a lower limit on the efficiency of a unit as measured at the test procedure 

load. Thus, for two units labeled 1 and 2, if EffTP(2) > EffTP(1), then according to the standard 

unit 2 is deemed more efficient than unit 1. However, this condition is not sufficient to guarantee 

that, at a different RMS load, unit 2 will still be more efficient. This uncertainty affects the 

energy savings that are predicted to result from the standard. The Department’s LCC analysis 

uses a distribution of loadings with a median of 25-30%, so any differences in performance 

between the test procedure load and the simulated field loading are accounted for in the LCC 

results. 

Figure 2 shows values of RMSopt as defined above, for a subset of the DL1 designs. The design

subset is defined by choosing the lowest price unit, for each design option, at a given efficiency. 

For reference, the price-efficiency curves for the same set of designs are shown in Figure 3, and

the design options (labeled C01...C09) are listed in Table 1. 

Table 1 List of design options

Label Design Specifications Label Design Specifications Label Design Specifications

C01 M5_CuAl_dgw_sh C04 M2_AlAl_dgw_sh C07 ZDMH_CuCu_dgw_sh

C02 M3_AlAl_dgw_sh C05 M2_CuAl_dgw_sh C08 SA1_AlAl_dgw_sh

C03 M3_CuAl_dgw_sh C06 ZDMH_AlAl_dgw_sh C09 SA1_CuCu_dgw_sh

0.988

0.989

0.99

0.991

0.992

0.993

0.994

0.995

0.996

0.988 0.99 0.992 0.994 0.996

Efficiency at RMS=35%

Efficiency at Test Procedure RMS=50%
Figure 2 RMSopt for the lowest-priced units for each design option modeled for DL1

By definition, the efficiency is at its maximum at RMSopt. This means that, if RMSopt < 50%, the 

design will have higher efficiency than predicted by the test procedure at lower loads; conversely 

if RMSopt > 50% the design will perform better than predicted at high loads. In general there is 

no relationship in the data between RMSopt and price. In the LCC simulation, there is also no 

relationship between the RMS load assigned to a purchaser, and the RMSopt of the design 

selected for that purchaser. In reality, a purchaser could request that a transformer be designed to 

perform well at a given RMS load, in addition to meeting the standard at the test procedure load. 

By neglecting this aspect of product choice, the LCC may be overestimating the performance 

degradation associated with a mismatch between the RMSopt of the design and the expected field 

loading. 

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10

RMS Load for Maximum Efficiency

Design Option Label

C01

C02

C03

C04

C05

C06

C07

C08

C09
Figure 3 Price vs. efficiency for the lowest price units shown in Figure 2.

As distribution transformers are engineered-to-order, the price-efficiency curve must be 

estimated by calculating the cost of producing specific designs. The design space sampled by the 

engineering analysis is not exhaustive, and does not include other design requirements that may 

be important to transformer purchasers. The efficiency standard is a performance requirement, 

not a design requirement, and it is possible that manufacturers will use different design options to 

meet the standard. This does not affect the LCC savings estimates, as long as the incremental 

cost due to increased efficiency is estimated correctly. It does however limit the usefulness of the 

LCC in predicting the market share of different core materials under a proposed standard. 

1500

1700

1900

2100

2300

2500

2700

2900

3100

3300

3500

0.990 0.991 0.992 0.993 0.994 0.995 0.996

Price of Least-Cost Transformer

Efficiency at Test Procedure Load

C01

C02

C03

C04

C05

C06

C07

C08

C09