0. ECE 476 Power System Analysis
Lecture 4: Three-Phase, Power System Operations
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign

1. Announcements Please read Chapter 4 HW 1 is due now
It does not need to be turned in, but will be covered by an in-class quiz on Sept 10
San Diego Gas & Electric is on campus for the ECE Career Fair on 9/9) (ARC Gym) and then for interviews on 9/10

2. Three-Phase - Wye Connection
There are two ways to connect 3 systems
Wye (Y)
Delta ()

3. Wye Connection Line Voltages
Van
Vcn
Vbn
Vab
Vca
Vbc
-Vbn
(α = 0 in this case)
Line-to-line
voltages are
also balanced

4. Wye Connection, cont’d
Define voltage/current across/through device to be phase voltage/current
Define voltage/current across/through lines to be line voltage/current

5. Delta Connection
Ica Ic
Iab
Ibc Ia Ib

6. Three-Phase Example
Assume a -connected load is supplied from a 3 kV (L-L) source with Z = 10020W

7. Three-Phase Example, cont’d

8. Delta-Wye Transformation

9. Delta-Wye Transformation Proof

10. Delta-Wye Transformation, cont’d

11. Three Phase Transmission Line

12. Per Phase Analysis
Per phase analysis allows analysis of balanced 3 systems with the same effort as for a single phase system
Balanced 3 Theorem: For a balanced 3 system with
All loads and sources Y connected
No mutual Inductance between phases

13. Per Phase Analysis, cont’d
Then
All neutrals are at the same potential
All phases are COMPLETELY decoupled
All system values are the same sequence as sources. The sequence order we’ve been using (phase b lags phase a and phase c lags phase a) is known as “positive” sequence; later in the course we’ll discuss negative and zero sequence systems.

14. Per Phase Analysis Procedure
To do per phase analysis
Convert all  load/sources to equivalent Y’s
Solve phase “a” independent of the other phases
Total system power S = 3 Va Ia*
If desired, phase “b” and “c” values can be determined by inspection (i.e., ±120° degree phase shifts)
If necessary, go back to original circuit to determine line-line values or internal  values.

15. Per Phase Example
Assume a 3, Y-connected generator with Van = 10 volts supplies a -connected load with Z = -j through a transmission line with impedance of j0.1 per phase. The load is also connected to a -connected generator with Va”b” = 10 through a second transmission line which also has an impedance of j0.1 per phase.
Find
1. The load voltage Va’b’
2. The total power supplied by each generator, SY and S

16. Per Phase Example, cont’d

17. Per Phase Example, cont’d

18. Per Phase Example, cont’d

19. Per Phase Example, cont’d

20. Power System Operations Overview
Goal is to provide an intuitive feel for power system operation
Emphasis will be on the impact of the transmission system
Introduce basic power flow concepts through small system examples

21. Power System Basics
All power systems have three major components: Generation, Load and Transmission/Distribution.
Generation: Creates electric power.
Load: Consumes electric power.
Transmission/Distribution: Transmits electric power from generation to load.
Lines/transformers operating at voltages above 100 kV are usually called the transmission system. The transmission system is usually networked.
Lines/transformers operating at voltages below 100 kV are usually called the distribution system (radial).

22. Simulation of the Eastern Interconnect

23. Small PowerWorld Simulator Case
Load with
green
arrows
indicating
amount
of MW
flow
Note the
power
balance at
each bus
Used
to control
output of
generator
Direction of arrow is used to indicate
direction of real power (MW) flow

24. Power Balance Constraints
Power flow refers to how the power is moving through the system.
At all times in the simulation the total power flowing into any bus MUST be zero!
This is know as Kirchhoff’s law. And it can not be repealed or modified.
Power is lost in the transmission system.

25. Basic Power Control
Opening or closing a circuit breaker causes the power flow to instantaneously(nearly) change.
No other way to directly control power flow in a transmission line.
By changing generation or load, or by switching other lines, we can indirectly change this flow.

26. Modeling Consideration – Change is Not Really Instantaneous!
The change isn’t really instantaneous because of propagation delays, which are near the speed of light; there also wave reflection issues
This will be addressed more in Chapters 5 and 13
Red is the vs end, green the v2 end

27. Transmission Line Limits
Power flow in transmission line is limited by heating considerations.
Losses (I2 R) can heat up the line, causing it to sag.
Each line has a limit; Simulator does not allow you to continually exceed this limit. Many utilities use winter/summer limits.

28. Overloaded Transmission Line

29. Interconnected Operation
Power systems are interconnected across large distances. For example most of North America east of the Rockies is one system, with most of Texas and Quebec being major exceptions
Individual utilities only own and operate a small portion of the system, which is referred to an operating area (or an area).

30. Operating Areas
Transmission lines that join two areas are known as tie-lines.
The net power out of an area is the sum of the flow on its tie-lines.
The flow out of an area is equal to total gen - total load - total losses = tie-flow

31. Area Control Error (ACE)
The area control error is the difference between the actual flow out of an area, and the scheduled flow.
There is also a frequency dependent component that we’ll address in Chapter 12
Ideally the ACE should always be zero.
Because the load is constantly changing, each utility must constantly change its generation to “chase” the ACE.

32. Automatic Generation Control
Most utilities use automatic generation control (AGC) to automatically change their generation to keep their ACE close to zero.
Usually the utility control center calculates ACE based upon tie-line flows; then the AGC module sends control signals out to the generators every couple seconds.

33. Three Bus Case on AGC Generation is automatically changed to match
change in load
Net tie flow is
close to zero

34. MISO Real-Time ACE
Previously individual utilities did their own ACE calculations; now we are part of MISO, which does one for the
region

35. MISO Real-Time ACE
MISO's real-time ACE is available online (along with lots of other data)