1. Master in Advanced Power Electrical Engineering © Copyright 2005 Techno-economic aspects of power systems Ronnie Belmans Dirk Van Hertem Stijn Cole

2. © Copyright 2005 – 2008 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. © Copyright 2005 – 2008 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

4. © Copyright 2005 – 2008 Control of active and reactive power Voltage regulation Voltage between sender and receiver Voltage related to reactive power: Angle related to active power: Sender Receiver

5. © Copyright 2005 – 2008 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 study o Congestion analysis o Need for redispatch o System development o Stability studies o...

6. © Copyright 2005 – 2008 N-1 Example Each line has capacity of 900 MW Equal, lossless lines between nodes P = 843 MW GG Load = 1500 MW P = 666 MW P = 166 MW Load = 500 MW P = 1500 MW GG Load = 1500 MW P = 0 MW P = 500 MW Load = 500 MW P = 1000 MW

7. © Copyright 2005 – 2008 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 = 843 MW GG Load = 1500 MW P = 666 MW P = 166 MW Load = 500 MW P = 900 MW congested GG Load = 1500 MW P = 500 MW P = 200 MW Load = 500 MW P = 1000 MW P = 1200 MWP = 800 MW If the load of gen B would increase, the profit would rise, but the line is congested B AB A

8. © Copyright 2005 – 2008 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 G G

9. © Copyright 2005 – 2008 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 IsIs IrIr Y/2 Z

10. © Copyright 2005 – 2008 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

11. © Copyright 2005 – 2008 Power flow Newton-Raphson Newton-Raphson has a quadratic convergence Normally +/- 7 iterations needed Principle Newton-Raphson iterative method:

12. © Copyright 2005 – 2008 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)

13. © Copyright 2005 – 2008 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

14. © Copyright 2005 – 2008 Power flow: Available computer tools Available programs:  PSS/E (Siemens)  DigSILENT (power factory)  Eurostag (tractebel)  ETAP  Powerworld (demo version available for download)  Matpower (free download, matlab based)  PSAT: power system analysis toolbox (free download, matlab based) ...

15. © Copyright 2005 – 2008 Optimal power flow (OPF) Optimal power flow = power flow with a goal Optimizing for highest objective  Minimum losses  Economic dispatch (cheapest generation) ... Problem formulation minimizeF(x, u, p) Objective function subject tog(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

16. © Copyright 2005 – 2008 Optimal power flow Flow chart Estimate control parametersSolve Normal Load FlowCompute the gradient of control variables Adjust control parameters Terminate process, solution reached Check if gradient is sufficiently small

17. © Copyright 2005 – 2008 Optimal power flow Example 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

18. © Copyright 2005 – 2008 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

19. © Copyright 2005 – 2008 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 known o Local or global control o Cross-border information o Output of power plants o Metering equipment is not always available or correct

20. © Copyright 2005 – 2008 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

21. © Copyright 2005 – 2008 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

22. © Copyright 2005 – 2008 Control problem Separation 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)

23. © Copyright 2005 – 2008 Turbine – Generator control

24. © Copyright 2005 – 2008 Why frequency control? Uncontrolled power variations affect machine speed Frequency has to remain between very strict limits 1 2 3 1.Start 2.P_consumed2 < P_consumed1 3.P_produced > P_consumed  acceleration

25. © Copyright 2005 – 2008 Why frequency control? Uncontrolled power variations affect machine speed Frequency has to remain between very strict limits 1 2 3 1.Start 2.P_consumed2 < P_consumed1 3.P_produced > P_consumed  acceleration (delta f) 4.Production has to be reduced (control action) Produced2

26. © Copyright 2005 – 2008 Frequency control Different 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 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 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 o integral control of the system time regarding UTC time, days Internationally controlled (UCTE, Nordel, and others) Operation handbook: http://www.ucte.org/publications/ophandbook/

27. © Copyright 2005 – 2008 UCTE

28. © Copyright 2005 – 2008 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)

29. © Copyright 2005 – 2008 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

30. © Copyright 2005 – 2008 Primary control principle Variations in the generating output of two generators Different droop Under equilibrium conditions Identical primary control reserves

31. © Copyright 2005 – 2008 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

32. © Copyright 2005 – 2008 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:

33. © Copyright 2005 – 2008 Primary and secondary control Example

34. © Copyright 2005 – 2008 Primary and secondary control Example (II)

35. © Copyright 2005 – 2008 Primary and secondary control Example (III)

36. © Copyright 2005 – 2008 Primary and secondary control Example (IV)

37. © Copyright 2005 – 2008 Primary and secondary control Example (V)

38. © Copyright 2005 – 2008 Primary and secondary control Example (VI) This phase happens simultaneously with the secondary control, and the “50.1 Hz” in reality doesn't occur

39. © Copyright 2005 – 2008 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 Cheap units (low marginal cost such as combined cycle or nuclear) o Highest security/stability o Loss minimalization o... How?  Redispatching of power generation  Redistributing output of generators participating in secondary control  Change power exchange with other areas  Load control (shedding)

40. © Copyright 2005 – 2008 Sequence overview

41. © Copyright 2005 – 2008 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. © Copyright 2005 – 2008 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. © Copyright 2005 – 2008 Voltage control Can the same control mechanism be used?  YES But  Good (sensitive) Q-production has to be available o Synchronous compensator: expensive o Capacitors: not accurate enough o 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

44. © Copyright 2005 – 2008 Voltage control Control scheme Automatic voltage regulator (e.g. IEEE AVR 1)

45. © Copyright 2005 – 2008 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. © Copyright 2005 – 2008 References Power System Stability and control, Prabha Kundur,1994, McGraw-Hill Operation handbook UCTE, http://www.ucte.org/ohb/cur_status.asp 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, 2 nd ed., Andersson and Fouad Dynamics and Control of Electric Power Systems, Goran Andersson