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Both load flow and fault current calculations can be performed for unbalanced networks.
The calculation can be performed both for LV and MV networks and the trace can be started from any optional point in the network.
If there is no description of the phase code for the conductor it is assumed to be a normal 3-phase distribution conductor. If the load points do not have a specific phase code they are assumed to have a symmetric 3 phase load.
As start voltage for the calculation the phase voltage is used. Only the value for phase 1 is needed, since the calculation automatically will set the start values for the other phases to the same value. If all start voltages are set they will all be used in the calculation.
Phase codes are entered in the attribute form, tab Project load. Press Add and enter the desired Phase code in the drop-down list.
No meshes are allowed
No parallel transformers are allowed
No one-phase transformers are allowed
•If the conductor has a phase code that is not included in the nearest feeding conductor
•If the load-point has a phase code that is not included in the phase code of the feeding conductor
•Parallel transformers
•Parallel conductors can only be calculated for a 3 phase configuration
1.Volt 1
2.Volt 2
3.Volt 3
4.Angle 1
5.Angle 2
6.Angle 3
7.Voltage drop 1
8.Voltage drop 2
9.Voltage drop 3
10.conductor current 1
11.conductor current 2
12.conductor current 3
13.Total current
14.Relative load-current 1
15.Relative load-current 2
16.Relative load-current 3
17.Active losses 1
18.Active losses 2
19.Active losses 3
20.Reactive losses 1
21.Reactive losses 2
22.Reactive losses 3
23.Three-phase active short-circuit power
24.Three-phase reactive short-circuit power
25.Three-phase apparent short-circuit power
26.Three-phase current in Node-point
27.Two-phase current in Node-point
28.Short-circuit phase-zero Ij in a node (if no generators this gives the result)
29.Short-circuit phase-zero 1 in a node L1-phase
30.Short-circuit phase-zero 2 in a node L2-phase
31.Short-circuit phase-zero 3 in a node L3-phase
32.Zk Positive
33.Rk Positive
34.Xk Positive
35.Three-phase current in conductor
36.Two-phase current in conductor
37.Short-circuit current phase neutral/ground in conductor (if no generators this gives the result)
38.Short-circuit current phase neutral/ground 1 in conductor from above.
39.Short-circuit current phase neutral/ground 2 in conductor from above.
40.Short-circuit current phase neutral/ground 3 in conductor from above.
41.Short-circuit current phase neutral/ground 1 in conductor from bottom.
42.Short-circuit current phase neutral/ground 2 in conductor from bottom.
43.Short-circuit current phase neutral/ground 3 in conductor from bottom.
44.Protection make
45.Protection rated current
46.Suggested make
47.Suggested maximum fuse IkMax (Based on maximum current of three, two and one-phase current)
48.Suggested maximum fuse IkMin (Based on maximum current of three, two and one-phase current)
49.Suggested minimum fuse
50.Suggested maximum fuse
51.Tripping time IkMax
52.Tripping time IkMin
53.Alarm conductor short time current
Make sure a delivery point has an unbalanced load by setting the phase code of a delivery point to L1-N. The load will be located between Phase L1 and neutral.
Make sure the conductor will include the correct phases (Phase L1-Neutral).
Make sure you have a result template with desired non symmetrical calculation results available. In the example - voltages and currents.
Start the calculation trace the same way as for a symmetric network calculation.
Select the unbalanced calculation and set at least one phase feeding point voltage as a start value.
Use the correct result template and show the result in the map.
Study the current direction phase by phase. Only one phase carries current.
Use fixed reports for further analysis.
Single phase generators
The generator is documented as a standard distribution generator but the correct phase code must be specified.
The result for an individual conductor can be presented in a tabular form.
For the conductors both fault currents from the feeding point and downwards to the faulty point and fault currents from the faulty point and upwards will be presented
Fault currents from above will receive contributions from other generators in the network and the feeding point. (Excluding any generation in fault object itself). The smallest of these fault currents will be the input for the protection tripping time evaluation.
Fault currents from below, will receive contributions from generators below the conductor in the feeding order.
For the nodes the fault current is shown phase by phase. Contributions from all involved generators in the network, including any generator in the object itself as well as from the supply point will be presented.
This section includes theory and solution of three-phase unbalanced load flow.
In a distribution system where balanced transposition of conductors is assumed (impedance symmetrical systems) and balanced three-phase loads at the customers dominate a single phase representation is commonly used in load flow studies. The phase inductance then includes the self impedance and the mutual inductance with the other two phases. If these prerequisites are not fulfilled a full three-phase representation must be used
VRR´ , VSS´ , VTT´ and VNN´ are voltage drops on the three phases
and the neutral
ZR , ZS , ZT and ZN are the self impedances
ZRS , ZST and ZRT are the phase to phase mutual impedances
ZRN , ZSN and ZRN are the phase to neutral mutual impedances
IR , IS , IT and IN are the currents in the phases and the neutral
In a multi-grounded system we can assume that
VNN´ = 0 (2)
If we can assume that the system is impedance symmetrical the impedance data is simplified to
ZR= ZS = ZT = ZE (7)
ZRS = ZST = ZRT = ZÖ (8)
ZRN = ZSN = ZRN = ZNÖ (9)
For a section with only one phase and grounded neutral almost all of the phase current returns in the neutral conductor,
Line section with a single phase and grounded neutral
The voltage drop across the phase conductor is calculated as
VRR´ = VRN - VR´N
= ZR IR + ZRN IN - ( ZN IN + ZRN IR ) (13)
Inserting IN = - IR in eq. (13) gives
VRR´ = ( ZR - 2 ZRN + ZN ) IR (14)
In conclusion, for the three phase load flow we use a impedance matrix for three phase sections. For two phase sections the matrix contains zeros for the missing phase. For single phase sections we use a single matrix element according to eq. (14).
For phase to neutral connected loads the load currents are calculated as
IR = (SR / VRN) *
IS = (SS / VSN) * (15)
IR = (ST / VTN) *
where
SR , SS and ST are the complex power loads on the three phases
IR , IS and IT are the complex currents
VRN , VSN and VTN are the complex phase to neutral voltages
For phase to phase connected loads we use a load representation
The complex phase currents and phase to phase voltages are calculated as
IR = IRS - ITR
IS = IST - IRS (16)
IT = ITR - IST
VRS = VR - VS
VST = VS - VT (17)
VTR = VT - VR
where
IR , IS and IT are the complex phase currents
IRS , IST and ITR are the complex phase to phase currents
VR , VS and VT are the complex phase to ground voltages
VRS , VST and VTR are the complex phase to phase voltages
Given the phase to phase complex power loads SRS , SST and STR the phase to phase currents are obtained as
IRS = ( SRS / VRS ) *
IST = ( SST / VST ) * (18)
ITR = ( STR / VTR ) *
from which the phase currents are obtained according to eq. (16).
For solution of the load flow we use a two step iterative method. In step one, the backward sweep, we calculate and sum up the phase load currents towards the feeding point (slack bus). In step two, the forward sweep, we calculate and sum up the voltage drops towards the end points of the network. We assume that the network is radially configured in normal operation(*), and use an efficient tree labeling technique in the forward and backward sweep procedures.
The solution starts with all voltages set equal to the given feeding point voltage. For each iteration the two step sweep procedures are performed, and the iterations proceed until the calculated voltage correction at the worst bus is below given threshold values for the real and imaginary parts of the voltage.
(*) In our program for balanced load flows we use a compensation technique to handle meshes in the network. This is not yet included in this program.
Beside the load flow we also calculate fault currents for three phase, two phase and single phase (phase to neutral) faults. The fault currents are calculated as
I3ph = Vph /(ZE - ZÖ) (19)
I2ph = Vph-ph /(2(ZE - ZÖ)) (20)
Iph-n = Vph /(ZE - 2 ZNÖ+ZN) (21)
where
I3ph, I2ph and Iph-n are the three phase, the two phase and the phase to neutral fault currents, respectively
Vph and Vph-ph are the phase to ground and phase to phase voltages
ZE , ZÖ , ZN and ZNÖ are the resulting (from the faulted bus to the feeding point, including the feeding point fault impedance) self and mutual impedance of the phases and self and mutual impedance of the neutral, respectively.
Coincidence of load is considered by representing the bus load Sk = Pk + jQk as a random variable with mean , (Pk)mean , (Qk)mean , and standard deviation , δPk , δQk. The load is assumed to be normally distributed, so that
(Pk- (Pk)mean)/δPk = N(0,1)
(Qk- (Qk)mean)/δQk = N(0,1)
Although Pk and Qk are not known, a statement can be made as to maximum values (Pk)max , (Qk)max , given with some probability p not being exceeded.
(Pk)max = (Pk)mean+ ΔPk
(Qk)max = (Qk)mean+ ΔQk
ΔPk is obtained from the condition
Prob((Pk- (Pk)mean)/δPk < kp ) = p
ΔPk = kp δPk
where kp is obtained from a normal distribution table. ΔQk is obtained in the same manner.
In order to facilitate a convenient data input to the computer program we have assumed that ΔPk = kp δPk is specified by a factor Δk
ΔPk = Δk (Pk)max
where (Pk)max is the bus load value given as input. ΔQk is obtained in the corresponding way.
From these input values the mean and variance of the bus phase load currents are calculated. The mean and variance of the branch currents, an thus their maximum values, are then obtained in the backward sweep of the load flow by summing up separately the mean and the variance of the phase load currents. In the forward sweep the voltage drop in each branch is calculated from its maximum branch current.