1 © alexis kwasinski, 2012 introduction field excitation q synchronous generators input: mechanical...
TRANSCRIPT
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)
2 © Alexis Kwasinski, 2012
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)
3 © Alexis Kwasinski, 2012
• 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
4 © Alexis Kwasinski, 2012
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
5 © Alexis Kwasinski, 2012
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
6 © Alexis Kwasinski, 2012
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
( ) syn
dt
dt
• (Micro) Grid’s angular frequency
7 © 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 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
8 © Alexis Kwasinski, 2012
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).
0 0( )Pf f k P P 0 0( )QV V k Q Q
0f
f
P0P
0V
V
Q0Q
9 © Alexis Kwasinski, 2012
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
P
V
Q
10 © Alexis Kwasinski, 2012
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.
genf
Gf
f
P Q
V
GV
11 © Alexis Kwasinski, 2012
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.
2P1P
f
P
Operating frequency
Higher commanded frequencies
No load droop line
Higher power output
12 © Alexis Kwasinski, 2012
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.
13 © Alexis Kwasinski, 2012
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
14 © Alexis Kwasinski, 2012
DC microgrids (droop control)
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
15 © Alexis Kwasinski, 2012
Tertiary control
Secondary control
16 © Alexis Kwasinski, 2012
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
Grid interface converter
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)
DC microgrids (droop control)
Voltage range “to allow for power sharing and voltage regulation using droop control”
17 © Alexis Kwasinski, 2012
DC bus (360 to 400 V)
MICRO-TURBINEMICRO-
TURBINE
DC microgrids (droop control)
IL DC bus (360 to 400 V)
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
Voltage range “to allow for power sharing and voltage regulation using droop control”
18 © Alexis Kwasinski, 2012
MICRO-TURBINEMICRO-
TURBINE
DC microgrids (droop control)
IL DC bus (360 to 400 V)
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
Voltage range “to allow for power sharing and voltage regulation using droop control”
19 © Alexis Kwasinski, 2012
MICRO-TURBINEMICRO-
TURBINE
DC microgrids (droop control)
IL DC bus (360 to 400 V)
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
Voltage range “to allow for power sharing and voltage regulation using droop control”
20 © Alexis Kwasinski, 2012
MICRO-TURBINEMICRO-
TURBINE
Ig
GRID
GIC
DC microgrids (droop control)
IL DC bus (360 to 400 V)
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
Voltage range “to allow for power sharing and voltage regulation using droop control”
21 © Alexis Kwasinski, 2012
MICRO-TURBINEMICRO-
TURBINE
Ig
GRID
GIC
DC microgrids (droop control)
IL DC bus (360 to 400 V)
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
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)
Voltage range “to allow for power sharing and voltage regulation using droop control”
22 © Alexis Kwasinski, 2012
MICRO-TURBINEMICRO-
TURBINE
Ig
GRID
GIC
DC microgrids (droop control)
IL DC bus (360 to 400 V)
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 is light, extra power being generated by the
microturbines can be injected back to the grid (see slide # 18)
Voltage range “to allow for power sharing and voltage regulation using droop control”
23 © Alexis Kwasinski, 2012
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
Grid interface converter
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
Primary control is combined with a secondary control to compensate voltage deviations
MICRO-TURBINE
MICRO-TURBINE
DC microgrids (droop control)
24 © Alexis Kwasinski, 2012
DC microgrids (droop control)
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
Primary control is combined with a secondary control to compensate voltage deviations
IL DC bus (380 V) LOAD
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
MICRO-TURBINE
MICRO-TURBINE
Nominal
Adjusted with δvref
25 © Alexis Kwasinski, 2012
VDC bus [V]
0
400
390
380
370
360
DC microgrids (droop control)
0IμT,1+IμT,2 = IL
IuT,1
IμT,2
IL DC bus (380 V) LOAD
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
IL DC bus (380 V) LOAD
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
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
26 © Alexis Kwasinski, 2012
MICRO-TURBINE
DC microgrids (droop control)
0IμT,1+IμT,2 = IL
IuT,1 IμT,2
VDC bus [V]
0
400
390
380
370
360
Notice same δvref for
both microturnines
IL DC bus (380 V) LOAD
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
IL DC bus (380 V) LOAD
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
MICRO-TURBINE
27 © Alexis Kwasinski, 2012
VDC bus [V]
0
400
390
380
370
360
MICRO-TURBINE
DC microgrids (droop control)
0
IuT,1 IμT,2
Notice lower δvref
than previous slide
IL DC bus (380 V) LOAD
Ig
GRID
GIC
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
IL DC bus (380 V) LOAD
Ig
GRID
GIC
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
MICRO-TURBINE
Ig
Ig+IμT,1+IμT,2 = IL
Now, δvref is changed in order to
control the current from or to the grid
28 © Alexis Kwasinski, 2012
VDC bus [V]
0
400
390
380
370
360
DC microgrids (droop control)
0
Ig
Ig+IμT,1+IμT,2 = IL
IuT,1IμT,2
IL DC bus (380 V) LOAD
Ig
GRID
GIC
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
IL DC bus (380 V) LOAD
Ig
GRID
GIC
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
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
29 © Alexis Kwasinski, 2012
VDC bus [V]
0
400
390
380
370
360
0
Ig
Ig+IμT,1+IμT,2 = IL
IuT,1 IμT,2
IL DC bus (380 V) LOAD
Ig
GRID
GIC
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
IL DC bus (380 V) LOAD
Ig
GRID
GIC
IuT IuT
Primary control is combined with a secondary control to compensate voltage deviations
MICRO-TURBINE
MICRO-TURBINE
DC microgrids (droop control)
30 © Alexis Kwasinski, 2012
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
Grid interface converter
Solar converter
Wind converter
Battery storage converter
Ibdsoc
Ig
GRID
GIC
DC microgrids (droop control)
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)
31 © Alexis Kwasinski, 2012
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
32 © Alexis Kwasinski, 2012
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 –”
DC microgrids (droop control)
33 © Alexis Kwasinski, 2012
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
Grid interface converter
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
DC microgrids (droop control)
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)
34 © Alexis Kwasinski, 2012
35 © Alexis Kwasinski, 2012
MICRO-TURBINE
DC bus (380 V)
VDC bus [V]
0
400
390
380
370
360
DC microgrids (droop control)
IgIuT,1
IμT,2
IL DC bus (380 V) LOAD
IuT IuT IL LOAD
Ig
DC GRID
IuT IuT
MICRO-TURBINE
0Ig+IμT,1+IμT,2 = IL
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)
36 © Alexis Kwasinski, 2012
DC bus (380 V)
MICRO-TURBINE
VDC bus [V]
0
400
390
380
370
360
0
Ig
Ig+IμT,1+IμT,2 = IL
IuT,1 IμT,2
IL DC bus (380 V) LOAD
Ig IuT IuT IL LOAD
Ig
DC GRID
IuT IuT
MICRO-TURBINE
DC microgrids (droop control)
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)
37 © Alexis Kwasinski, 2012
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.
38 © Alexis Kwasinski, 2012
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*