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ChE 391, Spring 2012

Power Systems Control

Introduction

• Control variables in dc power systems • Voltage

(

) 

• Control variables in ac power systems: • Voltage amplitude • Phase: (angular) frequency and angle 

cos(  

) • Phasors • Used to represent ac signals in single-frequency systems through a fixed vector in the complex plane.

Imaginary

 Real(

Ve j



V e

)





V Real

2 © Alexis Kwasinski, 2012

Introduction

• Power in ac systems • Instantaneous power:  

cos(  

 

2  cos( 

 

Constant part

)  

 

)  • 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.



2 cos( 

 

) 



V RMS I RMS I

2 cos( 

 

) © Alexis Kwasinski, 2012 

 

 

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).



V RMS I RMS

4 e.g. in an inductor:

 0



2 sin(90) 

(  2 

2 2 2 

Introduction

• Power in ac systems • Complex power • Notice that

 1 2 Real(

* ) ) ) ) )  • and that 1 2 Real     



 

I I I I I

      1 Real 2

 1 2 Imaginary(

* ) ) ) ) )  1 2 Imaginary     





I I I I I

      1 2 Imaginary • So a magnitude called complex power

is defined as

I I I I j j j j Q > 0 (inductive load) Q = 0 (resistive load) I I I

( ( ( ) ) )

Q < 0 (capacitive load)

• Power factor (in power systems with one frequency) is defined as • It provides an idea of how efficient is the process of using (and generating) electrical power in ac circuits: © Alexis Kwasinski, 2012 5

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) 6 Field Excitation

Introduction

• Synchronous generators • Open circuit voltage:



N S d



dt E



N S

 

E RMS

 4.44

K K fN d p S

   1 

l A N I R R E

Magneto-motive force (mmf) 7

I R

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.

Synchronous generators control

• Relationship between reactive power and field excitation http://baldevchaudhary.blogspot.co

m/2009/11/what-are-v-and inverted-v-curves.html

• 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 9 © Alexis Kwasinski, 2012 Field Excitation

Voltage and frequency control

• The simplified equivalent circuit for a generator and its output equation is:

LOAD 10 • Assumption: during short circuits or load changes

is • constant

is the output (terminal) voltage

p e



sin  

 Electric power provided to the load

XQ E

Voltage and frequency control

• It can be found that

  

 

syn

• Generator’s angular frequency • Grid’s angular frequency • Ideally, the electrical power equals the mechanical input power. The generator’s frequency depends dynamically on

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. © Alexis Kwasinski, 2012

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



0  



0 )



0  

(  0 )

f V f

0 12

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

f f

changed (and thus, changes P and then f).



0  

k P P



0 )



0  

V Q

(  0 )

0 13

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

f V Q

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.

f gen f G f V G V

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 16

2 © Alexis Kwasinski, 2012 No load droop line

Stability

• From mechanics

J d

2 

m dt

2 



Moment of inertia angular mechanical electrical acceleration torque torque • If a synchronous reference frame is considered then 

 

 

Mechanical equivalent of its Synchronous speed electrical homologous variable • Swing equation: 2



syn



2 

2 



where “p.u.” indicates per unit and



 ( )

 0.5

 2

S rated p



 , 

   

poles x m

2 17 © Alexis Kwasinski, 2012

Stability

• Equal area criterion: Assume that the mechanical power suddenly increases.

4) Because of rotor inertia increases up to here 2) The rotor accelerates

p e



p m

3) The rotor decelerates

p e



p m

1) Initial condition 5) After oscillating,

δ(t)

comes to a rest at 

  1

p e



sin  • The equal area criterion says that  2   3

= A



generator continues to accelerate.

• Sudden changes in

p m

are not common. But changes in

p e

do happen.

Stability

• Equal area criterion during faults a most critical case: a fault.

Both areas are equal

p e



p m

4) Because of  increases up to here

p e



sin  1) Initial condition

p e



p m

2) During the fault

p e

= 0 3) Fault is cleared here δ(t) will oscillate until losses and the load damp oscillations and  2   3    0

p e



p m

generator continues to accelerate.

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.

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).

Summer day Winter day

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)

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.

One grid or many grids?

•

US: The same nominal frequency but 3 main grids

•

Japan: Two different nominal frequencies and 3 grids

0.1Hz

Examples

Slow Frequency Variation Wednesday, November 7, 2007, 4:15 PM Texas 8 minutes

0.16Hz

Examples

Large Generator Trip Tuesday, November 13, 2007, 4:19 PM Texas 8 minutes

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.

0.10Hz

Examples

Multiple Generator Trips Saturday, August 25, 2007, 3:32 AM California 8 minutes

Examples

Onset of Rotating Blackout Monday, April 17, 2006, 4pm (Unusually hot day, and many generators out for maintenance) Texas

0.2Hz

Generator Trip Insufficient Spinning Reserve Generator Trip Voluntary load shedding begins 8 minutes Stage 1 of automatic load shedding (5%) kicks in at 59.7Hz

Slide 1

Transcript Slide 1

ChE 391, Spring 2012

Power Systems Control

Introduction

Introduction

Introduction

Introduction

Introduction

Introduction

Synchronous generators control

Synchronous generators control

Voltage and frequency control

Voltage and frequency control

  

Voltage and frequency control

Voltage and frequency control

Voltage and frequency control

Voltage and frequency control

Voltage and frequency control

Stability

Stability

Stability

A brief summary

Some additional comments

Some additional comments

One grid or many grids?

Examples

Examples

Examples

Examples

Examples

Directory