ED Problem Statement The Optimal Power Flow Smith College, EGR 35 A power system has four generators with the following cost characteristics C 1 = 1000 + 15P 1 + 0.05P 1 C = 100 + 5P + 0.1P C 3 = 060 + 0P 3 + 0.01P 3 C 4 = 500 + 1P 4 + 0.03P 4 Typical demand, P L, levels are: à 750MW, 1000MW, 1500MW, and 500MW Oct 3, 014 1 Visualizing Equal Marginal Cost; Quadratic Cost Curves Graphed Visualizing Equal Marginal Cost 3 4 1
5 6 Price à LMP Optimal Power Flow Electricity price = system lambda = LMP (locational marginal price) ISO New England: http://www.iso-ne.com/ PJM https://edata007.pjm.com/edata/index.html http://www.pjm.com/markets-and-operations/energy/real-time/monthlylmp.aspx - above link, linked from here NYISO http://www.nyiso.com/public/markets_operations/market_data/maps/index.jsp above linked under Market Data from: http://www.nyiso.com/public/markets_operations/index.jsp CAISO: Links to 3 LMP maps: http://oasis.caiso.com/mrtu-oasis/lmp/maps_home.html http://oasis.caiso.com/mrtu-oasis/lmp/rtm/pointmap.html MISO http://www.midwestmarket.org/page/lmp+contour+map+%8eor%9 (Need Adobe SVG plug-in) 7 Economic dispatch + power flow equations Objective Minimize total cost of supplying electricity Constrained by Total generation = total demand (energy balance) Generators must be within min and max bounds Transmission system must actually be able to support the flow of power (obey circuit laws) Optimal Power Flow = Power Flow + ED Referred to as OPF 8
Self-Quiz Questions 1) Define the physical significance of S, P, Q. What are the units of each? ) Define, compare and contrast Energy and power; include units 3) If you were a system operator, what questions/problems would you use a power flow program to answer/solve? 4) What input data do you need to run a power flow model? 5) What results/output do you get from a power flow model? and how do you use these results? 6) What is the slack bus and what role does it serve in the model? in the actual system? 7) How do we know if the model converges or not? What does it mean if it does not converge? 9 Self-Quiz Questions 8) If you were a system operator, what questions would you use an optimal power flow program to answer? 9) What input data do you need to run an optimal power flow model? 10) What results/output do you get from an optimal power flow model? and how do you use these results? 10 Recap: Power Flow Analysis Real Power Flow Equations For power systems, we know The system topology (the circuit diagram) The impedance of each line, Z -1 = Y = G + jb The load at each load bus, S = P + jq The capability of each generator, P & V The reference bus ( V and θ=0) We want to know The output of each generator (S = P + jq) The voltage at each bus (V = V θ) How many equations and how many unknowns? ( ) = P Gi P Di P i = Σ V i V k G ik cosθ ik + B ik sinθ ik Q i = Σ V i V k ( G ik sinθ ik B ik cosθ ik ) = Q Gi Q Di Numerical methods (iteration) Reference (Slack) bus Solution might not converge! The power flow on each line (P flow ) 11 1 3
Optimal Power Flow Economic dispatch + power flow equations Objective Minimize total cost of supplying electricity Constrained by Total generation = total demand (energy balance) Generators must be within min and max bounds Transmission system must actually be able to support the flow of power (obey circuit laws) Optimal Power Flow = Power Flow + ED Referred to as OPF 13 Optimal Power Flow Write out problem formulation 14 Discussion for ED & OPF If you do not obey constraints 1) Interpret: A power flow solution does not exist for a given economic dispatch solution (P Gi values) ) Discuss marginal unit for a system with hundreds of generators Many units are at their generating limits Only the marginal units participate in the ED solutions 3) ED and OPF solutions What is the role of network losses? What is the role of congestion/constraints? (Transmission congestion what is it?) 15 Transformer explosion, slow motion at end: http://www.youtube.com/watch?v=paej3g3f6y&nr=1 Residential line fire http://www.youtube.com/watch?v=eyumdqq94ao&nr=1 Night time city explosion http://www.youtube.com/watch?v=4yy7tgnsahw 16 4
Power World 37-bus Example Robustness of the system (example 6_13) As open lines around the system As open breakers connecting gens and loads Watch power flows change, look for patterns To start playing with the system: Open far right major line, JO345 AND Job138 to Lynn see other small lines in middle approach overload Open line from TIM to HANA and see overloads (upper left) Take out both major lines far right and top at buses JO345 AND Slack 345 Without these two major lines, the system is fine Without Tim-Hana two other lines overload What is the role of and importance of the power flow limit? 17 Power World HW: OPF Objective of next homework Practice playing with operating a power system Continue discovering patterns of system behavior Discover that intuition may not help in understanding behavior in all cases Familiarity with power system variables and behavior Example 1_11 Optimal power flow & electricity prices 18 Thoughts from HW 3 Experimenting with case 6_59 Power factor discussion Per unit system 19 5