STPM11ATR datasheet(35/46 Pages) STMICROELECTRONICS

35 / 46 page

STPM11, STPM12, STPM13, STPM14

Energy calculation algorithm

Doc ID 13167 Rev 8

35/46

In the STPM1x, after the pre-conditioning and the A/D conversion, the digital voltage signal

(which is dynamically more stable with respect to the current signal) is processed by a

differentiate stage which transforms:

Equation 9

v(t)

→ v’(t) = dv/dt = V

⋅ ω ⋅ cos tω; (see [5] in Figure 22);

The result, together with the pre-processed and digitalized current signal:

Equation 10

i(t) = I

⋅ sin (tω + ϕ); (see [6] in Figure 22)

can then be used to calculate. These digital signals are also used in two additional steps for

integration, obtaining:

Equation 11

dv/dt

→ v(t) = V

⋅ sin tω; (see [7] in Figure 22)

Equation 12

(see [8] in Figure 22)

Now four signals are available. Combining (pairing) them by two multiplication steps two

results are obtained:

Equation 13

(see [9] in Figure 22)

Equation 14

(see [10] in Figure 22)

After these two operations, another stage another step involves the subtraction of p1 from

p2 and dividing the result by 2, to obtain the active power:

Equation 15

(see [12] in Figure 22)

In this way, the AC part

)

cos(

)

(

)

(

⋅

−

⋅

∫

i(t)

⋅

)

cos(

cos

)

(

)

(

⋅

−

⋅

−

⋅

∫

)

cos(

cos

)

(

)

(

)

(

⋅

−

⋅

cos

))

(

)

(

)

(

⋅

−

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