E-36—Policy on loss compensation functions that influence legal units of measure in meters

Category: Electricity
Issue date:
Effective date:
Revision number: N/A
Supersedes: N/A


Table of contents


1.0 Scope

This bulletin applies to the calculation of loss compensation values for power transformers and power lines at specific site locations used with electricity meters and ancillary devices pursuant to the Electricity and Gas Inspection Act to establish source legal units of measure (SLUMs) or processed legal units of measure (PLUMs).

2.0 Purpose

The purpose of this bulletin is to communicate Measurement Canada's policy on applying loss compensation to quantity values declared in electricity trade transactions for both delivered and received energy.

3.0 References

4.0 Definitions

Actual current
(courant réel)

The current as determined from the meter's approved I2h function.

Actual voltage
(tension réelle)

The voltage as determined from the meter's approved V2h function.

Attestation
(attestation)

A binding document which solemnly declares in writing that a particular requirement of this document has been complied with and that this conclusion is an accurate representation of the facts as attested to by the signatory.

Blondel's theorem
(théorème de Blondel)

In a system of N conductors, N-1 meter elements, properly connected, will correctly measure the power or energy taken. The connection must be such that all potential coils have a common tie to the conductor in which there is no current coil.

Copper loss
(perte dans le cuivre)

The active and reactive power losses of the transformer or power line at the actual load current (also known as copper loss or winding loss for power transformers).

Core loss
(perte dans le noyau)

The active and reactive power consumed by the transformer's windings or power line at the actual voltage with no load current (also known as core loss or iron loss).

Full load loss (var)
(perte à pleine charge [en voltampères réactifs])

The reactive power consumed by the transformer's windings or power line at full load current.

Full load loss (watt)
(perte à pleine charge [en watts])

The active power consumed by the transformer's windings or power line at full load current.

Iron loss
(perte dans le fer)

The active and reactive power consumed by the transformer's windings or power line at the actual voltage with no load current (also known as core loss or iron loss).

Load loss
(perte due à la charge)

The active and reactive power losses of the transformer or power line at the actual load current (also known as copper loss or winding loss for power transformers).

Load loss (var)
(perte due à la charge [en voltampères réactifs])

The reactive power consumed by the transformer's windings or power line at actual load current.

Load loss (watt)
(perte due à la charge [en watts])

The active power consumed by the transformer's windings or power line at actual load current.

Load percent of short-circuit impedance
(pourcentage de la charge de l'impédance en court-circuit)

The short-circuit impedance of the power transformer expressed as a percentage of the primary voltage required to circulate full load current in the short-circuited secondary winding to the rated primary voltage.

Loss compensation
(compensation des pertes)

A means for establishing a legal unit of measure when the metering point and the point of service are physically separated resulting in measurable losses. These losses may be used to adjust meter registration for a final (compensated) legal unit of measure.

No-load loss
(perte à vide)

The active and reactive power consumed by the transformer's windings or power line at the actual voltage with no load current (also known as core loss or iron loss).

No-load loss (var)
(perte à vide [en voltampères réactifs])

The reactive power consumed by the transformer's windings or power line at the actual voltage with no load current.

No-load loss (watt)
(perte à vide [en watts])

The active power consumed by the transformer's windings or power line at the actual voltage with no load current.

No-load percent excitation current
(pourcentage du courant d'excitation à vide)

The percentage of a full load current that flows through the line terminals of a power transformer when all other windings are open circuited and rated voltage is applied.

Percent impedance
(pourcentage d'impédance)

The voltage drop on full load due to the winding resistance and leakage reactance expressed as a percentage of the rated voltage.

Rated (apparent) power
(puissance nominale [apparente])

The nominal volt-ampere power rating of the transformer as provided in the test sheet (typically provided in megavolt-amperes).

Rated current
(courant nominal)

The current at rated power of the transformer as provided in the test sheet.

Rated voltage
(tension nominale)

The voltage at rated power of the transformer as provided in the test sheet.

Test sheet
(feuille d'essai)

The source of the power transformer and/or power line technical information. The data can come from test sheets, reports or other acceptable sources.

Winding loss
(perte aux enroulements)

The active and reactive power losses of the transformer or power line at actual load current (also known as copper loss or winding loss for power transformers)..

Winding type
(type d'enroulement)

The type of winding which can be primary, secondary or tertiary.

5.0 Background

This bulletin has been established to support recommendations developed by the Electricity Loss Compensation Joint Working Group.

Loss compensation functions are a means to determine unmetered losses that occur when a meter's actual location is different from the declared trade point. Energy dissipated between the trade and metering points cannot be measured directly. The losses are calculated indirectly using transformer theory, circuit theory, as well as currents and voltages at the meter. Loss compensated meters operate with formulae that add or subtract losses to the metered legal unit of measure (LUM) registration.

An example of this is an installation where a meter is connected on the low-voltage side of a power transformer, and the ownership change and trade point occur on the high-voltage side of the transformer. This physical separation between the meter and actual declared trade point results in measurable losses. There are also cases where change of ownership and trade occurs halfway along a transmission line making it impractical or impossible to install a meter. In this case, the metered registration would be compensated to the declared trade point or location.

6.0 Policy for the application of loss compensation to site-specific legal units of measure

6.1 General

6.1.1 Application of formulae and processes

Loss compensation may be applied in accordance with the formulae and processes specified in S-E-11 and S-E-12.

6.1.2 Application of bulletin E-27

Loss compensation may be applied in accordance with bulletin E-27.

6.1.3 Application of type approval and other requirements

Meters used for loss compensation must meet the type approval requirements for the I2h and V2h functions of S-E-06 and LMB-EG-07, as well as the other applicable related type approval requirements of S-E-06 and LMB-EG-07.

6.1.4 Application of verification requirements

Meters used for loss compensation are to be verified in accordance with the requirements specified for the I2h and V2h functions of S-E-02, as well as the other applicable related metering verification requirements of S-E-02.

6.1.5 Implementation timeline

Loss compensation requirements are subject to the same implementation timelines referenced in bulletin E-31 for the type approval, verification and installation and use of devices pursuant to new requirements and policies.

Note: Fixed loss factors are not permitted to be applied to the LUM value as a means for calculating loss compensation (see: Units of measurement applied to the sale of electricity or natural gas in Canada and the provision of meter registration information for further information). However, contractors seeking to recover the cost of losses through billing adjustments may consider applying the adjustment to the unit cost (pricing) of electricity that does not adjust the declared LUM. Measurement Canada's responsibility is limited to the process used to determine the losses.

7.0 Requirements for the calculation of loss compensation

7.1 General

7.1.1 Methods to be used for loss compensation

The following two methods for determining losses and establishing compensated loss values are recognized.

  1. I2h/V2h method
  2. VA method

7.1.2 Preferred method

The I2h/V2h method is the preferred method for determining loss compensation and is the only method that will be used in approved meters.

7.2 I2h/V2h method

7.2.1 Use of I2h and V2h legal units of measurement

The I2h/V2h method for loss compensation uses I2h and V2h LUMs for calculating relevant power line and power transformer losses.

7.2.2 Inside the meter application with a two-winding power transformer

The I2h/V2h method can be used for inside the meter applications where the power transformer has two windings.

7.2.3 Method used outside the meter for power transformers having two or more windings

The I2h/V2h method can be used for loss determination outside the meter for power transformers having two or more windings and requires the use of SLUM legally relevant information (legally relevant in the form of I2h and V2h) from the meter(s).

7.3 VA method

7.3.1 Standards and guidance documents

The VA method for determining loss compensation must be based on the standards and guidance documents established by the Province of Ontario's Independent Electricity System Operator (IESO) in the following documents:

  1. MDP_STD_0005—Site-Specific Loss Adjustments: Requirements for Adjustment of Meter readings for site-specific losses in the IESO-administered market, Issue 4; and
  2. MDP_PRO_0011—Market manual 3: metering part 3.5 site-specific loss adjustments, Issue 8.

7.3.2 VA method limitations

The VA method is limited to those situations in which the nature of the equipment physically prevents the installation of the metering equipment required to apply I2h/V2h method. This method is only applicable to loss compensation determination outside of a meter where the I2h/V2h method cannot be used.

7.3.3 Formal attestation for coefficients used

A formal attestation of all the coefficients used in the loss calculations determination outside the meter is to be based on the provisions of MDP_STD_0005 and MDP_RRO_0011. The attestation must be signed by an authorized signing authority and this record must be kept by the owner/contractor in accordance with paragraph 11(2)(m) of the Electricity and Gas Inspection Regulations.

7.3.4 Phase equivalent circuit modelling

The VA method for loss compensation requires a per phase equivalent circuit modelling of the power lines and transformer(s) that represent the unmetered losses at a metering site. A load flow analysis is to be performed on the equivalent circuit model to determine active and reactive system losses over the range of operating conditions for the site. The loss data established by the load flow analysis is to be used in establishing a functional relationship between metered apparent power and active and reactive losses. The functional relationship must be of the form provided by the following two second-order polynomial equations:

Where:

  1. Wloss is the active power loss in the power system component
  2. Varloss is the reactive power loss in the power system component
  3. VA is the apparent power measured by the meters on the secondary and tertiary transformer windings
  4. Coefficients K1 through K6 are determined by the numerical methods described below

7.3.5 Requirements for establishing loss coefficients

Establishing loss adjustment coefficients under the VA method requires:

  1. establishing a one-line diagram and the electrical properties of the power system component;
  2. establishing the full range of load sharing possibilities between the windings, neutral current, power factor, upstream system voltage and under load tap changer tap position that may be reasonably expected over the life cycle of the installation;
  3. using the numerical curve fitting method (load-flow study) to calculate the losses at several points over the range of each variable;
  4. graphing the losses as a function of the demand that would be observed by the metering;
  5. using numerical curve fitting to determine the coefficients of the second-order polynomial function to be used to estimate losses;
  6. using the numerical curve fitting method to determine a measurement of the quality of the resulting predictions (R2).

7.3.6 R2 value limits

The R2 value is a measure of best fit and takes on values that range from zero to one. A value between 0.95 and 1.0 indicates that total VA can be used to reliably predict losses.

7.3.7 R2 values less than 0.95

The VA method for loss compensation must not be used in the case of R2 values less than 0.95.

7.3.8 Modelling data and curve example

An example of modelling data and curve fitted graphs of predicted loss data from modelling is provided in Appendix C.

7.4 Multiple transformations and/or line combinations

Loss compensation values for multiple transformations (cascaded or in series transformers) and/or line combinations may be calculated using the I2h/V2h method. Multiple transformations may be modelled as a single transformer and/or line. The model and associated parameters must be documented and signed off by an authorized signing authority. This record is to be kept by the owner or contractor in accordance with paragraph 11(2)(m) of the Electricity and Gas Inspection Regulations.

8.0 Information required for the calculation of loss compensation

8.1 Power distribution transformer parameters

The information recorded in Table 1 must be kept by the owner or contractor if power distribution transformer losses are applied to LUMs used for trade purposes.

Table 1—Record of power distribution transformer data
Item Short form Detailed description
1 VA rated Rated power of power transformer
2 Vpri / Vpri rated Primary rated voltage of power transformer
3 Vsec / Vsec rated Secondary rated voltage of power transformer
4 Ipri / Ipri rated Primary rated current of power transformer
5 Isec / Isec rated Secondary rated current of power transformer
6 %EXC Percent excitation current of the power transformer
7 %Z Percent impedance of the power transformer (from test data sheet, include reference temperature)
8 CTR Current transformer ratio for instrument transformers supplying current to the meter
9 VTR Voltage transformer ratio for instrument transformers supplying voltage to the meter
10 Elements Number of meter elements (use 3 for all 2 ½ element meters)
11 VAphase Per phase VA rating of power transformer
12 LWFeNL No-load loss (watts) (from test sheet data)
13 LVFeNL No-load loss (var) (typically calculated from test sheet data)
14 LWCuFL Load loss (watts) (from test sheet data, include reference temperature)
15 LVCuFL Load loss (var) (typically calculated from test sheet data, include reference temperature)
16 Irated Rated transformer current
17 Vrated Rated voltage (transformer)

Note: The policies and requirements provide by this bulletin and S-E-11 are established on the basis of certain transformer parameters. These parameters are commonly found on transformer test data sheets for transformers that are compliant with Institute of Electrical and Electronics Engineers (IEEE) standard C57.12.00—IEEE Standard for General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers or other applicable requirements found in the IEEE C57TM series of standards.

8.2 Power line parameters

The information recorded in Table 2 must be kept by the owner or contractor if line losses are applied to LUMs used for trade purposes.

Table 2—Record of power line loss data
Item Short form Detailed description
1 n Number of conductors
2 L Line length (units compatible with conductor resistance)
3 r Conductor resistance per unit length
4 xl Conductor inductive reactance per unit length
5 rt Conductor resistance corrected for temperature effect per unit length
6 Gl Conductance for service length of conductor
7 Bl Susceptance for service length of conductor

Note: The policies and requirements provide by this bulletin and S-E-11 are established on the basis of certain power line parameters. These parameters are commonly established in conformance with the Aluminum Electrical Handbook published by the aluminum association, IEEE 738—Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors and IEC 287—Electric Cables—Calculation of the Current Rating.

9.0 Losses and apportioning of losses for multiple points of metering

Where multiple points of metering occur at a common power system component (e.g. power transformer, power line, etc.), loss compensation is to be determined using the methods specified in S-E-11, section 6.2.3 e).

A record of the method and/or contractual agreements used for apportionment of the losses to each party must be kept by the contractor.

Where provisions of this section do not adequately accommodate the apportioning needs of a contractor, application can be made to Measurement Canada for special consideration of the apportioning method proposed by the utility.

Appendix A—Transformer loss compensation example calculations

A.1 Fixed tap power transformer on rated tap

A metering point located on the secondary side of a power transformer with the point of service located on the primary or high voltage side of the power transformer.

This example is based on a measured voltage of 2400 V line to line and measured line current of 3000 A.

Table A1—Power transformer data from transformer manufacturerFootnote 1
Parameters Phase 1 Phase 2 Phase 3
MVA rated 3.333 3.333 3.333
Vpri/Vpri rated 115,000 115,000 115,000
Vsec/Vsec rated 2,520 2,520 2,520
LWFeNL 9,650 9,690 9,340
LWCuFL 18,935 18,400 18,692
%EXC 1.00 1.06 0.91
%Z at 75 °C 8.16 8.03 8.12

Footnotes

Footnote 1

Handbook for Electricity Metering, 10th edition, Washington, DC: Edison Electric Institute, 2002, pp 258-262.

Return to footnote 1 referrer

Available voltage taps: 115,000; 112,125; 109,250; 106,375; 103,500

3 wire delta: 2 element metering

CTR= 3,000A/5A=600 line current

VTR= 2,400V/120V=20 line-line

A.2 Calculation of transformer no-load watt losses

  1. LWFe= [LWFe]_NL × (V_act/V_rated )^2
    1. V_act=2,400 V
    2. Vsec rated=2,520 V
    3. [LWFe]_NL=9,650+9,690+9,340=28,680 W
  2. LWFe=28,680 × ((2,400)/(2,520))^2=26,013.6 W (no load)

A.3 Calculation of transformer load watt losses

  1. LWCu= LWCu_FL × (I_act/I_rated)^2
    1. I_act=3,000 A
    2. I_rated= (√3× VAphase)/(V sec⁡[L−L])
    3. I_rated= (√3 × 3,333,000)/2,520=2,290.84 A
    4. [LWCu]_FL=18,935+18,400+18,962=56,027 W
  2. LWCu=56,027 × (3,000/2,290.84)^2=96,083.8 W

A.4 Calculation of transformer no-load var losses

  1. LVCFe=[LVFe]_NL × (V_act/V_rated)^4
    1. [LVFe]_NL= √(([VA]_(TXtest) × (%EXC)/100)^2−([LWFe]_NL)^2)
    2. [LVFe]_NL1=√((3,333,000 × 1.00%)^2−[9,650]^2)=31,902 vars
    3. [LVFe]_NL2=√((3,333,000 × 1.06%)^2−[9,690]^2)=33,974 vars
    4. [LVFe]_NL3=√((3,333,000 × 0.91%)^2−[9,340]^2)=28,856 vars
  2. [LVFe]_NL=31,902+33,974+28,856=94,732 vars
  3. LVFe=94,732[×(2,400/2,520)]^4=77,936 vars

A.5 Calculation of transformer load var losses

  1. LVCu= LVCu_FL ×(I_act/I_rated)^2
    1. LVCu_FL= √((VA_(TXtest)×(%Z)/100)^2−(LWCu_(FL))^2)
    2. [LVCu]_FL1= √((3,333,000×8.16%)^2−[18,935]^2)=271,313 vars
    3. [LVCu]_FL2= √((3,333,000×8.03%)^2−[18,400]^2)=267,007 vars
    4. [LVCu]_FL3= √((3,333,000×8.12%)^2−[18,682]^2)=269,994 vars
  2. [LVCu]_FL=271,313+267,007+269,994=808,314 vars
  3. LVCu=808,314 ×(3,000/2,290.84)^2=1,386,223 vars

Appendix B—Power line loss compensation example calculations

B.1 Line loss compensation based on climatic conditions

The metering point is located downstream of the point of service on bare overhead conductors. Line losses are to be added to the delivered power and energy quantities.

The power line data table based on the Aluminum Electrical Conductor Handbook (see Table 4-5 and Table 4-6 for the listed values included below).

Table B1—Power line data
Reference Item Value Unit
P Maximum power flow 18 MW
V Nominal voltage 130 kV
I Maximum current 79.94 A
L Length (L) 7.05 km
- Conductor code word Daisy -
n Number of wires 7 -
- Conductor diameter 0.586 in
Ro Positive sequence resistance per unit length at 50 °C (ra) 0.384 ohm/mile
xi Positive sequence self-reactance per unit length (xa) 0.489 ohm/mile

B.2 Calculation of line losses

1) Line loss (watts)

PLLW_t=(I_act )^2 × r_t × L

Where:

PLLWt = Power line loss in watts (climatic influence)

Iact = Actual current (derived from measure I2h)

rt = Resistance (corrected for climatic influences) per unit length

L = Conductor length

PLLW_t= [79.94]^2×0.2028×7.05=9,136.62 W

Note: Refer to the paragraph below in 2) to calculate rt.

2) Line loss (l var, inductive)

PLL_v=(I_act)^2 × x_i×L

Where:

PLLv = (Power) line loss (var)

Iact = Actual current (derived from measure I2h)

xi = Inductive resistance per unit length (ohm/km)

L = Conductor length

[PLL]_v=[79.94]^2 ×0.3039× 7.05=13,691.4 vars

Calculation of the resistance of the conductor rt is done according to IEEE standard 738-2006, p. 8, with equations (1a), (1b), (3a) and (3b). Equation (3a) applies at low wind speeds and equation (3b) applies at high wind speeds (assuming the following: wind direction is perpendicular to the axis and solar radiation and heat removal are negligible compared to I²R loss and convection).

Appendix C—Modelling examples for the VA method for loss compensation

Examples of how the VA method for loss compensation is applied are provided in Appendix B of MDP_STD_0005.

Table C1 shows the losses calculated at each load point.

Table C1—Calculated loss at load points
Total facility load Total losses
MW Mvar MVA kW kvar
- - 0.00 10.16 5.76
1.8 0.8718 2.00 11.86 50.22
3.6 1.7436 4.00 17.16 149.81
5.4 2.6153 6.00 26.06 320.14
7.2 3.4871 8.00 38.96 565.37
9 4.3589 10.00 56.06 890.27
10.8 5.2307 12.00 77.66 1300.43
12.6 6.1025 14.00 104.06 1802.36

The figures above develop the required loss adjustment coefficients. The curves shown below indicate the resulting graph. Curve-fitting software was used to develop the K coefficients and R2.

Figure 1 : kW losses curve using the VA method

the long description is located below the image
Description of Figure 1

kW losses plotted against the MVA loading of a power transformer respond exponentially. The exponential curve can be represented mathematically as Y=0.5059x2-0.4148x+10.16 R2=0.9998

Figure 2: kvar losses curve using the VA method

the long description is located below the image
Description of Figure 2

kvar losses plotted against the MVA rating values of a power transformer respond exponentially. The exponential curve can be represented mathematically as Y = 9.4407x2 - 4.7322x + 5.76 where R2 = 0.9997

Appendix D—Apportioning of losses

Figure 1 Appendix D: Two customers sharing the same power transformer

the long description is located below the image
Description of Figure 1 Appendix D

The primary transmission line is connected to a power transformer T1 and the point of sale even though there is no meter at the location, it is considered to be somewhere between the primary transmission and the power transformer T1. This point is considered to be the point of transaction and is acting like a virtual meter. The power transformer T1 could have meter M1 and load L1 connected to the grid along with meter M2 and load L2 connected to the grid after the power transformer T1.

D.1. Total usage = M1 + M2

  1. [Wh]_Total= [Wh]_M1+ [Wh]_M2
  2. [varh]_Total= [varh]_M1+ [varh]_M2
  3. [VAh]_Total=√([([Wh]_Total)]^2+ [([varh]_Total)]^2)
  4. I^2 h_Total=([VAh]_Total)^2/(V^2 h_((M1 or M2)))

D.2 Loss calculations

  1. [Wh]_LWFe= ([LWFe]_(NL )×[V^2 h]_((M1 or M2)))/[(V_rated )^2 × EL]
  2. [Wh]_LWCu=([LWCu]_FL× I^2 h_Total)/[(I_rated )^2 × EL]
  3. var_LWFe=([LVFe]_NL× iph× (V^2 h_((M1 or M2)))^2)/[(V_rated)^4×(EL)^2]
  4. var_LWCu=([LVCu]_FL× I^2 h_Total)/([[(I_rated)]^2× EL])
  5. [Wh]_Loss= [Wh]_LWFe+ [Wh]_LWCu
  6. [varh]_Loss= var_LWFe+ [var h]_LWCu

where:

iph = Number of intervals per hour

EL = Number of meter elements

Table D1—M1 data
Time kWhM1 kvarhM1 kVAhM1 kV2hM1 I2hM1
0:30 237.54 8.34 237.66 155.43 365.00
0:35 235.44 8.22 235.56 155.43 357.50
Table D2—M2 data
Time kWhM2 kvarhM2 kVAhM2
0:30 46.98 27.63 54.45
0:35 46.08 28.17 54.09
Table D3—Total values
Time kWhM1+M2 kvarhM1+M2 kVAhtotal calculated kV2hM1
measured
I2hTotal calculated
0:30 284.52 35.97 286.7847125 155.43 529.1357293
0:35 281.52 36.39 283.8621893 155.43 518.4062037
Table D4—Transformer losses
Time LWFe (kWh) LWCu (kWh) LVFe
(kvarh)
LVCu (kvarh) Transformer loss
kWh
Transformer loss
kvarh
0:30 6.00 0.021 7.89 0.76 6.02 8.65
0:35 6.00 0.021 7.89 0.75 6.02 8.64
Table D5.1—Apportioning of losses to L1
Time kWhM1 loss kvarhM1 loss
0:30 5.03 7.23
0:35 5.04 7.23
Table D5.2—Apportioning of losses to L2
Time kWhM2 loss kvarhM2 loss
0:30 0.99 1.43
0:35 0.99 1.41
Table D5.3—Legal units of measure for customers 1 and 2
Time kWhL1 kvarhL1 kWhL2 kvarhL2
0:30 242.57 15.57 47.97 29.06
0:35 240.48 15.45 47.07 29.58

D.3 Example of apportioning using a second transformer

For the example shown in figure D1 below, T1 is serving customer L1 and customer L2. Customer L2 meter is located on the secondary of a second transformer T2.

If reference to the installation and use requirements of section 6.2.3 e).i) of S-E-11, WhM1 and varh M1 are the legally relevant values established for customer L1. Whereas, WhM2 and varh M2 values are established from compensated PLUM values for customer L2 (legally relevant values of meter M2 + T2 loss values) as follows:

Figure D2: Use of two power transformers

the long description is located below the image
Description of Figure D2

The primary transmission line is connected to a power transformer T1 with the point of sale considered to be somewhere between the primary transmission line and the power transformer T1. There is actually no meter at the location considered to be the point of sale. The location considered to be the point of transaction is acting like a virtual meter. The power transformer T1 could have meter M1 and load L1 connected to the grid along with second transformer T2 using meter M2 and load L2 connected to the grid after the power transformer T2.

Figure D3: Customer and generator sharing the same power transformer

the long description is located below the image
Description of Figure D3

The primary transmission line is connected to a power transformer and metering the net value Mnet of 75 MW flowing back to the grid. Connected after this net meter (Mnet) is a second meter M1 measuring 25 MW of load used. In parallel with M1 is another meter M2 that measures the 100 MW of energy produced by a generator.

Two customers connected via one power transformer. Customer 1 is consuming energy and customer 2 is generating energy. The total energy flowing through the common power system component is net generation. Load losses may be apportioned among two or more different classes of connected customers using one of the following methods:

  1. Load loss apportionment based on absolute gross metered load at each customer
    1. M1 (gen 0 MW, load 25 MW): load losses apportioned based on 25 MW load for customer 1
      [Wh]_M1LoadLoss=25/(25+100)×[Wh]_LoadLoss
    2. M2 (gen 100 MW, load 0 MW): load losses apportioned based on 100 MW generation for customer 2
      [Wh]_M2LoadLoss=100/(25+100)×[Wh]_LoadLoss
  2. Load loss apportionment based on independent gross metered load at each customer.

    Each metering point is considered an independent single point metering installation. Losses must be established by the provisions of section 6.2.3 of S-E-11.

  3. Load loss apportionment based on net energy flow through a common power system component.

    Mnet (gen 75 MW, load 0 MW): load losses apportioned based on net 75 MW generation.

    • Wh_M1LoadLoss=0
    • Wh_M2LoadLoss= Wh_MnetLoadLoss

    Load losses could be attributed to customer 2 since they are causing net flow contributing to the load losses across the power transformer.

Appendix E—Example of I2h/V2h method loss parameter calculations for two transformers in series

Figure E.1: Single line diagram

the long description is located below the image
Description of Figure E.1

An electrical grid using two large power transformers in series can be represented with an equivalent single line diagram. The first power transformer T1 is rated 44 kVolts and typically connected in a delta configuration to wye configuration. T1 is comprised of T1R, T1W and T1B. The secondary voltages on the wye or secondary side of T1 would be 4.16 kVolts, line to line, and 2.4 kVolts line to neutral. The voltages of 4.16/2.4 kV supplies the primary voltage to the second power transformer in series represented by T2. This transformer configuration is wye on both the primary and secondary side of the transformer T2. The secondary voltage is 600 volts, line to line and 347 volts, line to neutral. The revenue metering is connected on the secondary side of T2 using 3 voltage transformers with a voltage transformer rating of 360:120, and 3 current transformers with a current transformer rating of 2000:5 amps.

E.1 Description

Transformer T1 is comprised of three single-phase transformers: T1R (red phase), T1W (white phase) and T1B (blue phase), each rated 1 MVA. The single-phase transformers are configured for delta/wye (D/Y) transformation and cascaded in series with T2, a 3-phase transformer, connected to the load bus. Revenue metering is done on the low voltage side of T2.

T1 3-phase bank rating: 3 MVA, 44 kV – 4.16/2.4 kV, connected D/Y. On-load tap changer on the 44 kV side.

T2 3-phase rating: 2.2 MVA, 4.16/2.4 kV – 600/347 V, connected Y/Y with ±10% taps on the 4.16 kV side.

E.2 Assumptions

The normal operating voltages are 44 kV and 4.16 kV.

The transformer's operating taps are 44 kV and 4.16 kV (i.e. rated phase to phase primary voltages for T1 and T2, respectively).

The voltage drop and losses in the cables between transformers T1 and T2 can be neglected.

The voltage drop in the metering voltage transformer secondary cables is 0.00%.

Table 1—Manufacturer's transformer ratings
Transformer Rated primary voltage
(V)
Rated secondary voltage
(V)
Rated power (MVA) No-load loss (iron)
(kW)
Load loss (copper)
(kW)
Percent excitation current
(%)
Percent impedance
(%)
T1R
(red phase)
44,000
p-p Footnote 2
2,400
p-n Footnote 3
1.0 2.03 7.83 1.46 5.46
T1W
(white phase)
44,000
p-p Footnote 2
2,400
p-n Footnote 3
1.0 2.02 8.02 1.072 5.46
T1B
(blue phase)
44,000
p-p Footnote 2
2,400
p-n Footnote 3
1.0 2.0 7.84 1.25 5.57
T2 4,160/2400
p-p Footnote 2/ p-nFootnote 3
600/347
p-p Footnote 2/ p-nFootnote 3
2.2 1.25 3.8 0.4 2.44

Footnotes

Footnote 2

p-p = phase to phase (line to line)

Return to first footnote 2 referrer

Footnote 3

p-n = phase to neutral (line to neutral)

Return to first footnote 3 referrer

E.3 Factory test results for transformer T1R

VATXtest = 1000 kVA Rated kVA, single phase

Vpri rated = 44000 V Rated primary voltage, p-p

Vsec rated = 2400 V Rated secondary voltage, p-n

LWFeTXtest = 2.03 kW No-load loss (iron loss)

%EXC = 1.46% Percent excitation current

LWCuTXtest = 7.83 kW Load loss (copper loss)

% Z = 5.46% Percent impedance

E.3.1 Calculation of transformer T1R active and reactive losses at rated voltage and power

T1R is operating on its principal taps at rated voltage and no adjustments to the manufacturer's no-load and load losses are required.

[T1]_R [LWFe]_NL=[LWFe]_TXtest=2.03 kW

[T1]_R [LWCu]_FL=[LWCu]_TXtest=7.83 kW

[T1]_R [LVFe]_NL=√(([VA]_TXtest×(%EXC)/100)^2−([[LWFe]_TXtest)]^2)

[T1]_R [LVFe]_NL=√((1000×1.46/100)^2−[2.03]^2 )=14.458k var

TI_R [LVCu]_FL= √(([VA]_TXtest ×(%Z)/100)^2−([[LWCu]_TXtest)]^2)

TI_R [LVCu]_FL= √((1000×5.46/100)^2−[7.83]^2)=54.036k var

E.4 Factory test results for transformer T1W

VATXtest = 1000 kVA Rated kVA, single phase

Vpri rated = 44000 V Rated primary voltage, p-p

Vsec rated = 2400 V Rated secondary voltage, p-n

LWFeTXtest = 2.02 kW No-load loss (iron loss)

%EXC = 1.072% Percent excitation current

LWCuTXtest = 8.02 kW Load loss (copper loss)

% Z = 5.46% Percent impedance

E.4.1 Calculation of transformer T1W active and reactive losses at rated voltage and power

T1W is operating on its principal taps at rated voltage and no adjustments to the manufacturer's no-load and load losses are required.

[T1]_W [LWFe]_NL=[LWFe]_TXtest=2.02 kW

[T1]_W [LWCu]_FL=[LWCu]_TXtest=8.02 kW

TI_W [LVCe]_NL=√(([VA]_TXtest ×(%EXC)/100)^2−([[LWFe]_TXtest)]^2)

TI_W [LVFe]_NL= √((1000×1.072/100)^2−[2.02]^2)=10.528k var

TI_W [LVCu]_FL=√(([VA]_TXtest ×(%Z)/100)^2−([[LWCu]_TXtest)]^2)

TI_W [LVCu]_FL= √((1000×5.46/100)^2−[8.02]^2)=54.008k var

E.5 Factory test results for transformer T1B

VATXtest = 1000 kVA Rated kVA, single phase

Vpri rated = 44000 V Rated primary voltage, p-p

Vsec rated = 2400 V Rated secondary voltage, p-n

LWFeTXtest = 2.0 kW No-load loss (iron loss)

%EXC = 1.25% Percent excitation current

LWCuTXtest = 7.84 kW Load loss (copper loss)

% Z = 5.57% Percent impedance

E.5.1 Calculation of transformer T1B active and reactive losses at rated voltage and power

T1B is operating on its principal taps at rated voltage and no adjustments to the manufacturer's no-load and load losses are required.

[T1]_B [LWFe]_NL=[LWFe]_TXtest=2.0 kW

[T1]_B [LWCu]_FL=[LWCu]_TXtest=7.84 kW

[T1]_B [LVFe]_NL= √(([VA]_TXtest ×(%EXC)/100)^2−([[LWFe]_TXtest)]^2)

[T1]_B [LVFe]_NL=√((1000×1.25/100)^2−[2.0]^2 )=12.339k var

[T1]_B [LVCu]_FL= √(([VA]_TXtest ×(%Z)/100)^2−([[LWCu]_TXtest)]^2)

[T1]_B [LVFe]_FL=√((1000×5.57/100)^2− [7.84]^2)=55.145k var

E.6 Active and reactive losses for T1 bank

[T1LWFe]_NL= [T1]_R LWFe_NL+ [T1]_W LWFe_NL+ [T1]_B LWFe_NL

[T1LWFe]_NL=2.03+2.02+2.0=6.05kW

[T1LWCu]_FL= [T1]_R [LWCu]_FL+ [T1]_W [LWCu]_FL+ [T1]_B [LWCu]_FL

[T1LWCu]_FL=7.83+8.02+7.84=23.69kW

[T1LVFe]_NL= [T1]_R LVFe_NL+ [T1]_W LVFe_NL+ [T1]_B LVFe_NL

[T1LVFe]_NL=14.458+10.528+12.339=37.325k var

[T1LVCu]_FL= [T1]_R LVCu_FL+ [T1]_W LVCu_FL+ [T1]_B LVCu_FL

[T1LVCu]_FL=54.036+54.008+55.145=163.189k var

E.6.1 Factory test results for transformer T2

VATXtest = 2200 kVA Rated kVA, single phase

Vpri rated = 4160/2400 V Rated primary voltage, p-p/p-n

Vsec rated = 600/347 V Rated secondary voltage, p-p/p-n

LWFeTXtest = 1.25 kW No-load loss (iron loss)

%EXC = 0.4% Percent excitation current

LWCuTXtest = 3.8 kW Load loss (copper loss)

% Z = 2.44% Percent impedance

E.6.2 Calculation of transformer T2 active and reactive losses at rated voltage and power

T2 is operating on its principal taps at rated voltage and no adjustments to the manufacturer's no-load and load losses are required.

[T2LWFe]_NL=[LWFe]_TXtest=1.25kW

[T2LWCu]_FL=[LWCu]_TXtest=3.8kW

[T2LVFe]_NL=√(([VA]_TXtest ×(%EXC)/100)^2−([[LWFe]_TXtest)]^2)

[T2LVFe]_NL=√((2200×0.4/100)^2−[1.25]^2)=8.711k var

[T2LVCu]_FL=√(([VA]_TXtest ×(%Z)/100)^2−([[LWCu]_TXtest)]^2)

[T2LVCu]_FL=√((2200×2.44/100)^2− [3.8]^2)=53.545k var

E.7 Losses for T1 and T2

LWFe_NL=[T1LWFe]_NL+ [T2LWFe]_NL

LWFe_NL=6.05+1.25=7.3kW

LWCu_FL=[T1LWCu]_FL+[T2LWCu]_FL

LWCu_FL=23.69+3.8=27.49kW

[LVFe]_NL=[T1LVFe]_NL+[T2LVFe]_NL

[LVFe]_NL=37.325+8.711=46.036k var

[LVCu]_FL=[T1LVCu]_FL+ [T2LVCu]_FL

[LVCu]_FL=163.189+53.545=216.734k var

E.8 Information and calculations for revenue metering on the LV side of T2

Metering is on the low voltage side of T2. The metering facility is comprised of a polyphase 3-element meter, three metering current transformers and three metering voltage transformers.

Elements = 3

Current transformer ratio = 2000:5 A

CTR= 2000A/5A=400

Voltage transformer ratio = 360:120 V

VTR= 360/120=3

V_TXtest= 2200kVA

V_rated=600 V phase to phase

I_rated=[VA]_TXtest/(V_rated ×√3)

I_rated= 2200/(600×√3)=2177 A (phase)

E.9 Calculation of loss parameters

The calculation of the loss parameters identified as A and B below are representative of no load and full load kW losses, per phase, and are proportional to the current and voltage dependent losses. The loss parameters identified as C and D below are representative of the no load and full load kvar losses, per phase, and are also proportional to the voltage and current dependent losses.

A= [LWFe]_NL/Elements ÷(V_rated/(VTR×√3))^2= 7.3/3 ÷(600/(3×√3))^2=[1.825×10]^(−4) kW/V^2 per phase

B= [LWCu]_FL/Elements ÷(I_rated/CTR)^2= 27.49/3 ÷(2117/400)^2= .03271 kW/I^2 per phase

C= [LVFe]_NL/Elements ÷(V_rated/(VTR×√3))^4= 46.036/3 ÷(600/(3×√3))^4=[8.631×10]^(−8) kvar/V^4 per phase

D= [LVCu]_FL/Elements ÷(I_rated/CTR)^2= 216.734/3 ÷(2117/400)^2= 2.5793 kvar/I^2 per phase

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