Secondary Current Calculations

Discussion in 'Homework Help' started by jonatha12, Aug 8, 2011.

  1. jonatha12

    Thread Starter New Member

    Aug 8, 2011
    When metering power (kW) or electrical energy (kWh), Blondel’s theorem states that total power for a system containing N conductors that it can be correctly metered with N-1 single phase watt-meter elements (Voltage x current). It is standard practice for a “delta primary transformer” (ex. 416V 3ph/3w to 120/208V 3ph/4w) to install 2 current sensors (CTs), one on A and one on C phase (i.e. I_A and I_C), and connect the voltage measurement from phases with CTs to the phase without CTs (i.e. V_AB and V_CB).

    NOTE: I am using capital letters (A, B, C) for primary values and lower-case letters (a, b, c) for secondary values.

    Ignoring losses due to transformer efficiency, by conservation of energy, the power on the primary must therefore be equal to the power on the secondary. Therefore:
    Power In = Power Out
    (V_AB) (I_A) (Cos θ_AB) + (V_CB) (I_C) (Cos θ_CB) = (V_a) (I_a) (Cos θ_a) + (V_b) (I_b) (Cos θ_b) + (V_c) (I_c) (Cos θ_c)

    NOTE: θ_AB is the phase angle between V_AB and I_A (+ 30 degrees for a resistive load) and θ_CB is the phase angle between V_CB and I_C (– 30 degrees for a resistive load)

    What I want to know is the secondary currents (I_a, I_b and I_c) and phase angles (θ_a, θ_b and θ_c) in order to determine if the load is balanced. I want to do this using existing “delta-connected” electricity meters that are readable from a remote location (AMR) to do this analysis.