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Determination of reactive power and compensation of power factor FP = COS(φ°).

Measure the power and power factor in each zone of the industrial plant and evaluate if reactive power needs to be compensated for the entire industrial plant:

Zone 1 = 60 [KVAR], current delayed phase current.

Zone 2 = 50 [KVAR] and 90 [KW], current-going phase current.

Zone 3 = 100 [KW], FP = COS(φ°) = 1, i.e. no phase angle between current and voltage.

Note: In real-world conditions, it is not possible to disassemble all electrical devices and measure their resistance, inductance, or capacitance to determine the power factor or COS(φ°) of each individual device, nor is it possible to have a wiring diagram for the entire system.

Therefore, we used a complex power formula for each zone:

For zone 1: Comp_S1 = S1.COS(φ°1) + j.S1.SIN(φ°1) = { P1 + j.Q1 }. There is no active power consumed in zone 1 (i.e., P1 = 0 [watts]), so: Comp_S1 = { 0 [KW] + j.60 [KVAR] } [KVA] = { 60.j } [KVA].

Region 2: Comp_S2 = S2.COS(φ°2) + j.S2.SIN(φ°2) = { P2 + j.Q2 } Region 2 consumes active power of P2 = 90 [KW] and reactive power of Q2 = 50 [KVAR]. On the other hand, the phase shift in zone 2 is leading, that is, the current leads the voltage, so that φ°2 is negative (i.e., -j). Therefore: Comp_S2 = { 90 [KW] - j.50 [KVAR] } [KVA] = { 90 - 50.j } [KVA].

In zone 3: Comp_S3 = S3.COS(φ°3) + j.S3.SIN(φ°3) = { P3 + j.Q3 }. In zone 3, FP = 1, i.e. Q3 = 0 [VAR], so no reactive power is consumed. Therefore: Comp_S3 = { 100 [KW] + j.0 [KVAR] } = { 100 } [KVA].

Since the complex power contains all the information about the circuit, we can add the three complex powers Comp_S1, Comp_S2, and Comp_S3 to get the total complex power of the electrical installation, Comp_S:

Comp_S = Comp_S1 + Comp_S2 + Comp_S3 = {60.j + (90 - 50.j) + 100}

Comp_S = Comp_S1 + Comp_S2 + Comp_S3 = {190 + 10.j} [kVA].

Comp_S = Comp_S1 + Comp_S2 + Comp_S3 = 190 262,98. in phase (3,013°) [kVA].

φ° = 3,013°.

The phase angle of the total complex power of the circuit represents the phase change between the total circuit current and the voltage at the terminals of the electrical device, so the power factor FP can be derived: FP = cos(φ°) = cos(3,013°) = 0,998 = 99,8%, which means that 99,8% of the apparent power is used as active power. The reactive power Q is only 0,2%, so no compensation for reactive power is needed. The power factor is almost 1, with FP = 0,998.