WO1996024070A1

WO1996024070A1 - Method of sizing transformers in an electrical utility service

Info

Publication number: WO1996024070A1
Application number: PCT/US1995/015311
Authority: WO
Inventors: John T. Voisine
Original assignee: Landis & Gyr Utilities Services, Inc.
Priority date: 1995-01-30
Filing date: 1995-11-28
Publication date: 1996-08-08

Abstract

A method for determining a source VA quantity related to the size of a transformer bank, or of individual transformers, needed to supply a load. The transformer bank (30) is connected to a source of line frequency AC power. Transformer currents and voltages are sampled at a desired rate from which RMS voltages and currents sampled over a time interval are determined. The RMS voltages and currents from each of the transformers are used to determine a source VA value for any of the transformers in the bank, or alternatively for the bank of transformers. Source VA data determined over a series of predetermined time intervals may provide electrical utility services with valuable information to be used in sizing transformers to appropriate VA ratings to meet loading demands. The method is applicable to any transformer bank configuration including four-wire systems, three-wire systems and four-wire delta systems.

Description

METHOD OF SIZING TRANSFORMERS IN AN ELECTRICAL UTILITY SERVICE

Field of the Invention:

The present invention relates generally to systems providing electrical power for commercial, industrial and residential applications, and more specifically to methods for determining VA values sourced by one or more transformers used for supplying power in such systems, further for sizing the transformers base on the VA values.

BACKGROUND OF THE INVENTION

In electric generators, it is commonly known that a magnetic field is set up by current flowing in a "field winding" coil which induces voltage in an "armature winding" coil. It is also known that the armature may be wound and taps brought out so that several voltages displaced in time from each other may be obtained to produce a polyphase system. If three voltages are brought out, displaced from each other by 120 degrees, the well known three-phase electrical system is obtained. Voltage and current levels supplied by such polyphase systems are often stepped up or stepped down to suit the requirements of a particular load through the use of transformers. Typically transformers are rated according to the maximum volt-amperes (VA) that may be supplied therefrom. For example, electrical service for a single family residence may be provided by a 10 kVA transformer.

The design of such transformers is based, in large part, on the total VA requirement of the load being served. Ideally, the transformer should be sized such that the maximum VA required by the load does not exceed the VA rating of the transformers supplying the service for extended periods of time. Electrical meters typically monitor watthour usage, a»d can further provide the utility with feedback information indicating whether the transformers are properly sized (rated) by providing the maximum VA required to supply the load. However, a standard representation and corresponding determination of VA seem to be lacking in the electric utility industry. Moreover, it has been observed that several of the commonly used calculations of VA can lead to significant errors in the presence of certain conditions. Such errors and inconsistencies lead to inaccurate calculation of transformer size and a correspondingly improperly designed electrical service.

For example, in the known 4-wire three-phase wye system 10 of FIG. 1, many electrical meters calculate VA according to the following equation:

^{VA = V}A(RMS)^IA(RMS) ^{+ V}B(RMS)^XB(RMS) ⁺ ^VC(RMS)^IC(RMS) (1)

where ^v _{A RMo\} represents the root-mean-square (RMS) value of the voltage from line A to neutral and Ϊ_{Λ DMCN} represents the RMS value to the current in line A, and so forth. For purely resistive and balanced loads 12, 14 and 16, VA is equal to the power requirement of the load, typically measured in watts (W) , and also equal to the appropriate VA rating of the transformer. However, when reactance (inductive or capacitive) is present in the circuit, the current is displaced or shifted out of phase with the voltage by an angle θ which depends on the relative amounts of resistance a d reactance present. When reactance is present, VA required to be supplied by the transformer includes an "in-phase" power producing component (W) and a non-power producing component that is 90 degrees out of phase with W, known as volt-ampere reactance (VAR) . It is well known that when the waveforms contain no harmonics, the three quantities are related by the equation:

It is further known that if the load is a single resistive load, such as the resistor 12 connected between lines A and B in FIG. 1 for example, equation (1) yields a VA representative of the appropriate transformer rating, but not representative of the actual VA of the load. In any event, because of the discrepancy between the size (rating) of the transformers needed to supply the load and the VA of the load itself, equation (2) is used by some meters in computing load VA for the system of FIG. 1. However, although equation (2) may yield a value equal to the load VA and the appropi ialt' transformer VA rating under some conditions, it assumes perfectly sinusoidal voltage and current waveforms. In practice, electrical service provided by most electrical utilities includes waveform distorting harmonics. In the presence of harmonics, the use of equation (2) in computing VA can yield significant errors.

As another example, in the 3-wire 3-phase delta system 20 of FIG. 2, some electricity meters calculate VA according to the following equation:

^VA " ^VAC(RMS)^IA(RMS) ^{+ V}BC(RMS) ^XB(RMS) ⁽³⁾'

where VA.C__/(_rR,.M-S--.) rep ^cresents the RMS value of the voltage between lines A and C, and

A(RMS) represents the RMS value of the current in line A, and so forth. One problem with equation (3) is that it yields a VA transformer rating that is 15.47% higher than the load VA for balanced and purely resistive loads 22, 24 and 26. For purely balanced and resistive loads, the VA transformer rating and the load VA values should be equal. To compensate for this apparent error, some electricity meters use the following equation in computing VA for the system shown in FIG. 2:

^VA " ^(VAC(RMS)^IA(RMS) ^{+ V}BC(RMS)^TB(RMS)* * ⁰.⁸⁶6 ⁽⁴⁾.

Although equation (4) yields a VA transformer rating equal to the load VA for balanced resistive loads, it can yield significant errors for unbalanced loads. In fact, for unbalanced loads, neither of equations (3) or (4) yield a quantity directly related to the transformer VA rating or the load VA.

To avoid the foregoing errors and inconsistencies, what is needed is a universal definition of VA for use with any polyphase electrical system, and a method of computing this quantity such that an accurate indication of the VA demanded of the various transformers may be determined. Peak VA determinations would enable appropriate sizing of the transformers, through a correspondingly appropriate choice of transformer VA rating, to thereby enable the transformers to efficiently meet maximum load VA requirements. Transformer VA, or source VA, information over predefined time intervals could further be used to determine VA demand on the individual transformers in a transformer bank. In any case, source VA data would provide valuable information to an electrical utility that was not previously known. SUMMARY OF THE INVENTION

The present invention overcomes some of the errors and inconsistencies in determining VA supplied by transformers in polyphase electrical utility service systems. In accordance witli one aspect of the present invention, a method of determining source VA supplied to a load by a transformer, wherein the transformer is connected to a line frequency AC power source and to the load to thereby supply VA from the power source to the load, comprises the steps of: (1) sampling current flowing through the transformer over at least a portion of a power source cycle to produce a number of sampled current values; (2) sampling the voltage across the transformer over at least a portion of the power source cycle to produce a number of sampled voltage values; (3) determining an RMS current value from the number of sampled current values; (4) determining an RMS voltage value from the number of sampled voltage values; and (5) multiplying the RMS current value by the RMS voltage value to produce the source VA. In accordance witli another aspect of the present invention, a method of determining a source VA supplied by a bank of transformers to at least one load, wherein the bank of transformers receives power to supply the source VA from a line frequency polyphase AC power source, comprises the steps of: (1) sampling current flowing through each of the transformers in the bank of transformers over at least a portion of a power source cycle to produce a number of sampled current values for each corresponding transformer; (2) sampling the voltage across each of the transformers in the bank of transformers over at least a portion of the power source cycle to produce a number of sampled voltage values for each corresponding transformer; (3) determining an RMS current value for each of the transformers from the number of sampled current values corresponding thereto; (4) determining an RMS voltage value for each of the transformers from the number of sampled voltage values corresponding thereto; and (5) multiplying the RMS current value by the RMS voltage ⁵ value for each of the transformers and summing the multiplied values to produce the source VA supplied by the bank of transformers.

One object of the present invention is to monitor the VA demanded of a polyphase transformer bank for sequential time

1₀ intervals over a predetermined time period.

Another object of the present invention is to monitor the VA demanded of the individual transformers in a polyphase transformer bank for sequential time intervals over a predetermined time period.

_!5 Yet another object of the present invention is to monitor the peak VA demanded of a polyphase transformer bank for sequential time intervals over a predetermined time period in order to appropriately size the transformer VA rating of each Still another object of the present invention is to

2o monitor the peak VA demanded of each transformer in a polyphase transformer bank for sequential time intervals over a predetermined time period in order to appropriately size the transformer VA rating of any of the transformers in the transformer bank to meet load VA demands.

2₅ These and other objects of the present invention will become more apparent from the following description of the preferred embodiment. BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a four-wire three phase wye transformer bank configuration having a balanced resistive load connected thereto. FIG. 2 is a schematic diagram of a three-wire three phase delta transformer bank configuration having a balanced resistive load connected thereto.

FIG. 3 is a schematic diagram of a four-wire three phase wye transformer bank configuration showing the voltages and currents to be sampled in calculating source VA values, in accordance with one embodiment of the present invention.

FIG. 4 is a schematic diagram of a three-wire three phase delta transformer bank configuration showing the voltages and currents to be sampled in calculating source VA values, in accordance with another embodiment of the present invention. FIG. 5 is a schematic diagram of a four-wire three phase delta transformer bank configuration showing the voltages and currents to be sampled in calculating source VA values, in accordance with yet another embodi erit of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiment illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope o the invention is thereby intended, such alterations and further modifications in the illustrated device, and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates .

In any electrical utility service, transformers are connected to the line frequency electrical power lines to either step up or step down the power provided by the utility. Typically, the line frequency is approximately GO Hz in the United States, although many European countries utilize line frequencies of approximately 50 Hz. In any case, the concepts of the present invention are applicable regardless of the line frequency value. In polyphase systems, the transformers are connected together in transformer banks to supply VA to various loads. Common transformer bank configurations include, for example, four-wire wye systems, three-wire delta systems and four-wir delta systems.

Source VA is a quantity that directly relates to the siz of the transformers and associated connections needed for th various types of electrical utility services to provide a given amount of energy to a load. Two assumptions are made in the calculation of source VA with respect to its use with polyphase delta configurations: (1) source voltages are balanced, and (2) source impedances are balanced. Transformer currents cannot be directly sampled in polyphase delta transformer banks and must be derived from sampled lin currents. These assumptions are therefore necessary in calculating the transformer currents from the measured line currents. The first assumption is believed to be valid because if the source voltages are not balanced, then excessive circulating currents will result in the delta connection. Voltages are therefore believed to be maintained in balance by the utility. The second assumption is also considered to be valid because the individual windings of a polyphase transformer bank are usually chosen to be identical to each other. Identical windings correspond to identical VA ratings and hence equal impedance. Although source impedances are commonly balanced in practice, known relationships between source impedances may be incorporated into the source VA calculations if the source impedances are not balanced.

In accordance with the present invention, source VA for any transformer within a bank of transformers may be computed by sampling the current through, and the voltage across, each transformer in the transformer bank. In some cases, such as with polyphase delta transformer bank configurations for example, the transformer currents must be calculated from sampled line currents. Root-mean-square (RMS) currents and voltages are then determined from the sampled data, and corresponding RMS currents and RMS voltages are multiplied together to yield a source VA value for each transformer within a given sampling period. The separate source VA values for each transformer in the transformer bank may then be summed to yield a source VA for the entire transformer bank. In either case, source VA can be continuously calculated for any desired time interval. Preferably, this time interval is approximately 15 minutes, although the present invention contemplates time intervals of between approximately one minute and a few hours. For a given sampling period, each of the sampled current and voltage data values are squared. Thereafter, an RMS current for the sampling period is determined by summing the squared sampled current values, dividing by the number of sampled current values and calculating the square root of this quotient. Similarly, an RMS voltage for the sampling period is determined by summing the squared sampled voltage values, dividing by the number of sampled voltage values and calculating the square root of this quotient. The number of source VA's calculated for the desired time interval may be averaged, using any desired averaging technique such as RMS and algebraic averaging for example, so that an average source VA supplied for the time interval, by any one of the transformers, or the entire bank of transformers, can be obtained. The sampling of current and voltage data and the calculation of an average source VA value may be repeated for subsequent time intervals for a predetermined time period. Preferably, this time period corresponds to a billing cycle of the utility so that periodic VA demand may be monitored. However, the present invention contemplates time peiiods of between one day and one year. Regardless of the length of the predetermined time period, the electrical utility service may reconstruct the average source VA values for the sequential time intervals so that a continuous VA demand for the predetermined time period may be observed. This time interval data may be useful to the utility for tracking historical source VA demand of a particular load and forecasting future source VA demand of that load, for example. While continuously repeating the calculation of an average source VA for subsequent time intervals, the present invention further contemplates that a peak source VA value may be maintained throughout the predetermined time period. For example, each calculated average source VA may be compared to the average source VA calculated for the previous time interval, and the largest of the two values is the current peak source VA value. At the end of the predetermined time period, the peak source VA value that occurred for the time period may be readily ascertained. An electrical utility service may choose to utilize peak source VA information, wliether for a single transformer in a bank of transformers or for the entire bank of transformers, for a variety of purposes. For example, the peak source VA may be used to size the transformer, or transformers, so that the transformer VA rating is greater than or equal to the peak VA value. This would ensure the ability of the transformer(s) to safely supply the demanded load VA, and would reduce the number of transformer failures due to overheating and electrical overstress due to excessive VA demand.

Alternatively, a utility could choose to penalize the load, through a fine assessment for example, for exceeding a predetermined maximum VA demand.

Typically, the current and voltage sampling period is approximately 0.3 seconds, corresponding to approximately 18 cycles. Higher sampling periods may also be used, but sample periods of less than one cycle should be avoided in order to provide accurate data. However, it is to be understood that sample periods of less than one cycle may be used if a predictive or interpolation algorithm is used to generate current and voltage data values corresponding to the remaining portion of the cycle.

A sampling rate of approximately 3.0 kHz is preferred, although the present invention contemplates higher sampling rates as well. A practical lower limit on the sampling rate exists in that it should be at least twice the frequency of the desired line frequency harmonic. For example, since most electrical power supplied by electrical utility services has a shape somewhat distorted from the ideal sinusoidal shape, accurate current and voltage sampling should include at least some of the source harmonics. Preferably, a sampling rate of at least twice the frequency of the twenty third harmonic is used for accuracy in waveform reproduction. However, the present invention contemplates that any number of harmonics, including only fundamental, may be sampled depending on the desired accuracy of the sampled data. Source VA is thus a valid measure of the VA needed to supply a load even in the presence of harmonics. By appropriately adjusting the current and voltage sampling rates, source VA determinations can include harmonic measurements to accurately yield the VA needed to supply the load.

The present invention contemplates utilizing a variety of means for determining source VA values. Preferably, such determinations are made within an electricity meter located on the customer's premises. Meter reading personnel may then read source VA information along with the standard kilowatt-hour information. Known circuitry may be employed in such a meter to sample and record the necessary data. The present invention further contemplates that such source VA determinations may be made at the transformer bank, at the utility, or at other convenient locations.

EXAMPLE 1

Referring now to FIG. 3, an example using the concepts of the present invention to determine source VA values for a four-wire three phase wye transformer bank configuration 30 is shown. The source VA for transformer 32, for a given sampling period, is defined as the RMS voltage V , measured between points A and N, multiplied by the RMS current I. flowing out of transformer 32. Similarly, the source VA for transformer 34, for a given sampling period, is defined as the RMS voltage _RN, measured between points B and N, multiplied by the RMS current I D_D flowing out of transformer 34. Finally, the source VA for transformer 36, for a given sampling period, is defined as the RMS voltage V_c„, measured between points C and N, multiplied by the RMS current I_, flowing out of transformer 36. The source VA for the transformer bank 30 is then defined by the following equation:

VAsource - VANIA + VBNTB + VCN1C (5°)' '

It is to be understood that the RMS voltage and current values described with respect to this example are determined, as previously described, by sampling voltage and current values for a predetermined sampling period and determining therefrom the RMS values.

EXAMPLE 2

Referring now to FIG. 4, an example using the concepts of the present invention to determine source VA values for a three-wire three phase delta transformer bank configuration 40 is shown. The source VA for transformer 42, for a given sampling period, is defined as the RMS voltage V , measured between points A and B, multiplied by the RMS current I A.D-, flowing between through transformer 42.

Similarly, the source VA for transformer 44, for a given sampling period, is defined as the RMS voltage V „, measured between points B and C, multiplied by the RMS current I_,„ flowing through transformer 44. Finally, the source VA for transformer 46, for a given sampling period, is defined as the RMS voltage V _, measured between points A and C, multiplied by the RMS current I„_A flowing through transformer 46. The source VA for the transformer bank 40 is then defined by the following equation:

^VAsource " ^VAB^ΣAB ⁺ VBC ^{+ V}AC^ΣCA <⁶>'

where the values I_AB I_BC and I_ are determined, using known circuit theory, from the sampled values of the line currents I., I and I,,. It is to be understood that the RMS voltage and current values described with respect to this example are determined, as previously described, by sampling voltage and current values for a predetermined sampling period and determining therefrom the RMS values.

EXAMPLE 3

Referring now to FIG. 5, an example using the concepts of the present invention to deter ine source VA values for a four-wire three phase delta transformer bank configuration 50 is shown. The source VA for transformer 52, for a given sampling period, is defined as the RMS voltage V , measured between points A and N, multiplied by the RMS current 1A..N. flowing between through transformer 52. Similarly, the source VA for transformer 54, for a given sampling period, is defined as the RMS voltage V , measured between points N and B, multiplied by the RMS current I„_ flowing through transformer 54. The source VA for transformer 56, for a given sampling period, is defined as the RMS voltage V , measured between points B and C, multiplied by the RMS current I_βC flowing through transformer 56. Finally, the source VA for transformer 58, for a given sampling period, is defined as the RMS voltage V_ , measured between points C and A, multiplied by the RMS current I_rA flowing through transformer 58. The source VA for the transformer bank 50 is then defined by the following equation:

VA = V I + V I + V I sou rce AN AN NB NB BC BC

where the values I_AN, I_N„, I_R{-, and I,,_A are determined, using known circuit theory, from the sampled values of the line currents I . , I_β and I,,. It is to be understood that the RMS voltage and current values described with respect to this example are determined, as previously described, by sampling voltage and current values for a predetermined sampling period and determining therefrom the RMS values.

While the invention has been illustrated and described in detail in the drawings and foregoing description, the same is to be considered as illustrative and not restrictive in character, it being understood that only the preferred embodiment has been shown and described and that all clianges and modi ications that come within the spirit of the invention are desired to be protected. For example, in the same way that demand meters measure peak kilowatt-hour demand, such meters can be constructed to incorporate the appropriate features for measuring peak VA demand. Such metering would facilitate achieving a desired goal of properly designing source VA to meet load VA demands.

Claims

PCI7US95/15311- 16-What is claimed is:

1. A method of sizing a transformer needed to supply a load, the transformer being connected to a source of line frequency AC power and requiring a VA of the power source sufficient to supply the load, the method comprising the steps of:

(1) sampling current representative of the current flowing through the transformer over at least a portion of a power source cycle and providing a number of sampled transformer current values therefrom;

(2) sampling the voltage across the transformer over at least a portion of said power source cycle to produce a number of sampled voltage values;

(3) determining an RMS current value from said number of sampled current values;

(4) determining an RMS voltage value from said number of sampled voltage values; and

(5) multiplying said RMS current by said RMS voltage value to produce a source VA value; and (6) sizing the transformer to have a VA rating at least as large as said source VA value.

2. The method of claim 1 wherein said current sampling and said voltage sampling occurs at a predetermined sampling rate.

3. The method of claim 2 wherein the line frequency AC power includes waveform distorting harmonic frequencies, and wherein said sampling rate is at least twice the frequency of a predetermined harmonic frequency.

4. The method of claim 3 wherein said predetermined harmonic frequency is the twenty third harmonic frequency of the line frequency.

5. The method of claim 2 wherein said current sampling and said voltage sampling occurs over a predetermined sampling period.

6. The method of claim 5 wherein said predetermined time period is approximately 0.3 seconds.

7. The method of claim 5 wherein step (3) includes the steps of:

(3) (a) squaring the value of each of said sampled current values; (3)(b) calculating a quotient of a sum of said squared current values divided by said number of sampled current values; and

(3)(c) calculating a square root of said quotient calculated in step (3)(b) to produce said RMS current value.

8. The method of claim 7 wherein step (4) includes the steps of:

(4) (a) squaring the value of each of said sampled voltage values ;

(4)(b) calculating a quotient of a sum of said squared voltage values divided by said number of sampled voltage values; and

(4)(c) calculating a square root of said quotient calculated in step (4)(b) to produce said RMS voltage value.

9. The method of claim 1 further including the following step to be performed after step (5) but before step (6);

(5) (a) repeating steps (1) - (5) for a predetermined time interval to thereby produce a number of source VA values;

(5)(b) determining an average source VA value within said predetermined time interval from said number of source VA values; and (5)(d) performing steps (1) - (5)(b) for a predetermined time period and defining said source VA value as the largest of said average source VA values determined.

10. The method of claim 9 wherein said predetermined time interval is approximately 15 minutes.

11. The method of claim 10 wherein the source of line frequency power is an electrical utility and said predetermined time period is a customer billing period.

12. The method of claim 9 wherein the transformer is part of a four-wire three phase wye transformer bank; and wherein step (I) is performed by sampling the current through the transformer.

13. The method of claim 9 wherein the transformer is part of a three-wire three phase delta transformer bank; and wherein step (1) is performed by sampling line currents flowing through two of the three wires and determining said sampled transformer current values therefrom.

14. The method of claim 9 wherein the transformer is part of a four-wire three phase delta transformer bank; and wherein step (1) is performed by sampling line currents flowing through the three of the four wires and determining said sampled transformer current values therefrom.

15. The method claim 1 wherein the transformer is one of a plurality of transformers in a polyphase transformer bank; and wherein the method includes performing steps (1) - (5) for each of the transformers in said transformer bank, and wherein the method further includes the following step to be performed after step (5) but before step (6): (5) (a) summing the source VA values of each of the transformers to yield a transformer bank source VA value; and further wherein step (6) includes sizing each of the transformers in said transformer bank to have a VA rating at least as large as said transformer bank source VA value.

16. The method of claim 15 further including the following step to be performed after step (5) (a) but before step (6);

(5)(b) repeating steps (1) - (5) (a) for a predetermined time interval to thereby produce a number of transformer bank source VA values;

(5)(d) determining an average transformer bank source VA value within said predetermined time interval from said number of transformer bank source VA values; and (5)(e) performing steps (1) - (5)(c) for a predetermined time period and defining said transformer bank source VA value as the largest of said average transformer bank source VA values determined.

17. The method of claim 16 wherein the source of line frequency power is an electrical utility and said predetermined time period is a customer billing period.

18. The method of claim 16 wherein the transformer bank is a four-wire three phase wye transformer bank; and wherein step (1) is performed by sampling the current through each of the transformers in the transformer bank.

19. The method of claim 16 wherein the transformer bank is a three-wire three phase delta transformer bank; and wherein step (1) is performed by sampling line currents flowing through two of the three wires and determining said sampled transformer current values for each of the transformers in the transformer bank therefrom. •20-

20. The method of claim 16 wherein the transformer bank is a four-wire three phase delta transformer bank; and wherein step (1) is performed by sampling line currents flowing through the three of the four wires and determining said sampled transformer current values for each of the transformers in the transformer bank therefrom.

21. A method of determining source VA of a transformer needed to supply a load, the transformer being connected to a source of line frequency AC power and requiring a VA of the power source sufficient to supply the load, the method comprising the steps of:

(1) sampling current flowing through the transformer over at least a portion of a power source cycle to produce a number of sampled current values; (2) sampling the voltage across the transformer over at least a portion of said power source cycle to produce a number of sampled voltage values;

(3) determining an RMS current value from said number of sampled current values; (4) determining an RMS voltage value from said number of sampled voltage values; and

(5) multiplying said RMS current value by said RMS voltage value to produce the source VA.

22 . The method of claim 21 wherein said current sampling and said voltage sampling occurs at a predetermined sampling rate.

23. The method of claim 22 wherein the line frequency AC power includes waveform distorting harmonic frequencies, and wherein said sampling rate is at least twice the frequency of a predetermined harmonic frequency.

24. The method of claim 23 wherein said predetermined harmonic frequency is the twenty third harmonic frequency of the line frequency.

25. The method of claim 24 wherein said current sampling a d said voltage sampling occurs over a predetermined sampling period.

26. The method of claim 25 wherein said predetermined time period is approximately 0.3 seconds.

27. The method of claim 25 wherein step (3) includes the steps of:

(3) (a) squaring the value of each of said sampled current values;

(3)(b) calculating a quotient of a sum of said squared current values divided by said number of sampled current values; and

28. The method of claim 27 wherein step (4) includes the steps of: (4)(a) squaring the value of each of said sampled voltage values;

(4)(b) calculating a quotient of a sum of said squared voltage values divided by said number of sampled voltage values; and (4)(c) calculating a square root of said quotient calculated in step (4)(b) to produce said RMS voltage value.

29. The method of claim 21 wherein the method includes determining a number of source VA values needed by the transformer to supply the load, the method further includiny the step of: (6) repeating steps (1) - (5) for a predetermined time interval to thereby produce the number of source VA values.

30. The method of claim 29 wherein said predetermined time interval is approximately 15 minutes.

31. The method of claim 29 further including the step of

(7) determining an average source VA value within said predetermined time interval from said number of source VA values.

32. The method of claim 31 further including the step of (8) repeating steps (1) - (7) for a predetermined time period to thereby produce a number of average source VA values.

33. The method of claim 32 further including the step of

(9) sequentially reconstructing said average source VA values for said second predetermined time period to thereby determine the average VA required of the source to supply the load for any of said time intervals within said predetermined time period.

34. The method of claim 33 wherein the line frequency power source is an electrical utility and said predetermined time period is a billing period.

35. The method of claim 31 further including the steps of:

(8) repeating steps (1) - (7); (9) saving said average source VA value as a peak VA value if it is larger than the previous average source VA value;

(10) performing steps (8) - (9) for a predetermined time period. -23-

36. The method of claim 35 wherein the transformer has a maximum VA rating corresponding to a maximum source VA value needed by the transformer to supply the load, the method further including the step of:

⁵ (11) sizing the transformer such that its maximum VA rating is at least as large as said peak VA value.

37. A method of determining a source VA supplied by a bank of transformers to at least one load, the bank of transformers receiving power to supply the source VA from a ° line frequency polyphase AC power source, the method comprising the steps of:

(1) sampling current representative of the current flowing through each of the transformers over at least a portion of a power source cycle and providing a number of 5 sampled transformer current values for each corresponding transformer therefrom;

(2) sampling the voltage across each of the transformers in the bank of transformers over at least a portion of said power source cycle to produce a number of sampled voltage ⁰ values for each corresponding transformer;

(3) determining an RMS current value for eacli of said transformers from said number of sampled current values corresponding thereto;

(4) determining an RMS voltage value for each of said 5 transformers from said number of sampled voltage values corresponding thereto; and

(5) multiplying said RMS current value by said RMS voltage value for each of said transformers and summing said multiplied values to produce the source VA supplied by the 0 bank of transformers.

38. The method of claim 37 wherein said current sampling and said voltage sampling occurs at a predetermined sampling rate. PCI7US95/15311

-24-

39. The method of claim 38 wherein said current sampling and said voltage sampling occurs over a predetermined sampling period.

40. The method of claim 39 wherein the method includes determining a number of source VA values needed by the bank of transformers, the method further including the step of: (6) repeating steps (1) - (5) for a predetermined time interval to thereby produce the number of source VA values.

41. The method of claim 40 further including the step of (7) determining an average source VA value within said predetermined time interval from said number of source VA values .

42. The method of claim 40 further including the step of

(8) repeating steps (1) - (7) for a predetermined time period to thereby produce a number of average source VA values .

43. The method of claim 42 further including the step o£ :

(9) sequentially reconstructing said average source VA values for said second predetermined time period to thereby determine the average VA needed by the bank of transformers for any of said time intervals within said predetermined time period.

44. The method of claim 40 further including the steps of: (8) repeating steps (1) - (7);

(9) saving said average source VA value as a peak VA value if it is larger than the previous average source VA value;

(10) performing steps (8) - (9) for a predetermined time period.

45. The method of claim 44 wherein each transformer in the bank of transformers has a maximum VA rating corresponding to a maximum source VA value that may be needed by the transformer, the method further including the step of: (11) sizing each of the transformers such that its maximum VA rating is at least as large as said peak VA value.

46. The method of claim 37 wherein said bank of transformers includes a three-phase four-wire wye configuration; and wherein step (1) is performed by sampling the currents through each of the transformer.

47. The method of claim 37 wherein said bank of transformers includes a three-phase three-wire delta configuration; and wherein step (i) is performed by sampling line currents flowing through two of the three wires and determining said sampled transformer current values for each of the transformers in the transformer bank therefrom.

48. The method of claim 37 wherein said bank of transformers includes a three-phase four-wire delta configuration; and wherein step (1) is performed by sampling line currents flowing through three of the four wires and determining said sampled transformer current values for each of the transformers in the transformer bank therefroin.