# Why the effect of a triphasic capacitor could be as twice as its rated kVar? *(check Update 1)*

Why the effect of a triphasic capacitor could be as twice as its rated kVar?

Please check Update 1, since if its true, then I think my issues are solved.

Intro

This is a real life case of a client of mine, which have a irrigation pumps station located in Chile. The power grid supplies their equipment through a power transformer dedicated to his consumption, where I don't know any of the transformer's plate data. The power transformer is providing in the low voltage stage a triphasic supply with neutral wire of 380 V rms among life wires with a frequency of 50 Hz (Chilean standard for triphasic low voltage), and the client consumption is registered on the high voltage side of the power transformer where just three power lines could be seen (I don't know their voltage).

About 50 meters from the power transformer, my client have two irrigation pumps connected within a cabin, each of them controlled by its own Variable Frequency Drives (VDF):

• Pump 1: SAER model IR65-160/B 15 HP (11 kW) with a power factor $$\\cos(\phi)=0.86\$$, controlled by a VDF Mitsubishi Electric model FR-D740-11K
• Pump 1: SAER model IR65-160/A 20 HP (15 kW) with a power factor $$\\cos(\phi)=0.87\$$, controlled by a VDF Mitsubishi Electric model FR-D740-15K

Every time the pumps are powered on by the VDF units, they took about $$\\approx 30\$$ seconds in achieve full load, and they work during the day at full load uninterrupted for the time required by the irrigation controllers.

The system from the Main Electric Board on forwards have a TN-S grounding system, but the original installer instead of building a grounding grid near the cabin, he connected the grounding wire to the neutral wire that is coming from the power transformer located near 50 meters away, so I think you could think in the installation of having a TN-C-S grounding scheme.

In Chile, the power factor penalization works as this:

• If the power factor is inductive then penalization starts when $$\\cos(\phi)< 0.93\$$, and the penalization factor is $$\\rho = 0.93-\cos(\phi)\$$ (commonly used)
• If the power factor is capacitive then penalization starts when $$\\cos(\phi)< 0.95\$$, and the penalization factor is $$\\rho = 0.95-\cos(\phi)\$$ (rare)

On my client electricity tariff segment (AT-4.3), the penalty fee due low power factor is calculated as: $$\begin{array}{r c l} \text{PF_fee} & = & \rho\, \cdot \left(C_1 + C_2 + C_3 + C_4 \right) \\ \text{PF_fee} & = & \text{fee due low power factor} \\ C_1 & = & \text{charge due kWh consumption} \\ C_2 & = & \text{charge due maximum registered power kW} \\ C_3 & = & \text{charge due maximum registered power kW on high demand hours} \\ C_3 & = & \text{charge due lecturing energy in the low voltage side} \\ \end{array}$$

Where for this client $$\C_4 = 0\$$ always since its power consumption is registered on the high voltage side of the power transformer.

Last year, my client electricity bills were as follows: $$\begin{array}{| c | c | c | r | r | r | c | r |} \hline \text{month} & \text{kWh} & \text{kVarh} & C_1 & C_2 & C_3 & \rho & \text{PF_fee} \\ \hline \text{jun-21} & 487.5 & 2,550 & 31,464 & 53,907 & 2,509 & 74\% & 65,031 \\ \text{jul-21} & 337.5 & 1,987.5 & 21,783 & 53,907 & 2,966 & 76\% & 59,779 \\ \text{aug-21} & 337.5 & 1,725 & 21,783 & 53,907 & 543 & 74\% & 56,412 \\ \text{sep-21} & 787.5 & 1,837.5 & 50,826 & 54,576 & 274 & 54\% & 57,065 \\ \text{oct-21} & 1,012.5 & 1,575 & 65,349 & 54,576 & 2,966 & 39\% & 47,927 \\ \text{nov-21} & 3,187.5 & 2,100 & 205,727 & 81,099 & 2,965 & 9\% & 26,081 \\ \text{dec-21} & 3,187.5 & 2,100 & 205,727 & 81,099 & 2,965 & 5\% & 17,166 \\ \text{jan-22} & 5,137.5 & 2,062.5 & 331,584 & 81,387 & 2,966 & 0\% & 0 \\ \text{feb-22} & 8,250 & 2,850 & 535,441 & 115,127 & 2,977 & 0\% & 0 \\ \text{mar-22} & 24,525 & 17,212.5 & 1,591,721 & 151,590 & 2,978 & 12\% & 209,555 \\ \text{apr-22} & 6,300 & 6,750 & 408,882 & 167,169 & 3,803 & 25\% & 144,964 \\ \text{may-22} & 450 & 2363 & 29,206 & 167,169 & 4,123 & 74\% & 148,369 \\ \hline \end{array}$$