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Techno-economic
aspects of power systems
Ronnie Belmans
Dirk Van Hertem
Stijn Cole
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Overview
•
•
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•
•
•
•
•
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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
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Outline
Power system analysis and control
• Power system analysis

Power flow
 Optimal power flow
• Power flow control

Primary control
 Secondary control
 Tertiary control
 Voltage control
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Control of active and reactive power
Voltage regulation
• Voltage between sender and receiver
S R  U R  I R  PR  j  QR
*
X
• Voltage related to reactive power:  U  U  QR
R
X
• Angle related to active power:   2  PR
U
R
R jX
Sender
PR  j  QR
PS  j  QS
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Receiver
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
o
o
o
o
o
N-1 contingency study
Congestion analysis
Need for redispatch
System development
Stability studies
...
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N-1
Example
• Each line has capacity of 900 MW
• Equal, lossless lines between nodes
P = 1000 MW
G
P = 1000 MW
P = 1000 MW
G
G
P = 166 MW
Load = 500 MW
P = 843 MW
P = 666 MW
G
P = 500 MW
Load = 500 MW
P = 1500 MW
P = 0 MW
Load = 1500 MW
Load = 1500 MW
© K.U.Leuven - ESAT/Electa
P = 1000 MW
/
Congestion and redispatch
Example
• 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 = 1000 MW
P = 1000 MW
G
G
A
P = 166 MW
Load = 500 MW
P = 843 MW
P = 666 MW
P = 800 MW
G A
B
P = 1200 MW
G B
P = 200 MW
Load = 500 MW
P = 900 MW
P = 500 MW
congested
Load = 1500 MW
Load = 1500 MW
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If the load of gen B would increase, the profit
would rise, but the line is congested
/
Power flow
Three 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
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G
G
G
G
Power flow
Assumptions 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
Z
Y/2
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Y/2
1


1  YZ
Z 

Vs 
Vr 
2
 
I     1 
 s  Y 1  YZ 1  1 YZ   I r 
  4 
2 
/
Power Flow
Equations
• I=Y.V is a set of (complex) linear equations
• But P and Q are needed ==> S=V.I*

Set of non-linear equations
Pk
 PGk  PLk 





  0



  0
Vk2Gkk VkVm Gkm cos  k  m  Bkm sin k m
Qk
 QGk  QLk 


Vk2 Bkk VkVm Gkm sin  k  m  Bkm cos k m
 P 
 Q 


i 
 P
 
 
 Q

 
P

V
V

Q 
V

V


J K
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i 1

/
i 
 
  V

 V




i 
Power flow
Newton-Raphson
• Newton-Raphson has a quadratic convergence
• Normally +/- 7 iterations needed
• Principle Newton-Raphson iterative method:
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Power Flow
Alternative 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)
P 
Q 
 
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(i )
 P
 
 
 0

(i )

i 
0    
  V 

Q
V   V 
V 
/
Power Flow
Alternative 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
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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)
...
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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
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Optimal power flow
Flow chart
Estimate control parameters
Solve Normal Load Flow
Compute the gradient of control variables
Check if gradient is
sufficiently small
Terminate process, solution
reached
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Adjust control
parameters
Optimal power flow
Example
Iter
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Directional
F-count f(x)
1
4570.1
3
9656.06
5.28e+003
6
7345.79
9
5212.76
11
5384.17
14
5305.59
17
5439.61
19
5328.32
22
5267.51
24
5301.72
26
5300.88
28
5295.95
30
5296.69
32
5296.69
34
5296.69
36
5296.69
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max
First-order
constraint
1.63
0.3196
1
0.2431
0.1449
0.02825
0.08544
0.07677
0.08351
0.1398
0.05758
0.004961
0.003562
4.436e-005
8.402e-007
4.487e-009
3.16e-011
0.5
0.5
1
0.5
0.5
1
0.5
1
1
1
1
1
1
1
Step-size derivative optimality
1.35e+004
506
1.41e+003
367
-132
958
144
-82.7
63.8
17.3
-0.325
1.15
0.0222
/
1.98e+003
4.32e+004
2.83e+003
696
859
1.04e+003
730
282
406
116
30.8
4.99
0.000728
0.431
2.75e-006
0.0113
Outline
Power system analysis and control
• Power system analysis

Power flow
 Optimal power flow
• Power flow control

Primary control
 Secondary control
 Tertiary control
 Voltage control
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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
o
o
o
o
Not every flow is known
Local or global control
Cross-border information
Output of power plants
Metering equipment is not always available or correct
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Control problem
Requirements
• 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
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Control problem
Assumptions
• P-f control and Q-U control can be separated
 QV   P f
• 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
fi
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Control problem
Separation of the problem
• P-f control
fi and Ptransfered   i  phase fault

Using feedback:
o
 i results in Pc ,i
Q-U control

Measuring
 Control signal U   Vi , generator excitation
and static Var compensation (capacitors or power
electronics) Qc ,i
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Turbine – Generator control
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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)
Pconsumed  f   1% / Hz 

Natural stability
f
Consumed
Produced
P
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Why frequency control?
• Uncontrolled power variations affect machine speed
• Frequency has to remain between very strict limits
f
Consumed 2
Consumed
Produced
P
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Frequency control
Different control actions
• 4 Phases

Primary control
o

Secondary control
o

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 control
o

maintains the balance between generation and demand in the network using turbine
speed governors. (tens of seconds)
any (automatic or) manual change in the working points of generators (mainly by rescheduling), in order to restore an adequate secondary control reserve at the right
time. (after 15 min)
Time control
o
integral control of the system time regarding UTC time, days
• Internationally controlled (UCTE, Nordel, en anderen)
• Operation handbook: http://www.ucte.org/ohb/
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UCTE
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Primary control
Grid characteristics
 f / fn
• Statism: SG 
PG / PGn


In %, typically 4 to 5 %
Highest droop = largest contribution
• Network stiffness   
 PG 
f

Also called `Network power frequency characteristic'

Includes self regulating effect (D) and influence of the feedback control
(K=1/R)
1
  D
R
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Primary control
principle
• 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
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Primary control
principle
•
•
•
•
Variations in the generating output of two generators
Different droop
Under equilibrium conditions
Identical primary control reserves
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Primary control
Principle (II)
• When f  1Hz , 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 f is too high ==> islanding
t
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Secondary control
Definition/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
1
• PI controlled:
Pdi   K   
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Tsec
/
  dt
Primary and secondary control
Example
50 Hz
P: X MW
pre-fault
50 Hz
0 MW
P: Y MW
C: Y MW
C: X MW
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Primary and secondary control
Example (II)
49,8 Hz
P: X MW
Initial
49,8 Hz
500 MW
P: Y MW
C: Y+1000 MW
C: X MW
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Primary and secondary control
Example (III)
49,9 Hz
P: X + 250 MW
primary control
500 MW
P: Y +250 MW
C: Y+1000 MW
C: X MW
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49,9 Hz
/
Primary and secondary control
Example (IV)
49,9+ Hz
P: X + 250 MW
Secondary control
500 - A/2 MW
49,9+ Hz
P: Y +250 + A MW
C: Y+1000 MW
C: X MW
+A MW
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/
G
Primary and secondary control
Example (V)
50,1 Hz
P: X + 250 MW
End secondary control
0 MW
50,1 Hz
P: Y + 1250 MW
C: Y+1000 MW
C: X MW
+1000 MW
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G
Primary and secondary control
Example (VI)
This phase happens simultaneously with the secondary control,
and the “50.1 Hz” in reality doesn't occur
50 Hz
Second primary control
50 Hz
P: X MW
0 MW
P: Y + 1000 MW
C: Y+1000 MW
C: X MW
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Tertiary control
Definition
• 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 considerations
o
o
o
o
Cheap units (low marginal cost such as combined cycle or nuclear)
Highest security/stability
Loss minimalization
...
• How?




Redispatching of power generation
Redistributing output of generators participating in
secondary control
Change power exchange with other areas
Load control (shedding)
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Sequence overview
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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



f
t

dt

20
s

• Sometimes `played' with (week – weekend)
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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
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Voltage control
• Can the same control mechanism be used?

YES
• But

Good (sensitive) Q-production has to be available
o
o
o


Synchronous compensator: expensive
Capacitors: not accurate enough
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
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Voltage control
Control scheme
• Automatic voltage regulator (e.g. IEEE AVR 1)
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/
Conclusions
• Power flow analysis

Performed through iterative method (NewtonRaphson)
 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
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/
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
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