© K.U.Leuven - ESAT/Electa / Techno-economic aspects of power systems Ronnie Belmans Dirk Van Hertem Stijn Cole.

© K.U.Leuven - ESAT/Electa

Techno-economic aspects of power

systems

Ronnie BelmansRonnie BelmansDirk Van HertemDirk Van Hertem

Stijn ColeStijn Cole


Overview

• Lesson 1: Liberalization• Lesson 2: Players, Functions and Tasks• Lesson 3: Markets• Lesson 4: Present generation park• Lesson 5: Future generation park• Lesson 6: Introduction to power systems• Lesson 7: Power system analysis and control• Lesson 8: Power system dynamics and security• Lesson 9: Future grid technologies: FACTS and

HVDC• Lesson 10: Distributed generation


OutlinePower system analysis and control

• Power system analysis Power flow Optimal power flow

• Power flow control Primary control Secondary control Tertiary control Voltage control


Control of active and reactive powerVoltage regulation

• Voltage between sender and receiver

• Voltage related to reactive power:

• Angle related to active power:

*

RR R R RS U I P j Q

RR

QUX

U

RR

PUX 2

Sender Receiver

XjR

S SP j Q R RP j Q


Power flow

• Normal conditions ==> steady state (equilibrium)• Basis calculations to obtain this state are called Power Flow

Also called Load Flow

• Purpose of power flow: Determine steady state situation of the grid Get values for P, Q, U and voltage angle Calculate system losses First step for

o N-1 contingency studyo Congestion analysiso Need for redispatcho System development o Stability studies o ...


N-1Example

• Each line has capacity of 900 MW• Equal, lossless lines between nodes

P = 843 MW

G G

Load = 1500 MW

P = 666 MW

P = 166 MWLoad = 500 MW

P = 1500 MW

G G

Load = 1500 MW

P = 0 MW

P = 500 MWLoad = 500 MW

P = 1000 MWP = 1000 MW P = 1000 MWP = 1000 MW


Congestion and redispatchExample

• Each line has capacity of 900 MW• Equal, lossless lines between nodes• The right generator is cheaper than the left, both have capacity 1500 MW

P = 843 MW

G G

Load = 1500 MW

P = 666 MW

P = 166 MWLoad = 500 MW

P = 900 MWcongested

G G

Load = 1500 MW

P = 500 MW

P = 200 MWLoad = 500 MW

P = 1000 MWP = 1000 MW P = 1200 MWP = 800 MW

If the load of gen B would increase, the profit would rise, but the line is congested

BA B A


Power flowThree types of nodes

• Voltage controlled nodes (P-U node) Nodes connected to a generator Voltage is controlled at a fixed value Active power delivered at a known

value• Unregulated voltage node (P-Q node)

A certain P and Q is demanded or delivered (non dispatched power plants, e.g. CHP)

In practice: mostly nodes representing a pure `load'

• Slack or swing bus (U-node) Variable P and Q Node that takes up mismatches

G

G

G

G


Power flowAssumptions and representation

• Properties are not influenced by small changes in voltage or frequency

• Linear, localized parameters• Balanced system==> Single line representation• Loads represented by their P and Q values• Current and power flowing to the node is positive• Transmission lines and transformers: equivalent

Is Ir

11

21 1

1 14 2

s r

s r

YZ ZV V

I IY YZ YZ

Y/2Y/2

Z


Power FlowEquations

• I=Y.V is a set of (complex) linear equations• But P and Q are needed ==> S=V.I*

Set of non-linear equations

2 cos sin

2 sin cos

0

0

k Gk Lk

V G V V G Bk kk k m km k m km k m

k Gk Lk

V B V V G Bk kk k m km k m km k m

P P P

Q Q Q

1i

ii

i

J K

P PV

P VV

Q Q QV V

V


Power flowNewton-Raphson

• Newton-Raphson has a quadratic convergence

• Normally +/- 7 iterations needed

• Principle Newton-Raphson iterative method:


Power FlowAlternative methods

• Gauss-Seidel Old method (solves I=Y.V), not used anymore Linear convergence

• Decoupled Newton-Raphson Strong coupling between Q and V, and between P and Weak coupling between P and V, and between Q and ==> 2 smaller systems to solve ==> faster (2-3 times faster)

ii

i

V

VV

V

Q

P

Q

P

)(

)(

0

0


Power FlowAlternative methods (II)

• Fast decoupled Newton-Raphson Neglects coupling as in decoupled Newton-Raphson Approximation: Jacobian considered constant

• Newton-Raphson with convergence parameter Step in right direction (first order) multiplied by factor

• DC load flow Consider only B (not Y) Single calculation (no iterations needed) Very fast ==> 7-10 times faster than normal Newton-Raphson In high voltage grids: 1 pu Sometimes used as first value for Newton-Raphson iteration (starting

value) Economic studies and contingency analysis also use DC load flow


Power flow:Available computer tools

• Available programs: PSS/E (Siemens) DigSILENT ETAP Powerworld (demo version available for download) Matpower (free download, matlab based) PSAT: power system analysis toolbox (free

download, matlab based) ...


Optimal power flow (OPF)

• Optimal power flow = power flow with a goal• Optimizing for highest objective

Minimum losses Economic dispatch (cheapest generation) ...

• Problem formulation minimize F(x, u, p)

Objective function subject to g(x, u, p) = 0 Constraints

• Build the Lagrangian function L = F(x, u, p) + T g(x, u, p)

• Other optimization algorithms can also be used


Optimal power flow Flow chart

Estimate control parameters

Solve Normal Load Flow

Compute the gradient of control variables

Adjust control parameters

Terminate process, solution reached

Check if gradient is sufficiently small


Optimal power flowExample

max Directional First-order

Iter F-count f(x) constraint Step-size derivative optimality

0 1 4570.1 1.63 1 3 9656.06 0.3196 1 1.35e+004

5.28e+003 2 6 7345.79 0.2431 0.5 506

1.98e+003 3 9 5212.76 0.1449 0.5 1.41e+003

4.32e+004 4 11 5384.17 0.02825 1 367

2.83e+003 5 14 5305.59 0.08544 0.5 -132 696 6 17 5439.61 0.07677 0.5 958 859 7 19 5328.32 0.08351 1 144

1.04e+003 8 22 5267.51 0.1398 0.5 -82.7 730 9 24 5301.72 0.05758 1 63.8 282 10 26 5300.88 0.004961 1 17.3 406 11 28 5295.95 0.003562 1 -0.325 116 12 30 5296.69 4.436e-005 1 1.15 30.8 13 32 5296.69 8.402e-007 1 0.0222 4.99 14 34 5296.69 4.487e-009 1 0.000728

0.431 15 36 5296.69 3.16e-011 1 2.75e-006

0.0113


OutlinePower system analysis and control

• Power system analysis Power flow Optimal power flow

• Power flow control Primary control Secondary control Tertiary control Voltage control


Control problem

• Complex MIMO system Thousands of nodes Voltage and angle on each node Power flows through the lines (P and Q) Generated power (P and Q), and voltage OLTC positions ... Not everything is known!

o Not every flow is knowno Local or global controlo Cross-border informationo Output of power plantso Metering equipment is not always available or correct


Control problemRequirements

• Voltage must remain between its limits 1 p.u. +/- 5 or 10 %

• Power flow through a line is limited Thermal limit depending on section

• Frequency has to remain between strict limits

• Economic optimum


Control problemAssumptions

• P-f control and Q-U control can be separated

• Voltage control is independent for each voltage controlled node

• Global system can be divided in control areas Control area = region of generators that

experience the same frequency perturbation

Q V P f

fi


Control problemSeparation of the problem

• P-f control

Using feedback: o results in

Q-U control Measuring Control signal , generator excitation

and static Var compensation (capacitors or power electronics)

i transfered if and P phase fault

i icP ,

iU V

icQ ,


Turbine – Generator control


Frequency control

• Power equilibrium Produced power(t) == consumed power(t)+grid losses Produced power is +/- constant with constant “steam” values Consumed power is a function of the grid frequency (motors)

Natural stability

P

Produced

Consumedf

1% /consumedP f Hz


Why frequency control?

• Uncontrolled power variations affect machine speed

• Frequency has to remain between very strict limits

Consumed 2

P

Produced

Consumedf


Frequency controlDifferent control actions

• 4 Phases Primary control

o maintains the balance between generation and demand in the network using turbine speed governors. (tens of seconds)

Secondary controlo centralised automatic function to regulate the generation in a control area based on

secondary control reserves in order to• maintain its interchange power flow at the control program with all other control areas• restore the frequency in case of a frequency deviation originating from the control area to its set value in order to free the capacity engaged by the primary control. (15 min)

Tertiary controlo any (automatic or) manual change in the working points of generators (mainly by re-

scheduling), in order to restore an adequate secondary control reserve at the right time. (after 15 min)

Time controlo integral control of the system time regarding UTC time, days

• Internationally controlled (UCTE, Nordel, en anderen)• Operation handbook: http://www.ucte.org/ohb/


UCTE


Primary controlGrid characteristics

• Statism:

In %, typically 4 to 5 % Highest droop = largest contribution

• Network stiffness Also called `Network power frequency characteristic' Includes self regulating effect (D) and influence of the feedback control

(K=1/R)

GnGG PP

fnfS

/

/

f

PG

DR

1


Primary controlprinciple

• Balancing generation and demand in a synchronous zone

• Device is called `governor'• Maximum allowed dynamic frequency deviation:

800 mHz• Maximum allowed absolute frequency deviation:

200 mHz


Primary controlprinciple

• Variations in the generating output of two generators• Different droop • Under equilibrium conditions• Identical primary control reserves


Primary controlPrinciple (II)

• When , a part of the load is shed

• Basic principle: P-control feedback to counter power fluctuations

• Primary control uses spinning reserves

• Each control area within the synchronous area (UCTE) has to maintain a certain reserve, so that the absolute frequency shift in case of a 3 GW power deviation remains below 200 mHz 3 GW are two of the largest units within UCTE

• If is too high ==> islanding

Hzf 1

t

f


Secondary controlDefinition/principle

• System frequency is brought back to the scheduled value

• Balance between generation and consumption within each area

• Primary control is not impaired

• Centralized `automatic generation control' adjusts set points

• Power sources are called secondary reserves

• PI controlled: dtT

KPdisec

1


Primary and secondary controlExample

C: X MW

P: X MW P: Y MW

50 Hz 50 Hz

C: Y MW

0 MW

pre-fault


Primary and secondary controlExample (II)

C: X MW

P: X MW P: Y MW

49,8 Hz49,8 Hz

500 MW

C: Y+1000 MW

Initial


Primary and secondary controlExample (III)

C: X MW

500 MW

C: Y+1000 MW

primary control49,9 Hz 49,9 Hz

P: X + 250 MW P: Y +250 MW


Primary and secondary controlExample (IV)

C: X MWC: Y+1000 MW

P: X + 250 MW

G

P: Y +250 + A MW

+A MW

49,9+ Hz49,9+ Hz Secondary control

500 - A/2 MW


Primary and secondary controlExample (V)

C: X MWC: Y+1000 MW

P: X + 250 MW

G

50,1 Hz 50,1 Hz

0 MW P: Y + 1250 MW

+1000 MW

End secondary control


Primary and secondary controlExample (VI)

C: X MWC: Y+1000 MW

0 MW

50 Hz

P: X MW P: Y + 1000 MW

50 HzSecond primary control

This phase happens simultaneously with the secondary control, and the “50.1 Hz” in reality doesn't occur


Tertiary controlDefinition

• Automatic or manual set point change of generators and/or loads in order to: Guarantee secondary reserves Obtain best power generation scheme in terms of

economic considerationso Cheap units (low marginal cost such as combined cycle or nuclear)o Highest security/stabilityo Loss minimalizationo ...

• How? Redispatching of power generation Redistributing output of generators participating in

secondary control Change power exchange with other areas Load control (shedding)


Sequence overview


Time control

• Limit discrepancies between synchronous time and universal time co-ordinated (UTC) within the synchronous zone

• Time difference limits (defined by UCTE) Tolerated discrepancy: +/- 20 s Maximum allowed discrepancy under normal

conditions: +/- 30 s Exceptional range: +/- 60 s

• Sometimes `played' with (week – weekend)

sdttf 20


Voltage control

• Voltage at busbar: Voltage is mainly controlled by reactive power Can be regulated through excitation, tap changers,

capacitors, SVC, ... Reactive power has a local nature


Voltage control

• Can the same control mechanism be used? YES

• But Good (sensitive) Q-production has to be available

o Synchronous compensator: expensiveo Capacitors: not accurate enougho SVC/STATCom: possible, but not cheap

U is `OK' between 0,95 and 1,05 p.u. Reactive power is less price (fuel) dependent (some

losses)

• Voltage is locally controlled


Voltage controlControl scheme

• Automatic voltage regulator (e.g. IEEE AVR 1)


Conclusions

• Power flow analysis Performed through iterative method (Newton-

Raphson) Basis for many power system studies Optimal power flow

• Power flow control happens in several independent stages Inter-area ties make the grid more reliable Voltage control is independent of power

(frequency) control


References

• Power System Stability and control, Prabha Kundur,1994, McGraw-Hill

• Operational handbook UCTE, http://www.ucte.org/ohb/cur_status.asp

• Power system dynamics: stability and control, K. Padiyar, Ansham, 2004

• Power system analysis, Grainger and Stevenson• Power system control and stability, 2nd ed.,

Andersson and Fouad• Dynamics and Control of Electric Power Systems,

Goran Andersson

© K.U.Leuven - ESAT/Electa / Techno-economic aspects of power systems Ronnie Belmans Dirk Van Hertem Stijn Cole.

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