Download Dc Microgrids Stability

ECE 2795
Microgrid Concepts and Distributed
Generation Technologies
Spring 2015
Week #8
© A. Kwasinski, 2014
Microgrids architectures and
operation
• dc vs. ac
• The discussion refers to the system’s main bus. Remember the
discussion in the first class about Edison’s electric system.
•No frequency/phase control is necessary in dc microgrids.
• From a general point of view dc systems are simpler to control.
• Lack of a monitoring variable may complicate fault detection
and autonomous controls implementation.
• Since most distributed sources and energy storage devices have
an inherently dc output, dc architectures are a more “natural” option
for integration of such components.
• Most modern loads inherently require a dc input. Even the “most
classical” ac loads, induction motors, rely more on inherently dc
input variable speed drives (VSDs) to achieve a more efficient and
flexible operation.
© A. Kwasinski, 2014
Microgrids architectures and
operation
• dc vs. ac
• Availability: dc is several times more reliable than ac (NTT data
from 30,000 systems [H. Ikebe, “Power Systems for Telecommunications in the
IT Age,” in Proc. INTELEC 2003, pp. 1-8.])
• Efficiency:
• Efficiency gains in energy conversion interfaces makes dc
systems 5 % to 7 % more efficient than ac systems.
• dc powered VSDs are 5 % more efficient than equivalent ac
powered VSDs because the rectification stage is avoided.
• Dc systems tend to be more modular and scalable than ac systems
because dc converters are easier to control and to parallel.
• dc systems components tend to be more compact that equivalent
ac ones because of higher efficiency and for not being frequency
dependent.
© A. Kwasinski, 2014
Microgrids architectures and
operation
• dc vs. ac
• Modular design makes dc systems more flexible and easier to
expand, allowing for a more effective capital investment
management and a better planning of the entire facility power
installation.
• Well designed dc grids can achieve both hardware and operational
cost savings over equivalent ac systems.
• Power conditioning to improve quality tends to be simpler in dc
systems.
• Stability control tends to be simpler in dc systems.
© A. Kwasinski, 2014
Microgrids architectures and
operation
• Stability issues
• Stability issues are more prevalent in microgrids than in a large
electric grid because power and energy ratings are much lower.
• Analysis of stability issues in ac microgrids tend to follow the same
concepts than in the main grid:
• Voltage and frequency values need both to be regulated
through active and reactive power control.
• If sources are traditional generators with an ac output and
are connected directly without power electronic interfaces,
stability is controlled through the machine shaft’s torque and
speed control.
• In dc systems there is no reactive power interactions, which
seems to suggest that there are no stability issues. System
control seems to be oriented to voltage regulation only
© A. Kwasinski, 2014
Conventional (ac) datacenters
• Typical configuration:
•Total power consumption: > 5 MW (distribution at 208V ac)
© A. Kwasinski, 2014
Conventional (ac) datacenters
• Data centers represent a noticeable fast increasing load.
• Increasing power-related costs, likely to equal and exceed
information and communications technology equipment cost in the
near to mid-term future.
• Servers are a dc load
• 860 W of equivalent coal power is needed to power a 100 W load
© A. Kwasinski, 2014
New (dc) datacenters
• Use of 380 Vdc power distribution for:
• Fewer conversion stages (higher efficiency)
• Integration of local sources (and energy storage).
• Reduced cable size
© A. Kwasinski, 2014
Data centers efficiency dc vs. ac
• A 380Vdc power distribution standard is currently under study by the IEC
Brian Fortenbery and Dennis P. Symanski, GBPF, 2010
© A. Kwasinski, 2014
New distributed (dc) datacenters
• Many “small” distributed data centers powered locally and with a
coordinated operation
• Energy is used more effectively.
• Generation inefficiencies is energy that is not harvested (i.e.
converted), contrary to inefficiencies in conventional power plants
which represent power losses.
• Latency may be a problem
© A. Kwasinski, 2014
Utility dc distribution
Jonbok Bae, GBPF 2011
© A. Kwasinski, 2014
dc Homes
• dc in homes allows for a better integration of distributed
generation, energy storage and dc loads.
• With a variable speed drive air conditioners can be operated
continuously and, hence, more efficiently (about 50%)
WIND
GENERATOR
PV MODULES
LED LIGHTS (DC)
MAIN DC BUS
REFRIGERATOR (LOAD)
ENERGY STORAGE
ELECTRIC
VEHICLE
AIR CONDITIONER
FUEL CELL
© A. Kwasinski, 2014
EPA 430-F-97-028
ac microgrids stability
• Main goal: be able to maintain frequency and voltage levels within a
relatively tight ranges.
•Stability issues can be considered at various time scales:
• seconds to minutes (or more):
• Need to continuously balance load + losses and generation
with load and losses being unknown.
• Generation ramp rates
• This is a more challenging problem in microgrids due to the
reduced stiffness when operating in islanded mode. General
solutions involve the use of energy storage devices and/or load
management (e.g. load shedding).
• milliseconds to seconds:
• Mostly a power quality issue that without a quick correction
may usually lead to loss of stability
• < milliseconds:
• Usually originated in non-linear devices and loads.
© A. Kwasinski, 2014
ac microgrids stability
• Consider an ac microgrid with one ac generator and one load.
Consider also a stiff grid with X>>R.
• The simplified equivalent circuit for the generator and its output
equation is:
LOAD
E.V
pe 
sin 
X
Electric power provided to the load
Assumption: Infinite bus (simplifies the analysis
but not true for micro-grids).
Also during shorts or load changes E is constant
• From mechanics:
Moment of inertia
d 2 m
J
 Tm (t )  Te (t )
2
dt
angular
acceleration
mechanical
torque
© A. Kwasinski, 2014
electrical
torque
ac microgrids stability
• If a synchronous reference frame is considered then
 m (t )  synt   m
Mechanical equivalent of its
electrical homologous
variable
Synchronous speed
x
• Swing equation:
# poles
xm
2
d 2 (t )
 p.u (t )
 pm, p.u. (t )  pe, p.u (t )
2
syn
dt
2H
where “p.u.” indicates per unit and
H
0.5 J m2 ,syn
Srated
• So if pe  pm  (t ) decreases and if pe  pm
© A. Kwasinski, 2014
 (t ) increases
Stability
• Equal area criterion and analysis during faults or sudden load changes
(particularly load increase). Let’s see the most critical case: a fault
Both areas are
equal
pe  pm
4) Because of
rotor inertia  (t )
increases up to
here
pe 
1) Initial condition
E.V
sin 
X
pe  pm
3) Fault is
cleared here
2) During the
fault pe = 0
• After reaching  2 δ(t) will oscillate until losses and the load damp
oscillations and  (t )   0
• If  2   3 the generator looses stability because pe  pm and the
generator continues to accelerate.
© A. Kwasinski, 2014
ac microgrids stability
• In ac systems, real and reactive power needs to be
controlled to maintain system 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,
mechanical power applied to the generator rotor must follow
load changes. If mechanical power cannot follow load,
energy storage must be used to compensate for the
difference.
• Reactive power is used to regulate voltage.
• Some autonomous control strategies will be
discussed in a future class.
© A. Kwasinski, 2014
ac microgrids stability
• Let’s review some assumptions:
– Stiff grid.
– In cables X>>R.
• A stiff grid is a basic assumption for the application of the
equal area criterion. However, microgrids cannot be
generally considered a stiff grid.
• A basic approach to address stability issues related to lack of
stiffness is to add energy storage with a power electronic
interface with fast controllers.
• The amount of necessary stored energy is
Consumed electrical energy
in the time interval under
consideration
Maximum allowed
frequency excursion
Microgrid inertia constant
© A. Kwasinski, 2014
ac microgrids stability
• Assumption:
– In cables X>>R (implies long cables)
• But in microgrids
– In cables X<R (implies short cables)
Pout 
VG E  RSL cos   X SL sin    VG2  RSL
Qout 
RSL 2  X SL 2
VG E  X SL cos   RSL sin    VG2  X SL
RSL  X SL
2
2
© A. Kwasinski, 2014
Pout , X
V E
 G
X SL
Pout , R 
Qout , X 
VG E  VG2 
RSL
VG E  VG2 
X SL
Qout , R  
VG E
RSL
ac microgrids stability
• Equations on the right assume that the phase difference δ
between both voltages is small
Pout 
VG E  RSL cos   X SL sin    VG2  RSL
Qout 
RSL 2  X SL 2
VG E  X SL cos   RSL sin    VG2  X SL
RSL  X SL
2
2
Pout , X
V E
 G
X SL
Pout , R 
VG E  VG2 
RSL
Qout , X 
VG E  VG2 
X SL
Qout , R  
VG E
RSL
Most islanded microgrids
• Notice that conventional relationships between real power
and frequency and reactive power and voltage in power
grids are inverted for microgrids. This fact has important
implications in terms of stability and control.
• Loss of stability will be also observed in microgrids as
voltage deviations.
© A. Kwasinski, 2014
Microgrids architectures and
operation
• distributed and centralized architectures
• Power systems with distributed architecture have their power
distribution and conversion functions spread among converters and
the distribution is divided among two or more circuits.
• There are two basic structures in distributed architectures:
• Parallel structures are used when the design focuses on
improved availability.
• Cascade structures are used to improve point-of-load
regulation, reduce cost, and improve system efficiency. Hence,
they have at least two conversion stages among three or more
voltage levels.
Cascade structure
Parallel structure
© A. Kwasinski, 2014
Microgrids architectures and
operation
• distributed and centralized architectures
• The possibility of having different connection structures and
different conversion stages makes distributed architectures more
flexible than centralized architectures.
• Hence, distributed architectures are the natural choice in systems
requiring integration of a variety of energy sources with several
different loads.
• When power converters are modular, the distributed architecture
allows the system capacity to expand gradually as the load
increases over time.
• Thus, distributed architectures have lower financial costs than
equivalent centralized architectures.
© A. Kwasinski, 2014
Microgrids architectures and
operation
• distributed and centralized architectures
• Examples of distributed and centralized architectures can be found
in telecommunications power plants (remember that telephony grids
can be considered a low power dc grid).
Only (centralized)
bus bars
Centralized architecture
© A. Kwasinski, 2014
Microgrids architectures and
operation
• distributed and centralized architectures
• Examples of distributed and centralized architectures can be found
in telecommunications power plants (remember that telephony grids
can be considered a low power dc grid).
Each cabinet with its own
bus bars connected to its
own battery string and
loads. Then all cabinets’
bus bars are connected
Distributed architecture
© A. Kwasinski, 2014
Power architectures topologies
• Some examples of different power distribution architectures:
Radial
Ring
Ladder
(analogous to
breaker-and-ahalf or Double
breaker-double
bus substation
configurations)
© A. Kwasinski, 2014
Dc microgrids stability
• Stability issues (this problem is also observed with power electronicbased ac power distribution architectures but its analysis in ac is more
complicated and out of the scope of this course).
• Consider a cascade distributed architecture. The point-of-load
(POL) converter tightly regulates the output voltage on the actual
resistive load. If Vout is kept fixed regardless of the input voltage and
R does not change, then the power dissipated in the load resistance
PL is constant. If the POL converter is lossless its input power is
constant so it acts as a constant-power load with input voltage and
current related by
P
v(t )  L
i (t )
© A. Kwasinski, 2014
Dc Microgrids Stability
• In reality CPLs have the following form:
0

i (t )   PL
 v(t )

if v(t )  Vlim
if v(t )  Vlim
• For the analysis we will assume that Vlim is close to zero.
• Then the dynamic impedance is
Z 
P
dv(t )
 2 L 0
di (t )
i (t )
• Hence, CPLs introduce a destabilizing effect.
© A. Kwasinski, 2014
Dc Microgrids Stability
• Consider the following simplified system of a POL converter behaving
like a CPL and a buck converter regulating the main bus voltage that
equals the POL converter input.
• Consider also the following circuit parameters: E = 400 V, D = 0.5, C =
1 mF, L = 0.5 mH, PL = 5 kW (the POL converter and load resistance are
represented by this parameter).
• The system will behave in two possible ways depending the initial
conditions for the inductor current and capacitor voltage
© A. Kwasinski, 2014
Dc Microgrids Stability
• If the initial capacitor voltage is high enough the system’s state
variables may oscillate. If the initial capacitor voltage is low enough
and/or the power and inductance are also high enough and/or the
capacitance is low enough, the inductor current will take very high
values and the capacitor voltage will tend to zero.
iL(t)
iL(t)
vC(t)
vC(t)
vC(0) = 120 V
vC(0) = 50 V
© A. Kwasinski, 2014
Dc Microgrids Stability
• The phase portrait for a buck converter with a constant power load with
a fixed duty cycle looks like this:
- Approximate for the separatrix:
PL CvC2
iL 

( E  vC )
vC LPL
- Necessary but not sufficient
condition for oscillations:
P
d (t ) E  vC 1  PL
   iL  2L
L
C  vC
 vC
Buck LRC with a PL = 5 kW, E =
400 V, L = 0.5 mH, C = 1 mF, D
= 0.5.
• For all dc-dc converters it looks similar.
© A. Kwasinski, 2014
Dc Microgrids Stability
• Regulating the output with a PI controller yields bad results:
Simulation results for an ideal buck converter with a PI controller both for a 100 W
CPL (continuous trace) and a 2.25 Ω resistor (dashed trace); E = 24 V, L = 0.2 mH,
PL = 100 W, C = 470 μF.
© A. Kwasinski, 2014
Dc Microgrids Stability
• Model for a buck converter with a CPL:
 diL
 L dt  q (t )( E  RS iL )  (1  q (t ))(VD  iL RD )  iL RL  vC
,
 dv
PL vC
C
C
 iL  
dt
vC Ro

with iL  0, vC  
 Ri
2   
L

PL
1  Ri


CVo2 Ro C  L
 1
P  1
 L2 
0

R
C
LC
CV
o 
 o
© A. Kwasinski, 2014
Dc Microgrids Stability
• Linearization yields that in order to achieve a stable regulation point
two conservative conditions are:
C
1 
PL  Vo2  Ri  
Ro 
L
 1
1 
PL  V   
 Ri Ro 
2
o
(Predominant condition)
where Ri equals the sum of RSD, RD(1-D), and RL.
• Hence, stability improves if:
• L is lower
• C is higher
• PL is lower
• Ri is higher
• R0 is lower (higher ohmic load)
© A. Kwasinski, 2014
Dc Microgrids Stability
• Consider the following dc microgrid:
E1 = 400 V, E2 = 450 V, PL1 = 5 kW, PL3 = 10 kW, LLINE = 25 μH,
RLINE = 9 mΩ, CDCPL = 1 mF, and buck LRCs with L = 0.5 mH, C = 1 mF,
D1 = 0.5, and D2 = 0.45.
© A. Kwasinski, 2014
Dc Microgrids Stability
• With an open loop control (fixed duty cycles) the system shows again
important oscillations, well distant of the desired dc behavior.
© A. Kwasinski, 2014
Dc Microgrids Stability
• OPTION #1: add resistors in series with the circuit inductors or in
parallel with the circuit capacitors.
• Resistors damp the resonating
excess energy in the circuit
•This solution is very inefficient.
• A minimum resistive load is needed
1 Ohm resistor added in
parallel with the CPL
© A. Kwasinski, 2014
Dc Microgrids Stability
• OPTION #2: Add filters, particularly capacitors.
• Oscillations decrease with
increased capacitances
• Since the oscillation
frequency is in the order of
hundreds of hertz, increasing
capacitance is expensive.
•Large capacitors tend to be
unreliable.
60 mF capacitance placed at
the CPL input and at the buck
converters output.
© A. Kwasinski, 2014
Dc Microgrids Stability
• OPTION #3: Bulk energy storage (primarily batteries) directly
connected to the main bus.
• Telecommunications power systems
is a typical example of this solution.
• This solution tends to be expensive.
• This solution is more suitable for
energy systems. For power systems,
such as microgrids, bulk energy
storage is not well suited.
• Additional disadvantages in microgrids
are issues related with reliability, safety,
and protections when stacking several
battery cells in series to reach dc bus
voltages over 150 V. Inadequate cell
equalization is another disadvantage
(indirect connection does not work).
© A. Kwasinski, 2014
1 F ultracapacitor located at
the CPL input
Dc Microgrids Stability
• OPTION #4: Load shedding.
• As PL decreases the oscillation
amplitude also decreases.
.
• This solution is not suitable for
critical mission loads.
• This solution is equivalent to
load shedding in ac systems
PL3 dropping from 10 kW to
2.5 kW at t = 0.25 s
© A. Kwasinski, 2014
Dc Microgrids Stability
• OPTION #5: Linear controllers.
• Linear controllers refer to PID-type of controllers in which output voltage
regulation is achieved by creating a duty cycle signal by comparing the
measured output voltage with a reference voltage and then passing that
error signal through a PID-type controller.
• PD controllers can stabilize constant-power loads. The controller adds
damping without losses through virtual resistances embedded in the
controller gains.
• An additional integral action is used to provide line regulation and to
compensate for internal losses.
• In some situations (particularly with buck converters) a PI controller is
enough. But, in general, stability is not ensured.
•Advantages:
•Simple
•Cost effective
•Disadvantages:
•Stability is still not global
•Derivative term create noise susceptibility.
© A. Kwasinski, 2014
Dc Microgrids Stability
• OPTION #5: Linear controllers.
vB1(t)
• PI controller
• ki = 1
• kp = 0.1
vB2(t)
• With PI controllers stability
is not insured and results
are poor.
vB3(t)
© A. Kwasinski, 2014
Dc Microgrids Stability
• OPTION #5: Linear controllers.
vB1(t)
• PID controller
• ki = 1 10-3
• kd = 50 10-6
vB2(t)
• kP = 0.5
• Fast dynamics are
achieved thanks to the high
proportional gain. However,
this high gain can be
usually implemented only
in buck converters.
© A. Kwasinski, 2014
vB3(t)
Dc Microgrids Stability
• OPTION #5: Linear controllers.
vB1(t)
• PD controller
• kp = 0.5
• kd = 50 10-6
vB2(t)
• Fast dynamics are
achieved thanks to the high
proportional gain. However,
this high gain can be
usually implemented only
in buck converters.
© A. Kwasinski, 2014
vB3(t)
Dc Microgrids Stability
• OPTION #6: Geometric controls (boundary).
• Geometric controls (e.g. hysteresis controllers) are based on eventtriggered switching instead of time-dependent switching.
• With an hysteresis control, the output voltage (or inductor current) is
controlled to be between a band. Whenever the voltage (or inductor
current) crosses the band’s boundaries a switch action is triggered (switch
is closed or opened).
• Advantages:
• High performance (fast)
• Global stabilization
• Disadvantages:
• Complicated output regulation: analysis may require to determine the
trajectories. Overshoots caused by capacitances and inductances are
difficult to control
• Lack of a fixed switching frequency
© A. Kwasinski, 2014
Dc Microgrids Stability
• OPTION #6: Geometric controls
• A line with a negative slope achieves an stable regulating point for all
converters. Regulation is simple to implement.
Boost
Buck
Buck-boost
© A. Kwasinski, 2014
Dc Microgrids Stability
• OPTION #6: Geometric controls.
© A. Kwasinski, 2014
Protections
• Microgrids are more sensitive to power quality issues because of
reduced stiffness and the typical values found in line impedances.
• Faults need to be interrupt fast so that short circuits in a given circuit
do not cause:
• Significant voltage sags in neighboring circuits, and/or
• make the system to lose stability.
• To interrupt faults it is first necessary to detect faults quickly. However,
except in the case of dc microgrids with batteries directly connected to a
dc microgrid bus, fault currents are limited so they may be difficult to
distinguish from a high-load condition. Also, their limited value may be
too low to make protection devices to act quickly.
• Inrush currents (e.g. caused by capacitors) also create power quality
issues in dc microgrids but these tend to be issues that are easier to
solve than fault protection.
© A. Kwasinski, 2014
Protections
• Consider as an example the power distribution system of a full electric
ship (which can be considered as an islanded microgrid)
© A. Kwasinski, 2014
Protections
• Circuit protection: conventional approach based on switch gear. Issues:
• Coordination
• Fault current detection and interruption
© A. Kwasinski, 2014
Protections
• Circuit protection: based on power electronics or solid state circuit breaker.
© A. Kwasinski, 2014
Dc systems faults management
• In power electronic distributed architectures, faults may not be properly detected
because, without a significant amount of stored energy directly connected to the system
buses, short-circuit currents are limited to the converter maximum rated current plus the
transitory current delivered by the output capacitor.
• If the latter is not high enough, the protection device will not trip and the fault will not be
cleared.
• In this case, the converter will continue operation delivering the maximum rated current
but with an output voltage significantly lower than the nominal value.
• Consider the following situation
© A. Kwasinski, 2014
Dc systems faults management
• With C = 600 μF, the fault is not properly cleared and voltage collapse occurs for both
loads.
© A. Kwasinski, 2014
Dc systems faults management
• To avoid the situation described above, the converter output capacitance has to be
dimensioned to deliver enough energy to trip the protection element.
• One approach is to calculate the capacitance based on the maximum allowed
converter output voltage drop. However, this is a very conservative approach that often
leads to high capacitance values.
• Another option is to calculate the capacitance so that it can store at least enough
energy to trip the protection device, such as a fuse.
1
WC  Cvc2  WF
2
• Fuse-tripping process can be divided into two phases:
• pre-arcing
• Lasts for 90% of the entire process.
• During this phase, current flows through the fuse, which heats up.
• arcing
• the fuse-conducting element melts and an arc is generated between the
terminals. The arc resistance increases very rapidly, causing the current to drop
and the voltage to increase. Eventually the arc is extinguished. At this point, the
current is zero and the voltage equals the system voltage.
© A. Kwasinski, 2014
Dc systems faults management
• The energy during pre-arcing is
WF , pa 
1 2
I C , F RF 0.9TF
4
where TF is the total fault current clearing time, RF is the fuse resistance before melting,
and IC,F is the limiting case capacitor current during the fault.
IC,F equals the fault current less the sum of the converter current limit and other circuit
currents. For larger capacitances than the limit case, the converter current may not
reach the rated limit value, so IC,F might be slightly higher than in the limit case.
• .If a linear commutation is assumed, the portion of the arcing phase energy supplied by
the capacitor is
WF ,a 
1
I C , FVF 0.1TF
6
• Thus,
C
1 1 2
1

I
R
0.9
T

I
V
0.1
T
F
C ,F F
F 
 C,F F
VS2  2
3

© A. Kwasinski, 2014
Dc systems faults management
• With VS = VF = 50 V, IC,F = 135 A, RF = 1 mΩ, and considering a typical value for TF of
0.1 s, the minimum value of C is 900 μF. If the previous system is simulated with C =
1mF, then
• Ringing on R2 occurring when the fault is
cleared can be eliminated by adding a
decoupling capacitance next to R2
© A. Kwasinski, 2014
Dc systems faults management
• Additional simulation plots
© A. Kwasinski, 2014
Series faults in ac systems
• Series faults occur when a cable is severed or a circuit breaker is
opened, or a fuse is blown…. Then an arc is observed between the
two contacts where the circuit is being opened.
• The arc is interrupted when the current is close to zero.
• Due to cable inductances, voltage spikes are observed when the
arc reignites.
© A. Kwasinski, 2014
Series faults in ac systems
• Visually, arcs in ac series faults are not very intense
© A. Kwasinski, 2014
Series faults in dc systems
• In dc arcs last longer (because there are no zero crossings for the
current) but no voltage spikes are generated.
© A. Kwasinski, 2014
Series faults in dc systems
• Dc arcs last longer than ac ones, are much more intense and may
damage the contacts.
© A. Kwasinski, 2014
Solid state switches
• DC currents are more difficult to interrupt than equivalent ac currents when
using conventional switchgear (physical separation of contacts).
• Proposed solution: solid state circuit breakers.
• Solid state circuit breakers do not provide a physical disconnection, but such
disconnection can be implemented by adding a conventional disconnect
switch in series with the solid state circuit breaker. The conventional
disconnect switch acts after the solid state switch interrupts the current.
• Other issues with solid state circuit breakers:
• ON-conduction losses
• May fail as a short circuit (although conventional switches may also fail
in this way)…. Solution: redundancy
• For higher voltages, series connection of devices is necessary leading to
coordination issues (“perfect” on-off action) and over-sizing to prevent
device damage from excessive voltages during transients due to switching
lack of coordination.
• Advantages of solid state switches:
• Allow for many ON-OFF cycles.
• Contacts are not worn out (because there are no contacts).
• Act quickly.
© A. Kwasinski, 2014
Solid state switches
• Examples
ac SCR
ac IGBT (no
redundancy)
dc IGBT
© A. Kwasinski, 2014