SIEMENS Xmer Loss Calc

QUAD4 Plus/MAXsys Products User’s Guide

Transformer Loss Calc Method C-1

Transformer Loss Calculation Method This document provides an explanation with examples of the standard transformer loss calculation method used in the meter. A detailed example is also presented at the end of this appendix. See the section of this document titled Setting Up TLC Totalizors for an explanation of what totalizors are needed for TLC. Refer to Multi-Level TLC/LLC in chapter 4 of the MAXsys 2510 User’s Guide for details on that special type of loss calculations.

FIGURE 1 - 4-Quadrant Meter MeasuringOnly Delivered Power Flow

Reactive Power Flow(+) * (+) = +

quadrant 2 | quadrant 1||_________| /|| / || vah / || / || / || / || / || / |

___________________|/________|__________ + Real Power Flow|\ || \ || \ || \ || \ || \ || vah \ || \ ||________\||

quadrant 3 | quadrant 4(+) * (-) = -

Reactive Power Flow

Figure 1 shows a vector diagram of a 4-quadrant meter measuring only positive power indicated as flowing from left to right. Vector rotation is assumed to be clockwise and by using voltage as a reference, lagging vars (inductive load) are assigned a positive sign. Note that all power is delivered power, in quadrants 1 or 4 because, AT THE METERING POINT, it is not possible for current to be out of phase with voltage by more than 90 degrees with reference to the voltage AT THE METERING POINT.



FIGURE 2 - 4-Quadrant Meter MeasuringOnly Received Power

Reactive Power Flow(-) * (+) = -

quadrant 2 | quadrant 1|

_________||\ || \ || \vah || \ || \ || \ || \ || \ |

- _________|________\|____________________ +| /|| / || / || / || / || / || / vah || / ||/________|

|quadrant 3 | quadrant 4

(-) * (-) = +Reactive Power Flow

Figure 2 shows the same meter with only received power flowing. Note that, AT THE METERING POINT, it is not possible to have the current out of phase by more than 90 degrees with the voltage AT THE METERING POINT. Note that the sign of the reactive power flow, which is positive for inductive reactance and negative for capacitive power flow, must now be multiplied by the sign for the direction of power flow (because we are combining 2 conventions here, the standard Cartesian coordinate system for describing real and imaginary numbers as applied to real and reactive power, and a convention which says that power delivered (from left to right) will have a positive sign, and power received (from right to left) will have a negative sign). It is permissible to suggest such a system since, AT THE METERING POINT,it is not possible for delivered power to exist in quadrants 2 and 3 and it is not possible for received power to exist in quadrants 1 and 4, and therefore no ambiguities can exist in the system.



FIGURE 3 - 4-Quadrant Meter Measuring EitherDelivered Or Received Power

Reactive Power Flow(-) * (+) = - (+) * (+) = +quadrant 2 | quadrant 1

|_________|_________

|\ | /|| \ | / || \vah | vah / || \ | / || \ | / || \ | / || \ | / || \ | / |

- _________|________\|/________|__________ +| /|\ || / | \ || / | \ || / | \ || / | \ || / | \ || / vah | vah \ || / | \ ||/________|________\|

|quadrant 3 | quadrant 4(-) * (-) = + (+) * (-) = -

Reactive Power Flow

It can be seen from the above diagram that the sign of the reactive power flow indicates the true leading or lagging condition of the current in each quadrant if + is assumed to be lagging current and - is therefore leading current. Thus we have the situation where the sign of the real power indicates direction of flow and the sign of the reactive power indicates current lagging (+) or current leading (-). It is now possible to algebraically sum the reactive power, to detent the reactive power, or to sum the absolute values of the reactive power independently for the delivered or the received power. It is also possible to algebraically sum the delivered and the received real power to obtain the net value.



FIGURE 4 - Transformer Loss as Measured at aDelivery or a Tie Point Between aUtility and a Customer, a Co-generator,or a Second Utility. The meter belongsto Utility 1, the transformer belongsto Utility 2.

________________ | | _______

| | | | | |UTLTY1--------------| MTR 1 |---| XFMR |---| MTR 2 |----------UTLTY2

|_______| | | |_______|| |_________| |

__________________|_________________________|__________________

Assume that MTR 2 is the actual 4-quadrant meter which is to be used for billing purposes. MTR 1 is shown for illustration.

CASE 1:

• In Figure 4, assuming that the transformer belongs to Utility 2, MTR 2 is the meter which we desire to perform transformer loss compensation when power is flowing from Utility 1 to Utility 2 (or customer). That is, the real power is flowing in the positive direction. By reference to Figure 3 above, the reactive power must lie in either Quadrant 1 or Quadrant 4.

• If a meter were installed at MTR 1 position, no loss compensation would be required since the transformer loss would be included in the meter data.

• Since reactive power caused by a transformer is inductive in nature MTR 1 would record this power as occurring in Quadrant 1 in Figure 3 above.

• Properly done, Transformer Compensation should enable MTR 2 to compensate for the transformer so that the readings would correspond to the readings of MTR 1 within reasonable accuracy. This means that the real component of Transformer Loss should carry a positive sign and be algebraically added to the real component of the load. The reactive component will be in Quadrant 1 and should carry a positive sign so that it can be algebraically added only to the inductive component of the reactive load thus appearing only in Quadrant 1 and emulating the results of MTR 1. It must be possible to sum in or net in any capacitive reactance which may occur (in Quadrant 4) so that billing may be done on total or net vars.

CASE 2:

• The above discussion assumes that power is flowing from Utility 1 to Utility 2. If we assume that the power flow is now reversed and the flow is from Utility 2 to Utility 1, and the transformer is still owned by Utility 2, reverse transformer compensation is required so that Utility 1 does not have to pay for losses incurred in Utility 2's transformer.

• If a meter were installed at MTR 1 position, it would read the true power supplied to Utility 1 and Utility 2 would absorb the transformer losses.

• The real power recorded in MTR 2 is now negative and includes the real components of the transformer losses. The calculated values of the real components of the transformer losses now must carry a positive sign and must be totalized algebraically with real component of the meter reading.



• Since reactive power caused by a transformer is inductive in nature, MTR 2 must calculate this power and assign it as occurring in Quadrant 3 in Figure 3 above. This is because in the receive direction, Quadrant 3 is the quadrant in which current is lagging voltage. The sign of the correction must be negative since it must be subtracted from the received inductive current flow. It must be possible to sum in or net in any capacitive reactance which may occur (in Quadrant 2) so that billing may be done on total or net vars.

CASE 3:

• If we now say that the transformer is owned by Utility 1, instead of Utility 2, the burden of the transformer loss shifts to Utility 1.

• If real power flow is positive, (left to right), MTR 2 now records the true power delivered to Utility 2 and no compensation is required.

• Also, if the power flow is negative, MTR 2 now records the true power flow to Utility 1, including the transformer losses, so no transformer compensation is required, since Utility 2 will bill Utility 1 for the total real and reactive power that it must provide.

For Cases 1 and 2 above the signs of the transformer loss constants are summarized as follows:

(+) WCU LOSS DLVD (kWh copper loss delivered due to load current)(+) WFE LOSS DLVD (kWh iron loss delivered due to voltage)(+) WCU LOSS RCVD (kWh copper loss received due to load current)(+) WFE LOSS RCVD (kWh iron loss received due to voltage)(+) VCU Q1 LOSS (kvarh copper loss quadrant 1 due to load current)(-) VCU Q3 LOSS (kvarh copper loss quadrant 3 due to load current)(+) VFE Q1 LOSS (kvarh iron loss quadrant 1 due to voltage)(-) VFE Q3 LOSS (kvarh iron loss quadrant 3 due to voltage)



FIGURE 5 - Transformer Loss as Measured at aDelivery or a Tie Point Between aUtility and a Customer, a Co-generator,or a Second Utility. The meter and thetransformer belongs to Utility 1.

________________ | |

| | | |UTLTY1--------------| METER |---| XFMR |--------------------------UTLTY2

|_______| | || |_________|

__________________|____________________________________________

Assume that the meter is a 4 quadrant meter which is to be used for billing purposes.

CASE 4:

When Utility 1 is delivering real power to Utility 2, the signs of the transformer loss constants must be reversed. So that the difference of the metered values are billed to Utility 2 when power flow is in the positive direction and the sums of the metered values are billed to Utility 1 when power flow is in the negative direction.

For Case 4 above the signs of the transformer loss constants are summarized as follows:

(-) WCU LOSS DLVD (kWh copper loss delivered due to load current)(-) WFE LOSS DLVD (kWh iron loss delivered due to voltage)(-) WCU LOSS RCVD (kWh copper loss received due to load current)(-) WFE LOSS RCVD (kWh iron loss received due to voltage)(-) VCU Q1 LOSS (kvarh copper loss quadrant 1 due to load current)(+) VCU Q3 LOSS (kvarh copper loss quadrant 3 due to load current)(-) VFE Q1 LOSS (kvarh iron loss quadrant 1 due to voltage)(+) VFE Q3 LOSS (kvarh iron loss quadrant 3 due to voltage)



The following diagram illustrates the values available in the meter (down the left hand side), and the suggested formatting of the register section of the meter for transformer compensation to satisfy CASES 1 and 2 above. The boxes marked with a + sign are totalizors. To convert this diagram for Case 4, it is only necessary to reverse the signs of the loss compensation factors.

_____| | ____| |\______________| |

(+) KWH DLVD_______/| | KWH DLVD (+) | |(-) KWH DLVD_______/| |\______________| |(+) KWH RCVD_______/| | WCU DLVD (+) | + |______________________(-) KWH RCVD_______/| |\______________| | | ____ KWH DLVD(+) KVARH Q1_______/| | WFE DLVD (+) | | | | |(-) KVARH Q1_______/| | |____| |___| |(+) KVARH Q2_______/| | ____ ___| + |________(-) KVARH Q2_______/| |\______________| | | | | KWH NET(+) KVARH Q3_______/| | KWH RCVD (-) | | | |____|(-) KVARH Q3_______/| |\______________| | |(+) KVARH Q4_______/| | WCU RCVD (+) | + |____|_________________(-) KVARH Q4_______/| |\______________| | KWH RCVD

| | WFE RCVD (+) | |(+) WCU LOSS DLVD__/| | |____|(+) WFE LOSS DLVD__/| |(+) WCU LOSS RCVD__/| | ____(+) WFE LOSS RCVD__/| |\______________| |

| | KVARH Q1 (+) | |(+) VCU Q1 LOSS____/| |\ _ _ _ _ _ _ _| |(-) VCU Q3 LOSS____/| | KVARH Q4 (-)* | |(+) VFE Q1 LOSS____/| |\ _ _ _ _ _ _ _| + |_______________________(-) VFE Q3 LOSS_____| | KVARH Q4 (+)* | | | KVARH DLVD

|\______________| | | ____| VCU Q1 LOSS(+)| | | | ||\______________| | |___| || VFE Q1 LOSS(+)| | | || |____| | + |___________| ____ ___| | KVARH NET|\______________| | | | || KVARH Q3 (+) | | | |____||\ _ _ _ _ _ _ _| | || KVARH Q2 (-)* | | ||\ _ _ _ _ _ _ _| + |__|____________________| KVARH Q2 (+)* | | KVARH RCVD|\______________| || VCU Q3 LOSS(-)| |\______________| |VFE Q3 LOSS(-)| |

|____|

NOTE: * One of or neither of these 2 inputs may be used to obtain netVARS, total VARS, or single quadrant VARS.



WCU LOSS DLVD = (ia**2 + ib**2 + ic**2) * WCU (While power is being delivered)WFE LOSS DLVD = (ea**2 + eb**2 + ec**2) * WFE (While power is being delivered)WCU LOSS RCVD = (ia**2 + ib**2 + ic**2) * WCU (While power is being received)WFE LOSS RCVD = (ea**2 + eb**2 + ec**2) * WFE (While power is being received)

VCU Q1 LOSS = (ia**2 + ib**2 + ic**2) * VCU (DLVD)VCU Q3 LOSS = (ia**2 + ib**2 + ic**2) * VCU (RCVD)VFE Q1 LOSS = (ea**4 + eb**4 + ec**4) * VFE (DLVD)VFE Q3 LOSS = (ea**4 + eb**4 + ec**4) * VFE (RCVD)

WCU = factor for kwatt hours loss in transformer due to load currentWFE = factor for kwatt hours loss in transformer due to voltageVCU = factor for kvar hours loss in transformer due to load currentVFE = factor for kvar hours loss in transformer due to voltage

ia, ib, and ic = current for phase a, phase b, and phase cea, eb, and ec = voltage for phase a, phase b, and phase cThese are either primary OR secondary currents and voltages based on theresponse to the prompt Use CT*PT ratio for line value displays, Yes/No?. YES =primary; NO = secondary, that is, not using CT*PT ratio.

The following are the prompts in the download list for Transformer LossCalculations in the Q4COM program. The second column lists the associatedvariable names used in the Transformer Loss calculations listed in thefollowing pages of this appendix.

Q4COM Prompts Variable NameNumber of lines, excluding N and G: NptsTransformer connection, meter side TCmDelvd real power transformer loss sign TLCsTotal connection resistance, phase current RIpTotal connection resistance, line current RIl

Per phase values:Rated voltage, metered side: EmRated kVA per phase: KVAmPhase A copper loss: WCUlaPhase B copper loss: WCUlbPhase C copper loss: WCUlcPhase A iron loss: WFElaPhase B iron loss: WFElbPhase C iron loss: WFElcPhase A exciting current: %IxaPhase B exciting current: %IxbPhase C exciting current: %IxcPhase A % impedance at operating temp: %ZaPhase B % impedance at operating temp: %ZbPhase C % impedance at operating temp: %ZcCT primary current: CTPCT secondary current: CTSPT primary voltage required for TLC: PTPPT secondary voltage required for TLC: PTSUse CT * PT ratio for line value displays: None



TRANSFORMER LOSS CONSTANT CALCULATIONSThis section lists the standard loss constant calculations used in the meter.

Refer to Multi-Level TLC/LLC in chapter 4 of the MAXsys 2510 User’s Guide fordetails on that special type of TLC with its own loss constant calculationmethods.

Given:Transformer connection, metered side = TCm = (Delta, Wye, Open Delta)Sign of loss compensation for delivered power = TLCs = (plus or minus)Total Ip resistance = RIp (Total connection resistance in series

with phase current)Total Il resistance = RIl (Total connection resistance in series

with line current)

Rated Voltage = Em (Per phase)Rated KVA = KVAm (Per phase)Phase A copper loss = WCUlaPhase B copper loss = WCUlbPhase C copper loss = WCUlcPhase A iron loss = WFElaPhase B iron loss = WFElbPhase C iron loss = WFElcCT primary current = CTPCT secondary current= CTSPT primary voltage = PTPPT secondary voltage= PTSPhase A % Exciting I= %IxaPhase B % Exciting I= %IxbPhase C % Exciting I= %Ixc% Imp. a at op temp = %Za% Imp. b at op temp = %Zb% Imp. c at op temp = %ZcNumber of measured points = Npts

Calculated Values:

CT ratio = CTR = CTP / CTSPT ratio = PTR = PTP / PTSVAm = KVAm * 1000 (Per phase)Phase Current Rated = Ipm = VAm / Em (Per phase)

If TCm = Delta thenLine Current Rated = Ilm = Ipm * √3 (Per phase)

else if TCm = Wye thenLine Current Rated = Ilm = Ipm (Per phase)

else if TCm = Open Delta thenLine Current Rated = Ilm = .866 * Ipm * √3 (Per phase)

Ilm Rated Metered = Ilmm = Ilm / CTR (Per phase)E Rated metered = Emm = Em / PTR (Per phase)

Calculated Watt Hours Copper Loss:

Copper Loss Max = WCUlm = WCUla + WCUlb + WCUlc + ((Ipm**2) * RIp) +((Ilm**2) * RIl)

Copper Loss Max Metered = WCUlmm = WCUlm / (CTR * PTR)Copper Loss Constant = WCU = WCUlmm / (Npts * (Ilmm**2))

If TLCs = minus thenWCU = - WCU

Calculated Watt Hours Iron Loss:

Iron Loss Max = WFElm = WFEla + WFElb + WFElc



Iron Loss Max Mtrd = WFElmm = WFElm / (CTR * PTR)Iron Loss Constant = WFE = WFElmm / (Npts * (Emm**2))

If TLCs = minus thenWFE = - WFE

VARS LOSSCalculated VAR Hours Iron Loss:

VARS FE exciting a = Vxa = VAm * %Ixa / 100VARS FE exciting b = Vxb = VAm * %Ixb / 100VARS FE exciting c = Vxc = VAm * %Ixc / 100phase a max FE VARS = VFEa = Vxa * (sin (arc cos (WFEla / Vxa)))phase b max FE VARS = VFEb = Vxb * (sin (arc cos (WFElb / Vxb)))phase c max FE VARS = VFEc = Vxc * (sin (arc cos (WFElc / Vxc)))total max FE VARS = VFEt = VFEa + VFEb + VFEctotal max metered FE VARS = VFEtm = VFEt / (CTR * PTR)VARS FE loss constant = VFE = VFEtm / (Npts * (Emm**4))

If TLCs = minus thenVFE = - VFE

Calculated VAR Hours Core Loss:

Full load CU VA = VACUfla = VAm * %Za / 100Full load loss b = VACUflb = VAm * %Zb / 100Full load loss c = VACUflc = VAm * %Zc / 100phase a max CU VARS = VCUa = VACUfla * (sin (arc cos (WCUla / VACUfla)))phase b max CU VARS = VCUb = VACUflb * (sin (arc cos (WCUlb / VACUflb)))phase c max CU VARS = VCUc = VACUflc * (sin (arc cos (WCUlc / VACUflc)))total max CU VARS = VCUt = VCUa + VCUb + VCUctotal max metered CU VARS = VCUtm = VCUt / (CTR * PTR)VARS CU loss constant = VCU = VCUtm / (Npts * (Ilmm**2))

If TLCs = minus thenVCU = - VCU

Setting Up TLC Totalizors

The compensated readings are what a "phantom" meter located on the other side of the transformer would read.

WFEd - Watts Iron loss, delivered

WFEr - Watts Iron loss, received

WCUd - Watts Copper loss, delivered

WCUr - Watts Copper loss, received

VFEd - VARs Iron loss, delivered

VFEr - VARs Iron loss, received

VCUd - VARs Copper loss, delivered

VCUr - VARs Copper loss, received

If the Meter is "upstream" of the Utility Owned Transformer: The Ke's for the WFEd, WCUd, VFEd, and VCUd should be positive and the Ke's

for the WFEr, WCUr, VFEr, and VCUr should be negative. If the Meter is "downstream" of the Customer Owned Transformer:



The Ke's for the WFEd, WCUd, VFEd, and VCUd should be negative and the Ke's

for the WFEr, WCUr, VFEr, and VCUr should be positive. When beginning recording (either from cold start or when the X6 command is received) the totalizor configuration is scanned to detect TLC calculations. If one of the TLC configurations listed in the following table is not detected, that totalizor simply adds the inputs specified. The result of these calculations will always be a positive number. They can be used as inputs to recorder channels and be routed to output relays. The TLC calculations supported by the meter are listed in the following table are supported.

NOTE:You must configure totalizors for compensated Delivered PWR and compensated Received PWR if any compensated VAR totalizors are to be used. This is because the compensated VAR calculations must know which way compensated power is flowing.

To get

Compensated: Totalize inputs: (Input numbers)

(See notes below)

Deliv'd PWR + Watts Del + WFEd + WCUd (2,20,21)

(2,63,64)

Receiv'd PWR + Watts Rec + WFEr + WCUr (1,22,23)

(1,65,66)

Q1 Vars + Q1 + VFEd + VCUd (6,24,25)

(6,67,68)

Q2 Vars + Q2 + VFEr + VCUr (4,26,27)

(4,69,70)

Q3 Vars + Q3 + VFEr + VCUr (3,26,27)

(3,69,70)

Q4 Vars + Q4 + VFEd + VCUd (5,24,25)

(5,67,68)

Q1 + Q4 Vars + Q1 + Q4 + VFEd + VCUd (6,5,24,25)

(6,5,67,68)

Q2 + Q3 Vars + Q2 + Q3 + VFEr + VCUr (4,3,26,27)

(4,3,69,70)

Q1 + Q2 Vars + Q1 + Q2 + VFEd + VCUd + VFEr + VCUr (6,4,24,25,26,27)

(6,4,67,68,69,70)

Q3 + Q4 Vars + Q3 + Q4 + VFEd + VCUd + VFEr + VCUr (3,5,24,25,26,27)

(3,5,67,68,69,70)



NOTES:

1.THESE ARE THE ONLY VALID TLC TOTALIZORS SUPPORTED BY THE METER.

2.THERE CAN BE ONLY ONE EACH OF THE ABOVE TLC TOTALIZORS DEFINED IN A METER.

3.The top set of input numbers for meters with 39 meter inputs;

The bottom set of input numbers for meters with 85 meter inputs.

The following are "normal" totalizor functions and no special action is taken. They can be considered as "NET VARs". They are only listed here for reference. These could have a negative value and thus can not be used as inputs to recorder channels and not be routed to output relays.

Q1 - Q4 Vars + Q1 - Q4 + VFEd + VCUd (6,11,24,25)

Q3 - Q2 Vars + Q3 - Q2 + VFEr + VCUr (3,10,26,27)

In Delivered PWR: If the one-second total is negative, the one second value of this totalizor is set to

zero and the negative value is transferred to the Received PWR totalizor as a positive value. If one second total is positive, the meter sets that compensated power is delivered.

In Received PWR: If the one second total is negative, the one second value of this totalizor is set to

zero and the negative value is transferred to the Delivered PWR totalizor as a positive value. If one second total is positive, the meter clears that compensated power is delivered (i.e. compensated power is received).

In Q1: If the uncompensated VARS are in Q4, the VFEd and VCUd inputs are not added

in. If the one second total is negative, the one second value of this totalizor is set to zero and the negative value is transferred to either the Q4 totalizor or the Q3 totalizor as a positive value. If the compensated power is delivered, it goes to the Q4 totalizor; if not, to the Q3 totalizor.

In Q2: If the uncompensated VARS are in Q3, the VFEr and VCUr inputs are not added in.

If the uncompensated VARS are in Q2, the VFEr and VCUr are subtracted instead of added (i.e. the sign is reversed). If the one second total is negative, the one second value of this totalizor is set to zero and the negative value is transferred to either the Q3 totalizor or the Q4 totalizor as a positive value. If the compensated power is delivered, it goes to the Q4 totalizor; if not, to the Q3 totalizor.

In Q3:



If the uncompensated VARS are in Q2, the VFEr and VCUr inputs are not added in. If the one second total is negative, the one second value of this totalizor is set to zero and the negative value is transferred to either the Q2 totalizor or the Q1 totalizor as a positive value. If the compensated power is delivered, it goes to the Q1 totalizor; if not, to the Q2 totalizor.

In Q4: If the uncompensated VARS are in Q1, the VFEd and VCUd inputs are not added

in. If the uncompensated VARS are in Q4, the VFEd and VCUd are subtracted instead of added (i.e. the sign is reversed). If the one second total is negative, the one second value of this totalizor is set to zero and the negative value is transferred to either the Q1 totalizor or the Q2 totalizor as a positive value. If the compensated power is delivered, it goes to the Q1 totalizor; if not, to the Q2 totalizor.

In Q1 + Q4:

If the uncompensated VARS are in Q4, the VFEd and VCUd inputs are subtracted instead of added (i.e. the sign is reversed). If the one second total is negative, the one second value is either added to this totalizor or transferred to the Q2 + Q3 totalizor as a positive number. If the compensated power is delivered, it is added here; if not, it is transferred to the Q2 + Q3 totalizor.

If the one second total is positive and the power is not delivered, the one second value is transfered to the Q2 + Q3 totalizor.

In Q2 + Q3: If the uncompensated VARS are in Q2, the VFEd and VCUd inputs are subtracted

instead of added (i.e. the sign is reversed). If the one second total is negative, the one second value is either added to this totalizor or transferred to the Q1 + Q4 totalizor as a positive number. If the compensated power is delivered, it is transferred to the Q1 + Q4 totalizor; if not, it is added here.

If the one second total is positive and the power is delivered, the one second value

is transfered to the Q1 + Q4 totalizor. In Q1 + Q2: If the uncompensated VARS are in Q3 or Q4, the VFEr, VFEd, VCUr, and VCUd

are not added in. If the uncompensated VARs are in Q2, the VFEr and VCUr are subtracted instead of added (i.e. the sign is reversed). (Note that the VFEd and VCUd are both zero when in Q2). If the one second total is negative, the one second value is transferred to the Q3 + Q4 totalizor as a positive value.

In Q2 + Q3: If the uncompensated VARS are in Q1 or Q2, the VFEr, VFEd, VCUr, and VCUd

are not added in. If the uncompensated VARs are in Q4, the VFEd and VCUd are subtracted instead of added (i.e. the sign is reversed). (Note that the VFEr and



VCUr are both zero when in Q4). If the one second total is negative, the one second value is transferred to the Q1 + Q2 totalizor as a positive value.

When negative values are transferred to another totalizor as a positive value, they are only done so when the negative value is more negative than two units of the meter Ke value times the transformer ratio. This is to allow for the "quantizing" of the meter. Losses can accumulate for one second without a power (or VAR) pulse in that second but, in subsequent seconds, power pulses can arrive to more than offset the loss. The losses can yield a short term negative value which should not be shifted to another totalizor. These short term negative values are remembered. Due to this memory, very very small values can be time shifted (delayed) but these delayed values will always be less than two units of the meter Ke (compensated for the transformer ratio). If there are VARh's accumulated in the totalizors before there are 2 units of Ke power delivered or received, the VARh's may be put in the wrong totalizor as the "previous power flow" is incorrect. This small error would only occur on startup.

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SIEMENS Xmer Loss Calc