STPMC1 datasheet(69/77 Pages) STMICROELECTRONICS

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STPMC1

Energy calculation algorithm

Doc ID 15728 Rev 6

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In case of a non Rogowski sensor, the corresponding products are:

Equation 32

P1 = vd vsi = - AC kDIFkINT cos (ω t) cos (ω t + ϕ) = - AC [cos ϕ + cos (2 ω t + ϕ)] / 2

Equation 33

P2 = vdi vs = AC kDIFkINT sin (ω t) sin (ω t + ϕ) = AC [cos ϕ - cos (2 ω t + ϕ)] / 2

Then a subtraction of P1 from P2 is performed:

Equation 34

P = (P2 - P1) / 2 = (AB cos ϕ) kINT / 2 = (UkDIkL cos ϕ) kINT / 2 = URMS IRMS cos ϕ kP

where:

Equation 35

kP = kD kL kINT

This gives the same result for P in case of non Rogowski sensor, substituting B and kL kINT

with C and kS:

Equation 36

P = (P2 - P1) / 2 = (AC cos ϕ) / 2 = (UkDIkS cos ϕ) / 2 = URMS IRMS cos ϕ kP

where:

Equation 37

kP = kD kS

The result in

Equation 35 and Equation 36 is proportional to the DC part of active power of

line. The division by 2 is a feature of

ΔΣ subtractor. The absence of harmonic components

eliminates the spread of results due to asynchronism with the line. This fact enables fast a

calibration procedure which is used to set the target constant of meter kP.

A sensitivity analysis of kP yields:

Equation 38

ΔkP/kP = ΔL/L + R1 / (R1+R2)(ΔR2/R2 - ΔR1/R1) + ΔAU/AU + ΔAI/AI - 2 ΔVREF/VREF

Equation 39

ΔkP/kP = ΔRS / RS + R1 / (R1+R2)(ΔR2/R2 - ΔR1/R1) + ΔAU/AU + ΔAI/AI - 2 ΔVREF/VREF

It is clear that the device is responsible for AU, AI and VREF parts. The parts kU, kI and kINT

are omitted, because they are not subject to aging or temperature variations due to digital

implementation.

10.2

Reactive energy calculation

The natural reactive power (ART = 0) of the line is computed as follows.

First, 16-bit voltage from the 3rd stage (

Equation 20 or Equation 28) is multiplied by the

current stream from the 1st stage (

Equation 14 or Equation 23) and the frequency

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