0. ECE 476 POWER SYSTEM ANALYSIS
Lecture 3
Three Phase, Power System Operation
Professor Tom Overbye
Department of Electrical and Computer Engineering

1. Reading and Homework For lecture 3 please be reading Chapters 1 and 2
For lectures 4 through 6 please be reading Chapter 4
we will not be covering sections 4.7, 4.11, and 4.12 in detail
HW 1 is 2.7, 12, 21, 26; due Thursday 9/4

2. Balanced 3 Phase () Systems
A balanced 3 phase () system has
three voltage sources with equal magnitude, but with an angle shift of 120
equal loads on each phase
equal impedance on the lines connecting the generators to the loads
Bulk power systems are almost exclusively 3
Single phase is used primarily only in low voltage, low power settings, such as residential and some commercial

3. Balanced 3 -- No Neutral Current

4. Advantages of 3 Power
Can transmit more power for same amount of wire (twice as much as single phase)
Torque produced by 3 machines is constrant
Three phase machines use less material for same power rating
Three phase machines start more easily than single phase machines

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

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

7. 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

8. Delta Connection
Ica Ic
Iab
Ibc Ia Ib

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

10. Three Phase Example, cont’d

11. Delta-Wye Transformation

12. Delta-Wye Transformation Proof

13. Delta-Wye Transformation, cont’d

14. Three Phase Transmission Line

15. 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

16. 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.

17. 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.

18. 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

19. Per Phase Example, cont’d

20. Per Phase Example, cont’d

21. Per Phase Example, cont’d

22. Per Phase Example, cont’d

23. 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

24. 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).

25. 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

26. 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.

27. Basic Power Control
Opening 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 we can indirectly change this flow.

28. 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.

29. Overloaded Transmission Line

30. 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).

31. 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

32. Area Control Error (ACE)
The area control error is the difference between the actual flow out of an area, and the scheduled flow.
Ideally the ACE should always be zero.
Because the load is constantly changing, each utility must constantly change its generation to “chase” the ACE.

33. 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.

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

35. Generator Costs
There are many fixed and variable costs associated with power system operation.
The major variable cost is associated with generation.
Cost to generate a MWh can vary widely.
For some types of units (such as hydro and nuclear) it is difficult to quantify.
For thermal units it is much easier. These costs will be discussed later in the course.

36. Economic Dispatch
Economic dispatch (ED) determines the least cost dispatch of generation for an area.
For a lossless system, the ED occurs when all the generators have equal marginal costs. IC1(PG,1) = IC2(PG,2) = … = ICm(PG,m)

37. Power Transactions
Power transactions are contracts between areas to do power transactions.
Contracts can be for any amount of time at any price for any amount of power.
Scheduled power transactions are implemented by modifying the area ACE: ACE = Pactual,tie-flow - Psched

38. 100 MW Transaction Scheduled 100 MW Transaction from Left to Right
Net tie-line
flow is now
100 MW

39. Security Constrained ED
Transmission constraints often limit system economics.
Such limits required a constrained dispatch in order to maintain system security.
In three bus case the generation at bus 3 must be constrained to avoid overloading the line from bus 2 to bus 3.

40. Security Constrained Dispatch
Dispatch is no longer optimal due to need to keep line
from bus 2 to bus 3 from overloading

41. Multi-Area Operation
If Areas have direct interconnections, then they may directly transact up to the capacity of their tie-lines.
Actual power flows through the entire network according to the impedance of the transmission lines.
Flow through other areas is known as “parallel path” or “loop flows.”

42. Seven Bus Case: One-line
System has
three areas
Area top
has five
buses
Area left
has one
bus
Area right has one
bus

43. Seven Bus Case: Area View
Actual
flow
between
areas
System has
40 MW of
“Loop Flow”
Scheduled
flow
Loop flow can result in higher losses

44. Seven Bus - Loop Flow? Note that Top’s Losses have increased from
7.09MW to
9.44 MW
Transaction has actually decreased
the loop flow
100 MW Transaction
between Left and Right

45. Pricing Electricity
Cost to supply electricity to bus is called the locational marginal price (LMP)
Presently some electric makets post LMPs on the web
In an ideal electricity market with no transmission limitations the LMPs are equal
Transmission constraints can segment a market, resulting in differing LMP
Determination of LMPs requires the solution on an Optimal Power Flow (OPF)

46. 3 BUS LMPS - OVERLOAD IGNORED
Gen 2’s
cost
is $12
per
MWh
Gen 1’s
cost
is $10
per
MWh
Line from Bus 1 to Bus 3 is over-loaded; all buses have same marginal cost

47. LINE OVERLOAD ENFORCED
Line from 1 to 3 is no longer overloaded, but now
the marginal cost of electricity at 3 is $14 / MWh