1. ChE 391, Spring 2012
Power Systems Control

2. Introduction Control variables in dc power systems Voltage
Control variables in ac power systems:
Voltage amplitude
Phase: (angular) frequency and angle
Phasors
Used to represent ac signals in single-frequency systems through a fixed vector in the complex plane.

3. Introduction Power in ac systems Instantaneous power:
Real power: related with irreversible energy exchanges (work or dissipated heat). That is, real power represents energy that leaves or enters the electrical circuit under analysis per unit of time, so the energy exchanges occur between the circuit and its environment.
Constant part

4. Introduction Power in ac systems
Reactive power: related with reversible energy exchanges. That is, reactive power represents energy that is exchanged between the circuit and electric or magnetic fields in a cyclic way. During half of the cycle energy from the sources are used to build electric fields (charge capacitors) or magnetic fields (charge machines) and during the other half cycle exactly the same energy is returned to the source(s).
e.g. in an inductor:

5. Introduction Power in ac systems Complex power Notice that and that
So a magnitude called complex power S is defined as
Power factor (in power systems with one frequency) is defined as
Q > 0 (inductive load)
Q = 0 (resistive load)
Q < 0 (capacitive load)
It provides an idea of how efficient is the process of using (and generating) electrical power in ac circuits:

6. Introduction Synchronous generators Input:
Mechanical power applied to the rotor shaft
Field excitation to create a magnetic field constant in magnitude and that rotates with the rotor.
Output:
P and Q (electric signal with a given frequency for v and i)
Field Excitation Q

7. Introduction Synchronous generators Open circuit voltage:
Magneto-motive force
(mmf)

8. Synchronous generators control
Effect of varying field excitation in synchronous generators:
When loaded there are two sources of excitation:
ac current in armature (stator)
dc current in field winding (rotor)
If the field current is enough to generate the necessary mmf, then no magnetizing current is necessary in the armature and the generator operates at unity power factor (Q = 0).
If the field current is not enough to generate the necessary mmf, then the armature needs to provide the additional mmf through a magnetizing current. Hence, it operates at an inductive power factor and it is said to be underexcited.
If the field current is more than enough to generate the necessary mmf, then the armature needs to provide an opposing mmf through a magnetizing current of opposing phase. Hence, it operates at a capacitive power factor and it is said to be overexcited.

9. Synchronous generators control
Relationship between reactive power and field excitation
The frequency depends on the rotor’s
speed. So frequency is controlled
through the mechanical power.
Pmec is increased to increase f
Pmec is decreased to decrease f
Field Excitation Q

10. Voltage and frequency control
The simplified equivalent circuit for a generator and its output equation is:
LOAD
Assumption: during short circuits or load changes E is constant
V is the output (terminal) voltage
Electric power provided to the load

11. Voltage and frequency control
It can be found that
Ideally, the electrical power equals the mechanical input power. The generator’s frequency depends dynamically on δ which, in turn, depends on the electrical power (=input mechanical power). So by changing the mechanical power, we can dynamically change the frequency.
Likewise, the reactive power controls the output voltage of the generator. When the reactive power increases the output voltage decreases.
Generator’s angular frequency
Grid’s angular frequency

12. Voltage and frequency control
Droop control
It is an autonomous approach for controlling frequency and voltage amplitude of the generator and, eventually, the grid.
It takes advantage that real power controls frequency and that reactive power controls voltage

13. Voltage and frequency control
Droop control
Then a simple (e.g. PI) controller can be implemented. It considers a reference voltage and a reference frequency:
If the output voltage is different, the field excitation is changed (and, thus, changes Q and then V).
If the frequency is different, the prime mover torque is changed (and thus, changes P and then f).

14. Voltage and frequency control
Operation of a generator connected to a large grid
A large grid is seen as an infinite power bus. That is, it is like a generator in which
Changes in real power do not cause changes in frequency
Changes in reactive power do not originate changes in voltage
Its droop control curves are horizontal lines

15. Voltage and frequency control
Operator of a generator connected to a large grid
When connected to the grid, the voltage amplitude and frequency is set by the grid.
In order to synchronize the oncoming generator, its frequency needs to be slightly higher than that of the grid, but all other variables need to be the same.

16. Higher commanded frequencies
Voltage and frequency control
Operator of a generator connected to a large grid
After the generator is paralleled to the grid then its output frequency and voltage will remain fixed and equal to the grid’s frequency and voltage, respectively.
Output power is controlled by attempting a change in frequency by controlling the prime mover’s torque. By “commanding” a decrease in frequency, the output power will increase.
A similar approach is followed with reactive power control, by controlling field excitation in an attempt to change output voltage.
Higher commanded frequencies
Higher power output
Operating frequency
No load droop line

17. Mechanical equivalent of its electrical homologous variable
Stability
From mechanics
If a synchronous reference frame is considered then
Swing equation:
where “p.u.” indicates per unit and
So if decreases and if increases
Moment of inertia
electrical torque
angular acceleration
mechanical torque
Mechanical equivalent of its electrical homologous variable
Synchronous speed

18. Stability
Equal area criterion: Assume that the mechanical power suddenly increases.
The equal area criterion says that A1 = A2
If the generator looses stability because and the generator continues to accelerate.
Sudden changes in pm are not common. But changes in pe do happen.
4) Because of rotor inertia increases up to here
3) The rotor decelerates
2) The rotor accelerates
5) After oscillating, δ(t) comes to a rest at
1) Initial condition

19. 4) Because of rotor inertia increases up to here
Stability
Equal area criterion during faults a most critical case: a fault.
After reaching δ(t) will oscillate until losses and the load damp oscillations and
If the generator looses stability because and the generator continues to accelerate.
4) Because of rotor inertia increases up to here
Both areas are equal
1) Initial condition
3) Fault is cleared here
2) During the fault pe = 0

20. A brief summary
In ac systems, large machine inertia helps to maintain stability.
Since frequency needs to be regulated at a precise value, imbalances between electric and mechanical power may make the frequency to change. In order to avoid this issue, mechanical power applied to the generator rotor must follow load changes. If the mechanical power cannot follow the load alone (e.g. due to machine’s inertia), energy storage must be used to compensate for the difference. This is a situation often found in microgrids.
Reactive power is used to regulate voltage.
Droop control is an effective autonomous controller.

21. Some additional comments
Large machine’s inertia contributes to system stability but makes it difficult to follow fast changing loads.
At every time instant the goal is power generation = load + losses.
Hence a combination of generation technologies are used to achieve good stability performance while still be able to follow the load.
A dispatch center solves the power flow equations and commands the generation units so generation = load + losses in an optimally economical and technically feasible way (economic dispatch problem).
Peaking plants (gas turbines and some diesel
Load following plants (gas turbines and some hydro and nuclear)
Base load plants (coal-fired and most nuclear plants)

22. Some additional comments
Although not explicitly mentioned before, the analysis considered some implicit assumptions:
single phase equivalent for the circuits
No harmonics
Linear loads and components (e.g. no saturation in machines)
Ideal lumped components
The fast average frequency is the same everywhere in the grid.
The voltage changes along the grid. Hence, then voltage is compensated everywhere along the grid with capacitors and voltage compensators (autotransformers) and other means (e.g. static VAR compensators).
Although it seems that control of a dc grid is simpler, the need for power electronic interfaces create nonlinear instantaneous constant-power loads that have a de-stabilizing effect on the dc grid. Moreover, autonomous controllers are more difficult to implement because the only static existing variable is bus voltages.

23. One grid or many grids?
US: The same nominal frequency but 3 main grids
Japan: Two different
nominal frequencies and
3 grids
Tie
Source: NPR
Source: Tosaka

24. Slow Frequency Variation Wednesday, November 7, 2007, 4:15 PM
Examples
Slow Frequency Variation
Wednesday, November 7, 2007, 4:15 PM
Texas
0.1Hz
8 minutes

25. Examples Large Generator Trip Tuesday, November 13, 2007, 4:19 PM
Texas
0.16Hz
8 minutes

26. Unusual Wind-Related Event?
Examples
Unusual Wind-Related Event?
Sunday, May 13, 2007, 3:11am
8 minutes
Intermittent (non-dispatchable) generation sources, such as wind generators or PV modules) may have a severe negative effect on grid’s stability if they are not properly controlled.

27. Multiple Generator Trips
Examples
Multiple Generator Trips
Saturday, August 25, 2007, 3:32 AM
California
0.10Hz
8 minutes

28. Examples Onset of Rotating Blackout Monday, April 17, 2006, 4pm
(Unusually hot day, and many generators out for maintenance)
Texas
0.2Hz
Insufficient
Spinning
Reserve
Generator
Trip
Generator
Trip
Voluntary load shedding begins
8 minutes
Stage 1 of automatic load shedding (5%) kicks in at 59.7Hz