APPENDIX 8I. TRIAL STANDARD LEVEL CONSISTENCY OF SINGLE-PHASE AND 

THREE-PHASE TRANSFORMERS 

TABLE OF CONTENTS 

8I.1 INTRODUCTION ................................................................................................................. 2 

8I.2 Final Rule Trial Standard Levels ........................................................................................... 2

8I.3 Single-Phase Transformers – Inter-Phase Consistency ......................................................... 4 

8I.4 Three-Phase Transformers – Inter-Phase Consistency .......................................................... 6 

8I.5 Consistency Between Single-Phase and Three-Phase ........................................................... 9 

LIST OF TABLES 

Table 8I.1 Efficiency Values for Single-Phase kVA Ratings and all Trial Standard Levels ..........3 

Table 8I.2 Efficiency Values for Three-Phase kVA Ratings and all Trial Standard Levels ...........3 

Table 8I.3 Increase in Efficiency Values for Single-Phase kVA Ratings .......................................4 

Table 8I.4 Increase in Efficiency Values for Three-Phase kVA Ratings ........................................7 

LIST OF FIGURES 

Figure 8I.1 Incremental Increases in Single-Phase Efficiency for TSL2 .......................................5 

Figure 8I.2 Incremental Increases in Single-Phase Efficiency for TSL4 .......................................5 

Figure 8I.3 Incremental Increases in Single-Phase Efficiency for TSL5 .......................................6 

Figure 8I.4 Incremental Increases in Three-Phase Efficiency for TSLC........................................7 

Figure 8I.5 Incremental Increases in Three-Phase Efficiency for TSL3 ........................................8 

Figure 8I.6 Incremental Increases in Three-Phase Efficiency for TSL4 ........................................8 

Figure 8I.7 Inconsistency Between Phases at TSL2.......................................................................9 

Figure 8I.8 Inconsistency Between Phases at TSL3.....................................................................10 

Figure 8I.9 Inconsistency Between Phases at TSL4.....................................................................10 

Figure 8I.10 Inconsistency Between Phases at TSL5 ...................................................................11 

Figure 8I.11 Inconsistency Between Phases at TSL6 ...................................................................12 

Figure 8I.12 Inconsistency Between Phases at TSLD ..................................................................12 

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 EE-RM/STD-00-550 COMMENT 196
APPENDIX 8I. TRIAL STANDARD LEVEL CONSISTENCY OF SINGLEPHASE AND THREE-PHASE TRANSFORMERS 

8I.1 INTRODUCTION 

This appendix contains a review of the degree of consistency of the efficiency ratings 

within the trial standard levels considered for single-phase and three-phase transformers. The 

issue of consistency only affects liquid-immersed distribution transformers, because single-phase 

and three-phase units were analyzed separately. For medium-voltage dry-type units, the higher 

shipment volume three-phase units were analyzed, and the single-phase standard levels were 

scaled from the three-phase standard levels. 

There are two kinds of consistency issues associated with the trial standard levels 

considered for liquid-immersed distribution transformers, 1) continuity across capacities (or kVA 

ratings) at the interfaces between design lines, called “Inter-Phase Consistency”, and 2) 

consistency of minimum efficiency values for single and three phase transformers, called 

“Between-Phase Consistency.” 

1) Inter-Phase Consistency – this concerns consistency issues as they relate to the efficiency 

values within all the single-phase or all the three-phase transformers. DOE analyzed 

multiple baseline models, three single-phase kVA ratings and two three-phase kVA 

ratings. Each of these five baseline models analyzed had its only range of applicable kVA 

ratings, called ‘design lines’. Inter-Phase consistency pertains to the interface between the 

design lines, and whether the step increase in efficiency is consistent with the other 

increments above and below. This issue is discussed in sections 8I.3 and 8I.4. 

2) Between-Phase Consistency – this concerns consistency of the efficiency values between 

single-phase transformers and the per-phase kVA equivalent three-phase transformers. 

Because single-phase units were analyzed separately from three-phase units, the resultant 

efficiency values were not always consistent. Between-Phase consistency pertains to trial 

standard levels 2 through 6, but is not an issue for trial standard level 1, A, B, C or D. 

This issue is discussed and illustrated in section 8I.5. 

8I.2 FINAL RULE TRIAL STANDARD LEVELS 

The following two tables present all the trial standard levels that were considered by 

DOE in its Energy Conservation Standards Final Rule for Distribution Transformers. The 

second table, which presents the three-phase efficiency ratings has a column marked 

‘kVA/phase’, which shows the kVA rating per phase for these three-phase transformers. When 

making a comparison of the efficiency value between the single-phase table and the three-phase 

table, the kVA/phase column of values should be used to determine equivalency. For example, 

note that in the first table, the 50 kVA single-phase transformer has a TSL1 efficiency value of 

98.9. In the second table, the 150 kVA three-phase (kVA per phase equivalent to the 50 kVA 

single-phase) transformer has a TSL1 efficiency value of 98.9. Thus, a comparison of these two 

transformers in these two tables reveals no consistency issue between single-phase and threephase at that kVA rating. 

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 EE-RM/STD-00-550 COMMENT 196
An Inter-Phase consistency problem can be observed in the second (three-phase) table of 

efficiency values, considering the efficiency ratings under TSL4 for 500 and 750 kVA 

transformers. The efficiency level drops for the higher kVA rating, which is counter-intuitive. A 

Between-Phase consistency problem can be observed comparing the efficiency requirements at 

TSL for 50 kVA single-phase (99.04%) with the 150 kVA three-phase (99.26%) – the threephase is considerably higher, and is inconsistent with its single-phase counterpart. 

Table 8I.1 Efficiency Values for Single-Phase kVA Ratings and all Trial Standard Levels 

kVA TSL1 TSL2 TSL3 TSL4 TSL5 TSL6 TSLA TSLB TSLC TSLD 

10 98.4 98.40 98.44 98.48 98.69 99.32 98.79 98.62 98.62 98.56 

15 98.6 98.56 98.59 98.63 98.82 99.39 98.91 98.76 98.76 98.70 

25 98.7 98.73 98.76 98.79 98.96 99.46 99.04 98.91 98.91 98.79 

37.5 98.8 98.85 98.88 98.91 99.06 99.51 99.13 99.01 99.01 98.97 

50 98.9 98.90 98.90 99.04 99.19 99.59 99.19 99.08 99.08 99.04 

75 99.0 99.04 99.06 99.08 99.21 99.59 99.27 99.17 99.17 99.13 

100 99.0 99.10 99.12 99.14 99.26 99.62 99.32 99.23 99.23 99.19 

167 99.1 99.21 99.23 99.25 99.35 99.66 99.40 99.32 99.27 99.29 

250 99.2 99.26 99.36 99.45 99.69 99.70 99.45 99.37 99.31 99.26 

333 99.2 99.31 99.40 99.49 99.71 99.72 99.49 99.41 99.36 99.31 

500 99.3 99.38 99.46 99.54 99.74 99.75 99.54 99.47 99.42 99.38 

667 99.4 99.42 99.50 99.57 99.76 99.77 99.57 99.51 99.46 99.42 

833 99.4 99.45 99.52 99.60 99.77 99.78 99.60 99.53 99.49 99.45 

Table 8I.2 Efficiency Values for Three-Phase kVA Ratings and all Trial Standard Levels 

kVA kVA / 

Phase 

TSL1 TSL2 TSL3 TSL4 TSL5 TSL6 TSLA TSLB TSLC TSLD 

15 5 98.1 98.36 98.68 98.68 99.25 99.31 98.56 98.36 98.36 98.36 

30 10 98.4 98.62 98.89 98.89 99.37 99.42 98.79 98.62 98.62 98.62 

45 15 98.6 98.76 99.00 99.00 99.43 99.47 98.91 98.76 98.76 98.76 

75 25 98.7 98.91 99.12 99.12 99.50 99.54 99.04 98.91 98.91 98.91 

112.5 38 98.8 99.01 99.20 99.20 99.55 99.58 99.13 99.01 99.01 99.01 

150 50 98.9 99.08 99.26 99.26 99.58 99.61 99.19 99.08 99.08 99.08 

225 75 99.0 99.17 99.33 99.33 99.62 99.65 99.27 99.17 99.17 99.17 

300 100 99.0 99.23 99.38 99.38 99.65 99.67 99.32 99.23 99.23 99.23 

500 167 99.1 99.32 99.45 99.45 99.69 99.71 99.40 99.32 99.27 99.32 

750 250 99.2 99.24 99.31 99.37 99.66 99.66 99.45 99.37 99.31 99.31 

1000 333 99.2 99.29 99.36 99.41 99.68 99.68 99.49 99.41 99.36 99.36 

1500 500 99.3 99.36 99.42 99.47 99.71 99.71 99.54 99.47 99.42 99.42 

2000 667 99.4 99.40 99.46 99.51 99.73 99.73 99.57 99.51 99.46 99.46 

2500 833 99.4 99.44 99.49 99.53 99.74 99.74 99.60 99.53 99.49 99.49 

8I-3

 EE-RM/STD-00-550 COMMENT 196
8I.3 SINGLE-PHASE TRANSFORMERS – INTER-PHASE CONSISTENCY 

The following table presents the incremental increases in efficiency observed for all the 

trial standard levels considered for liquid-immersed single-phase transformers. The smaller kVA 

ratings (i.e., 10 through 167) are represented by analysis on a 25 kVA pole-mount and a 50 kVA 

pad-type distribution transformer. The larger kVA ratings (i.e., 250 through 833) are represented 

by analysis on a 500 kVA single-phase round-tank. Generally, the numerical increase in 

efficiency is greatest at the smaller kVA ratings, and decreases gradually as the kVA rating 

increases. 

Table 8I.3 Increase in Efficiency Values for Single-Phase kVA Ratings 

kVA TSL1 TSL2 TSL3 TSL4 TSL5 TSL6 TSLA TSLB TSLC TSLD 

10 

15 0.200 0.160 0.150 0.150 0.130 0.070 0.117 0.133 0.133 0.138 

25 0.100 0.170 0.170 0.160 0.140 0.070 0.134 0.153 0.153 0.087 

37.5 0.100 0.120 0.120 0.120 0.100 0.050 0.090 0.101 0.101 0.178 

50 0.100 0.050 0.020 0.130 0.130 0.080 0.060 0.069 0.069 0.072 

75 0.100 0.140 0.160 0.040 0.020 - 0.078 0.089 0.089 0.093 

100 - 0.060 0.060 0.060 0.050 0.030 0.051 0.058 0.058 0.060 

167 0.100 0.110 0.110 0.110 0.090 0.040 0.082 0.093 0.044 0.097 

250 0.100 0.050 0.130 0.200 0.340 0.040 0.052 0.050 0.044 (0.027) 

333 - 0.050 0.040 0.040 0.020 0.020 0.038 0.044 0.044 0.051 

500 0.100 0.070 0.060 0.050 0.030 0.030 0.049 0.057 0.062 0.066 

667 0.100 0.040 0.040 0.030 0.020 0.020 0.032 0.037 0.040 0.043 

833 - 0.030 0.020 0.030 0.010 0.010 0.023 0.027 0.029 0.031 

The following figure illustrates the incremental increases in efficiency values for TSL2, 

the level that DOE proposed in the 2006 notice of proposed rulemaking. In this histogram, the 

general trend of decreasing incremental increases in efficiency with larger kVA ratings is 

evident. In addition, the transition between the small and large kVA ratings (which occurs 

between 167 and 250kVA) is hardly perceivable. The incremental change in efficiency between 

those two ratings is in line with the magnitude of other incremental changes at similar kVA 

ratings. 

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 EE-RM/STD-00-550 COMMENT 196
0.180

0.160

0.140

0.120

0.100

0.080

0.060

0.040

0.020

-

Change in Percent Efficiency 

15 25 37.5 50 75 100 167 250 333 500 667 833 

kVA ratings 

Figure 8I.1 Incremental Increases in Single-Phase Efficiency for TSL2 

The following two plots illustrate where the inter-phase consistency issue is particularly 

problematic, TSLs 4 and 5. For these two plots, the required increase in efficiency for the 250 

kVA is not in line with the transformers above and below the 250 kVA, and consequently, the 

standard level is inconsistent across the kVA ratings. 

-

0.050 

0.100 

0.150 

0.200 

0.250 

Change in Percent Efficiency 

15 25 37.5 50 75 100 167 250 333 500 667 833 

kVA ratings 

Figure 8I.2 Incremental Increases in Single-Phase Efficiency for TSL4 

8I-5 

 EE-RM/STD-00-550 COMMENT 196
The relative magnitude of that difference is even more pronounced at TSL5, where the 

efficiency increase between 167 and 250 is more than double any other efficiency increase Change in Percent Efficiency 

between any other two single-phase liquid-immersed kVA ratings. 

0.400 

0.350 

0.300 

0.250 

0.200 

0.150 

0.100 

0.050 

-

15 25 37.5 50 75 100 167 250 333 500 667 833 

kVA ratings 

Figure 8I.3 Incremental Increases in Single-Phase Efficiency for TSL5 

8I.4 THREE-PHASE TRANSFORMERS – INTER-PHASE CONSISTENCY 

The following table presents the incremental increases in efficiency observed for all the 

trial standard levels considered for liquid-immersed three-phase transformers. The smaller kVA 

ratings (i.e., 15 through 500) are represented by analysis on a 150 kVA pad-mount three-phase 

distribution transformer. The larger kVA ratings (i.e., 750 through 2500) are represented by 

analysis on a 1500 kVA three-phase pad mount. The transition between the smaller and larger 

kVA ratings occurs between the 500 and 750 kVA ratings, and is presented in the 750 kVA row 

of the table. The discontinuity between the smaller and larger kVA ratings analyzed for threephase liquid-immersed transformers is immediately evident in the negative increment shown for 

several TSLs, between 500 and 750: TSL2, TSL3, TSL4, TSL5, TSL6 and TSLD. In all of these 

cases, the efficiency rating for the 750 kVA unit is lower than the requirement of the 500 kVA 

unit. 

As for the single-phase units, the general trend is for the incremental increase in 

efficiency to decrease as the kVA rating increases. 

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 EE-RM/STD-00-550 COMMENT 196
Table 8I.4 Increase in Efficiency Values for Three-Phase kVA Ratings 

kVA TSL1 TSL2 TSL3 TSL4 TSL5 TSL6 TSLA TSLB TSLC TSLD 

15 

30 0.300 0.260 0.210 0.210 0.120 0.110 0.229 0.260 0.260 0.260 

45 0.200 0.140 0.110 0.110 0.060 0.050 0.117 0.133 0.133 0.133 

75 0.100 0.150 0.120 0.120 0.070 0.070 0.131 0.149 0.149 0.149 

112.5 0.100 0.100 0.080 0.080 0.050 0.040 0.093 0.105 0.105 0.105 

150 0.100 0.070 0.060 0.060 0.030 0.030 0.060 0.069 0.069 0.069 

225 0.100 0.090 0.070 0.070 0.040 0.040 0.078 0.089 0.089 0.089 

300 - 0.060 0.050 0.050 0.030 0.020 0.051 0.058 0.058 0.058 

500 0.100 0.090 0.070 0.070 0.040 0.040 0.082 0.093 0.044 0.093 

750 0.100 (0.080) (0.140) (0.080) (0.030) (0.050) 0.052 0.051 0.044 (0.009) 

1000 - 0.050 0.050 0.040 0.020 0.020 0.038 0.044 0.044 0.048 

1500 0.100 0.070 0.060 0.060 0.030 0.030 0.049 0.057 0.062 0.062 

2000 0.100 0.040 0.040 0.040 0.020 0.020 0.032 0.037 0.040 0.040 

2500 - 0.040 0.030 0.020 0.010 0.010 0.023 0.027 0.029 0.029 

The following figure illustrates the incremental increases in efficiency values for TSLC. 

In this histogram, the general trend of decreasing incremental increases in efficiency with larger 

kVA ratings is evident. In addition, the transition between the small and large kVA ratings 

(which occurs between 500 and 750kVA) is hardly perceivable. The incremental change in 

efficiency between those two ratings is in line with the magnitude of other incremental changes 

at similar kVA ratings. 

-

y 

0.050 

0.100 

0.150 

0.200 

0.250 

0.300 

Change in Percent Efficienc

30 

45 

75

11

5

1

0

50 

225 

300 

500 

750

10

0

0

0

2.

0

50

00

50

1

2

2

kVA ratings 

Figure 8I.4 Incremental Increases in Three-Phase Efficiency for TSLC 

The following two plots illustrate where the inter-phase consistency issue is particularly 

problematic, TSLs 3 and 4. For these two plots, the efficiency transition between the 500 and 

750 kVA transformer is negative, depicting a lower efficiency requirement for the higher kVA 

rating. 

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 EE-RM/STD-00-550 COMMENT 196
(0.200) 

(0.150) 

(0.100) 

(0.050) 

-

0.050 

0.100 

0.150 

0.200 

0.250 

30 

45 

75 

112.5 

150 

225 

300 

500 

750

1000

1500

2000

2500

Change in Percent Efficiency 

kVA ratings 

Figure 8I.5 Incremental Increases in Three-Phase Efficiency for TSL3 

(0.100) 

(0.050) 

-

0.050 

0.100 

0.150 

0.200 

0.250 

30 

45 

75

112.5 

150 

225 

300 

500 

750

1000

1500

2000

2500

Change in Percent Efficiency 

kVA ratings 

Figure 8I.6 Incremental Increases in Three-Phase Efficiency for TSL4 

8I-8 

 EE-RM/STD-00-550 COMMENT 196
8I.5 CONSISTENCY BETWEEN SINGLE-PHASE AND THREE-PHASE 

This section presents plots for all the TSLs which have inconsistent efficiency 

requirements for the kVA ratings. Only those TSLs which have inconsistent values between Efficiency at 50% Load (%) 

single-phase and their three-phase equivalents are presented. Thus, TSL1, TSLA, TSLB, and 

TSLC are not plotted in this section. For each of these four TSLs, the efficiency requirements of 

the single-phase liquid-immersed transformers is identical to their three-phase per kVA liquidimmersed equivalents. 

For TSL2, the three-phase standard is higher (more stringent) than the single-phase 

standard at smaller kVA ratings, but lower (less stringent) than the single-phase at larger kVA 

ratings. 

99.60 

99.40 

99.20 

99.00 

98.80 

98.60 

98.40 

98.20 

0 100 200 300 400 500 600 700 800 900 

Sing e-Phase l

Three-Phase 

kVA Rating 

Figure 8I.7 Inconsistency Between Phases at TSL2 

For TSL3, the three-phase standard is higher (more stringent) than the single-phase 

standard at smaller kVA ratings, but lower (less stringent) than the single-phase at larger kVA 

ratings. 

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 EE-RM/STD-00-550 COMMENT 196
98.20 

98.40 

98.60 

98.80 

99.00 

99.20 

99.40 

99.60 

(%) 

Singl

Efficiency at 50% Load 

e-Phase 

Three-Phase 

0 100 200 300 400 500 600 700 800 900 

kVA Rating 

Figure 8I.8 Inconsistency Between Phases at TSL3 

For TSL4, the three-phase standard is higher (more stringent) than the single-phase 

standard at smaller kVA ratings, but lower (less stringent) than the single-phase at larger kVA 

ratings. 

98.40 

98.60 

98.80 

99.00 

99.20 

99.40 

99.60 

99.80 

(%) 

l

Efficiency at 50% Load

Sing e-Phase 

Three-Phase 

0 100 200 300 400 500 600 700 800 900 

kVA Rating 

Figure 8I.9 Inconsistency Between Phases at TSL4 

8I-10 

 EE-RM/STD-00-550 COMMENT 196
For TSL5, the three-phase standard is higher (more stringent) than the single-phase 

standard at smaller kVA ratings, but lower (less stringent) than the single-phase at larger kVA 

ratings. In addition, there is considerable disparity in the efficiency requirements between the 

phases for the smaller kVA transformers. Efficiency at 50% Load (%) 

100.00 

99.80 

99.60 

99.40 

99.20 

99.00 

98.80 

98.60 

0 100 200 300 400 500 600 700 800 900 

Sing e-Phase l

Three-Phase 

kVA Rating 

Figure 8I.10 Inconsistency Between Phases at TSL5 

For TSL6, the three-phase standard is higher (more stringent) than the single-phase 

standard at smaller kVA ratings, but lower (less stringent) than the single-phase at larger kVA 

ratings. 

8I-11

 EE-RM/STD-00-550 COMMENT 196
99.20 

99.30 

99.40 

99.50 

99.60 

99.70 

99.80 

99.90 

(%) 

l

Efficiency at 50% Load

Sing e-Phase 

Three-Phase 

0 100 200 300 400 500 600 700 800 900 

kVA Rating 

Figure 8I.11 Inconsistency Between Phases at TSL6 

For TSLD, the three-phase standard is higher (more stringent) than the single-phase 

standard at all kVA ratings. 

98.20 

98.40 

98.60 

98.80 

99.00 

99.20 

99.40 

99.60 

(%) 

Si

Efficiency at 50% Load

ngle-Phase 

Three-Phase 

0 100 200 300 400 500 600 700 800 900 

kVA Rating 

Figure 8I.12 Inconsistency Between Phases at TSLD 

8I-12 

 EE-RM/STD-00-550 COMMENT 196