- Email: [email protected]
The optimum adjustment of motor protection relays in an industrial complex
Microe/ectron. Re/iab., Vol. 35, Nos 9-10, pp. 1245-1256, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain 0026-2714/95 $9.50+.00
Pergamon
THE OPTIMUM ADJUSTMENT OF MOTOR PROTECTION RELAYS IN AN INDUSTRIAL COMPLEX
P. Massee 1 and H. Rijanto 1
Abstract In this paper a distribution network is considered supplying electricity to a number of factories belonging to one industrial complex. The costs of interruption may vary more than one order of magnitude from one factorY to another. The problem studied in this paper is how to adjust the time lags of the undervoltage protection relays in each factory in order to obtain a minimum in the total costs of interruptions of all factories together. By properly adjusting the time lags of the relays it may be provoked that factories with low interruption costs are disconnected from the network rather fast after the occurrence of a short circuit through which action the chance that a factory with high interruption cost is switched off is decreased. 1. Introduction In this paper the distribution
network for an industrial complex
is
considered which provides electrical power to a large number of factories. Characteristic for this situation is that the load at each factory rail consists of a large number of asynchronous motors. Each factory rail is provided with an undervoltage relay with the aim to protect the motors connected to it. The problem adressed in the paper is how to adjust the different undervoltage relays such that the sum of the interruption costs of the different factories over a chosen period of time is minimum. The costs per interruption for the various factories are determined by the temporary market position for the different products and may vary by t w o orders of magnitude from one factory to another. Thus it is reasonable to switch off a factory with small interruption costs rather fast after the occurrence of a short circuit in order to try to prevent a factory with large Eindhoven University of Technology, Group Electrical Energy Systems, P.O. Box 513, 5600 MB Eindhoven, The Netherlands 1245
1246
E Massee and H. Rijanto
interruption costs from being switched off. The effect on the distribution network
when
a certain factory
is switched
off,
depends
on the
behaviour of the motors comprising the considered plant. In the paper each factory is represented by one motor, the behaviour of which during the disturbance is described by a simple model. This model takes into account the loss of kinetic energy of the motor when the voltage is less than nominal and the fact that the motor requires 6 times the nominal current in order to reaccelerate after the short circuit has been taken out of the network. A computer program has been written to calculate the interruption costs after choosing the various adjustments of the undervoltage relays which are used as inputs. The occurrence of short circuits in the network is described by negative exponential distributions and the duration of the short circuits depends on the chosen protection strategy for the various connections and rails. The optimum adjustment of the undervoltage relays has to be reached through an interactive approach in which previous results are coupled back. In this way the optimum adjustment of the motor protection relays can be approached very closely.
2. The distribution network The electricity distribution network considered in the paper is shown in figure 1. The configuration in this figure is a simplified version of the actual situation but contains the essential features of an electricity network in practice (Fransen,1989). The typical, characteristic that the loads mainly consist of a number of large motors has also been indicated in figure 1. It can also be seen that the principle of single reserve has been used in the supply to the factories. When one of the connections to a factory has to be switched off due to the presence of a short circuit the above implies that the electricity supply can be resumed very fast through the parallel connection. However, this does not imply that the voltage returns very fast to its nominal value due to the behaviour of the
Motor
protection
asynchronous motors as has been sketched As
long
as the
decelerate from
energy
current.
circuit
and loose kinetic
the network
kinetic
short
is present
energy.
1241
relay adjustment
After
by the protection
in figure 2 (Schreurs,l989). in the
network
the
the short has been eliminated
the motors
have to regain the lost
and during this process they draw six times the nominal
In this way the fact that the voltage at the factory
rather slowly
motors
after a sh,ort circuit,
rail builds up
as shown in figure 2, can be explained.
More details of the model which is used to describe the motor behaviour are given below.
factory
2 1
1
power(MVA) 2
Figure 1:
3 2
The industrial
4 1
5 0.1
electricity
6 5
7 5
network
3. Short circuits and the protection Short circuits
can occur anywhere
to be taken into account on the occurrence
simple.
connection
in the computer
program.
network
and this has
However,
the chance
of a short circuit depends on the involved
Since we concentrate kept
in the distribution
on electrical
For instance
is obtained
the
phenomena total
chance
statistical on
calculations
a short
by adding the chances on a short
component.
circuit
are in a
1248
E Massee and H. Rijanto
VlVn
m
i
...............
I
o o Figure 2:
0.5
t (s)
J
I
I
1.0
1.5
The reaction of a network with a motor to a voltage dip and the used approximation (dotted line).
circuit in the different components comprising that connection. Similarly the total chance on interruption of a certain factory is obtained by adding the chances on interruption due to the different short circuits. The chances on short circuits in the different components have been taken from the industrial practice (Fransen,1989) and are given in table 1. Another point to decide is how long a short circuit will be present in the network which depends on the chosen protection strategy.
Here a
simplification is introduced by assuming that the primary protection will never fail. Since the transformer connections are protected by differential relays a short circuit in such a connection is normally disconnected after 0.2 sec. Short circuits at rails occur less frequent than short circuits in connections
so that special rail protections are not installed in the
considered industrial application. Thus short circuits at rails have to be disconnected by overcurrent-time backup protections in the connections. In order to maintain selectivity the short circuits at the 10 kV rails are
Motor protection relay adjustment
1249
disconnected after 0.5 see and at the 30 kV rails after 0.8 sec. Finally there is one other type of protection which has to be discussed and that is the protection of the motors inside a certain factory. For this protection an undervoltage relay is used which starts its time counter when the voltage at the factory rails sinks below for instance 85% of the nominal voltage and disconnects the motor after a preset time. The problem adressed in this paper is how to adjust the time lags of the motor protection relays in order to obtain a minimum in the total of the costs of interruptions of all factories together. In order to avoid unacceptably large damage to the motors it is assumed that the time delay may not be larger than one second. It should be mentioned that short circuits at the factory rails are not taken into account since their contribution to the costs of interruptions of the factories can not be influenced by the adjustment of the undervoltage relays.
Table 1 :
Chance on the occurrence of a failure (short circuit) in the most important components comprising the connections in an electricity network (Fransen, 1989). Component
Chance (per year)
Cable
0.0051
Transformer
0.0114
Circuit breaker
0.0011
Rail
0.01
Relay
0.0071
4. The costs of interruption
The costs of interruption of the various factories have also been taken from the industrial practice (Fransen,1989) and appear to vary from Dfl
1250
P. Massee and H. Rijanto
7 , 0 0 0 to Dfl 6 7 5 , 0 0 0 per interruption.
In the paper only the fixed costs
(the costs that have to be made when the factory is started up again) are considered and not the time dependent
costs of interruption since the duration of the
interruptions is not determined. Note that the costs depend on the type of factory and especially on the value of its product. Thus the costs depend on the market situation and when this changes the costs may change considerably.
5. The model of the asynchronous motor As has been discussed above and as shown in figure 2 the voltage at the factory rail comes back rather slowly after a short circuit has been disconnected from the network. This is caused by the behaviour of the motors. Also indicated in figure 2 is the approximation to the actual voltage curve, which is used in this paper. From this approximation three different
states
of
a motor
can
be distinguished
namely
nominal
operation, "short circuit" operation and "starting" operation. In contrast to a realistic motor model in which the motor is represented by 5 impedances
which
are
partly
connected
in
series,
partly
parallel
(Lerch,1991) a very simple model is used with only one impedance representing the motor. The value of this impedance, however, depends on the state of operation of the motor. In the model the motor behaviour is described by the impedance of the motor ZM,.the power factor of the motor
cos
q),
the
voltage
at the factory
rail V and the
power
consumption of the load PL- As load a mechanical tool is considered such as a pump, a compressor, a stirrer etc. It is assumed that the power consumption of the load PL is constant. In nominal operation the power produced by the motor equals the power consumption of the load so that p, = V2c°s(I)-
IZMol
(1)
Motor protection relay adjustment
125 I
This equation can be used to calculate the motor impedance in nominal operation ZM, from the power of the load taking into account that in this situation cos ~ , = 0.8. As can be seen from the approximation curve in figure 2 it is assumed in the model that the parameters describing the motor behaviour change instantaneously. During the short circuit the voltage at the factory rail will be very low. It is assumed that the motor will draw the motor starting current in this situation which equals 6 times the nominal current. This implies that the "short .circuit" motor impedance ZM,c then equals the starting impedance ZM,t so that ZM,~ = ZM,t = 1/6 ZM,. In this situation the power factor will also be very low and is assumed to have the value cos ~,c = 0.3. Because of the lower values of V, ZM and cos q~ the power produced by the motor PM = V~ 2 cos q~,~/IZM,¢] is less than PL SO that the motor will loose kinetic energy AE. The kinetic energy lost during the "short circuit", operati.o.n can then be calculated from the formula
AE=
V~cosq~=
_pL ~ At=
[2)
I where At~c equals the duration of the short circuit. After the short circuit has been taken out of the network the motor has to
reaccelerate
and is therefore still characterized
by the starting
impedance (ZM,t = 1/6 ZM,) and by the low value of the power factor (cos q~,t = 0.3). However, not only the lost kinetic energy has to be replenished but also the magnetic field inside the motor which has decreased strongly while the short circuit was present, has to be built up again. It has been estimated that the energy needed to build up the magnetic field again equals the lost kinetic energy AE. Thus the time that the motor needs
to
reaccelerate
during
calculated from the formula MR 35:9/i0-0
the
"startin.q"
operation
At,~ can be
E MasseeandH.Rijanto
1252 At,,
= -2Ae
,
v,=,cos *.,
}-1 (3)
- p'
After the time At, t the motor has completely reaccelerated and the motor impedance and the power factor will then change instantaneously to their nominal values. Note that the lost kinetic energy AE is negative (see formula (2)) so that equation (3) leads to a positive value for At, t when the power produced by the motor V,t 2 cos q~,t /IZM,tl is larger than the power consumption of the load PL. When the power produced by the motor is smaller than PL the motor cannot reaccelerate anymore and the value from equation (3) is negative. This is interpreted as At,, is infinite which means in practice that the motor is connected to the network until the undervoltage protection disconnects it. The advantage of the simple motor model described
above is that it is not necessary to solve
differential equations in order to determine the motor behaviour. This implies that the transient behaviour of the motor is neglected which is a reasonable assumption since it will hardly influence the chance on interruption of the factories in which we are mainly interested. Thus it is only necessary to calculate the voltages at any moment that changes take place in the network i.e. when a short circuit occurs or is removed or when the operating state of one of the motors is changed. Note that each factory is represented by one motor only which is consistent with the
simple
motor
model
described
above.
Since
the
motors
are
represented by only one impedance the voltages in the network are easily calculated by means of the bus impedance matrix approach which has been described before already (Massee,1990).
6. Results In the computer program each possible short circuit is considered and at
Motor protection relay adjustment
1253
any moment that changes take place in the network the voltages are
calculated and it is decided if a factory is disconnected by its motor protection relay. Thus after each possible short circuit has been worked out, it is known which factories have been switched off. Using the probability of occurrence of the various short circuits the chance that a certain factory is switched off due to the considered short circuit is thus known and adding these chances the total chance on disconnection of the considered factory is obtained. Thus the result of the calculations can be given as the expected number of interruptions for the various factories over a period of for instance 10 years (see figures 3 and 4).
f/ //
/! f/ // // // /J
I
// // /J
½ 2
J/ i/ fJ i1
/J // //
//
// // // //
N
N // /J // //
lJ /J lJ
N /J ,,,/
i
,,,j fJ
0
~4
½ 1
Z/
2
3
4
6
e
7
0,3
0.3
factory number O.S
Figure 3:
The estimated
1
1
1
0.6
Number of interruptions in the base case and with "optimally" adjusted time lags of motor protection relays (hatched) cost of interruption per year is easily calculated
by
multiplying the total chance that a certain factory is disconnected due to the occurrence of short circuits by its cost of interruption. For ease of comparison, however, the figures 3 and 4 do not show the result of one
1254
P. Massee and H. Rijanto
calculation but the difference between the results of two calculations. In the base case the undervoltage protection relays of all factories are set at the standard time delay of 1.0 sec. The next step is to adjust the time delay for factories with small interruption costs to a smaller value and in this way to try to prevent factories with high interruption costs from being disconnected. In figure 3 the difference in the expected number of interruptions
between the base case and the case with "optimally"
adjusted motor protection relays is indicated. // //
7"7
/ / / / / /
/J
I /
/ i
/ /
II / i
n
ii ii ii ii /i ii ii ii
/ / i/ / / I i i i i i /i
¢.-A
",4
~ .r A
II li ii Ii ii II ii ii
f/ /I
e'iA
,1~
¢/.4
/I II fl /I /I /I ~1
~ l/ ~ Ii
".6 1
¢~A
i/
ii
2
3
elA ¢1A ¢1A ¢~A
~
¢/Jl ¢/A
¢iA
~
¢1J
¢'/'A r'/A
¢1A ¢/A
rl~ ¢1A F/A ¢1.1
4
6
6
7
factory number 0.3
Figure 4:
I
0.3
1
0.4
1
0.3
Number of interruptions in the base case and with "optimally" adjusted time lags of motor protection relays (hatched) when the market situation has changed.
The economic benefit, however, cannot be judged from figure 3 alone. It can be mentioned that the adjustment of the motor protection relays which resulted in figure 3 led to a decrease in yearly interruption costs for all factories together from Dfl. 185,000 for the base case to Dfl. 9 6 , 0 0 0 for the "optimum"
Motor protection relay adjustment
1255
case. Thus it is clear that a considerable reduction of interruption costs can be obtained by adjusting the time delays of the various motor protection relays. It is clear,
however,
from figure
3 that the expected
number of
interruptions varies much from one factory to the other both in the base case as in the "optimum" case. The way in which the number of interruptions is distributed over the factories depends on the layout of the electricity network as well as on the different powers of the various factories
(see figure
1). This implies that the expected
number of
interruptions cannot be adjusted at wish by adjusting the time lags of the motor protection relays. This is shown in figure 4 for which it has been assumed that the market situation has changed which led to an exchange of the interruption costs of the factories 3 and 6. Figure 4 again shows the difference in the expected number of interruptions between the base case and the situation with "optimally" adjusted motor protection relays. A comparison of figure 4 with figure 3 shows that now less reduction in number of interruptions could be obtained for the factories with high interruption costs. This is reflected by the fact that the yearly interruption costs for all factories together is now only reduced from Dfl. 185,000 for the base case to Dfl. 154,000 for the "optimum" case.
7. Discussion
When an electricity network for a large industrial complex is designed it may turn out that the expected number of interruptions due to short circuits is unevenly distributed over the different factories. Depending on the market situation the difference in interruption costs of the various factories may vary to a much larger extent. By properly adjusting the undervoltage relays protecting the motors in the factories it can be stimulated that factories with small interruption costs are disconnected rather fast. In this way it may be hoped that the expected number of interruptions will be small for factories with large interruption costs so
1256
E Massee and H. Rijanto
that a net economic benifit may result. This has been verified in this paper by means of a computer program showing that significant reduction in interruption costs for all factories together may be obtained in this way.
References Fransen, H., "Single reserve in the electricity supply of a chemical industry", Elektrotechniek, Vol. 67, 1989, p.719-722 (in dutch). Lerch, E. and Simons, J., "Identification methods to solve complex network problems", Elektrotechnische Zeitschrift, Vol. 112, 1991, p.712-716 (in german). Massee, P. and Bollen, M.H.J., "Reliability analysis of industrial electricity supply", Proceedings Third International Conference on Probabilistic Methods Applied to Electric Power Systems, London, July 1991, p.220-223. Schreurs, C., "The behaviour of motors and adjustable drives during short duration voltage dips", Elektrotechniek, Vol. 67, 1989, p.706-714 (in dutch).
Pergamon
THE OPTIMUM ADJUSTMENT OF MOTOR PROTECTION RELAYS IN AN INDUSTRIAL COMPLEX
P. Massee 1 and H. Rijanto 1
Abstract In this paper a distribution network is considered supplying electricity to a number of factories belonging to one industrial complex. The costs of interruption may vary more than one order of magnitude from one factorY to another. The problem studied in this paper is how to adjust the time lags of the undervoltage protection relays in each factory in order to obtain a minimum in the total costs of interruptions of all factories together. By properly adjusting the time lags of the relays it may be provoked that factories with low interruption costs are disconnected from the network rather fast after the occurrence of a short circuit through which action the chance that a factory with high interruption cost is switched off is decreased. 1. Introduction In this paper the distribution
network for an industrial complex
is
considered which provides electrical power to a large number of factories. Characteristic for this situation is that the load at each factory rail consists of a large number of asynchronous motors. Each factory rail is provided with an undervoltage relay with the aim to protect the motors connected to it. The problem adressed in the paper is how to adjust the different undervoltage relays such that the sum of the interruption costs of the different factories over a chosen period of time is minimum. The costs per interruption for the various factories are determined by the temporary market position for the different products and may vary by t w o orders of magnitude from one factory to another. Thus it is reasonable to switch off a factory with small interruption costs rather fast after the occurrence of a short circuit in order to try to prevent a factory with large Eindhoven University of Technology, Group Electrical Energy Systems, P.O. Box 513, 5600 MB Eindhoven, The Netherlands 1245
1246
E Massee and H. Rijanto
interruption costs from being switched off. The effect on the distribution network
when
a certain factory
is switched
off,
depends
on the
behaviour of the motors comprising the considered plant. In the paper each factory is represented by one motor, the behaviour of which during the disturbance is described by a simple model. This model takes into account the loss of kinetic energy of the motor when the voltage is less than nominal and the fact that the motor requires 6 times the nominal current in order to reaccelerate after the short circuit has been taken out of the network. A computer program has been written to calculate the interruption costs after choosing the various adjustments of the undervoltage relays which are used as inputs. The occurrence of short circuits in the network is described by negative exponential distributions and the duration of the short circuits depends on the chosen protection strategy for the various connections and rails. The optimum adjustment of the undervoltage relays has to be reached through an interactive approach in which previous results are coupled back. In this way the optimum adjustment of the motor protection relays can be approached very closely.
2. The distribution network The electricity distribution network considered in the paper is shown in figure 1. The configuration in this figure is a simplified version of the actual situation but contains the essential features of an electricity network in practice (Fransen,1989). The typical, characteristic that the loads mainly consist of a number of large motors has also been indicated in figure 1. It can also be seen that the principle of single reserve has been used in the supply to the factories. When one of the connections to a factory has to be switched off due to the presence of a short circuit the above implies that the electricity supply can be resumed very fast through the parallel connection. However, this does not imply that the voltage returns very fast to its nominal value due to the behaviour of the
Motor
protection
asynchronous motors as has been sketched As
long
as the
decelerate from
energy
current.
circuit
and loose kinetic
the network
kinetic
short
is present
energy.
1241
relay adjustment
After
by the protection
in figure 2 (Schreurs,l989). in the
network
the
the short has been eliminated
the motors
have to regain the lost
and during this process they draw six times the nominal
In this way the fact that the voltage at the factory
rather slowly
motors
after a sh,ort circuit,
rail builds up
as shown in figure 2, can be explained.
More details of the model which is used to describe the motor behaviour are given below.
factory
2 1
1
power(MVA) 2
Figure 1:
3 2
The industrial
4 1
5 0.1
electricity
6 5
7 5
network
3. Short circuits and the protection Short circuits
can occur anywhere
to be taken into account on the occurrence
simple.
connection
in the computer
program.
network
and this has
However,
the chance
of a short circuit depends on the involved
Since we concentrate kept
in the distribution
on electrical
For instance
is obtained
the
phenomena total
chance
statistical on
calculations
a short
by adding the chances on a short
component.
circuit
are in a
1248
E Massee and H. Rijanto
VlVn
m
i
...............
I
o o Figure 2:
0.5
t (s)
J
I
I
1.0
1.5
The reaction of a network with a motor to a voltage dip and the used approximation (dotted line).
circuit in the different components comprising that connection. Similarly the total chance on interruption of a certain factory is obtained by adding the chances on interruption due to the different short circuits. The chances on short circuits in the different components have been taken from the industrial practice (Fransen,1989) and are given in table 1. Another point to decide is how long a short circuit will be present in the network which depends on the chosen protection strategy.
Here a
simplification is introduced by assuming that the primary protection will never fail. Since the transformer connections are protected by differential relays a short circuit in such a connection is normally disconnected after 0.2 sec. Short circuits at rails occur less frequent than short circuits in connections
so that special rail protections are not installed in the
considered industrial application. Thus short circuits at rails have to be disconnected by overcurrent-time backup protections in the connections. In order to maintain selectivity the short circuits at the 10 kV rails are
Motor protection relay adjustment
1249
disconnected after 0.5 see and at the 30 kV rails after 0.8 sec. Finally there is one other type of protection which has to be discussed and that is the protection of the motors inside a certain factory. For this protection an undervoltage relay is used which starts its time counter when the voltage at the factory rails sinks below for instance 85% of the nominal voltage and disconnects the motor after a preset time. The problem adressed in this paper is how to adjust the time lags of the motor protection relays in order to obtain a minimum in the total of the costs of interruptions of all factories together. In order to avoid unacceptably large damage to the motors it is assumed that the time delay may not be larger than one second. It should be mentioned that short circuits at the factory rails are not taken into account since their contribution to the costs of interruptions of the factories can not be influenced by the adjustment of the undervoltage relays.
Table 1 :
Chance on the occurrence of a failure (short circuit) in the most important components comprising the connections in an electricity network (Fransen, 1989). Component
Chance (per year)
Cable
0.0051
Transformer
0.0114
Circuit breaker
0.0011
Rail
0.01
Relay
0.0071
4. The costs of interruption
The costs of interruption of the various factories have also been taken from the industrial practice (Fransen,1989) and appear to vary from Dfl
1250
P. Massee and H. Rijanto
7 , 0 0 0 to Dfl 6 7 5 , 0 0 0 per interruption.
In the paper only the fixed costs
(the costs that have to be made when the factory is started up again) are considered and not the time dependent
costs of interruption since the duration of the
interruptions is not determined. Note that the costs depend on the type of factory and especially on the value of its product. Thus the costs depend on the market situation and when this changes the costs may change considerably.
5. The model of the asynchronous motor As has been discussed above and as shown in figure 2 the voltage at the factory rail comes back rather slowly after a short circuit has been disconnected from the network. This is caused by the behaviour of the motors. Also indicated in figure 2 is the approximation to the actual voltage curve, which is used in this paper. From this approximation three different
states
of
a motor
can
be distinguished
namely
nominal
operation, "short circuit" operation and "starting" operation. In contrast to a realistic motor model in which the motor is represented by 5 impedances
which
are
partly
connected
in
series,
partly
parallel
(Lerch,1991) a very simple model is used with only one impedance representing the motor. The value of this impedance, however, depends on the state of operation of the motor. In the model the motor behaviour is described by the impedance of the motor ZM,.the power factor of the motor
cos
q),
the
voltage
at the factory
rail V and the
power
consumption of the load PL- As load a mechanical tool is considered such as a pump, a compressor, a stirrer etc. It is assumed that the power consumption of the load PL is constant. In nominal operation the power produced by the motor equals the power consumption of the load so that p, = V2c°s(I)-
IZMol
(1)
Motor protection relay adjustment
125 I
This equation can be used to calculate the motor impedance in nominal operation ZM, from the power of the load taking into account that in this situation cos ~ , = 0.8. As can be seen from the approximation curve in figure 2 it is assumed in the model that the parameters describing the motor behaviour change instantaneously. During the short circuit the voltage at the factory rail will be very low. It is assumed that the motor will draw the motor starting current in this situation which equals 6 times the nominal current. This implies that the "short .circuit" motor impedance ZM,c then equals the starting impedance ZM,t so that ZM,~ = ZM,t = 1/6 ZM,. In this situation the power factor will also be very low and is assumed to have the value cos ~,c = 0.3. Because of the lower values of V, ZM and cos q~ the power produced by the motor PM = V~ 2 cos q~,~/IZM,¢] is less than PL SO that the motor will loose kinetic energy AE. The kinetic energy lost during the "short circuit", operati.o.n can then be calculated from the formula
AE=
V~cosq~=
_pL ~ At=
[2)
I where At~c equals the duration of the short circuit. After the short circuit has been taken out of the network the motor has to
reaccelerate
and is therefore still characterized
by the starting
impedance (ZM,t = 1/6 ZM,) and by the low value of the power factor (cos q~,t = 0.3). However, not only the lost kinetic energy has to be replenished but also the magnetic field inside the motor which has decreased strongly while the short circuit was present, has to be built up again. It has been estimated that the energy needed to build up the magnetic field again equals the lost kinetic energy AE. Thus the time that the motor needs
to
reaccelerate
during
calculated from the formula MR 35:9/i0-0
the
"startin.q"
operation
At,~ can be
E MasseeandH.Rijanto
1252 At,,
= -2Ae
,
v,=,cos *.,
}-1 (3)
- p'
After the time At, t the motor has completely reaccelerated and the motor impedance and the power factor will then change instantaneously to their nominal values. Note that the lost kinetic energy AE is negative (see formula (2)) so that equation (3) leads to a positive value for At, t when the power produced by the motor V,t 2 cos q~,t /IZM,tl is larger than the power consumption of the load PL. When the power produced by the motor is smaller than PL the motor cannot reaccelerate anymore and the value from equation (3) is negative. This is interpreted as At,, is infinite which means in practice that the motor is connected to the network until the undervoltage protection disconnects it. The advantage of the simple motor model described
above is that it is not necessary to solve
differential equations in order to determine the motor behaviour. This implies that the transient behaviour of the motor is neglected which is a reasonable assumption since it will hardly influence the chance on interruption of the factories in which we are mainly interested. Thus it is only necessary to calculate the voltages at any moment that changes take place in the network i.e. when a short circuit occurs or is removed or when the operating state of one of the motors is changed. Note that each factory is represented by one motor only which is consistent with the
simple
motor
model
described
above.
Since
the
motors
are
represented by only one impedance the voltages in the network are easily calculated by means of the bus impedance matrix approach which has been described before already (Massee,1990).
6. Results In the computer program each possible short circuit is considered and at
Motor protection relay adjustment
1253
any moment that changes take place in the network the voltages are
calculated and it is decided if a factory is disconnected by its motor protection relay. Thus after each possible short circuit has been worked out, it is known which factories have been switched off. Using the probability of occurrence of the various short circuits the chance that a certain factory is switched off due to the considered short circuit is thus known and adding these chances the total chance on disconnection of the considered factory is obtained. Thus the result of the calculations can be given as the expected number of interruptions for the various factories over a period of for instance 10 years (see figures 3 and 4).
f/ //
/! f/ // // // /J
I
// // /J
½ 2
J/ i/ fJ i1
/J // //
//
// // // //
N
N // /J // //
lJ /J lJ
N /J ,,,/
i
,,,j fJ
0
~4
½ 1
Z/
2
3
4
6
e
7
0,3
0.3
factory number O.S
Figure 3:
The estimated
1
1
1
0.6
Number of interruptions in the base case and with "optimally" adjusted time lags of motor protection relays (hatched) cost of interruption per year is easily calculated
by
multiplying the total chance that a certain factory is disconnected due to the occurrence of short circuits by its cost of interruption. For ease of comparison, however, the figures 3 and 4 do not show the result of one
1254
P. Massee and H. Rijanto
calculation but the difference between the results of two calculations. In the base case the undervoltage protection relays of all factories are set at the standard time delay of 1.0 sec. The next step is to adjust the time delay for factories with small interruption costs to a smaller value and in this way to try to prevent factories with high interruption costs from being disconnected. In figure 3 the difference in the expected number of interruptions
between the base case and the case with "optimally"
adjusted motor protection relays is indicated. // //
7"7
/ / / / / /
/J
I /
/ i
/ /
II / i
n
ii ii ii ii /i ii ii ii
/ / i/ / / I i i i i i /i
¢.-A
",4
~ .r A
II li ii Ii ii II ii ii
f/ /I
e'iA
,1~
¢/.4
/I II fl /I /I /I ~1
~ l/ ~ Ii
".6 1
¢~A
i/
ii
2
3
elA ¢1A ¢1A ¢~A
~
¢/Jl ¢/A
¢iA
~
¢1J
¢'/'A r'/A
¢1A ¢/A
rl~ ¢1A F/A ¢1.1
4
6
6
7
factory number 0.3
Figure 4:
I
0.3
1
0.4
1
0.3
Number of interruptions in the base case and with "optimally" adjusted time lags of motor protection relays (hatched) when the market situation has changed.
The economic benefit, however, cannot be judged from figure 3 alone. It can be mentioned that the adjustment of the motor protection relays which resulted in figure 3 led to a decrease in yearly interruption costs for all factories together from Dfl. 185,000 for the base case to Dfl. 9 6 , 0 0 0 for the "optimum"
Motor protection relay adjustment
1255
case. Thus it is clear that a considerable reduction of interruption costs can be obtained by adjusting the time delays of the various motor protection relays. It is clear,
however,
from figure
3 that the expected
number of
interruptions varies much from one factory to the other both in the base case as in the "optimum" case. The way in which the number of interruptions is distributed over the factories depends on the layout of the electricity network as well as on the different powers of the various factories
(see figure
1). This implies that the expected
number of
interruptions cannot be adjusted at wish by adjusting the time lags of the motor protection relays. This is shown in figure 4 for which it has been assumed that the market situation has changed which led to an exchange of the interruption costs of the factories 3 and 6. Figure 4 again shows the difference in the expected number of interruptions between the base case and the situation with "optimally" adjusted motor protection relays. A comparison of figure 4 with figure 3 shows that now less reduction in number of interruptions could be obtained for the factories with high interruption costs. This is reflected by the fact that the yearly interruption costs for all factories together is now only reduced from Dfl. 185,000 for the base case to Dfl. 154,000 for the "optimum" case.
7. Discussion
When an electricity network for a large industrial complex is designed it may turn out that the expected number of interruptions due to short circuits is unevenly distributed over the different factories. Depending on the market situation the difference in interruption costs of the various factories may vary to a much larger extent. By properly adjusting the undervoltage relays protecting the motors in the factories it can be stimulated that factories with small interruption costs are disconnected rather fast. In this way it may be hoped that the expected number of interruptions will be small for factories with large interruption costs so
1256
E Massee and H. Rijanto
that a net economic benifit may result. This has been verified in this paper by means of a computer program showing that significant reduction in interruption costs for all factories together may be obtained in this way.
References Fransen, H., "Single reserve in the electricity supply of a chemical industry", Elektrotechniek, Vol. 67, 1989, p.719-722 (in dutch). Lerch, E. and Simons, J., "Identification methods to solve complex network problems", Elektrotechnische Zeitschrift, Vol. 112, 1991, p.712-716 (in german). Massee, P. and Bollen, M.H.J., "Reliability analysis of industrial electricity supply", Proceedings Third International Conference on Probabilistic Methods Applied to Electric Power Systems, London, July 1991, p.220-223. Schreurs, C., "The behaviour of motors and adjustable drives during short duration voltage dips", Elektrotechniek, Vol. 67, 1989, p.706-714 (in dutch).