1 © alexis kwasinski, 2012 introduction field excitation q synchronous generators input: mechanical...

1 © Alexis Kwasinski, 2012

Introduction

Field Excitation Q

• 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)


Introduction

• Synchronous generators• Open circuit voltage:

S

de N

dt

4.44RMS d p SE K K fN

E

SE N

1R RN I

l

A

RI

Magneto-motive force(mmf)


• 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


Synchronous generators control

Field Excitation Q

• 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

http://baldevchaudhary.blogspot.com/2009/11/what-are-v-and-inverted-v-curves.html


Voltage and frequency control

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

. .sine

E V E Vp

X X

LOAD

• Assumption: during short circuits or load changes E is constant• V is the output (terminal) voltage

Electric power provided to the load

XQE V

E

, EQ p



• 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

( ) syn

dt

dt

• (Micro) Grid’s angular frequency



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

0 0( )Pf f k P P 0 0( )QV V k Q Q

0f

f

P0P

0V

V

Q0Q



• 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).

0 0( )Pf f k P P 0 0( )QV V k Q Q

0f

f

P0P

0V

V

Q0Q



• 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

P

V

Q



• 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.

genf

Gf

f

P Q

V

GV



• 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.

2P1P

f

P

Operating frequency

Higher commanded frequencies

No load droop line

Higher power output


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.


DC microgrids (droop control)

NOTE: Based on Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization”

• Consider a microturbine in a microgrid controlled by droop control.• Primary control:

• Secondary control (voltage deviation compensation)

,ref ref NL T Dv v I R , / 2ref NL n Rv v V ,maxR T DV I R

, ,( ) ( )ref p MG ref MG i MG ref MGv K v v K v v dt ,( )ref ref ref NL T Dv v v I R

Co

nv

ert

er

rati

ng

V [V]

0

IμT

400

390

380

370

360

Source Interface

vn

vref,NL

IμT,max

ΔVRδvref

Depends on microgrid bus voltage



NOTE: Based on Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization”

• Tertiary control (associated with a grid tie):

• Could be the input for a grid interface converter or the input for the distributed generation sources interface. The latter applies when there is a direct connection to a stiff grid because the stiff grid fixes the microgrid voltage. When there is a grid outage, the tertiary control is replaced by the secondary control. When the grid is present the secondary control is replaced by the tertiary control.

, ,( ) ( )ref p g ref g i g ref gv K I I K I I dt ,( )ref ref ref NL T Dv v v I R

V [V]

0

400

390

380

370

360

vref,NL

Co

nve

rter

ra

tin

g

Co

nve

rter

ra

tin

g

IgIg,max-Ig,max

Grid interface converter

δvref

Depends on current to or from the grid


Tertiary control

Secondary control


IL DC bus (360 to 400 V)

MICRO-TURBINE

LOAD

Ig

GRID

GIC

IμT

Cu

rren

t L

imit

Co

nve

rter

rat

ing

“Power” demand

Co

nve

rter

rat

ing

V [V]

0

400

390

380

370

360

V [V]

0 IμT


Microturbine

Cu

rren

t L

imit

V [V]

Microturbine

0 IμT

MICRO-TURBINE

IμT

Set by the utility company

Droop slope (virtual dc output

resistance)


Voltage range “to allow for power sharing and voltage regulation using droop control”


DC bus (360 to 400 V)

MICRO-TURBINEMICRO-

TURBINE



MICRO-TURBINE

LOAD

IuT

MICRO-TURBINE

IμT IL LOAD

IuT,1 IμT,2

VDC bus [V]

0

400

390

380

370

360

0IμT,1+IμT,2 = IL

IuT,1 IμT,2

DC bus voltage



MICRO-TURBINEMICRO-

TURBINE



MICRO-TURBINE

LOAD

IuT

MICRO-TURBINE

IμT IL DC bus (360 to 400 V) LOAD

IuT,1 IμT,2

VDC bus [V]

0

400

390

380

370

360

0IμT,1+IμT,2 = IL

IuT,1

IμT,2

When the load increases, current is shared between the two microturbines with the one

with the highest capacity providing more current to the load



MICRO-TURBINEMICRO-

TURBINE



MICRO-TURBINE

LOAD

IuT

MICRO-TURBINE

IμT IL DC bus (360 to 400 V) LOAD

IuT,1 IμT,2

VDC bus [V]

0

400

390

380

370

360

0IμT,1+IμT,2 = IL

IuT,1 IμT,2

As the load increases, the voltage drops so current output from the microturbines can

increase. Still, the microturbine with the highest capacity providing more current to the load



MICRO-TURBINEMICRO-

TURBINE

Ig

GRID

GIC



MICRO-TURBINE

LOAD

Ig

GRID

GIC

IuT

MICRO-TURBINE

IμTIg

GRID

GIC

IL DC bus (360 to 400 V) LOAD

Ig

GRID

GIC

IuT,1 IμT,2

VDC bus [V]

0

400

390

380

370

360

0

Ig

Ig+IμT,1+IμT,2 = IL

IuT,1 IμT,2

When the load increases even further the grid needs to provide the extra current in

order to prevent voltage collapse



MICRO-TURBINEMICRO-

TURBINE

Ig

GRID

GIC



MICRO-TURBINE

LOAD

Ig

GRID

GIC

IuT

MICRO-TURBINE

IμTIg

GRID

GIC


Ig

GRID

GIC

IuT,1 IμT,2

VDC bus [V]

0

400

390

380

370

360

0

Ig


IuT,1 IμT,2

Current from the grid can be used to reduce the current from the microturbines and

increase the dc bus voltage (see the voltage in the case with the same load in slide #19)



MICRO-TURBINEMICRO-

TURBINE

Ig

GRID

GIC



MICRO-TURBINE

LOAD

Ig

GRID

GIC

IuT

MICRO-TURBINE

IμTIg

GRID

GIC


Ig

GRID

GIC

IuT,1 IμT,2

VDC bus [V]

0

400

390

380

370

360

0

Ig


IuT,1

IμT,2

When the load is light, extra power being generated by the

microturbines can be injected back to the grid (see slide # 18)



IL DC bus (380 V)

MICRO-TURBINE

LOAD

Ig

GRID

GIC

IuT

MICRO-TURBINE

IuT

Primary control is combined with a secondary control to compensate voltage deviations

Cu

rren

t L

imit

Co

nve

rter

rat

ing

Co

nve

rter

rat

ing

V [V]

0

400

390

380

370

360

V [V]

0 IμT


Microturbine

Cu

rren

t L

imit

V [V]

Microturbine

0 IμT

Now, vref,NL can

be adjusted with

a δvref

Now, vref,NL can be adjusted with a δvref

IL DC bus (380 V)

MICRO-TURBINE

LOAD

Ig

GRID

GIC

IuT IuT


MICRO-TURBINE

MICRO-TURBINE




VDC bus [V]

0

400

390

380

370

360

0IμT,1+IμT,2 = IL

IuT,1 IμT,2

IL DC bus (380 V) LOAD

IuT IuT



IuT IuT


MICRO-TURBINE

MICRO-TURBINE

Nominal

Adjusted with δvref


VDC bus [V]

0

400

390

380

370

360


0IμT,1+IμT,2 = IL

IuT,1

IμT,2


IuT IuT



IuT IuT


MICRO-TURBINE

MICRO-TURBINE

Notice that the currents are the same than in the case with no secondary control (slide #18)

but now the voltage is kept at 380 V


MICRO-TURBINE


0IμT,1+IμT,2 = IL

IuT,1 IμT,2

VDC bus [V]

0

400

390

380

370

360

Notice same δvref for

both microturnines


IuT IuT



IuT IuT


MICRO-TURBINE


VDC bus [V]

0

400

390

380

370

360

MICRO-TURBINE


0

IuT,1 IμT,2

Notice lower δvref

than previous slide


Ig

GRID

GIC

IuT IuT



Ig

GRID

GIC

IuT IuT


MICRO-TURBINE

Ig


Now, δvref is changed in order to

control the current from or to the grid


VDC bus [V]

0

400

390

380

370

360


0

Ig


IuT,1IμT,2


Ig

GRID

GIC

IuT IuT



Ig

GRID

GIC

IuT IuT


MICRO-TURBINE

MICRO-TURBINE

Secondary control can be used to optimize efficiency but when optimizing efficiency the controller may not do a proportional load sharing because the load sharing condition of a given source may not be its optimal operating point


VDC bus [V]

0

400

390

380

370

360

0

Ig


IuT,1 IμT,2


Ig

GRID

GIC

IuT IuT



Ig

GRID

GIC

IuT IuT


MICRO-TURBINE

MICRO-TURBINE



IwIs Ib

IL DC bus (360 – 400 V)

SOLARARRAY

WINDTURBINE

ENERGYSTORAGE

LOAD

Op

erat

ing

ran

ge

Co

nve

rter

rat

ing

Act

ual

M

PP

T

Co

nve

rter

rat

ing

Act

ual

M

PP

T

Co

nve

rter

rat

ing

“Power” demand

Co

nve

rter

rat

ing

V [V]

0 Ig 0

400

390

380

370

360

Is

V [V] V [V]V [V]

00 IbIw

Ibcsoc


Solar converter

Wind converter

Battery storage converter

Ibdsoc

Ig

GRID

GIC


NOTE: Slide prepared by Prof. Dushan Boroyevich from VT

Paper: Boroyevich et al “Future Electronic Power Distribution Systems – A contemplative view –”

Voltage range “to allow for power sharing and voltage regulation using the droop control”

Set by the utility company

Droop slope (virtual dc output

resistance)


DC microgrids (droop control)• In the presence of constant-power loads, regulators in source converters

cannot use PI controllers. From a static perspective, regulators designed for constant-power loads will make the source converter output characteristic to look like MPP trackers.

• Battery interfaces have different characteristic depending on the state of charge of the batteries. For example, at the float voltage, the battery may take no current (if the state of charge is 100 %) or may take some current if the state of charge is less than 100 %. Droop controllers without secondary controls cannot be used if batteries are directly connected to the microgrid main bus.

Op

erat

ing

ran

ge

Co

nve

rter

rat

ing

Constant Power Output

0IμT

V [V] V [V]

0 Ib

Ibcsoc

Microturbine with Constant Power Load

Battery storage converter

Ibdsoc


VDC bus [V]

0

400

390

380

370

360

Iw Is

0Iw+Is= IL0= IL

Iw IsIg

Iw+Is+Ig = IL

IgIw Is

Iw+Is+Ig+Ib = IL

Iw Is IgIb

IL DC bus 360 – 400 V

Is

SOLARARRAY

Iw

WINDTURBINE

Ib

ENERGYSTORAGE

LOAD

Ig

GRID

GIC

Iw+Is+Ig = IL

Iw IsIb

Iw+Is+Ib = IL

NOTE: Slide prepared by Prof. Dushan Boroyevich from VT

Paper: Boroyevich et al “Future Electronic Power Distribution Systems – A contemplative view –”



MICRO-TURBINEMICRO-

TURBINE

DC bus (380 V)IL

DC bus (380 V)

MICRO-TURBINE

LOAD

Ig

DC GRID

IuT

MICRO-TURBINE

IuT

Cu

rren

t L

imit

V [V]

0

400

390

380

370

360

V [V]

0 IμT


Microturbine

Cu

rren

t L

imit

V [V]

Microturbine

0 IμT

With a stiff grid there is no limit

to Ig

Ig is regulated by adjusting δvref

IL LOAD

IuT IuT

MICRO-TURBINE


Voltage is kept fixed by the stiff grid so no voltage regulation is necessary (but it is not possible to have batteries directly connected to the main bus)


MICRO-TURBINE

DC bus (380 V)

VDC bus [V]

0

400

390

380

370

360


IgIuT,1

IμT,2


IuT IuT IL LOAD

Ig

DC GRID

IuT IuT

MICRO-TURBINE

0Ig+IμT,1+IμT,2 = IL



DC bus (380 V)

MICRO-TURBINE

VDC bus [V]

0

400

390

380

370

360

0

Ig


IuT,1 IμT,2


Ig IuT IuT IL LOAD

Ig

DC GRID

IuT IuT

MICRO-TURBINE




AC microgrids revisited (droop control)• Sources with a dc output or an ac output with a frequency different from

that of the microgrid main bus need to use an inverter to be integrated into an ac microgrid. When implementing droop control, the P-ω and Q-E droop regulators are used to emulate the inertia of an ac machine.

• Issues when implementing conventional droop control in ac systems with inverters:– Droop current-sharing methods are affected by harmonic content created by

non-linear loads. These issues can be solved by distorting the voltage signal intentionally which leads to further issues.

– Frequency is dependent on load levels in the same way that voltage levels depend on load levels. Also, frequency goals for two inverters with different capacity may be different. Frequency deviations dependant on load levels may lead to loss of synchronization when attempting to connect the microgrid directly to a main grid. Hence, it is only applicable to islanded operation and makes transition into grid connected operation complicated.

– In islanded mode there is both frequency and voltage deviations leading to tradeoffs inherent to droop control in islanded mode.

• Secondary controls have been proposed in order to solve these issues without the need for communication links.


NOTE: Figure from Guerrero et al “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization”

Now tertiary control depends on real and

reactive power flow from or to the grid

Now secondary control depends on microgrid

bus voltage and frequency

* ( )( *)

* ( )( *)P

Q

G s P P

E E G s Q Q

- GP(s) and GQ(s) represent PI or P controllers.

- ω*, E*, P* and Q* are reference signals, so when P=P*, ω=ω* and when Q=Q*, E=E*

1 © alexis kwasinski, 2012 introduction field excitation q synchronous generators input: mechanical...

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