Overview
•
Homework #2: Posted tonight and due next Monday
•
Review
–
Power Factor Correction
•
Today
–
Node Equations
–
Three-phase power
1
Lyles College of Engineering, Fresno State
Dr. K. McBee

Review - Example 2.4
How do we solve?
Identify the current VARS
2
Lyles College of Engineering, Fresno State
Dr. K. McBee
p.f. angle

Review - Example 2.4
b) Identify the added load
3
Lyles College of Engineering, Fresno State
Dr. K. McBee

Review
•
Real Power, Complex Power, Apparent Power
•
Power and Impedance Triangle
•
Power Factor Corrections
4
Lyles College of Engineering, Fresno State
Dr. K. McBee

Review
- PowerWorld
•
A software designed for assisting engineers in performing “
Power System
Simulations
”
•
An electric grid is too large to build a laboratory model to examine how
fluctuations in load and generation will affect the power system
•
Power engineers rely upon simulation tools to
–
Design upgrades
–
Evaluate system voltage (ANSI Standard C84.1
–
voltage limits)
–
Evaluate system stability
–
Recreate failure events
•
Software example
5
Lyles College of Engineering, Fresno State
Dr. K. McBee

Power Grid is a network
•
How do we analyze a large system consisting of numerous lines, nodes, and
buses?
•
How do we model a system?
•
Powerflow software is useful in modeling entire system, but how to engineers
add to the model when changes occur?
6
Lyles College of Engineering, Fresno State
Dr. K. McBee

Power System Analysis
•
Picture of Denver
–
distribution system
7
Lyles College of Engineering, Fresno State
Dr. K. McBee

Power System Analysis
•
Picture of Denver
8
Lyles College of Engineering, Fresno State
Dr. K. McBee

Power System Analysis
•
Picture of Denver
- with transmittion lines
9
Lyles College of Engineering, Fresno State
Dr. K. McBee

Network Equations
10
Lyles College of Engineering, Fresno State
Dr. K. McBee

Network Equations
•
Circuit operating in sinusoidal-steady
–
state, Kirchhoff’s current and voltage law
still apply to phasors
•
Many times a network (grid) is analyzed as
complete system, instead of analyzing a
single quantity
•
Transmission systems can consists of
hundreds of nodes, which limits simple
solutions
•
A system is modelled by connection to
buses (or nodes)
11
Lyles College of Engineering, Fresno State
Dr. K. McBee
4 Bus Example

Node Analysis Review
Node
v
1
Node
v
2
12
𝑖
1
= 𝑖
2
+ 𝑖
3
𝑖
3
= 𝑖
4
+ 𝑖
5
Lyles College of Engineering, Fresno State
Dr. K. McBee

Node
v
1
13
10v − 𝑣
1
1Ω
=
𝑣
1
4Ω
+
𝑣
1
− 𝑣
2
3Ω
1.58𝑣
1
− 0.33𝑣
2
= 10
𝑖
1
= 𝑖
2
+ 𝑖
3
Lyles College of Engineering, Fresno State
Dr. K. McBee

14
𝑣
1
=
7.33v
𝑣
2
=
4.77v
1.58𝑣
1
− 0.33𝑣
2
= 10
−0.33𝑣
1
+ 1.03𝑣
2
= 2.5
Lyles College of Engineering, Fresno State
Dr. K. McBee

Network Equations
•
For system with over hundreds of nodes, computer simulations are formulated
from nodal equations, which are systematically applied to circuits
•
Assumptions
–
Sinusoidal
–
Source voltages
represented by phasors
–
Circuit impedances are measured in Ohms
15
Lyles College of Engineering, Fresno State
Dr. K. McBee

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- Fall '17
- QUTAB GHULAM