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STPM01 Datasheet(PDF) 44 Page - STMicroelectronics |
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STPM01 Datasheet(HTML) 44 Page - STMicroelectronics |
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44 / 56 page ![]() Theory of operation STPM01 44/56 [Eq. 6 - see (9)] [Eq. 7 - see (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: [Eq. 8 - see (11)] In this way, the AC part V•I•cos(2 ωt + ϕ)/2 has been then removed from the instantaneous power. In the case of current sensors like “Rogowski coils”, which provide the rate of the instantaneous current signal (di/dt), the initial voltage signal differentiated stage will be switched off. In this case the signals coming from the A/D conversion and their consequent integrations will be: v(t) = V•sin ωt [Eq. 9] [Eq. 10] [Eq. 11][ [Eq. 12] The signals process flow will be the same as shown in the previous case, and even with the formulas above, the result will be the same. The absence of any AC component allows a very fast calibration procedure: it requires just to set (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 need for line synchronization. 8.24.2 Reactive power The reactive power is produced using the already computed signals. In case of shunt sensor the voltage signal is derived while the current signal is not. A first computation is to multiply 2 ) 2 cos( 2 cos ) ( ) ( 1 ϕ ω ϕ + ⋅ ⋅ − ⋅ ⋅ − = ⋅ ⋅ = / ∫ t I V I V dt t i dt dv t p 2 ) 2 cos( 2 cos ) ( ) ( ) ( 2 ϕ ω ϕ + ⋅ ⋅ − ⋅ ⋅ = ⋅ = / t I V I V t i t v t p 2 cos 2 )) ( ) ( ( ) ( 1 2 ϕ ⋅ ⋅ = / − / = I V t p t p t p ) cos( ) ( ) ( ϕ ω ω + ⋅ ⋅ − = = ′ t I dt t di t i t V dt t v t V ω ω cos ) ( ) ( ⋅ − = ⋅ = ∫ ) sin( ) ( ) ( ) ( ϕ ω + ⋅ − = = ⋅ ′ = ′′ ∫ t I t i dt t i t i |
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