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

Category: Electricity
Issue date: 2017-08-31
Effective date: 2018-07-01
Revision number: N/A
Supersedes: N/A

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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 site-specific legal units of measure
  • 6.1 General
    • 6.1.1 Application of formulae and processes
    • 6.1.2 Application of bulletin E-27
    • 6.1.3 Application of type approval and other requirements
    • 6.1.4 Application of verification requirements
    • 6.1.5 Implementation timeline
• 7.0 Requirements for the calculation of loss compensation
  • 7.1 General
    • 7.1.1 Methods to be used for loss compensation
    • 7.1.2 Preferred method
  • 7.2 I²h/V²h method
    • 7.2.1 Use of I²h and V²h legal units of measurement
    • 7.2.2 Inside the meter application with a two-winding power transformer
    • 7.2.3 Method used outside the meter for power transformers having two or more windings
  • 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 R² value limits
    • 7.3.7 R² 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
  • 8.1 Power distribution transformer parameters
  • 8.2 Power line parameters
• 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 I²h/V²h method loss parameter calculations for two transformers in series

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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
• LMB-EG-07—Specifications For Approval of Type of Electricity Meters, Instrument Transformers and Auxiliary Devices
• MDP_STD_0005—Site-Specific Loss Adjustments: Requirements for Adjustment of Meter Readings for Site-Specific Losses in The IESO-Administered Market, Issue 4
• MDP_PRO_0011—Market Manual 3: Metering—Part 3.5: Site-Specific Loss Adjustments, Issue 8
• S-E-03—Specification for the Installation and Use of Electricity Meters Input Connections and Ratings
• S-E-06—Specification for the Approval of Type of Electricity Meters and Auxiliary Devices—Amendments to Measurement Canada Specification LMB-EG-07
• S-E-11—Specification for the Installation And Use of Approved and Verified Electricity Meters Used to Establish Processed Legal Units of Measure
• S-E-12 —Specifications for the Approval of Type of Electricity Meters Equipped With Loss Compensation Functions
• S-EG-02—Specifications for Approval of Physical Sealing Provisions for Electricity and Gas Meters
• S-EG-05—Specifications for the Approval of Software Controlled Electricity and Gas Metering Devices
• S-EG-06—Specifications Relating to Event Loggers for Electricity and Gas Metering Devices
• E-30—Policy Decisions and Interpretations Related to Specification LMB-EG-07
• E-27—Policy on the Use of Electricity Meters in Net Metering Applications
• E-31—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 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.

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:

• $W_{\mathrm{loss}}=K1\left({\mathrm{VA}}^2\right)+K2\left(\mathrm{VA}\right)+K3$
• ${\mathrm{var}}_{\mathrm{loss}}=K4\left({\mathrm{VA}}^2\right)+K5\left(\mathrm{VA}\right)+K6$

Where:

1. W_loss is the active power loss in the power system component
2. Var_loss 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)

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

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 manufacturer^{Footnote 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, 10^th 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

$\mathrm{CTR}=\frac{\mathrm{3,000 }A}{5A}=\mathrm{600 }\mathrm{line }\mathrm{current}$

$\mathrm{VTR}=\frac{\mathrm{2,400 }V}{\mathrm{120 }V}=\mathrm{20 }\mathrm{line}-\mathrm{line}$

A.2 Calculation of transformer no-load watt losses

1. $\mathrm{LWFe}={\mathrm{LWFe}}_{\mathrm{NL}}\times {\left(\frac{V_{\mathrm{act}}}{V_{\mathrm{rated}}}\right)}^2$
   1. $V_{\mathrm{act}}=\mathrm{2,400 }V$
   2. $V\mathrm{sec }\mathrm{rated}=\mathrm{2,520 }V$
   3. ${\mathrm{LWFe}}_{\mathrm{NL}}=\mathrm{9,650}+\mathrm{9,690}+\mathrm{9,340}=\mathrm{28,680 }W$
2. $\mathrm{LWFe}=\mathrm{28,680}\times {\left(\frac{\mathrm{2,400}}{\mathrm{2,500}}\right)}^2=\mathrm{26,013.6 }W\left(\mathrm{no load}\right)$

A.3 Calculation of transformer load watt losses

1. $\mathrm{LWCu}={\mathrm{LWCu}}_{\mathrm{FL}}\times {\left(\frac{1_{\mathrm{act}}}{1_{\mathrm{rated}}}\right)}^2$
   1. $I_{\mathrm{act}}=\mathrm{3,000 }A$
   2. $I_{\mathrm{rated}}=\frac{\sqrt{3}\times \mathrm{VAphase}}{\mathrm{V }\mathrm{sec }L-L}$
   3. $I_{\mathrm{rated}}=\frac{\sqrt{3}\times \mathrm{3,333,000}}{\mathrm{2,520}}=\mathrm{2,290.84 }A$
   4. ${\mathrm{LWCu}}_{\mathrm{FL}}=\mathrm{18,935}+\mathrm{18,400}+\mathrm{18,962}=\mathrm{56,027 }W$
2. $\mathrm{LWCu}=\mathrm{56,027}\times {\left(\frac{\mathrm{3,000}}{\mathrm{2,290,84}}\right)}^2=\mathrm{96,083.8 }W$

A.4 Calculation of transformer no-load var losses

1. $\mathrm{LVCFe}={\mathrm{LVFe}}_{\mathrm{NL}}\times {\left(\frac{V_{\mathrm{act}}}{V_{\mathrm{rated}}}\right)}^4$
   1. ${\mathrm{LVFe}}_{\mathrm{NL}}=\sqrt{{({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%\mathrm{EXC}}{100})}^2-{\left({\mathrm{LWFe}}_{\mathrm{NL}}\right)}^2}$
   2. ${\mathrm{LVFe}}_{\mathrm{NL1}}=\sqrt{{(\mathrm{3,333,000}\times 1.00\%)}^2-{\mathrm{9,650}}^2}=\mathrm{31,902 }\mathrm{var}$
   3. ${\mathrm{LVFe}}_{\mathrm{NL2}}=\sqrt{{(\mathrm{3,333,000}\times 1.06\%)}^2-{\mathrm{9,690}}^2}=\mathrm{33,974 }\mathrm{var}$
   4. ${\mathrm{LVFe}}_{\mathrm{NL3}}=\sqrt{{(\mathrm{3,333,000}\times 0.91\%)}^2-{\mathrm{9,340}}^2}=\mathrm{28,856 }\mathrm{var}$
2. ${\mathrm{LVFe}}_{\mathrm{NL}}=\mathrm{31,902}+\mathrm{33,974}+\mathrm{28,856}=\mathrm{94,732 }\mathrm{var}$
3. $\mathrm{LVFe}=\mathrm{94,732}\times {\left(\frac{\mathrm{2,400}}{\mathrm{2,520}}\right)}^4=\mathrm{77,936 }\mathrm{var}$

A.5 Calculation of transformer load var losses

1. $\mathrm{LVCu}={\mathrm{LVCu}}_{\mathrm{FL}}\times {\left(\frac{I_{\mathrm{act}}}{I_{\mathrm{rated}}}\right)}^2$
   1. ${\mathrm{LVCu}}_{\mathrm{FL}}=\sqrt{{({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%Z}{100})}^2-{\left({\mathrm{LWCu}}_{\mathrm{FL}}\right)}^2}$
   2. ${\mathrm{LVCu}}_{\mathrm{FL1}}=\sqrt{{(\mathrm{3,333,000}\times 8.16\%)}^2-{\mathrm{18,935}}^2}=\mathrm{271,313 }\mathrm{var}$
   3. ${\mathrm{LVCu}}_{\mathrm{FL2}}=\sqrt{{(\mathrm{3,333,000}\times 8.03\%)}^2-{\mathrm{18,400}}^2}=\mathrm{267,007 }\mathrm{var}$
   4. ${\mathrm{LVCu}}_{\mathrm{FL3}}=\sqrt{{(\mathrm{3,333,000}\times 8.12\%)}^2-{\mathrm{18,682}}^2}=\mathrm{269,994 }\mathrm{var}$
2. ${\mathrm{LVCu}}_{\mathrm{FL}}=\mathrm{271,313}+\mathrm{267,007}+\mathrm{269,994}=\mathrm{808,314 }\mathrm{var}$
3. $\mathrm{LVCu}=\mathrm{808,314 }\times {\left(\frac{\mathrm{3,000}}{\mathrm{2,290,94}}\right)}^2=\mathrm{1,386,223 }\mathrm{var}$

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)

${\mathrm{PLLW}}_t={\left(I_{\mathrm{act}}\right)}^2\times r_t\times L$

Where:

PLLW_t = Power line loss in watts (climatic influence)

I_act = Actual current (derived from measure I²h)

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

L = Conductor length

${\mathrm{PLLW}}_t={79.94}^2\times 0.2028\times 7.05=\mathrm{9,136.62 }W$

2) Line loss (l var, inductive)

${\mathrm{PLL}}_v={\left(I_{\mathrm{act}}\right)}^2\times x_i\times L$

Where:

PLLv = (Power) line loss (var)

I_act = Actual current (derived from measure I²h)

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

L = Conductor length

${\mathrm{PLL}}_v={79.94}^2\times 0.3039\times 7.05=\mathrm{13,691.4 }\mathrm{var}$

Calculation of the resistance of the conductor r_t 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

• 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 two-winding 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 three-winding 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.

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.

Appendix D—Apportioning of losses

D.1. Total usage = M1 + M2

1. ${\mathrm{Wh}}_{\mathrm{total}}={\mathrm{Wh}}_{M1}+{\mathrm{Wh}}_{M2}$
2. ${\mathrm{varh}}_{\mathrm{total}}={\mathrm{varh}}_{M1}+{\mathrm{varh}}_{M2}$
3. ${\mathrm{VAh}}_{\mathrm{total}}=\sqrt{{\left({\mathrm{Wh}}_{\mathrm{total}}\right)}^2+{\left({\mathrm{varh}}_{\mathrm{total}}\right)}^2}$
4. ${I^{2}h}_{\mathrm{total}}=\frac{{\left({\mathrm{VAh}}_{\mathrm{total}}\right)}^2}{{V^{2}h}_{\left(M1\mathrm{or M}2\right)}}$

D.2 Loss calculations

1. ${\mathrm{Wh}}_{\mathrm{LWFe}}=\frac{{\mathrm{LWFe}}_{\mathrm{NL}}\times {V^{2}h}_{\left(M\mathrm{1 }\mathrm{or M}2\right)}}{[{\left(V_{\mathrm{rated}}\right)}^2\times \mathrm{EL}]}$
2. ${\mathrm{Wh}}_{\mathrm{LWCu}}=\frac{{\mathrm{LWCu}}_{\mathrm{FL}}\times {I^{2}h}_{\mathrm{total}}}{[{\left(I_{\mathrm{rated}}\right)}^2\times \mathrm{EL}]}$
3. ${\mathrm{var}}_{\mathrm{LWFe}}=\frac{{\mathrm{LVFe}}_{\mathrm{NL}}\times \mathrm{iph}\times {{\left({V^{2}h}_{\left(M\mathrm{1 }\mathrm{or M}2\right)}\right)}^2}^{}}{[{\left(V_{\mathrm{rated}}\right)}^4\times {\left(\mathrm{EL}\right)}^2]}$
4. ${\mathrm{var}}_{\mathrm{LWCu}}=\frac{{\mathrm{LVCu}}_{\mathrm{FL}}\times {I^{2}h}_{\mathrm{total}}}{[{\left(I_{\mathrm{rated}}\right)}^2\times \mathrm{EL}]}$
5. ${\mathrm{Wh}}_{\mathrm{loss}}={\mathrm{Wh}}_{\mathrm{LWFe}}+{\mathrm{Wh}}_{\mathrm{LWCu}}$
6. ${\mathrm{varh}}_{\mathrm{loss}}={\mathrm{var}}_{\mathrm{LWFe}}+{\mathrm{var h}}_{\mathrm{LWCu}}$

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, Wh_M1 and varh _M1 are the legally relevant values established for customer L1. Whereas, Wh_M2 and varh _M2values are established from compensated PLUM values for customer L2 (legally relevant values of meter M2 + T2 loss values) as follows:

• ${\mathrm{Wh}}_{\mathrm{total}}=\Sigma {\mathrm{Wh}}_{\mathrm{MI}}\mathrm{ where I}=\mathrm{1, }\mathrm{ 2}={\mathrm{Wh}}_{M1}+({\mathrm{Wh}}_{M2}+{\mathrm{Wh}}_{T\mathrm{2 }\mathrm{loss}})$
• ${\mathrm{VARh}}_{\mathrm{total}}=\Sigma {\mathrm{VARh}}_{\mathrm{MI}}\mathrm{ where I}=\mathrm{1, }\mathrm{ 2}={\mathrm{VARh}}_{M1}+({\mathrm{VARh}}_{M2}+{\mathrm{VARh}}_{T\mathrm{2 }\mathrm{loss}})$

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
      ${\mathrm{Wh}}_{M1\mathrm{load} \mathrm{loss}}=\frac{25}{25+100}\times {\mathrm{Wh}}_{\mathrm{load} \mathrm{loss}}$
   2. M2 (gen 100 MW, load 0 MW): load losses apportioned based on 100 MW generation for customer 2
      ${\mathrm{Wh}}_{M2\mathrm{load} \mathrm{loss}}=\frac{100}{25+100}\times {\mathrm{Wh}}_{\mathrm{load} \mathrm{loss}}$

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.

   • ${\mathrm{Wh}}_{M1\mathrm{load} \mathrm{loss}}=0$
   • ${\mathrm{Wh}}_{M2\mathrm{load} \mathrm{loss}}={\mathrm{Wh}}_{\mathrm{M net load} \mathrm{loss}}$

   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

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 T1_R

VA_TXtest = 1000 kVA Rated kVA, single phase

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

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

LWFe_TXtest = 2.03 kW No-load 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 no-load and load losses are required.

${T1}_R{\mathrm{LWFe}}_{\mathrm{NL}}={\mathrm{LWFe}}_{\mathrm{TXtest}}=\mathrm{2.03 }\mathrm{kW}$

${T1}_R{\mathrm{LWCu}}_{\mathrm{FL}}={\mathrm{LWCu}}_{\mathrm{TXtest}}=\mathrm{7.83 }\mathrm{kW}$

${T1}_R{\mathrm{LVFe}}_{\mathrm{NL}}=\sqrt{{({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%\mathrm{EXC}}{100})}^2-{\left({\mathrm{LWFe}}_{\mathrm{TXtest}}\right)}^2}$

${T1}_R{\mathrm{LVFe}}_{\mathrm{NL}}=\sqrt{{({1000}_{}\times \frac{\mathrm{1.46}}{100})}^2-{{\mathrm{2.03}}_{}}^2}=\mathrm{14.458 }\mathrm{kvar}$

${\mathrm{TI}}_R{\mathrm{LVCu}}_{\mathrm{FL}}=\sqrt{{({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%Z}{100})}^2-{\left({\mathrm{LWCu}}_{\mathrm{TXtest}}\right)}^2}$

${T\mathrm{I}}_R{\mathrm{LVCu}}_{\mathrm{FL}}=\sqrt{{({1000}_{}\times \frac{\mathrm{5.46}}{100})}^2-{{7.83}_{}}^2}=\mathrm{54.036 }\mathrm{kvar}$

E.4 Factory test results for transformer T1_W

VA_TXtest= 1000 kVA Rated kVA, single phase

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

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

LWFe_TXtest = 2.02 kW No-load 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 no-load and load losses are required.

${T1}_W{\mathrm{LWFe}}_{\mathrm{NL}}={\mathrm{LWFe}}_{\mathrm{TXtest}}=\mathrm{2.02 }\mathrm{Kw}$

${T1}_W{\mathrm{LWCu}}_{\mathrm{FL}}={\mathrm{LWCu}}_{\mathrm{TXtest}}=\mathrm{8.02 }\mathrm{Kw}$

${\mathrm{TI}}_W{\mathrm{LVCe}}_{\mathrm{NL}}=\sqrt{{({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%\mathrm{EXC}}{100})}^2-{\left({\mathrm{LWFe}}_{\mathrm{TXtest}}\right)}^2}$

${\mathrm{TI}}_W{\mathrm{LVFe}}_{\mathrm{NL}}=\sqrt{{(1000\times \frac{1.072}{100})}^2-{2.02}^2=}\mathrm{10.528 }\mathrm{kvar}$

${\mathrm{TI}}_W{\mathrm{LVCu}}_{\mathrm{FL}}=\sqrt{{({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\mathrm{\%Z}}{100})}^2-{{\left({\mathrm{LWCu}}_{\mathrm{TXtest}}\right)}^2}^{}}$

${\mathrm{TI}}_W{\mathrm{LVCu}}_{\mathrm{FL}}=\sqrt{{\left(1000\times \frac{5.46}{100}\right)}^2-{8.02}^2}=\mathrm{54.008 }\mathrm{kvar}$

E.5 Factory test results for transformer T1_B

VA_TXtest = 1000 kVA Rated kVA, single phase

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

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

LWFe_TXtest = 2.0 kW No-load 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 no-load and load losses are required.

${T1}_B{\mathrm{LWFe}}_{\mathrm{NL}}={\mathrm{LWFe}}_{\mathrm{TXtest}}=\mathrm{2.0 }\mathrm{kW}$

${T1}_B{\mathrm{LWCu}}_{\mathrm{FL}}={\mathrm{LWCu}}_{\mathrm{TXtest}}=\mathrm{7.84 }\mathrm{kW}$

${T1}_B{\mathrm{LVFe}}_{\mathrm{NL}}=\sqrt{{\left({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%\mathrm{EXC}}{100}\right)}^2-{{\left({\mathrm{LWFe}}_{\mathrm{TXtest}}\right)}^2}^{}}$

${T1}_B{\mathrm{LVFe}}_{\mathrm{NL}}=\sqrt{{\left(1000\times \frac{\mathrm{1.25}}{100}\right)}^2-{2.0}^2}=\mathrm{12.339 }\mathrm{kvar}$

${T1}_B{\mathrm{LVCu}}_{\mathrm{FL}}=\sqrt{{\left({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%Z}{100}\right)}^2-{\left({\mathrm{LWCu}}_{\mathrm{TXtest}}\right)}^2}$

${T1}_B{\mathrm{LVFe}}_{\mathrm{FL}}=\sqrt{{\left(1000\times \frac{\mathrm{5.57}}{100}\right)}^2-{7.84}^2}=\mathrm{55.145 }\mathrm{kvar}$

E.6 Active and reactive losses for T1 bank

${T1\mathrm{LWFe}}_{\mathrm{NL}}={T1}_R{\mathrm{LWFe}}_{\mathrm{NL}}+{T1}_W{\mathrm{LWFe}}_{\mathrm{NL}}+{T1}_B{\mathrm{LWFe}}_{\mathrm{NL}}$

${T1\mathrm{LWFe}}_{\mathrm{NL}}=2.03+2.02+2.0=\mathrm{6.05 }\mathrm{kW}$

${T1\mathrm{LWCu}}_{\mathrm{FL}}={T1}_R{\mathrm{LWCu}}_{\mathrm{FL}}+{T1}_W{\mathrm{LWCu}}_{\mathrm{FL}}+{T1}_B{\mathrm{LWCu}}_{\mathrm{FL}}$

${T1\mathrm{LWCu}}_{\mathrm{FL}}=7.83+8.02+7.84=\mathrm{23.69 }\mathrm{kW}$

${T1\mathrm{LVFe}}_{\mathrm{NL}}={T1}_R{\mathrm{LVFe}}_{\mathrm{NL}}+{T1}_W{\mathrm{LVFe}}_{\mathrm{NL}}+{T1}_B{\mathrm{LVFe}}_{\mathrm{NL}}$

${T1\mathrm{LVFe}}_{\mathrm{NL}}=14.458+10.528+12.339=\mathrm{37.325 }\mathrm{kvar}$

${T1\mathrm{LVCu}}_{\mathrm{FL}}={T1}_R{\mathrm{LVCu}}_{\mathrm{FL}}+{T1}_W{\mathrm{LVCu}}_{\mathrm{FL}}+{T1}_B{\mathrm{LVCu}}_{\mathrm{FL}}$

${T1\mathrm{LVCu}}_{\mathrm{FL}}=54.036+54.008+55.145=\mathrm{163.189 }\mathrm{kvar}$

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, p-p/p-n

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

LWFe_TXtest = 1.25 kW No-load 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 no-load and load losses are required.

${T2\mathrm{LWFe}}_{\mathrm{NL}}={\mathrm{LWFe}}_{\mathrm{TXtest}}=\mathrm{1.25 }\mathrm{kW}$

${T2\mathrm{LWCu}}_{\mathrm{FL}}={\mathrm{LWCu}}_{\mathrm{TXtest}}=\mathrm{3.8 }\mathrm{kW}$

${T2\mathrm{LVFe}}_{\mathrm{NL}}=\sqrt{{({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%\mathrm{EXC}}{100})}^2-{\left({\mathrm{LWFe}}_{\mathrm{TXtest}}\right)}^2}$

${T2\mathrm{LVFe}}_{\mathrm{NL}}=\sqrt{{\left(2200\times \frac{0.4}{100}\right)}^2-{1.25}^2}=8.711\mathrm{k var}$

${T2\mathrm{LVCu}}_{\mathrm{FL}}=\sqrt{{({\mathrm{VA}}_{\mathrm{TXtest}}\times \frac{\%Z}{100})}^2-{\left({\mathrm{LWCu}}_{\mathrm{TXtest}}\right)}^2}$

${T2\mathrm{LVCu}}_{\mathrm{FL}}=\sqrt{{\left(2200\times \frac{2.44}{100}\right)}^2-{3.8}^2}=53.545\mathrm{k var}$

E.7 Losses for T1 and T2

${\mathrm{LWFe}}_{\mathrm{NL}}={T1\mathrm{LWFe}}_{\mathrm{NL}}+{T2\mathrm{LWFe}}_{\mathrm{NL}}$

${\mathrm{LWFe}}_{\mathrm{NL}}=6.05+1.25=\mathrm{7.3 }\mathrm{kW}$

${\mathrm{LWCu}}_{\mathrm{FL}}={T1\mathrm{LWCu}}_{\mathrm{FL}}+{T2\mathrm{LWCu}}_{\mathrm{FL}}$

${\mathrm{LWCu}}_{\mathrm{FL}}=23.69+3.8=\mathrm{27.49 }\mathrm{kW}$

${\mathrm{LVFe}}_{\mathrm{NL}}={T1\mathrm{LVFe}}_{\mathrm{NL}}+{T2\mathrm{LVFe}}_{\mathrm{NL}}$

${\mathrm{LVFe}}_{\mathrm{NL}}=37.325+8.711=\mathrm{46.036 }\mathrm{kvar}$

${\mathrm{LVCu}}_{\mathrm{FL}}={T1\mathrm{LVCu}}_{\mathrm{FL}}+{T2\mathrm{LVCu}}_{\mathrm{FL}}$

${\mathrm{LVCu}}_{\mathrm{FL}}=163.189+53.545=\mathrm{216.734 }\mathrm{kvar}$

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

$\mathrm{CTR}=\frac{\mathrm{2000 }A}{\mathrm{5 }A}=400$

Voltage transformer ratio = 360:120 V

$\mathrm{VTR}=\frac{360}{120}=3$

$V_{\mathrm{TXtest}}=\mathrm{2200 }\mathrm{kVA}$

$V_{\mathrm{rated}}=\mathrm{600 }\mathrm{V phase }\mathrm{to }\mathrm{phase}$

$I_{\mathrm{rated}}=\frac{{\mathrm{VA}}_{\mathrm{TXtest}}}{V_{\mathrm{rated}}\times \sqrt{3}}$

$I_{\mathrm{rated}}=\frac{2200}{600\times \sqrt{3}}=\mathrm{2177 }\mathrm{A }\left(\mathrm{phase}\right)$

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.

$A=\frac{{\mathrm{LWFe}}_{\mathrm{NL}}}{\mathrm{elements}}÷{\left(\frac{V_{\mathrm{rated}}}{\mathrm{VTR}\times \sqrt{3}}\right)}^2=\frac{7.3}{3}÷{\left(\frac{600}{3\times \sqrt{3}}\right)}^2=1.825\times {10}^{-4}\frac{\mathrm{kW}}{V^2}\mathrm{ per }\mathrm{phase}$

$B=\frac{{\mathrm{LWCu}}_{\mathrm{FL}}}{\mathrm{elements}}÷{\left(\frac{I_{\mathrm{rated}}}{\mathrm{CTR}}\right)}^2=\frac{27.49}{3}÷{\left(\frac{2117}{400}\right)}^2=.03271\frac{\mathrm{kW}}{I^2}\mathrm{ per }\mathrm{phase}$

$C=\frac{{\mathrm{LVFe}}_{\mathrm{NL}}}{\mathrm{elements}}÷{\left(\frac{V_{\mathrm{rated}}}{\mathrm{VTR}\times \sqrt{3}}\right)}^4=\frac{46.036}{3}÷{\left(\frac{600}{3\times \sqrt{3}}\right)}^4=8.631\times {10}^{-8}\frac{\mathrm{kvar}}{V^4}\mathrm{ per }\mathrm{phase}$

$D=\frac{{\mathrm{LVCu}}_{\mathrm{FL}}}{\mathrm{elements}}÷{\left(\frac{I_{\mathrm{rated}}}{\mathrm{CTR}}\right)}^2=\frac{216.734}{3}÷{\left(\frac{2117}{400}\right)}^2=2.5793\frac{\mathrm{kvar}}{I^2}\mathrm{ per }\mathrm{phase}$