Transcript Class Notes

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Cyber Physical Power Systems
Fall 2015
Week #1
© A. Kwasinski, 2015
Cyber-physical systems
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• From NSF:
• Cyber-physical systems (CPS) are engineered systems that are built from,
and depend upon, the seamless integration of computational algorithms
and physical components.
• In this course the cyber-physical system under consideration is built by
combining power and communications infrastructures (physical components)
through integrated sensing, data management and control (implicit
computational algorithms).
© A. Kwasinski, 2015
Historical Perspective
Competing technologies for electrification in 1880s:
• Edison:
• dc.
• Relatively small power plants (e.g. Pearl Street Station).
• No voltage transformation.
• Short distribution loops – No transmission
• Loads were incandescent lamps and possibly dc motors (traction).
Pearl Street Station:
6 “Jumbo” 100 kW, 110 V
generators
“Eyewitness to dc history” Lobenstein, R.W. Sulzberger, C.
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History
Competing technologies for electrification in 1880s:
•Tesla:
• ac
• Large power plants (e.g. Niagara Falls)
• Voltage transformation.
• Transmission of electricity over relatively long distances
• Loads were incandescent lamps and induction motors.
Niagara Falls historic power plant:
38 x 65,000 kVA, 23 kV, 3-phase
generatods
http://spiff.rit.edu/classes/phys213/lectures/niagara/niagara.html
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Power Grids Topology
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• Divided among the following parts
Generation
Distribution /
consumption
Transmission
Generation
Generation
Distribution /
consumption
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Power Grids Topology
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• Often standard grid configurations are used based on IEEE case studies.
IEEE 14 bus
case
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Generation
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• Electric power is generated at power stations.
• Generated power = load + losses
• Electric power generators are classified between base and peaking units.
Wind + PV
Peaking units
Natural gas, liquid fuels
Hydroelectric
Base units
Coal
Nuclear
© A. Kwasinski, 2015
Generation
• Peaking units:
• The tend to be used to follow the load.
• Most of them are fueled by natural gas but some units using liquid fuels
are also used.
• They tend to have a relatively faster response (their power output can be
adjusted relatively fast) and they tend to come online and offline relatively
often.
• Their power output is in the range of a few 100s MW to a very few 1000s
MW.
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Generation
• Coal fired power plants:
• Equipped with base generation units
• They operate continuously at a constant
output.
• Power stations rating could reach a few
1000s MW.
• They tend to have a slow response
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Generation
• Nuclear power plants:
• Equipped with base generation units
• They operate continuously at a constant output.
• Power stations rating is typically of a few 1000s MW.
• They tend to have a slow response
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Transmission
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• High Voltage: from 69 kV to 800 kV ac and more. Few dc lines are also found.
• Power Capacity of each line: from 50 to 1,000 MW
• Carry power long distances from buses
of a substation to buses in
another substation.
• Low power losses
• Passive portion of a grid
• Generally in a mesh configuration
with some redundancy
© A. Kwasinski, 2015
Distribution
• Primary distribution (feeders and laterals) voltage levels: 12 – 34 kV ac
(medium voltage)
• Secondary distribution: 480 V – 120 V ac (low voltage)
• Power capacity for each circuit 10 – 40 MW
• Passive grid.
• Spans shorter distances than the transmission
portion. Distribution circuits have relatively
higher losses than transmission lines.
• Generally in a radial configuration from a substation.
• Typically, no redundancy
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Consumers
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• Generally classified among:
• Residential
• Industrial
• Commercial
• Each type of consumer group tend to have a different demand profile that may
change depending on the seasons.
• Electric meters represent the border between electric utilities and consumers.
• Some consumers are now adding local electric power generation.
© A. Kwasinski, 2015
Substations
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• Divide transmission from
distribution and generation
(substations are highlighted in red in
the figure on the left).
• Transformers are a main
equipment found at substations.
• Circuit breakers are also another
key component found at
substations.
• Actuation and sensing equipment
is also found at substations.
• Capacitors and inductors can also
be found at substations.
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Substations
Layout examples:
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Substations
Another layout example and transformers
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Substations
Circuit breakers.
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Substations
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Sensing and actuation components (a lot more about this throughout this
course).
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Dispatch Center
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• Centralized location.
• Responsible for monitoring power flow and coordinating operations so
demand and generation are match in an economically optimal way. That is,
from a stability perspective demand (plus losses) needs to equal generation but
from an operational perspective, such match needs to be achieve in an
economically optimal way.
Source: Scientific
American
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Introduction
• Control variables in dc power systems
• Voltage
v (t )  V
• Control variables in ac power systems:
• Voltage amplitude
• Phase: (angular) frequency and angle
v(t )  V cos(t  V )
• Phasors
• Used to represent ac signals in single-frequency systems through
a fixed vector in the complex plane.
Imaginary
v(t )  Real(Ve jV e jt )
V
V  V V
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V
Real
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Introduction
• Power in ac systems
• Instantaneous power:
p(t )  v(t )i(t )  V cos(t  V ) I cos(t   I )
p(t )  v(t )i(t ) 
VI
cos(V   I )  cos(2t  V   I )
2
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.
P
VI
V I
cos(V   I ) 
cos(V   I )
2
2 2
P  VRMS I RMS cos( )
© A. Kwasinski, 2015
V   I  
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Introduction
• Power in ac systems
• Complex power
• Notice that
P



1
1
1
Real(VI* )  Real VI V   I  Real VI 
2
2
2

and that
1
1
1
Q  Imaginary(VI* )  Imaginary VI V   I  Imaginary VI  
2
2
2
• So a magnitude called complex power S is defined as

S  VI*  VRMS I RMS (cos   j sin  )
2
S  I RMS
( R  jX )

Q > 0 (inductive load)
Q = 0 (resistive load)
Q < 0 (capacitive load)
• Power factor (in power systems with one frequency) is defined as
• It provides an idea of how efficient is the
P
P
p. f .  cos   
process of using (and generating) electrical
S
P2  Q2
power in ac circuits:
© A. Kwasinski, 2015
Introduction
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• 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).
Q  VRMS I RMS sin( )
e.g. in an inductor:
P0
VI
I ( L) I LI 2 2
Q  sin(90) 

2
2
2 T
© A. Kwasinski, 2015
Power flow along lines
• Consider the following example of a generator on the left connected to
the rest of the grid through a line.
• Assumptions:
• The rest of the grid is “stiff” as a result of many large interconnected
generators with a combined large inertia. When it is “stiff” the voltage
at the rest of the grid side cannot be changed. Since the combined
power output of the generators of the rest of the grid is much more
than that of the generator on the left, then it is as if the rest of the grid
acts as an ideal infinite power source. The generator on the left is
considered to be a “real” one with an internal impedance Zs. The
interconnecting line has an impedance ZL. Usually XL>>RL
© A. Kwasinski, 2015
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Power flow along lines
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• Output real and reactive power of an inverter (or any source) equal
PSL 
VG E  RSL cos   X SL sin    VG2  RSL
RSL 2  X SL 2
QSL 
VG E  X SL cos   RSL sin    VG2  X SL
RSL 2  X SL 2
• In conventional power grids XL>>RL, and in generators XS>>RS. Also δ is
also usually small, so
PSL, X
VG E sin  VG E


X SL
X SL
QSL , X 
VG E  VG2 
X SL
– Hence, real power flow is dependent on the angle difference
between the two ends and reactive power is dependent on
the voltage differences between the two ends
© A. Kwasinski, 2015
Power flow along lines
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• Consider now the following example of a small 4-bus grid.
• Important information:
• Parameters: Line impedances (includes transformer
impedances).
• State: bus voltages, real and reactive powers provided at each
bus (conventionally, a generated power at the bus is positive and
a consumed power by loads at the bus is negative)
© A. Kwasinski, 2015
Power flow along lines
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• Notice that in reality generators output power and maximum power
that can be transmitted through lines are constrained. Grid operators
need to consider these constrains and economical aspects to decide
how much power to generate at each generator.
• Using the previous relationships the power flow along lines and
voltages in buses can be calculated from:
where Pk and Qk are the real and reactive powers provided at a bus
k, and
if k  j (Upper case:
 ( gkj  jbkj )
admittance matrix

1
N
elements
Ykj 
 Gkj  jBkj   g  jb 
g

jb
if
k

j



k
kj
kj
Zkj
Lower case:
 k
j 1
line admittance
j k

components)
(Bus voltages)
Vk  Vk k
© A. Kwasinski, 2015
Power flow along lines
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• Considering once again X/R ratios much higher than 1, small angle
differences, and per unit relative voltage magnitudes at each bus
close to 1, the previous equations can be simplified to the dc power
flow equations
Pk  VkV j  Bkj (k   j )     Bkj (k   j ) 
N
N
j 1
j k
j 1
j k
Qk  V b  Vk bkj Vk  V j   V   bkj Vk  V j 
N
2
k k
N
2
k
j 1
j k
j 1
j k
• Then, the power flow along lines is given by
Pkj  Bkj ( k   j )
Qk  bkjVk Vk  V j 
© A. Kwasinski, 2015
Power flow along lines
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• To find the power flow along lines we need to calculate:
Pkj  Bkj ( k   j )
• To calculate the above equation we need to solve
Pk    Bkj ( k   j ) 
N
j 1
j k
• This is an undetermined system of equations (the matrix is
singular) then, the voltage (magnitude and angle) at a bus (called
slack or swing bus) is set (usually a relative per unit voltage of 1 with
an angle of 0). As a result, the equation for the slack bus replaced
by this set voltage value and the real and reactive power at this bus
are now unknown.
• Other knows and unknows are:
• In a PQ (load) bus: P and Q are known, voltage is unknown
• In a PV (generator) bus: P and V are known, reactive power
and voltage angle are unknown.
© A. Kwasinski, 2015
Power flow along lines
• Important conclusions:
• P relates to angle differences and Q relates to voltage differences.
• System operators need to balance demand and generation in an
economically optimal way.
• To achieve their objective system operators need to know the state of
the system (i.e. know voltages and power flow).
•To know voltages at buses and power flow along lines system
operators need to compute an algorithm that solves a system of
equation (notice that a real power systems may have thousands of
buses).
• To solve such system of equations operators need to know system
parameters (e.g. line impedances) and demand levels (i.e. need to
measure voltages and currents).
• Notice that all basic components of a cyber-physical system are
mentioned: algorithms, physical components, computation and
sensing… However, power grids are cyber-physical system with
basic capabilities and limited cyber-physical integration.
© A. Kwasinski, 2015
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Electric Power Generation Concepts
• 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
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Electric Power Generation Concepts
• Synchronous generators
• Open circuit voltage:
e  NS
d
dt
ERMS  4.44 K d K p fN S 
E  N S 

1
NR IR
l
A
E
Magneto-motive force
(mmf)
IR
© A. Kwasinski, 2015
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Electric Power Generation Concepts
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• 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.
© A. Kwasinski, 2015
Electric Power Generation Concepts
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• Relationship between reactive power and field excitation
http://baldevchaudhary.blogspot.co
m/2009/11/what-are-v-andinverted-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
Field
Excitation
© A. Kwasinski, 2015
Q
Electric Power Generation Concepts
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• As we saw before, the simplified equivalent circuit for a generator and
its output equation is:
Q, pE
Rest of the grid
• Assumption: the rest of the grid is “stiff” so during short
circuits or load changes E is constant
• V is the output (terminal) voltage
pe 
E.V
E.V
sin  

X
X
Electric power provided to the rest of the grid
XQ
E V 
E
© A. Kwasinski, 2015
Electric Power Generation Concepts
• It can be found that
d
  (t )  syn
dt
• Generator’s angular frequency
(rotor’s speed)
• Grid’s angular frequency
• Output frequency of a generator is proportional to its rotor angular
velocity.
• 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 (ideally it equals the 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.
© A. Kwasinski, 2015
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Voltage and frequency control
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• Matching generation and demand (plus losses) is essential for power
grid stability. If generation is less than demand, frequency drops. If
demand is less than generation, frequency increases.
• Additionally, voltage needs to be controlled within a given range
• To achieve these goals in an economically optimal way, power grids
control system is structured in mainly 3-levels.
• Primary control: Local control using locally measured variables.
Main goal: adjust electrical power output (i.e. adjust mechanical
power input) to compensate for mismatches between generation and
demand.
• Secondary control: Local control using locally measured variables.
Main goal: frequency (or voltage in some cases) regulation to a given
nominal set point.
• Tertiary control: Performed at a central location. Main goal:
determine operation nominal set points in order for optimal operation.
• Primary control is often implemented through droop controllers.
© A. Kwasinski, 2015
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Voltage and frequency control
• Droop control
• It is an autonomous approach for controlling frequency and voltage
amplitude of the generator.
• It takes advantage that real power controls frequency and that
reactive power controls voltage. A droop controller is based on the
following static laws to adjust a new set point with respect to a
nominal one
f  f0  kP ( P  P0 )
Drooped
frequency
f
V  V0  kQ (Q  Q0 )
Nominal
frequency
V
f0
V0
P0
P
© A. Kwasinski, 2015
Q0
Q
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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).
V  V0  kQ (Q  Q0 )
f  f0  kP ( P  P0 )
V
f
f0
V0
P0
P
© A. Kwasinski, 2015
Q0
Q
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Voltage and frequency control
• Operation of a generator connected to a large “stiff” 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
V
f
P
© A. Kwasinski, 2015
Q
Voltage and frequency control
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• Operator of a generator connected to a large “stiff” 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.
V
f
f gen
VG
fG
P
© A. Kwasinski, 2015
Q
Voltage and frequency control
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• Real grids are not ideally “stiff” so frequency can change.
• In large grids with many generators with a high inertia and normal load
changes frequency changes relatively slowly. However, frequency
changes faster than changes in generators rotational speed (because of
the relatively high inertia). So,
• when the load changes, the
grid frequency changes, too.
• when the frequency changes,
the primary droop controller
adjusts the generator output
to match generation and
demand based on the new
frequency.
• If there is a sufficiently large mismatch between generation and
demand that cannot be compensated with a droop controller,
stability can be lost and the system may collapse.
© A. Kwasinski, 2015
Voltage and frequency control
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• Real grids are not ideally “stiff” so frequency can change.
• Once the frequency deviates from its nominal value due to a mismatch
between generation and demand, it is desirable to bring it to its nominal
value. This is accomplished by the secondary controller:
© A. Kwasinski, 2015
Voltage and frequency control
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• Grid-connected operation of a generator
• After the generator is paralleled to the grid then its power output
can be adjusted in order to minimize overall system cost for
generating electricity.
• That is, it is desirable to generate more power from the least costly
units.
• At a central location, the grid operator determines how much power
to generate at each unit based on load estimates.
• The, droop lines are adjusted to change the generator power
output
Adjusted droop lines
f
Higher power output
Operating frequency
No load droop line
P1
P2
© A. Kwasinski, 2015
P
Additional comments
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• In conventional ac grids, 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.
• The same approach described with real power output can be
used to adjust reactive power based on voltage regulation.
•
Droop control is an effective decentralized controller.
•
Optimal operation set points need to be transmitted from the
central operations center to the generators.
© A. Kwasinski, 2015
Additional comments
• Operation and monitoring of electric power grids is usually
performed with a SCADA (supervisory control and data
acquisition) system. At a basic level a SCADA system
includes:
• Remote terminals
• Central processing unit
• Data acquisition (sensing) units
• Telemetry
• Human interfaces (usually computers).
• SCADA systems require communication links but, usually,
these are dedicated links separate from the public
communication networks used by people for their every day
lives.
© A. Kwasinski, 2015
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Additional comments
• Operating a power grids involves dealing with a broad time
scale range:
Source: NERC
© A. Kwasinski, 2015