Calculating and Compensating for Power Transformer and Cable (or Line) Losses – Standard Methods |
Guidance Note |
This guidance sets out basic standard methods for calculating electrical loss compensation factors for power transformers and cables (or lines) that need to be applied to
Half Hourly Metering Systems (HHMS) used for
Settlements purposes. This is in the event the measurement transformers for a HHMS cannot be located at the Defined
Metering Point (DMP), as set out in the relevant metering
Code of Practice (CoP). Due to this non-compliance with the requirements of the CoP the
Registrant of the HHMS needs to apply for a
Metering Dispensation and it may be necessary to compensate the HHMS for electrical losses in any power transformers and/or cables (or lines) between the Actual
Metering Point (AMP) and the DMP.
The purpose of this guidance is to assist Registrants/Meter Operators Agents (MOAs) in calculating these compensation factors and to provide assurance to the BSC Panel and industry participants that, where compensation is to be applied to a new HHMS under a Metering Dispensation, suitable compensation factors for electrical losses in any power transformer and/or cable (or line), between the AMP and the DMP, are applied to that HHMS before the Metering System Effective From Date.
The Electrical Loss Validation Agent (ELVA) will validate the compensation factors provided for any new
Metering System as part of the
Metering Dispensation application process (
BSCP32).
In addition, as part of the Technical Assurance of
Metering (TAM) technique as set out in
Section L (7) of the Balancing and
Settlement Code (BSC) and
BSCP27, the
Technical Assurance Agent (TAA) will continue to request values of any compensation applied (including evidence to support the applied values) to any HHMS (i.e. existing or new) from the
Registrant or its MOA.
Section K of the BSC requires
Active Energy, and where relevant,
Reactive Energy flowing across
Boundary Points to the
Total System, and flowing between
Systems at
Systems Connection Points (SCPs), to be measured and recorded by compliant
Metering Equipment.
Section L of the BSC requires Metering Equipment to comply with the relevant CoP at the time the Metering Equipment is first registered as a Metering System for Settlement purposes.
The metering
CoPs set out the DMPs at which overall accuracy of the
Metering System is to be maintained. Where measurement cannot take place at the DMP for a particular circuit then a
Metering Dispensation needs to be applied for and approved.
Where the AMP and the DMP do not coincide, CoPs 1, 2, 3 and 5 require compensation for any electrical losses in any power transformer and/or cable (or line) between the AMP and the DMP to be considered and, if necessary, applied to the Settlement Meter(s) or via the Data Collector’s system. This may need to be done to ensure that overall accuracy is maintained within the limits set out in the relevant CoP at the DMP (e.g. for CoP1 the overall accuracy limits at the DMP for Active Energy are ± 0.5% for 120% to 10% rated current at Unity Power Factor).
A standard method for deriving compensation factors for power transformer losses
In order to calculate the electrical losses in a power transformer it will be necessary to obtain relevant information about the power transformer, including the power transformer test sheet.
Power transformers are typically tested to determine the electrical losses associated with them when operating under no-load conditions and full load conditions. Electrical losses at other loads will need to be derived from these figures.
The two tests used to determine the Active Power (watt) losses (and sometimes the Reactive Power (var) losses) associated with a power transformer are:
In the open circuit test the no-load (iron) watt losses are determined by applying the rated voltage to one of the power transformer’s windings and measuring the winding current (known as the no-load, exciting or excitation current) and power (watts). This is done with the other winding open circuited (i.e. with no load connected).
In the short circuit test the full load (copper) watt losses of the power transformer are determined by shorting one of the power transformer’s windings (through an ammeter - a device for measuring current) and applying a small voltage to the other winding which is gradually increased until the rated full load current flows in the shorted winding. The current that flows in the other winding as a result is measured and the power (watts) being supplied to the other winding is also measured. Since full load current is circulating in the shorted winding, the windings have the same power loss as on full load.
Calculating power transformer electrical losses
The results from the power transformer test sheet can also be used to calculate losses that aren’t directly provided (e.g. no load (iron) and full load (copper) var losses). Also, the losses that occur at different load conditions other than no-load or full load can be calculated by appropriate scaling factors.
Some Meters can be programmed with the relevant parameters from the transformer test sheet and automatically calculate and add or subtract the losses to/from the measured quantities (known as dynamic compensation) seen by the Meter (i.e. taking into account the correct measurement transformer ratios). Different Meter types will have different methods of calculating and applying loss compensation so the Meter manufacturer’s documentation should be consulted.
The power transformer test sheet will usually provide the following information:
rated apparent power of the power transformer (
${VA}_{test}$
);
rated primary voltage of the power transformer (
$kV$
);
rated secondary voltage (
$kV$
);
no-load (iron) watt losses (
$N{LWFe}_{test}$
) – the Active Power consumed by the transformer’s core at rated voltage with no load current (during the open circuit test)
full load (copper) watt losses (
$F{LWCu}_{test}$
) - the Active Power consumed by the transformer’s windings at full load current for rated VA (during the short circuit test);
% excitation current - the ratio of the no-load test current (at rated voltage) to the full load test current; and
% impedance - the ratio of the full load test voltage (at rated current) to the rated voltage.
If the no-load (iron) var losses and full load (copper) var losses are not provided these can be calculated using some of the information provided above, as follows:
$NLV{Fe}_{test}$
is the no-load vars lost in the power transformer’s iron core under test conditions.
$FLV{Cu}_{test}$
is the full load vars lost in the power transformer’s copper windings under test conditions.
To determine the losses at actual operating voltages and currents the test losses must be scaled by the actual voltage or current:
${NLWFe}_{actual}={NLWFe}_{test}*{\left(\frac{{V}_{actual}}{{V}_{test}}\right)}^{2}$
${FLWCu}_{actual}={FLWCu}_{test}*{\left(\frac{{I}_{actual}}{{I}_{test}}\right)}^{2}$
${NLVFe}_{actual}={NLVFe}_{test}*{\left(\frac{{V}_{actual}}{{V}_{test}}\right)}^{4}$
${FLVCu}_{actual}=F{LVCu}_{test}*{\left(\frac{{I}_{actual}}{{I}_{test}}\right)}^{2}$
If the actual voltages and current are the secondary voltages and currents from the measurement transformers, as seen by the Meter, then these readings need to be scaled by the current transformer ratio (CTR) or the voltage transformer ratio (VTR), as appropriate, to give the primary circuit values:
${NLWFe}_{actual}={NLWFe}_{test}*{\left(\frac{{V}_{secondary}*VTR}{{V}_{test}}\right)}^{2}$
${FLWCu}_{actual}={FLWCu}_{test}*{\left(\frac{{I}_{secondary}*CTR}{{I}_{test}}\right)}^{2}$
${NLVFe}_{actual}={NLVFe}_{test}*{\left(\frac{{V}_{secondary}*VTR}{{V}_{test}}\right)}^{4}$
${FLVCu}_{actual}={FLVCu}_{test}*{\left(\frac{{I}_{secondary}*CTR}{{I}_{test}}\right)}^{2}$
Care should be taken when performing loss calculations where equipment other than the power transformer lies between the DMP and the AMP, for example, power factor correction equipment, other ‘parasitic’ loads (e.g. lighting or heating in a substation for instance) and lengths of cable or line.
A standard method for deriving compensation factors for cable (or line) losses
Cables and lines are not 100% efficient at transferring power. Energy (Active and Reactive Energy) is lost (or generated in the case of Reactive Energy due to capacitance) transmitting power over the length of the cable or line due to the following factors:
the (series) resistance
$\left(R\right)$
of the cable or line;
the (series) inductive reactance
$\left({X}_{L}\right)$
of the cable or line;
the (shunt or parallel) capacitive reactance
$\left({X}_{C}\right)$
of the cable or line; and
the (shunt or parallel) leakage resistance
$\left({r}_{leakage}\right)$
of the cable or line.
For short cables or lines the main factors to consider when estimating the losses are the series resistance (which contribute to the watt losses) and series inductive reactance (which contribute to the var losses).
Remember that the resistance of the conductors changes with temperature so the typical operating temperature of the conductor must be taken into account when performing loss calculations.
With longer lengths of cable or line the effects of capacitive reactance and leakage resistance need to be considered. These calculations are more complex and are not covered in this guidance.
The manufacturer of the cable or line will provide the tested electrical parameters of the cable or line, e.g.:
resistance (r) per unit length (
$\raisebox{1ex}{$\mathrm{\Omega}$}\!\left/ \!\raisebox{-1ex}{$m$}\right.)$
per conductor (at a given temperature)
reactance (x) per unit length (
$\raisebox{1ex}{$\mathrm{\Omega}$}\!\left/ \!\raisebox{-1ex}{$m$}\right.)$
per conductor
If the impedance (z) per unit length (
$\raisebox{1ex}{$\mathrm{\Omega}$}\!\left/ \!\raisebox{-1ex}{$m$}\right.)$
of conductor is given in complex (notation) form, e.g. r +jx, then r and x can be taken from this.
Knowing the total length
$\left(l\right)$
of the conductors that form the cable or line, the total series resistance
$\left(R\right)$
and total series inductive reactance
$\left({X}_{L}\right)$
of each conductor can be calculated by multiplying the per unit length figure (r or x) by the length
$\left(l\right)$
:
The total resistance
$\left(R\right)$
of the each conductor contributes to Active Power losses (P) and the inductive reactance
$\left({X}_{L}\right)$
contributes to the Reactive Power losses (Q).
Since the power lost due to resistance is:
and the power lost due to inductive reactance is:
Then, for a 3 phase system, the losses for each phase are calculated separately according to the current flowing in each phase (a, b and c):
${P}_{a}={{I}_{a}}^{2}*{R}_{a}$
${P}_{b}={{I}_{b}}^{2}*{R}_{b}$
${P}_{c}={{I}_{c}}^{2}*{R}_{c}$
${Q}_{a}={{I}_{a}}^{2}*{X}_{La}$
${Q}_{b}={{I}_{b}}^{2}*{X}_{Lb}$
${Q}_{c}={{I}_{c}}^{2}*{X}_{Lc}$
The total Active Power loss is:
${P}_{total}={P}_{a}+{P}_{b}+{P}_{c}={{(I}_{a}}^{2}*{R}_{a})+{({I}_{b}}^{2}*{R}_{b})+{({I}_{c}}^{2}*{R}_{c})$
and the total Reactive Power loss is
${Q}_{total}={Q}_{a}+{Q}_{b}+{Q}_{c}={({I}_{a}}^{2}*{X}_{La})+({{I}_{b}}^{2}*{X}_{Lb})+({{I}_{c}}^{2}*{X}_{Lc})$
If the resistance (and the inductive reactance) is the same for each conductor then the equations can be simplified to:
${P}_{total}=({{I}_{a}}^{2}+{{I}_{b}}^{2}+{{I}_{c}}^{2})*R$
${Q}_{total}=({{I}_{a}}^{2}+{{I}_{b}}^{2}+{{I}_{c}}^{2})*{X}_{L}$
In the case where the currents in each conductor are very similar (i.e. a balanced load), the average of the square of the three currents could be used:
${P}_{total}=\left(\frac{{{I}_{a}}^{2}+{{I}_{b}}^{2}+{{I}_{c}}^{2}}{3}\right)*R={{3*I}^{2}}_{average}*R$
${Q}_{total}=\left(\frac{{{I}_{a}}^{2}+{{I}_{b}}^{2}+{{I}_{c}}^{2}}{3}\right)*X={{3*I}^{2}}_{average}*{X}_{L}$
Some Meters can be programmed with the relevant parameters from the cable manufacturer’s sheet and automatically calculate and add or subtract the losses to/from the measured quantities (known as dynamic compensation) seen by the Meter (i.e. taking into account the correct measurement transformer ratios^{14}). Different Meter types will have different methods of calculating and applying loss compensation so the Meter manufacturer’s documentation should be consulted.
Applying loss compensation factors for power transformer losses and/or cable (or line) losses
Care should also be taken when applying loss compensation factors such that the losses are correctly added or subtracted from the measured quantities depending on the location of the measurement transformer (AMP) relative to the DMP and the direction of flow of energy through the measurement transformers.
e.g. if the DMP is the on the higher voltage side of the power transformer and the measurement transformers are located on the lower voltage side of the power transformer, and an Import is defined as a flow of Active (and Reactive) Energy away from the lower voltage side towards a Customer’s site, then the power transformer loss compensation factor(s) for Active Energy will be added to the Active Import (AI) Energy measured quantity in order to refer the Meter register readings back to the higher voltage side for Active Import (AI) Energy. In the same DMP/AMP scenario, in the case of an Export from a Generating Plant towards the lower voltage side of the power transformer then the power transformer loss compensation factor(s) for Active Energy will be subtracted from the Active Export (AE) Energy measured quantity in order to refer the Meter register readings to the higher voltage side for Active Export (AE) Energy.
For further information please contact the
BSC Service Desk or call
0370 0106950.
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