STPM10_V01 datasheet(38/47 Pages) STMICROELECTRONICS

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Theory of operation

STPM10

38/47

DocID17728 Rev 5

Equation 11:

��1(��) =

��

⋅ ∫ i(t) ⋅ dt = −

V ⋅ I ⋅ cosϕ

−

V ⋅ I ⋅ cos⁡(2wt + ϕ)

See figure above (9)

Equation 12:

��2(��) = ��(��) ⋅ i(t) = −

V ⋅ I ⋅ cosϕ

−

V ⋅ I ⋅ cos⁡(2wt + ϕ)

See Figure 26: "Active energy computation diagram" (10)

After these two operations, another stage performs the subtraction between the results p2

and p1 and a division by 2, obtaining the active power:

Equation 13:

p(��) =

(��2(t)−��1(t))

V⋅I⋅cosφ⁡

See Figure 26: "Active energy computation diagram" (11)

In this way, the AC part V

⋅ I⋅ cos(2ωt + ϕ)/2 has been removed from the instantaneous

power.

The absence of any AC component allows a very fast calibration procedure. It only requires

the setting of (using the internal device programming registers) the voltage and current

sensor conversion constants, using the effective voltage and current (Vrms, Irms) readings

provided by the device built-in communication port, avoiding the time-averaged readings of

the active power or the need for line synchronization.

7.23.2

Reactive power

The reactive power is produced using the previously-computed signals. In case of shunt

sensor the voltage signal is derived while the current signal is not. A first computation is to

multiply the DS value of the integrated voltage channel with the value of the integrated

current channel, which yields:

Eqaution 14:

��1(��) = ∫ ��(��)�� ⋅ l(t) = ��(��) ⋅ I(t) = (Vsinωt) ⋅ (−

��

cos(�� + ��)) =

2��

∙ (�� −

sin(2�� + ��))

The second is to multiply the filtered DS value of the voltage channel with the value of the

filtered current channel:

Equation 15:

��2(��) = ��(��) ⋅ I(t) = Vωcosωt ⋅ Isin(ωt + ��) =

��

∙ �� ∙ ((�� + sin(2�� + ��))

From the above results, Q1(t) is proportional to 1/ω, while Q2(t) is proportional to ω. The

correct reactive power would result from the following formula:

Equation 16:

�� =

⋅ ��1(��) ⋅ ω + ��2(t) ⋅

��

Since the above computation needs a significant additional circuitry, the reactive power in

the STPM10 is calculated using only the Q1(t) multipli

ed by ω, which means:

Equation 17:

��3(��) =

⋅ ��1(��) ⋅ ω =

��

⋅ (�� − sin(2�� + ��))

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