Transformer Loadings and Ef ficiency

DOE Distribution Transformer Negotiating Subcommittee Memo November 28, 2011

T he efficiency of a transformer is d efined 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 . I t c an be shown that maximum
effi ciency 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

RMS opt = (NL/LL )

1

/2

.

The test procedure efficiency ( Eff TP ) 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 Eff TP , 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 mo re efficient at 35% RMS than at 50%, for m any 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 loa d (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 th e 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 Eff TP (2) > Eff TP (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 analysi s 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 RMS opt as defined above, for a subset of the DL1 designs. Th e 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 0.996Efficiency at RMS=35%

Efficiency at Test Procedure RMS=50%Figure 2 RMS opt for the lowest

- priced units for each design option modeled for DL1

By definition, the efficiency is at its maximum at RMS opt . This means that, if RMS opt < 50%, the design will have higher efficiency than predicted by the test procedure at lower loads; conversely
if RMS opt > 50% the design will perform better than predicted at high loads. In general there is no relationship in the data between RMS opt and price. In the LCC simulation, there is also no relationship between the RMS load assigned to a purchaser, and the RMS opt of the design selected for that purchaser. In reality, a purchaser could request that a tr ansformer 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 RMS opt 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 10RMS Load for Maximum Efficiency

Design Option Label C01

C02

C03

C04

C05

C06

C07

C08

C09Figure 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 b e 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 prop osed standard. 1500 1700 1900 2100 2300 2500 2700 2900 3100 3300 3500

0.990 0.991 0.992 0.993 0.994 0.995 0.996Price of Least-Cost Transformer

Efficiency at Test Procedure Load C01

C02

C03

C04

C05

C06

C07

C08

C09