STPMC1 datasheet(72/77 Pages) STMICROELECTRONICS

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Energy calculation algorithm

STPMC1

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Doc ID 15728 Rev 6

The DSP performs also an integration of powers (P, Q) into energies:

Equation 54

AW = URMS IRMS cos ϕ kP kUD

Equation 55

AW = URMS IRMS sin ϕ kP kUD

These integrators are implemented as up/down counters and they can roll over.

20-bit output buses of the counters are assigned as the most significant part of the energy

data records. It is a responsibility of the application to read the counters at least every

second so as not to miss any rollover. The integration of power can be suspended due to

detected error on the source signals or due to no load condition. From AW, stepper output

signals are generated.

10.5

Fundamental power calculation

The fact that integration suppresses all but fundamental components of signals is used to

compute the fundamental active power, which is in case of Rogowski coil:

Equation 56

F1 = vuic viiic = - ABkINT cos (ω t) cos (ω t + ϕ) = - ABkINT [cos ϕ + cos (2 ω t + ϕ)] / 2

Equation 57

F2 = viic vuiic = - ABkINT sin (ω t) sin (ω t + ϕ) = ABkINT [cos ϕ - cos (2 ω t + ϕ)] / 2

Equation 58

F = (F2 - F1) / 2 = (AB cos ϕ) kINT / 2 = (UkDIkLcos ϕ) kINT / 2 = URMS IRMS cos ϕ kP

Similar result are found in case of non Rogowski sensor:

Equation 59

F1 = vdic vsiic = - AC sin (ω t) sin (ω t + ϕ) = - AC [cos ϕ - cos (2 ω t + ϕ)] / 2

Equation 60

F2 = vsic vdiic = - ACkDIFkINT cos (ω t) cos (ω t + ϕ) = - AC [cos ϕ + cos (2 ω t + ϕ)] / 2

Equation 61

F = (F2 - F1) / 2 = - AC cos (2 ω t + ϕ) = UkDIks cos (2 ω t + ϕ) / 2 = URMS IRMS cos (2 ω t +

ϕ) kP

The fundamental reactive power in case of a Rogowski coil is:

Equation 62

Q = vuiic viiic ω / kINT = - ABkINT cos (ω t) sin (ω t + ϕ) = ABkINT [sin ϕ - sin (2 ω t + ϕ)] / 2

Similar results are found in cases of non Rogowski sensors:

Equation 63

Q = vdiic vsiic ω / kINT = - AC cos (ω t) sin (ω t + ϕ) = AC [sin ϕ - sin (2 ω t + ϕ)] / 2.

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