-
Tripping
John Undrill 12 January 2016
-
Engineering realities - residential air conditioners
Not all single phase motors on a feeder will stall if voltage
depression is in the threshold range
All motors will stall/stop of voltage depression goes far below
the threshold range
Single phase motors that do stall will not all stall
simultaneously
Motors driving reciprocating compressors are unlikely to
restart
Significant fraction of air conditioner motors driving scroll
compressors will reverse and reaccelerate running backwards
Older residential thermostats do not trip motors
Trend is for newer thermostats to trip motors promptly to ensure
against backward rotation
-
Engineering realities - three phase motors
Three phase motors are more likely than single phase motors to
be - controlled by a energy management system or process controller
- protected by a relay with overcurrent and undervoltage trips
Motor control may be by - very simple relay logic - extensive
process-oriented control systems
Simple relay/contactor control my drop-out very nearly
instantaneously - but quick operation of a control relay is not
universal - relays and/or contractors may have deliberate delay
before tripping
-
Block and progressive processes
In a block process the entire category of load (eg motor-d)
changes state at the same instant
Stalling as a block is not realistic
Makes sensitivity studies impractical
In a progressive process the change of state of a load category
takes place over a time interval of, at least, a few simulation
time steps
Allows study of sensitivity to the fraction of the load that
changes state
-
Progressive stalling/tripping model
Fraction of motors that will stall at stall threshold
voltage
Fraction of motors that have not stalled and are still
running
Fraction of motors that have actually stalled
Temperature of thermal cutouts in motors that have stalled
Current in motors that have stalled
SfracfrfstalledTthistalled
fr =1− Sfrac1 + sTstall
fstalled = max((1− fr), fstalled)
fcon = fstalled (1− tth)
fr =i2stalled − 1
1 + s Ttherm
-
Sfrac increases with decreased terminal voltage
V>Vstall — No stalling
V
-
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
1.2
Term
inal
vol
tage
0 1 2 3 4 5 6 7 8 9 100
50
100
150
200
250
Load
Pto
tal
0 1 2 3 4 5 6 7 8 9 10-50
0
50
100
150
200
Load
Qto
tal
0 1 2 3 4 5 6 7 8 9 10Time, sec.
0
0.2
0.4
0.6
0.8St
alle
d no
t trip
ped
case2l
Vstall=0.6 Sfrac=0.7 Tc=0.025,0.050,0.075 Vstall=0.6 Sfrac=0.7
Tc=0.025,0.050,0.075
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
1.2
Term
inal
vol
tage
0 1 2 3 4 5 6 7 8 9 100
50
100
150
200
250
Load
Pto
tal
0 1 2 3 4 5 6 7 8 9 10-50
0
50
100
150
200
Load
Qto
tal
0 1 2 3 4 5 6 7 8 9 10Time, sec.
0
0.2
0.4
0.6
0.8
Stal
led
not t
rippe
d
case1l
~60% of motors stall >60% of motors stall
-
Depressed voltage close to Vstall
Vstall=0.6
Sfrac=0.7
Tc=0.025,0.050,0.075
Stalling starts when motor terminal voltage goes below 0.7
Stalled fraction increases according to time constant until
voltage goes above 0.7
Increasing time constant causes smaller fraction of motors to
stall
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.40
0.2
0.4
0.6
0.8
1
1.2
Term
inal
vol
tage
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.450
100
150
200
250
Load
Pto
tal
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4-50
0
50
100
150
200
Load
Qto
tal
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4Time, sec.
0
0.2
0.4
0.6
0.8
Stal
led
not t
rippe
d
case1s
Tstall - controls rate and extent of stalling
Tc=0.025 0.050 0.075
-
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.40
0.2
0.4
0.6
0.8
1
Term
inal
vol
tage
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.40
50
100
150
200
250
Load
Pto
tal
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4-50
0
50
100
150
200
Load
Qto
tal
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4Time, sec.
0
0.2
0.4
0.6
0.8
Stal
led
not t
rippe
d
case2s
Depressed voltage far below Vstall
Vstall=0.6
Sfrac=0.7
Tc=0.025,0.050,0.075
Stalling starts when motor terminal voltage goes below 0.7
Stalled fraction increases according to time constant until
voltage goes above 0.7
Stalled fraction goes above Sfrac because motor terminal voltage
goes far below 0.7
Tstall - controls rate and extent of stalling
Tc=0.025 0.050 0.075
