### 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 Singl e-Phase and Three-Phase
........................................................... 9 LIST OF TABLES Table 8I.1 Efficiency Values for Single-PhasekV A Ratings and all Trial Standard Levels
.......... 3 Table 8I.2 Efficiency Values for Three-Phase kV A 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 inSingle-Phase Efficiency for TSL2
....................................... 5 Figure 8I.2 Incremental Increases inSingle-Phase Efficiency for TSL4
....................................... 5 Figure 8I.3 Incremental Increases inSingle-Phase Efficiency for TSL5
....................................... 6 Figure 8I.4 Incremental Increases inThree-Phase Efficiency for TSLC
........................................ 7 Figure 8I.5 Incremental Increases inThree-Phase Efficiency for TSL3
........................................ 8 Figure 8I.6 Incremental Increases inThree-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

8I-1

### 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 th e trial standard levels considered for single-phase and three-phase transformers. The issue of consistency only affects liquid-immerseddistribution transformers, because single-phase and three-phase units were analy zed separately. For medium-vol tage 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 a sso ciated with the trial standard levels considered for liquid-immersed distribution tran sformers, 1) continuityacross capacities (or kVA ratings) at the interfaces between design lines, called “Inter-Phase Consistency”, and 2 ) consistency of minimum efficiency values fo r single and three phasetransformers, called “Between-Phase Consistency.” 1) Inter-Phase Consistency – this concerns consiste ncy issues a s 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 ba seline models analyzed had it s 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 c onsistency 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 consiste ncy pertains to trial standard levels 2 through 6, but is not an issu e for trial standard level 1, A, B, C or D. This issue is discussed and illustrated in section 8I.5. 8I.2 FINAL RULE T RIAL STANDARD LEVELS The following two tables present all the trial stan dard levels that were considered by DOE in its Energy Conservation Standards Final Rule for Distribution Transformers. The second table, which presents the three-phaseefficiency ratings has a column marked ‘kVA/phase’, which shows the kVA rating per phas e for these three-phase transformers. When making a comparison of the efficiency value betw een 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, th e 50 kVA single-phase transformer ha s a TSL1 efficiency value of 98.9. In the second table, the 150 kVA three-ph ase (kVA per phase equi valent 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.

8I-2

### An Inter-Phase consistency problem can be obs erved in the second (three-phase) table of efficiency values, considering the effici ency ratings under TSL4 for 500 and 750 kVA transformers. The efficiency level drops for th e 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 th e 150 kVA three-phase (99.26%) – the threephase is considerably higher, and is incons istent with its single-phase counterpart. Table 8I.1 Efficiency Values for Single-PhasekVA Ratings and all Trial Standard Levels

kVA TSL1 TSL2TSL3 TSL4TSL5 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 TSL2TSL3 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

### 8I.3 SINGLE-PHASE TRANSFORMERS – INTER-PHASE CONSISTENCY The following table presents the incremental in creases in efficiency obs erved 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 rati ngs, and decreases gradually as the kVA rating increases. Table 8I.3 Increase in Efficiency Va lues for Single-Phas e kVA Ratings

kVA TSL1 TSL2 TSL3 TSL4TSL5 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 tran sition between the small and larg e kVA ratings (which occurs between 167 and 250kVA) is hardly perceivable. The incremental change in efficiency between those two ratings is in line w ith the magnitude of other incremental changes at similar kVA ratings.

8I-40.180 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 Si ngle-Phase Efficiency for TSL2 The following two plots illustrate where the inter-phase consistency issue is particularly problem atic, TSLs 4 and 5. For these two plots, the required increase in efficiency for the 250 kVA is not in line with the transformers aboveand below the 250 kVA, and consequently, the standard level is inconsis tent across the kVA ratings.

- 0.050 0.100 0.150 0.200 0.250Change in Percent Efficiency

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

### Figure 8I.2 Incremental Increases in Si ngle-Phase Efficiency for TSL4

8I-5

### The relative magnitude of that difference is even more pronounced at TSL5, where the efficiency increase between 167 and 250 is morethan double any other efficiency increaseChange 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 Si ngle-Phase Efficiency for TSL5
8I.4 THREE-P HASE TRANSFORMERS – INTER-PHASE CONSISTENCY The following table presents the incremental in creases in efficiency obs erved 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. Th e larger kVA ratings (i.e., 750 through 2500) are represented by analysis on a 1500 kVA three-phase pad mount. Th e 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 sm aller and larger kVA ratings analyzed for threephase liquid-immersed transformers is immediatel y evident in the negati ve increment shown for several TSLs, between 500 and 750: TSL2, TSL3, TS L4, 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 f or the incremental increase in efficiency to decrease as the kVA rating increases.

8I-6

### Table 8I.4 Increase in Efficiency Values for Three-Phase kVA Ratings kVA TSL1 TSL2 TSL3 TSL4TSL5 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 th e 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 0.300Change in Percent Efficienc

30 45 75 11 5 1 0 50 2 25 3 00 5 00 7 50 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 problem atic, TSLs 3 and 4. For these two plots, the efficiency transi tion between the 500 and 750 kVA transformer is negative, depicting a lower efficiency requirement for the higher kVA rating.

8I-7(0.200) (0.150) (0.100) (0.050) - 0.050 0.100 0.150 0.200 0.250

30 45 7 5 1 12.

5 1 50 225 300 50 0 750 1000 15 00 2 0

00 25 0 0Change 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 11 2.

5 150 225 300 50 0 75 0 1000 1 5

00 2 0

00 25 0 0Change in Percent Efficiency

kVA ratings 

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

8I-8

### 8I.5 CONSISTENCY BETWEEN SINGLE- PHASE AND THREE-PHASE This section presents plots for all the TS Ls which have inconsistent efficiency requirements for the kVA ratings. Only those TS Ls which have inconsistent values betweenEfficiency 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 th e 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 l Sing e-Phase 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 th e single-phase at larger kVA ratings.

8I-998.20 98.40 98.60 98.80 99.00 99.20 99.40 99.60(%)

SinglEfficiency 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 th e single-phase at larger kVA ratings.

98.40 98.60 98.80 99.00 99.20 99.40 99.60 99.80(%)

lEfficiency 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

### For TSL5, the three-phase standard is higher (more stringent) than the single-phase standard at smaller kVA ratings, but lower (less stringent) than th e single-phase at larger kVA ratings. In addition, there is c onsiderable disparity in the effi ciency 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 l Sing e-Phase 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 th e single-phase at larger kVA ratings.

8I-1199.20 99.30 99.40 99.50 99.60 99.70 99.80 99.90(%)

lEfficiency 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(%)



### SiEfficiency 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