1. Techno-economic aspects of power systems
Ronnie Belmans
Dirk Van Hertem
Stijn Cole /

2. 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 /

3. Outline Power system analysis and control
Power flow
Optimal power flow
Power flow control
Primary control
Secondary control
Tertiary control
Voltage control /

4. Control of active and reactive power Voltage regulation
Voltage between sender and receiver
Voltage related to reactive power:
Angle related to active power:
The assumption is that R is small compared to X, which is true for overhead high voltage lines.
The angle between sending and receiving voltage is defined by the active power transported along the line. The voltage drop is defined by the reactive power.
So if too much reactive power is demanded by the receiver, a high voltage drop is seen. Therefore, a low power factor is not acceptable.
Sender
Receiver /

5. 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
N-1 contingency study
Congestion analysis
Need for redispatch
System development
Stability studies
...
N-1 contingency: The grid operation should stay intact even if one of the grid elements fails (large generator, high voltage line, transformer, …)
The N-1 rule only takes into account failures of major electrical components, but totally disregards control system failures! (Electra Dec 2005)
Congestion: when a line is overloaded, this leads to congestion, for instance a specific generator can not be dispatched and is curtailed in its output.
Redispatch: if there are problems in the grid, changing the output of power plants locally may alliviate the problems, the overload of grid elements
System development: if for instance a voltage problem is noticed at a node, investments can be planned there to solve that
Stability studies are dynamic, but need a starting value, given by a steady state solution by a power flow analysis /

6. N-1 Example Each line has capacity of 900 MW
Equal, lossless lines between nodes
P = 1000 MW
P = 1000 MW
P = 1000 MW
P = 1000 MW G G G G
P = 166 MW
P = 500 MW
Load = 500 MW
Load = 500 MW
P = 843 MW
P = 1500 MW
P = 666 MW
When considering the power production constant (or at their maximum), this system is not N-1 secure because when one line opens, the system is no longer able to operate (due to a line overload).
N-1 secure when any single incident, line switching or alteration in load/generation can occur without the system being faulted
P = 0 MW
Load = 1500 MW
Load = 1500 MW /

7. 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
P = 800 MW
P = 1200 MW G A G B G A G B
P = 166 MW
P = 200 MW
Load = 500 MW
Load = 500 MW
P = 843 MW
P = 900 MW
congested
P = 666 MW
Congestion occurs when the optimal state of the system can not be reached due to network constraints.
If generator A produces electricity at 2 euro/MWh and B at 1 euro/MWh, it is obvious that we should use B until its limit.
It would be optimal if the 2000 MW load would be produced by B for 1500 MW and 500 MW by A (cost 2500).
However, the network is limited. The flow from B to the main load can be only 900 MW, and therefore the maximum production in B is 1200 MW (2/3*PB+1/3*(1500-PB)=900).
The cost in this case is 2800.
redispatch:
Reassessment or reassignment of dispatch, in other words the modification of generating schedules and/or demand-side management to change patterns of customer energy use. Redispatch is usually used to reduce congestion in transmission systems.
P = 500 MW
Load = 1500 MW
Load = 1500 MW
If the load of gen B would increase, the profit
would rise, but the line is congested /

8. 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 G G
Mismatch: for instance you know all power generated and used at each node, you calculate the currents, then you get the losses and these losses have to be balanced by extra generation at the slack or swing bus G G /

9. 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
Frequency dependence is low, for reactance proportional
PI network: J.C. Das Is Ir Z
Y/2
Y/2 /

10. 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
J Jacobian
Hier gebruik je theta en voorheen delta, be concise  delta theta = delta /

11. Power flow Newton-Raphson
Newton-Raphson has a quadratic convergence
Normally +/- 7 iterations needed
Principle Newton-Raphson iterative method:
f(x) is a function of which we want to know the zeros. we search the zeros by taking a tangent to the curve in our starting value X0, we calculate the intersection of this linear tangent with the x-axis. This is our second value X1. In X1 we do the same until f(Xn) is small enough. /

12. 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)
Ref: Grainger and arrillaga /

13. 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
DC Load Flow: max 5% deviation from real flows (Electric Power Research Institute, 1999) /

14. 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)
...
PSS/E
DigSILENT
ETAP
Powerworld
Matpower
PSAT

15. 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
May be a combination of targets, in a weighed way /

16. Optimal power flow Flow chart
Estimate control parameters
Solve Normal Load Flow
Compute the gradient of control variables
Check if gradient is sufficiently small
Adjust control parameters
Terminate process, solution reached /

17. Optimal power flow Example
max Directional First-order
Iter F-count f(x) constraint Step-size derivative optimality
e e+003
e+003
e e+004
e+003
e+003 e e e
e e
Matpower 9-bus network optimization: economic dispatch: 15 iteration until the stop criterion is reached (directional derivative below threshold).
Command to test this yourself in Matpower (
> runopf /

18. Outline Power system analysis and control
Power flow
Optimal power flow
Power flow control
Primary control
Secondary control
Tertiary control
Voltage control /

19. 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!
Not every flow is known
Local or global control
Cross-border information
Output of power plants
Metering equipment is not always available or correct
MIMO: Multiple input, multiple output
You have to model one voltage level lower than the one you want to study to get the results correct (Peter Van Roy)
OLTC: On line Tap Changing transformers, sometimes also referred to as ULTC: Under-Load Tap Changer
Frequency is not part of the load flow because we assume a equilibrium (production == consumption), and therefore constant frequency. If you need to include the frequency  dynamic calculations /

20. 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
If voltage is not correct: dangerous situations /

21. Control problem Assumptions
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
Define time constants, make a loose link with Jacobian
The control of active power is much more subject to inertia: steam cycle, while the reactive energy/voltage regulation is only determined by the excitation /

22. Control problem Separation of the problem
P-f control
Using feedback:
results in
Q-U control
Measuring
Control signal , generator excitation and static Var compensation (capacitors or power electronics)
P-f: OVERALL balance of active power to be attained
Q-U: LOCAL balance of reactive power is key /

23. Turbine – Generator control
Steam stands for any mechanical input (gas, hydro, even wind for future systems)
Frequency signal may be local or from a distance (Laufen) as overall European control system
Voltage signal is locally measured by reactive power signal may also come from grid dispatch /

24. 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
Grid equilibrium is key
Consumed power is unpredictable
Predictability of generation (replace produced by generated) is decreasing (wind for instance) /

25. Why frequency control?
Uncontrolled power variations affect machine speed
Frequency has to remain between very strict limits
When there is a change in consumption (consumed2 < consumed), meaning less energy is drawn from the grid. Without control, the system will initially move from equilibrium 1 to point 2. At this point, the produced power exceeds the consumed power, and the generators accellorate. At point 3, the balance between production and consumption is restored and the system is back in steady-state. However, the frequency has risen. When we want to return to normal operation, the production has to be lowered (until position 2). /

26. Frequency control Different control actions
4 Phases
Primary control
maintains the balance between generation and demand in the network using turbine speed governors. (tens of seconds)
Secondary control
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
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 control
integral control of the system time regarding UTC time, days
Internationally controlled (UCTE, Nordel, en anderen)
Operation handbook: /

27. UCTE /

28. Primary control Grid 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)
Statism: relative change of the frequency with respect to relative power changes
Droop control can even be introduced via control electronics with power electronic converters /

29. 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
Governor: typically for steam and hydro: governors the speed of the system
800 and 200 mHz are UCTE values
Is deze D dezelfde als de vorige: blijkbaar wel… nog eens nakijken met kundur en arrillaga in de buurt /

30. Primary control principle
Variations in the generating output of two generators
Different droop
Under equilibrium conditions
Identical primary control reserves
The figure shows a diagram of variations in the generating output of two generators a and b of different droop under equilibrium conditions, but with identical PRIMARY CONTROL RESERVES (operation handbook ucte) /

31. Primary control Principle (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
This load shedding should not be mixed with interuptable contracts
Advantage: one big strong grid:
1GW loss in a 15 GW system gives /

32. 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
PI controlled:
Epsilon is the error, the difference between expected and real value
T and K are constants /

33. Primary and secondary control Example
pre-fault: two systems in balance, no power transfer /

34. Primary and secondary control Example (II)
in the yellow system, 1 GW of power is extra produced. This power is taken over by the entire system (both zones). Because there is initially a lack of power in the total system, the frequency drops (same in both systems no matter which relative size). If both systems are of similar size, there will be a power transfer of 500 MW from the blue zone to the yellow zone. No control action yet /

35. Primary and secondary control Example (III)
Primary control starts: the mismatch in frequency causes generators in both zones to accelerate (produce more electricity). The frequency does not go to 50 Hz. /

36. Primary and secondary control Example (IV)
After a while, secondary control starts. This only happens in the zone where there is not enough generation (the yellow one in this case).
Secondary control == setting the steam tap setting to the required/desired value
the frequency rises and the power transfer between the zones reduces with half of the extra secondary power.
In the blue zone, nothing happens /

37. Primary and secondary control Example (V)
at the end of secondary control, the shortage of 1 GW of power in the yellow zone is additionally produced in the yellow zone
There is no power transfer
The frequency has risen above 50 Hz because of the extra energy that is produced by the primary energy control (250 MW) /

38. Primary and secondary control Example (VI)
This phase happens simultaneously with the secondary control,
and the “50.1 Hz” in reality doesn't occur
The second primary control corrects the frequency mismatch (no changing of settings) and while the secondary control takes place, the additional power produced by the primary control is again reduced until we have again a state of balance with no power transfer and 50 Hz. /

39. 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
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)
Oppassen: primaire en secundaire zijn voor het net, tertiaire lijkt mij hier voor de producenten
Ik denk niet dat er daar nog naar security/stability gekeken wordt, loss minimalization lijkt mij helemaal niet ter zake
==> todo: nog eens goed bekijken in operations handbook (dirk) /

40. Sequence overview
operations handbook UCTE /

41. 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) /

42. 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 /

43. Voltage control Can the same control mechanism be used? But
YES
But
Good (sensitive) Q-production has to be available
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
Synchronous generators can be used, be careful, if too much reactive is needed, active may need to be curtailed, resulting in costs. Sometimes a power plant has to be used to locally support the voltage. Then a generator can not use its best power plant. These are so-called « must run » power plants, and the generator involved will send an invoice for that.
Synchronous compensator: synchronous generator not delivering any active power
Synchronous motors can also contribute
SVC: Static Var Compensator
STATCom: Static Compensator, Voltage Source Converter based FACTS device /

44. Voltage control Control scheme
Automatic voltage regulator (e.g. IEEE AVR 1)
Heb je geen europese ?
==> zal eens zoeken, deze stond in Kundur, en was ook gedefinieerd in de Eurostag modellen (en die gebruikten voornamelijk Belgische en franse voorbeelden als ik me dat goed herinnerde...) (dirk) /

45. 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 /

46. References
Power System Stability and control, Prabha Kundur,1994, McGraw-Hill
Operational handbook UCTE,
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
Weedy and Cory
todo /