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Techno-economic aspects of power systems

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

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Techno-economic aspects of power systems

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  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. OutlinePower system analysis and control • Power system analysis • Power flow • Optimal power flow • Power flow control • Primary control • Secondary control • Tertiary control • Voltage control

  4. Control of active and reactive powerVoltage regulation • Voltage between sender and receiver • Voltage related to reactive power: • Angle related to active power: Receiver Sender

  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 • ...

  6. N-1Example • 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 =500 MW P =166 MW Load = 500 MW Load = 500 MW P =1500 MW P =843 MW P =0 MW P =666 MW Load = 1500 MW Load = 1500 MW

  7. 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 =800 MW P =1200 MW P =1000 MW P =1000 MW G G A B G G A B P =200 MW P =166 MW Load = 500 MW Load = 500 MW P =900 MW congested P = 500 MW P =843 MW P =666 MW Load = 1500 MW If the load of gen B would increase, the profit would rise, but the line is congested Load = 1500 MW

  8. 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

  9. 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 Z Y/2 Y/2

  10. 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

  11. Power flowNewton-Raphson • Newton-Raphson has a quadratic convergence • Normally +/- 7 iterations needed • Principle Newton-Raphson iterative method:

  12. 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)

  13. 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

  14. 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. 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

  16. 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 Optimal power flow Flow chart

  17. 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

  18. OutlinePower system analysis and control • Power system analysis • 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

  20. 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

  21. 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

  22. Control problemSeparation 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)

  23. Turbine – Generator control

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

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

  26. Frequency controlDifferent 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, a nd others) • Operation handbook: http://www.ucte.org/publications/ophandbook/

  27. UCTE

  28. 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)

  29. 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

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

  31. 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

  32. 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:

  33. Primary and secondary controlExample

  34. Primary and secondary controlExample (II)

  35. Primary and secondary controlExample (III)

  36. Primary and secondary controlExample (IV)

  37. Primary and secondary controlExample (V)

  38. Primary and secondary controlExample (VI) This phase happens simultaneously with the secondary control, and the “50.1 Hz” in reality doesn't occur

  39. 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 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)

  40. Sequence overview

  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? • 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

  44. Voltage controlControl scheme • Automatic voltage regulator (e.g. IEEE AVR 1)

  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 • Operation 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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