Recap: Power Flow Analysis
•  For power systems, we know
–  The system topology (the circuit diagram)
–  The impedance of each line, Z-1 = Y = G + jB
–  The load at each load bus, S = P + jQ
–  The capability of each generator, P & |V|
–  The reference bus (|V| and ∠θ=0)
The Power Flow & Optimal
Power Flow Problems
Smith College, EGR 325
Sept 19, 2014
•  We want to know
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–  The output of each generator (S = P + jQ)
–  The voltage at each bus (V = V∠θ)
–  The power flow on each line (Pflow)
Power System Diagrams
Real Power Flow Equations
•  How many equations and how many
unknowns?
•  One-line diagram
Pi = Σ Vi Vk (Gik cosθ ik + Bik sin θ ik ) = PGi − PDi
16.8 MW
16.0 MW
6.4 MVR
0.0 MVR
44.94 kV
Qi = Σ Vi Vk (Gik sin θ ik − Bik cosθ ik ) = QGi − QDi
16.8 MW
6.4 MVR
•  Numerical methods (iteration)
– Reference (Slack) bus
– Solution might not converge!
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Generators
are shown as
circles
40.0 kV
16.0 MW
16.0 MVR
Transmission lines
are shown as a single
line
16.0 MVR
Arrows are
used to
show loads
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New England 39-Bus Test System
To Obtain Simulator Yourself
http://www.powerworld.com/gloversarmaoverbye
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Power World Simulator – Open Case
Finding
Power
World
Simulator
Open PowerWorld Simulator and Click
the file menu to get the drop down
menu and dialog to open a case
(now version 18)
in …
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Power World Simulator – Open Case
Open PowerWorld Simulator and Click
the file menu to get the drop down
menu and dialog to open a case
Or… double-click PowerWorld Case
in Windows Explorer
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To zoom so you can see things
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Small PowerWorld Simulator Case
Load with
green
arrows
indicating
amount
of MW
flow
Bus 2
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20 MW
-4 MVR
Bus 1
1.00 PU
204 MW
102 MVR
1.00 PU
106 MW
0 MVR
150 MW AGC ON
116 MVR AVR ON
-14 MW
4 MVR
-34 MW
10 MVR
34 MW
-10 MVR
Home Area
Used
to control
output of
generator
-20 MW
4 MVR
100 MW
Note the
power
balance at
each bus
14 MW
-4 MVR
1.00 PU
Bus 3
102 MW
51 MVR
150 MW AGC ON
37 MVR AVR ON
Direction of arrow is used to indicate
direction of real power (MW) flow
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Three Bus Case on AGC
Bus 2
-40 MW
8 MVR
40 MW
-8 MVR
Bus 1
1.00 PU
266 MW
133 MVR
1.00 PU
101 MW
5 MVR
150 MW AGC ON
166 MVR AVR ON
-39 MW
12 MVR
-77 MW
25 MVR
78 MW
-21 MVR
Home Area
Generation
is automatically
changed to match
change in load
To run the Power World Simulator – Using a One-line Diagram
Bus 3
100 MW
39 MW
-11 MVR
1.00 PU
133 MW
67 MVR
250 MW AGC ON
34 MVR AVR ON
To view the power system data: Select Network
Simulate the system operation by
selecting the ‘Tools’ tab and
clicking the green ‘Go’ arrow
Switch to ‘Run’ mode
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TO EDIT: Make sure you are in edit mode, and
select the correct table in “Network” to edit data
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Self-Quiz Questions
1)  Define the physical significance of
§  S, P, Q. What are the units of each?
2)  Define, compare and contrast
§  Energy and power; include units
3)  If you were a system operator, what questions/problems
would you use a power flow program to answer/solve?
4)  What input data do you need to run a power flow model?
5)  What results/output do you get from a power flow model?
… and how do you use these results?
6)  What is the slack bus and what role does it serve in the
model? in the actual system?
7)  How do we know if the model converges or not? What
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does it mean if it does not converge?
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Power Flow: Iterative Solution
•  We assume we know the following at
each bus (input data to program)
–  Generator buses: P and |V|
–  Load buses: P and Q
–  Slack bus: |V| and <θv
–  …Along with the system topology
–  How buses are connected
–  Impedance (as admittance) of each
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line
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Power World Simulator
Power Flow: Iterative Solution
•  In order to know P, Q, V and <θv at each
bus, we solve the power flow eq’ns
Pi = Σ Vi Vk (Gik cosθ ik + Bik sin θ ik ) = PGi − PDi
•  Open PowerWorld
•  Do practice problems (next slides)
•  Then, open the homework and begin it
Qi = Σ Vi Vk (Gik sin θ ik − Bik cosθ ik ) = QGi − QDi
•  Which we cannot solve in closed form
à We must iterate
à Computer programs do this for us
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Power World Simulator
Power World Simulator
•  Open Example2_3.pwb
•  Change the ‘kvar’ generation at the
Load to minimize the kvar
generation at the Generator
•  Change both Load kW and kVAr
•  What is the physical phenomenon
being simulated?
•  Open Example1_3.pwb
•  Change the Load MW at each load
•  Watch the changes in line flows and
bus voltages
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– What happens that you expect?
– What happens that you don’t expect?
– Why?
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Summary
•  Third look at the power flow problem
•  Thinking about numerical methods
–  Iterating to find a solution
–  Significance of lack of convergence
–  Reference (slack) bus
•  Introduction to the power flow program
PowerWorld
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