E36—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
 2.0 Purpose
 3.0 References
 4.0 Definitions
 5.0 Background
 6.0 Policy for the application of loss compensation to sitespecific legal units of measure
 7.0 Requirements for the calculation of loss compensation
 7.1 General
 7.2 I^{2}h/V^{2}h method
 7.3 VA method
 7.3.1 Standards and guidance documents
 7.3.2 VA method limitations
 7.3.3 Formal attestation for coefficients used
 7.3.4 Phase equivalent circuit modelling
 7.3.5 Requirements for establishing loss coefficients
 7.3.6 R^{2} value limits
 7.3.7 R^{2} values less than 0.95
 7.3.8 Modelling data and curve example
 7.4 Multiple transformations and/or line combinations
 8.0 Information required for the calculation of loss compensation
 9.0 Losses and apportioning of losses for multiple points of metering
 Appendix A—Transformer loss compensation example calculations
 Appendix B—Power line loss compensation example calculations
 Appendix C—Modelling examples for the VA method for loss compensation
 Appendix D—Apportioning of losses
 Appendix E—Example of I^{2}h/V^{2}h method loss parameter calculations for two transformers in series
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
 Handbook for Electricity Metering, 10th Edition, Edison Electric Institute
 LMBEG07—Specifications For Approval of Type of Electricity Meters, Instrument Transformers and Auxiliary Devices
 MDP_STD_0005—SiteSpecific Loss Adjustments: Requirements for Adjustment of Meter Readings for SiteSpecific Losses in The IESOAdministered Market, Issue 4
 MDP_PRO_0011—Market Manual 3: Metering—Part 3.5: SiteSpecific Loss Adjustments, Issue 8
 SE03—Specification for the Installation and Use of Electricity Meters Input Connections and Ratings
 SE06—Specification for the Approval of Type of Electricity Meters and Auxiliary Devices—Amendments to Measurement Canada Specification LMBEG07
 SE11—Specification for the Installation And Use of Approved and Verified Electricity Meters Used to Establish Processed Legal Units of Measure
 SE12 —Specifications for the Approval of Type of Electricity Meters Equipped With Loss Compensation Functions
 SEG02—Specifications for Approval of Physical Sealing Provisions for Electricity and Gas Meters
 SEG05—Specifications for the Approval of Software Controlled Electricity and Gas Metering Devices
 SEG06—Specifications Relating to Event Loggers for Electricity and Gas Metering Devices
 E30—Policy Decisions and Interpretations Related to Specification LMBEG07
 E27—Policy on the Use of Electricity Meters in Net Metering Applications
 E31—Implementation of policies and specifications relating to standardized electricity energy and demand legal units of measure
4.0 Definitions
 Actual current
(courant réel) 
The current as determined from the meter's approved I^{2}h function.
 Actual voltage
(tension réelle) 
The voltage as determined from the meter's approved V^{2}h 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, N1 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 shortcircuit impedance
(pourcentage de la charge de l'impédance en courtcircuit) 
The shortcircuit impedance of the power transformer expressed as a percentage of the primary voltage required to circulate full load current in the shortcircuited 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.
 Noload 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).
 Noload 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.
 Noload 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.
 Noload 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 voltampere power rating of the transformer as provided in the test sheet (typically provided in megavoltamperes).
 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 lowvoltage side of a power transformer, and the ownership change and trade point occur on the highvoltage 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 sitespecific 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 SE11 and SE12.
6.1.2 Application of bulletin E27
Loss compensation may be applied in accordance with bulletin E27.
6.1.3 Application of type approval and other requirements
Meters used for loss compensation must meet the type approval requirements for the I^{2}h and V^{2}h functions of SE06 and LMBEG07, as well as the other applicable related type approval requirements of SE06 and LMBEG07.
6.1.4 Application of verification requirements
Meters used for loss compensation are to be verified in accordance with the requirements specified for the I^{2}h and V^{2}h functions of SE02, as well as the other applicable related metering verification requirements of SE02.
6.1.5 Implementation timeline
Loss compensation requirements are subject to the same implementation timelines referenced in bulletin E31 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.
 I^{2}h/V^{2}h method
 VA method
7.1.2 Preferred method
The I^{2}h/V^{2}h method is the preferred method for determining loss compensation and is the only method that will be used in approved meters.
7.2 I^{2}h/V^{2}h method
7.2.1 Use of I^{2}h and V^{2}h legal units of measurement
The I^{2}h/V^{2}h method for loss compensation uses I^{2}h and V^{2}h LUMs for calculating relevant power line and power transformer losses.
7.2.2 Inside the meter application with a twowinding power transformer
The I^{2}h/V^{2}h 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 I^{2}h/V^{2}h 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 I^{2}h and V^{2}h) 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:
 MDP_STD_0005—SiteSpecific Loss Adjustments: Requirements for Adjustment of Meter readings for sitespecific losses in the IESOadministered market, Issue 4; and
 MDP_PRO_0011—Market manual 3: metering part 3.5 sitespecific 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 I^{2}h/V^{2}h method. This method is only applicable to loss compensation determination outside of a meter where the I^{2}h/V^{2}h 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 secondorder polynomial equations:
Where:
 W_{loss} is the active power loss in the power system component
 Var_{loss} is the reactive power loss in the power system component
 VA is the apparent power measured by the meters on the secondary and tertiary transformer windings
 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:
 establishing a oneline diagram and the electrical properties of the power system component;
 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;
 using the numerical curve fitting method (loadflow study) to calculate the losses at several points over the range of each variable;
 graphing the losses as a function of the demand that would be observed by the metering;
 using numerical curve fitting to determine the coefficients of the secondorder polynomial function to be used to estimate losses;
 using the numerical curve fitting method to determine a measurement of the quality of the resulting predictions (R^{2}).
7.3.6 R^{2} value limits
The R^{2} 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 R^{2} values less than 0.95
The VA method for loss compensation must not be used in the case of R^{2} 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 I^{2}h/V^{2}h 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.
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  I_{pri} / Ipri rated  Primary rated current of power transformer 
5  I_{sec} / 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  LWFe_{NL}  Noload loss (watts) (from test sheet data) 
13  LVFe_{NL}  Noload loss (var) (typically calculated from test sheet data) 
14  LWCu_{FL}  Load loss (watts) (from test sheet data, include reference temperature) 
15  LVCu_{FL}  Load loss (var) (typically calculated from test sheet data, include reference temperature) 
16  I_{rated}  Rated transformer current 
17  V_{rated}  Rated voltage (transformer) 
Note: The policies and requirements provide by this bulletin and SE11 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 LiquidImmersed Distribution, Power, and Regulating Transformers or other applicable requirements found in the IEEE C57^{TM} 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.
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  x_{l}  Conductor inductive reactance per unit length 
5  r_{t}  Conductor resistance corrected for temperature effect per unit length 
6  G_{l}  Conductance for service length of conductor 
7  B_{l}  Susceptance for service length of conductor 
Note: The policies and requirements provide by this bulletin and SE11 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 CurrentTemperature 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 SE11, 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.
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 
LWFe_{NL}  9,650  9,690  9,340 
LWCu_{FL}  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, 10^{th} edition, Washington, DC: Edison Electric Institute, 2002, pp 258262.
Available voltage taps: 115,000; 112,125; 109,250; 106,375; 103,500
3 wire delta: 2 element metering
A.2 Calculation of transformer noload watt losses
A.3 Calculation of transformer load watt losses
A.4 Calculation of transformer noload var losses
A.5 Calculation of transformer load var losses
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 45 and Table 46 for the listed values included below).
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 
R_{o}  Positive sequence resistance per unit length at 50 °C (ra)  0.384  ohm/mile 
x_{i}  Positive sequence selfreactance per unit length (xa)  0.489  ohm/mile 
B.2 Calculation of line losses
1) Line loss (watts)
Where:
PLLW_{t} = Power line loss in watts (climatic influence)
I_{act} = Actual current (derived from measure I^{2}h)
r_{t} = Resistance (corrected for climatic influences) per unit length
L = Conductor length
Note: Refer to the paragraph below in 2) to calculate r_{t}.
2) Line loss (l var, inductive)
Where:
PLLv = (Power) line loss (var)
I_{act} = Actual current (derived from measure I^{2}h)
x_{i} = Inductive resistance per unit length (ohm/km)
L = Conductor length
Calculation of the resistance of the conductor r_{t} is done according to IEEE standard 7382006, 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
 C.1 Examples for the VA method can be found in IESO documents MDP_STD_0005 and MDP_PRO_0011.
 C.2 The per phase equivalent circuit for a twowinding transformer can be found in Figure 4.2 of IESO standard MDP_STD_0005, section 4.2.
 C.3 The per phase equivalent circuit for a threewinding transformer used for the VA method for loss compensation can be found in Figure 9.1 of IESO standard MDP_STD_0005, section 9.
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.
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. Curvefitting software was used to develop the K coefficients and R^{2}.
Figure 1 : kW losses curve using the VA method
Figure 2: kvar losses curve using the VA method
Appendix D—Apportioning of losses
Figure 1 Appendix D: Two customers sharing the same power transformer
D.1. Total usage = M1 + M2
D.2 Loss calculations
where:
iph = Number of intervals per hour
EL = Number of meter elements
Time  kWh_{M1}  kvarh_{M1}  kVAh_{M1}  kV^{2}h_{M1}  I^{2}h_{M1} 

0:30  237.54  8.34  237.66  155.43  365.00 
0:35  235.44  8.22  235.56  155.43  357.50 
Time  kWh_{M2}  kvarh_{M2}  kVAh_{M2} 

0:30  46.98  27.63  54.45 
0:35  46.08  28.17  54.09 
Time  kWh_{M1+M2}  kvarh_{M1+M2}  kVAh_{total} calculated  kV^{2}h_{M1} measured 
I^{2}h_{Total} 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 
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 
Time  kWh_{M1} loss  kvarh_{M1} loss 

0:30  5.03  7.23 
0:35  5.04  7.23 
Time  kWh_{M2} loss  kvarh_{M2} loss 

0:30  0.99  1.43 
0:35  0.99  1.41 
Time  kWh_{L1}  kvarh_{L1}  kWh_{L2}  kvarh_{L2} 

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 SE11, Wh_{M1} and varh_{ M1} are the legally relevant values established for customer L1. Whereas, Wh_{M2} 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
Figure D3: Customer and generator sharing the same power transformer
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:
 Load loss apportionment based on absolute gross metered load at each customer
 M1 (gen 0 MW, load 25 MW): load losses apportioned based on 25 MW load for customer 1
 M2 (gen 100 MW, load 0 MW): load losses apportioned based on 100 MW generation for customer 2
 M1 (gen 0 MW, load 25 MW): load losses apportioned based on 25 MW load for customer 1
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 SE11.
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.
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 I^{2}h/V^{2}h method loss parameter calculations for two transformers in series
Figure E.1: Single line diagram
E.1 Description
Transformer T1 is comprised of three singlephase transformers: T1R (red phase), T1W (white phase) and T1B (blue phase), each rated 1 MVA. The singlephase transformers are configured for delta/wye (D/Y) transformation and cascaded in series with T2, a 3phase transformer, connected to the load bus. Revenue metering is done on the low voltage side of T2.
T1 3phase bank rating: 3 MVA, 44 kV – 4.16/2.4 kV, connected D/Y. Onload tap changer on the 44 kV side.
T2 3phase 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%.
Transformer  Rated primary voltage (V) 
Rated secondary voltage (V) 
Rated power (MVA)  Noload loss (iron) (kW) 
Load loss (copper) (kW) 
Percent excitation current (%) 
Percent impedance (%) 

T1_{R} (red phase) 
44,000 pp ^{Footnote 2} 
2,400 pn ^{Footnote 3} 
1.0  2.03  7.83  1.46  5.46 
T1_{W} (white phase) 
44,000 pp ^{Footnote 2} 
2,400 pn ^{Footnote 3} 
1.0  2.02  8.02  1.072  5.46 
T1_{B} (blue phase) 
44,000 pp ^{Footnote 2} 
2,400 pn ^{Footnote 3} 
1.0  2.0  7.84  1.25  5.57 
T2  4,160/2400 pp ^{Footnote 2}/ pn^{Footnote 3} 
600/347 pp ^{Footnote 2}/ pn^{Footnote 3} 
2.2  1.25  3.8  0.4  2.44 
Footnotes
 Footnote 2

pp = phase to phase (line to line)
 Footnote 3

pn = phase to neutral (line to neutral)
E.3 Factory test results for transformer T1_{R}
VA_{TXtest} = 1000 kVA Rated kVA, single phase
Vpri rated = 44000 V Rated primary voltage, pp
Vsec rated = 2400 V Rated secondary voltage, pn
LWFe_{TXtest} = 2.03 kW Noload loss (iron loss)
%EXC = 1.46% Percent excitation current
LWCu_{TXtest} = 7.83 kW Load loss (copper loss)
% Z = 5.46% Percent impedance
E.3.1 Calculation of transformer T1_{R} active and reactive losses at rated voltage and power
T1_{R} is operating on its principal taps at rated voltage and no adjustments to the manufacturer's noload and load losses are required.
E.4 Factory test results for transformer T1_{W}
VA_{TXtest} = 1000 kVA Rated kVA, single phase
Vpri rated = 44000 V Rated primary voltage, pp
Vsec rated = 2400 V Rated secondary voltage, pn
LWFe_{TXtest} = 2.02 kW Noload loss (iron loss)
%EXC = 1.072% Percent excitation current
LWCu_{TXtest} = 8.02 kW Load loss (copper loss)
% Z = 5.46% Percent impedance
E.4.1 Calculation of transformer T1_{W} active and reactive losses at rated voltage and power
T1_{W} is operating on its principal taps at rated voltage and no adjustments to the manufacturer's noload and load losses are required.
E.5 Factory test results for transformer T1_{B}
VA_{TXtest} = 1000 kVA Rated kVA, single phase
Vpri rated = 44000 V Rated primary voltage, pp
Vsec rated = 2400 V Rated secondary voltage, pn
LWFe_{TXtest} = 2.0 kW Noload loss (iron loss)
%EXC = 1.25% Percent excitation current
LWCu_{TXtest} = 7.84 kW Load loss (copper loss)
% Z = 5.57% Percent impedance
E.5.1 Calculation of transformer T1_{B} active and reactive losses at rated voltage and power
T1_{B} is operating on its principal taps at rated voltage and no adjustments to the manufacturer's noload and load losses are required.
E.6 Active and reactive losses for T1 bank
E.6.1 Factory test results for transformer T2
VA_{TXtest} = 2200 kVA Rated kVA, single phase
Vpri rated = 4160/2400 V Rated primary voltage, pp/pn
Vsec rated = 600/347 V Rated secondary voltage, pp/pn
LWFe_{TXtest} = 1.25 kW Noload loss (iron loss)
%EXC = 0.4% Percent excitation current
LWCu_{TXtest} = 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 noload and load losses are required.
E.7 Losses for T1 and T2
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 3element meter, three metering current transformers and three metering voltage transformers.
Elements = 3
Current transformer ratio = 2000:5 A
Voltage transformer ratio = 360:120 V
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.
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