Power System Harmonics, True Power Factor & DPF Measure

October 18, 2009

Displacement Power Factor (DPF) is the power factor as we know at fundamental system frequency (50Hz in UK). However, True Power Factor (PF) or just Power Factor is the product of the distortion power factor and DPF. Check out the Wikipedia article on this  topic. The following equation related components:

PF=DPF\cdot  \frac{1}{\sqrt{1+I_{THD}^2}}=DPF\cdot\frac{I_{1,RMS}}{I_{RMS}}

Where, I_{THD} is the total current harmonic distortion at the point of measurement, I_{1,RMS} and I_{1,RMS} are fundamental and total harmonic RMS currents, and \left [\sqrt{1+I_{THD}^2} \right ]^{-1} is the distortion power factor (in other words distortion factor associated with power factor).

The above equation leads to the following conclusions:

  • PF≤DPF, True Power Factor is always less than or equal to Displacement Power Factor.
  • PF = DPF, True Power Factor equals Displacement Power Factor when there are current harmonics at the point of measurement;
  • PF<DPF, suggests presence of harmonics, take it easy: awareness is good.
  • PF<<DPF, means its time to take action.

The above observations, comparing DPF and PF will give you a quick assessment of harmonic severity, however if detail assessment is required then you will need to monitor both I_{THD} and V_{THD}.

As I understand, most meters or monitoring equipment that display PF and DFC also may have the ability to calculate both current and voltage total harmonic distortion factors: I_{THD} and V_{THD}, sometimes including individual harmonics levels as numbers and/or as a harmonic spectrum bar chart. Now if have measured these values, i.e. both THD for current and voltage, and individual harmonics levels in %, then compare them against the harmonics standards that govern your electric network, and you will know the severity of the harmonic problem.

In UK, DNOs are required to comply with EN50160 Std. and consumers with G5/4-1 Std.


Power Factor Capacitor Discharge Resistor Design

August 27, 2009

When a Power Factor Capacitor (PFC) step, a single unit in a bank of several capacitors, is disconnected or switched off, the discharging resistor connected across the capacitor will discharge it to designed retained voltage V value in discharge time t seconds. Typical discharge resistor ratings for a given power factor capacitor C  in μF or MVAR include: maximum normal operation system voltage V_0  in kV and required retained discharge voltage V  in Volts (around 50V) at discharge time t  in seconds (usually <60s). The discharge resistor R  in kΩ  is given as,

R=\left | \frac{-t}{ln(\frac{V}{V_0})C} \right |          (1)

Depending whether the PFC bank step is star or delta connected (usually star connected), for given system frequency f  and capacitor step’s rated reactive power output Q in MVAR, the capacitor step’s capacitance C  in μF is given as:

  • If star connected, C=\frac{Q}{2 \pi f V_0^{2}}
  • If delta connected, C=\frac{3Q}{2 \pi f V_0^{2}}

Explanation:

Capacitor voltage decay across the resistor is given as, V=V_{0}e^{\frac{-t}{RC}}. Rearrange this for Discharge Resistor ‘R’ and you get (1). Simple!


Power Factor Capacitor Detuning

August 17, 2009

Power Factor Capacitor (PFC) banks are commonly detuned to specific frequencies to reduce or remove harmonic resonances. This is done by introducing a detuning reactor in series with the capacitor cluster at each three phase leg.

At the detuning frequency, detuning reactor will have the same impedance as the PFC capacitance per phase leg, i.e. X_{L}=X_{C}.

Detune reactor inductance is then given as: L=\frac{1}{(2\Pi f_{d})^{2}C}Henry

Where, f_{d} is the PFC detune frequency and C is the PFC capacitance per phase leg.


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