electricpete
Electrical
- May 4, 2001
- 16,774
I have seen many reference which advocate setting the motor instantaneous trip setting in the range of 170%-175% of motor locked rotor current.
In trying to understand the basis for that number, I use the following logic.
Three-phase ungrounded-wye or delta motor should act similar to one-phase L-R circuit upon sudden application of a voltage... worst case phase closing would give a current that goes from 0 to 2*I_LRC (ignoring any decay of the DC component). If I compute the rms value of this waveform, I see it is composed of DC component of rms magnitude I_LRC and ac component of rms magnitude I_LRC/sqrt(2). Total rms is the sqrt of sum of squares of two components
or I_tot_rms = sqrt(I_LRC^2+(I_LRC/sqrt2)^2) = sqrt((1+0.5)*I_LRC^2) = sqrt(3/2)*I_LRC. If I compare this to the symmetrical (ac) portion of LRC which has rms of sqrt(1/2)*I_LRC, I see the ratio is sqrt(3).
Is that the basis for the sqrt(3). If so, why would we use the ratio of the rms currents instead of the ratio of the peak currents (which is 2.0). Doesn't an instantaneous element respond to the peak value of current?
It occurs to me the other possible explanation is that they are assuming some decay of the DC component prior to the first peak. But without knowing the L/R of the circuit, that seems non-conservative (might lead to trip during starting).
In trying to understand the basis for that number, I use the following logic.
Three-phase ungrounded-wye or delta motor should act similar to one-phase L-R circuit upon sudden application of a voltage... worst case phase closing would give a current that goes from 0 to 2*I_LRC (ignoring any decay of the DC component). If I compute the rms value of this waveform, I see it is composed of DC component of rms magnitude I_LRC and ac component of rms magnitude I_LRC/sqrt(2). Total rms is the sqrt of sum of squares of two components
or I_tot_rms = sqrt(I_LRC^2+(I_LRC/sqrt2)^2) = sqrt((1+0.5)*I_LRC^2) = sqrt(3/2)*I_LRC. If I compare this to the symmetrical (ac) portion of LRC which has rms of sqrt(1/2)*I_LRC, I see the ratio is sqrt(3).
Is that the basis for the sqrt(3). If so, why would we use the ratio of the rms currents instead of the ratio of the peak currents (which is 2.0). Doesn't an instantaneous element respond to the peak value of current?
It occurs to me the other possible explanation is that they are assuming some decay of the DC component prior to the first peak. But without knowing the L/R of the circuit, that seems non-conservative (might lead to trip during starting).