1 © a. kwasinski, 2015 cyber physical power systems fall 2015 week #1

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© A. Kwasinski, 2015

Cyber Physical Power Systems

Fall 2015

Week #1

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Cyber-physical systems

• 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).

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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).

“Eyewitness to dc history” Lobenstein, R.W. Sulzberger, C.

Pearl Street Station:6 “Jumbo” 100 kW, 110 Vgenerators

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HistoryCompeting 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.

http://spiff.rit.edu/classes/phys213/lectures/niagara/niagara.html

Niagara Falls historic power plant:38 x 65,000 kVA, 23 kV, 3-phase

generatods

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Power Grids Topology

• Divided among the following parts

Generation

Generation

Generation

Transmission

Distribution / consumption

Distribution / consumption

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Power Grids Topology

• Often standard grid configurations are used based on IEEE case studies.

IEEE 14 bus case

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Generation

• Electric power is generated at power stations.

• Generated power = load + losses

• Electric power generators are classified between base and peaking units.

Peaking units

Base units

Wind + PV

Natural gas, liquid fuelsHydroelectric

Coal

Nuclear

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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

• 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

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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• 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.

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Substations

• 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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Layout examples:

Substations

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Another layout example and transformers

Substations

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Substations

Circuit breakers.

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Substations

Sensing and actuation components (a lot more about this throughout this course).

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Dispatch Center

• 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

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

• Phasors• Used to represent ac signals in single-frequency systems through a

fixed vector in the complex plane.

( ) cos( )Vv t V t

Vtv )(

( ) Real( )Vj j tv t Ve e

VV VV

V

Imaginary

Real

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Introduction• Power in ac systems

• Instantaneous power:

• 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.

( ) ( ) ( ) cos( ) cos( )V Ip t v t i t V t I t

( ) ( ) ( ) cos( ) cos(2 )2 V I V I

VIp t v t i t t

Constant part

cos( ) cos( )2 2 2

V I V I

VI V IP

cos( )RMS RMSP V I

V I

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• Complex power• Notice that

and that

• So a magnitude called complex power S is defined as

• Power factor (in power systems with one frequency) is defined as

*1 1 1Real( ) Real Real

2 2 2V IP VI VI VI

2 ( )RMSI R jX S

2 2. . cos

P Pp f

S P Q

*1 1 1Imaginary( ) Imaginary Imaginary

2 2 2V IQ VI VI VI

• It provides an idea of how efficient is the process of using (and generating) electrical power in ac circuits:

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

Q < 0 (capacitive load)

* (cos sin )RMS RMSV I j S VI


2 2 2V IP VI VI VI


2 2 2V IQ VI VI VI



2 2 2V IP VI VI VI


2 2 2V IQ VI VI VI

2 ( )RMSI R jX S



2 2 2V IP VI VI VI


2 2 2V IQ VI VI VI

2 ( )RMSI R jX S



2 2 2V IP VI VI VI


2 2 2V IQ VI VI VI

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• 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).

0P e.g. in an inductor:

2( ) 2sin(90)

2 2 2

VI I L I LIQ

T

sin( )RMS RMSQ V I

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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

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• Output real and reactive power of an inverter (or any source) equal

• In conventional power grids XL>>RL, and in generators XS>>RS. Also δ is also usually small, so

– 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

2

2 2

cos sinG SL SL G SL

SLSL SL

V E R X V RP

R X

2

2 2

cos sinG SL SL G SL

SLSL SL

V E X R V XQ

R X

,

sinG GSL X

SL SL

V E V EP

X X

2

,

G G

SL XSL

V E VQ

X

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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)


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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


1

( ) if 1

if

kj kj

N

kj kj kjk k kj kj

kj jj k

g jb k j

G jB g jb g jb k j

YZ

(Upper case: admittance matrix elementsLower case: line admittance components)(Bus voltages)k k kV V

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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

• Then, the power flow along lines is given by


1 1

( ) ( )N N

k k j kj k j kj k jj jj k j k

P V V B B

2 2

1 1

N N

k k k k kj k j k kj k jj jj k j k

Q V b V b V V V b V V

( )kj kj k jP B

k kj k k jQ b V V V

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• To find the power flow along lines we need to calculate:

• To calculate the above equation we need to solve

• 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.


1

( )N

k kj k jjj k

P B

( )kj kj k jP B

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• 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.


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Electric Power Generation Concepts

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)

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• 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)


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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.


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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


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• As we saw before, the simplified equivalent circuit for a generator and its output equation is:

. .sine

E V E Vp

X X

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

Electric power provided to the rest of the grid

XQE V

E

, EQ p


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• It can be found that

• 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.

• Generator’s angular frequency

(rotor’s speed)

( ) syn

dt

dt

• Grid’s angular frequency


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Voltage and frequency control• 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.

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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

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

0f

f

P0P

0V

V

Q0Q

Nominal frequency

Drooped frequency

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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).

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

0f

f

P0P

0V

V

Q0Q

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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

f

P

V

Q

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Voltage and frequency control• 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.

genf

Gf

f

P Q

V

GV

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Voltage and frequency control• 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.

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Voltage and frequency control• 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:

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Voltage and frequency control• 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

2P1P

f

P

Operating frequency

Adjusted droop lines

No load droop line

Higher power output

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Additional comments

• 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.

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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.

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Additional comments• Operating a power grids involves dealing with a broad time

scale range:

Source: NERC

1 © a. kwasinski, 2015 cyber physical power systems fall 2015 week #1

Documents

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