EE544 Distribution 1

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EE544 Distribution 1

• Distribution Feeder Analysis

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Feeder Analysis

• Explore modeling and performance of a feeder
  Section with various Assumptions
• How to look at performance
• Voltage drop
• Unbalance
• Distribution Power Flow
• Analysis of a complete feeder

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Feeder Analysis

• Examples will use following Data

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Feeder Analysis
a b c n
a b c n
z
Feeder
z
z
VRan VR VRbn VRcn
VSan VS VSbn VScn
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Feeder Analysis-Phase Domain
Convenient way to get ll voltage VabVan-Vbn
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Feeder Analysis-Sequence Domain
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Feeder Analysis-Sequence Domain
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Feeder Analysis-Sequence Domain
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Feeder Analysis Capacitance Included
Insignificant Difference because feeder is lt 1mi
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Feeder Analysis Power and Power Loss
Per phase loss may not be very intuitive Because
of mutual coupling between phase (per phase real
power loss can sometimes even be negative)
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Feeder Analysis Unbalance
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Feeder Analysis Constant KVA Load-Gauss
a 1 b 2 c 3 n 0
a 4 b 5 c 6 n 0
S
z
Feeder
z
z
VSan V1 VS VSbn V2 VScn
V3
VRan V4 VR VRbn V5
VRcn V6
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Feeder Analysis Constant KVA Load--Gauss
Conventional rules for Y - Positive( or
Negative or Zero) Sequence or single phase
network - No coupling between branches I Y V
V1,V2,V3 Node Voltages I1, I2, I3 Injected
Currents Z12, Z13, Z23 Line Series Impedance Y12,
Y23, Y13 Line shunt admittance (1/2 of Total
for Pi model)
Ykk sum of all admittances at node
k Yki -sum of admittances directly
between node k and i
V2 I2
I1 V1
Z12,Y12
2
1
Z13,Y13
Z23,Y23
3
V3 I3
I1 Y12Y131/Z121/Z13 -1/Z12 -1/Z13 V1
I2 -1/Z12
Y12Y231/Z121/Z23 -1/Z23 V2 I3
-1/Z13 -1/Z23 Y13Y231/Z131/Z23 V3
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Feeder Analysis Constant KVA Load--Gauss
Extended rules for Y - Lines(branches) modeled
by 3x3 or 4x4 impedance and admittance matrix -
No coupling between branches - remember there is
coupling within branch I Y V
V2 I2
I1 V1
Z12,Y12
2
1
Z13,Y13
Z23,Y23
3
Ykk sum of all admittance matrices at
node k Yki -sum of admittances matrices
directly between node k and i
V3 I3
1 a 2 b 3 c
I1 V1 I2
Y12Y13Z12-1Z13-1 -Z12-1 -Z13-1 V2 I3
V3 I4 V4 I5
-Z12-1
Y12Y23Z12-1Z23-1 -Z23-1 V5
I6 V6 I7


V7 I8 -Z13-1 -Z23-1 Y13Y23Z13-1Z23-1
V8 I9 V9
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Feeder Analysis Constant KVA Load--Gauss
Zohp-1Yohp/2 -Zohp-1 Y -Zohp-1
Zohp-1Yohp/2
a 1 b 2 c 3 n 0
a 4 b 5 c 6 n 0
S
z
Feeder
z
z
VSan V1 VS VSbn V2 VScn
V3
VRan V4 VR VRbn V5
VRcn V6
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Feeder Analysis Constant KVA Load--Gauss
Gauss Seidel Review A network with N buses can
be described by the admittance matrix(KCL)
equation I YV I is the N vector of
currents, V the N vector of voltages and Y is
the NxN admittance matrix Expanding row
k N Ik ? Ykm Vm m1 The
power injected into node k N Sk ? VkYkm Vm
m1 These Power Flow Equations
are an equivalent description of the system
Ik Vk Sk
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Feeder Analysis Constant KVA Load--Gauss
Gauss Seidel Review These Power Flow
Equations are nonlinear N Sk ? VkYkm Vm
m1 These can be solved using Newton
Raphson or Gauss Seidel The Gauss Seidel version
moves the unknown voltage to the left hand side
to create an iterative Equation N Vk (1/Ykk)
(Sk/Vk) - ?Ykm Vm m1
m?k We classify buses as slack load or generator
based on what is given and Iteratively solve the
equations. We guess Vk, k1,2..N and plug into
the RHS To get an updated value of Vk
Ik Vk Sk
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Feeder Analysis Constant KVA Load--Gauss
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Feeder Analysis Constant KVA Load--Gauss
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Feeder Analysis Constant KVA Load- Impedance
Matrix - Iterative
V Z I where Impedance matrix Z Y-1
Ik (Sk/Vk)
Start with imitial guess for V, Calculate I,
update V Repeat to convergence Without
connections to ground ( Source impedance, line
capacitance..) Y will be singular In this method
we model the impedance of the source and model
the source As a current source Is
Vs/Zs This means we add 1/ Zs to the the
diagonal term corresponding to the three source
nodes
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Feeder Analysis Constant KVA Load- Impedance
Matrix - Iterative
Given Source Voltage
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Feeder Analysis Constant KVA Load- Ladder
Radial systems - component model generalized
matrices VS A VR B Ir VR A VS B
IS IS C VR D IR IR C VS D IS
Zp
V2
V1
I2
I1
If capacitance ignored V1 I V2 Zp
I2 I1 0 V2 I I2 V2 I V1
-Zp I1 I2 0 V2 I I2 I is 3x3
Identity
Initial Guess V2 Find I2 I1I2 Find
V1 Set V1 to original Value Find V2
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Feeder Analysis Constant KVA Load- Ladder
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Feeder Analysis Constant KVA Load- Ladder
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Feeder Analysis Constant KVA Load

• Analysis Methods
• All three methods are in the Gauss-Seidel Class
• Newton-methods can also be applied
• Impedance Matrix Iterative /Newton
• Some Extra Operations ( Need feeder admittance
  matrix, Invert(Factor)
• System admittance matrix)
• Can handle Loops
• Generalize by setting up component admittance
  matrix ( easily done)
• Used in many commercial codes
• Ladder
• Excellent for radial
• Can adapt to loops
• Requires presorting of nodes to define
  forward/backward pass
• Generalize by setting up Generalized Matrices (
  ABCD parameter format
• See Kersting Text
• Used in many commercial codes