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  1. Electric Power Markets:Process and Strategic Modeling HUT (Systems Analysis Laboratory) & Helsinki School of Economics Graduate School in Systems Analysis, Decision Making, and Risk Management Mat-2.194 Summer School on Systems Sciences Prof. Benjamin F. Hobbs Dept. of Geography & Environmental Engineering The Johns Hopkins University Baltimore, MD 21218 USA bhobbs@jhu.edu

  2. I. Overview of Course Multifirm Models with Strategic Interaction Single Firm Models Single Firm Models Design/ Investment Models Design/ Investment Models Operations/ Control Models Operations/ Control Models Demand Models Market Clearing Conditions/Constraints

  3. Why The Power Sector? • Scope of economic impact • ~$1000/person/yr in US (~petroleum use) • Almost half of US energy use • Ongoing restructuring and reforms • Vertical disintegration • separate generation, transmission, distribution • Competition in bulk generation • grant access to transmission • creation of regional spot & forward markets • Competition in retail sales • Horizontal disintegration, mergers • Privatization • Emissions trading Finland`s 1995 Elect. Market Act X X EL-EX, Nord Pool X Fingrid None

  4. Why Power? (Continued) • Scope of environmental impact • Transmission lines & landscapes • 3/4 of SO2, 1/3 of NOx, 3/8 of CO2 in US; CO2 increasing (+50% by 2020 despite goals?) • Power: A horse of a different color • Difficult to store  must balance supply & demand in real time • Physics of networks • North America consists of three synchronized machines • What you do affects everyone else  pervasive externalities; must carefully control to maintain security. Example of externalities: parallel flows resulting from Kirchhoff`s laws

  5. II. “Process” or “Bottom-Up” Analysis:Company & Market Models • What are bottom-up/engineering-economic models? And how can they be used for policy analysis? • = Explicit representation & optimization of individual elements and processes based on physical relationships D

  6. Process Optimization Models • Elements: • Decision variables. E.g., • Design: MW of new combustion turbine capacity • Operation: MWh generation from existing coal units • Objective(s). E.g., • Maximize profit or minimize total cost • Constraints. E.g., • S Generation = Demand • Respect generation & transmission capacity limits • Comply with environmental regulations • Invest in sufficient capacity to maintain reliability • Traditional uses: • Evaluate investments under alternative scenarios (e.g., demand, fuel prices) (3-40 yrs) • Operations Planning (8 hrs - 5 yrs) • Real time operations (<1 second - 1 hr)

  7. Bottom-Up/Process Models vs. Top-Down Models • Bottom-up models simulate investment & operating decisions by an individual firm, (usually) assuming that that the firm can’t affect prices for its outputs (power) or inputs (mainly fuel) • Examples: capacity expansion, production costing models • Individual firm models can be assembled into market models • Top-down models start with an aggregate market representation (e.g., supply curve for power, rather than outputs of individual plants). • Often consider interactions of multiple markets • Examples: National energy models

  8. Functions of Process Model: Firm Level Decisions • Real time operations: • Automatic protection (<1 second): auto. generator control (AGC) methods to protect equipment, prevent service interruptions. (Responsibility of: Independent System Operator ISO) • Dispatch (1-10 minutes): optimization programs (convex) min. fuel cost, s.t. voltage, frequency constraints (ISO or generating companies GENCOs) • Operations Planning: • Unit commitment (8-168 hours). Integer NLPs choose which generators to be on line to min. cost, s.t. “operating reserve” constraints (ISO or GENCOs) • Maintenance & production scheduling (1-5 yrs): schedule fuel deliveries & storage and maintenance outages (GENCOs)

  9. Firm Decisions Made Using Process Models, Continued • Investment Planning • Demand-side planning (3-15 yrs): implement programs to modify loads to lower energy costs (consumer, energy services cos. ESCOs, distribution cos. DISCOs) • Transmission & distribution planning (5-15 yrs): add circuits to maintain reliability and minimize costs/ environmental effects (Regional Transmission Organization RTO) • Resource planning (10 - 40 yrs): define most profitable mix of supply sources and D-S programs using LP, DP, and risk analysis methods for projected prices, demands, fuel prices (GENCOs) • Pricing Decisions • Bidding (1 day - 5 yrs): optimize offers to provide power, subject to fuel and power price risks (suppliers) • Market clearing price determination (0.5- 168 hours): maximize social surplus/match offers (Power Exchange PX, marketers)

  10. Emerging Uses • Profit maximization rather than cost minimization guides firm’s decisions • Market simulation: • Use model of firm’s decisions to simulate market. Paul Samuelson: MAX {consumer + producer surplus}  Marginal Cost Supply = Marg. Benefit Consumption  Competitive market outcome Other formulations for imperfect markets • Price forecasts (averages, volatility) • Effects of environmental policies on market outcomes (costs, prices, emissions & impacts, income distribution) • Effects of market design & structure upon market outcomes

  11. Advantages of Process Models for Policy Analysis • Explicitness: • changes in technology, policies, prices, objectives can be modeled by altering: • decision variables • objective function coefficients • constraints • assumptions can be laid bare • Descriptive uses: • show detailed cost, emission, technology choice impacts of policy changes • show changes in market prices, consumer welfare • Normative: • identify better solutions through use of optimization • show tradeoffs among policy objectives

  12. Dangers of Process Models for Policy Analysis • GIGO • Uncertainty disregarded, or misrepresented • Ignore “intangibles”, behavior (people adapt, and are not profit maximizers) • Basic models overlook market interactions • price elasticity • power markets • multimarket interactions • Optimistic bias--overestimate performance of selected solutions

  13. The Overoptimism of Optimization (e.g., B. Hobbs & A. Hepenstal, Water Resources Research, 1988; J. Kangas, Silvia Fennica, 1999) • Auctions: The winning bidder is cursed: • If there are many bidders, the lowest bidder is likely to have underestimated its cost--even if, on average, cost estimates are unbiased. • Further, bidders whose estimates are error prone are more likely to win. • Process models: if many decision variables, and if their objective function coefficients are uncertain: • the cost of the “winning” (optimal) solution is underestimated (in expectation) • investments whose costs/benefits are poorly understood are more likely to be chosen by the model • E.g.: • this results in a downward bias in the long run cost of CO2 reductions • there will be a bias towards choosing supply resources with more uncertain costs

  14. Conclusion What can process-based policy models do well? • Exploratory modeling: examining implications of assumptions/scenarios upon impacts/decisions Exploratory modeling is becoming easier because of increasingly nimble models, and is becoming more important because of increased uncertainty/complexity

  15. Conclusions, continued What don´t process-based models do well? • Consolidative modeling: assembling the best/most defensible data/assumptions to derive a single “best” answer Although computer technology makes comprehensive models more practical than ever, increased complexity and diverse perspectives makes consensus difficult Models are for insight, not numbers (Geoffrion)

  16. III. Operations Model: System Dispatch LP • Basic model (cost minimization, no transmission, pure thermal system, no storage, deterministic, no 0/1 commitment variables, no combined heat/power). In words: • Choose level of operation of each generator to minimize total system cost subject to demand level • Decision variable: yift = megawatt [MW] output of generating unit i (i=1,..,I) during period t (t=1,..,T) using fuel f (f=1,…,F(i)) • Coefficients: CYift = variable operating cost [$/MWh] for yift Ht= length of period t [h/yr]. (Note: in pure thermal system, periods do not need to be sequential) Xi = MW capacity of generating unit i. (Note: may be “derated” for random “forced outages” FORi [ ]) CFi = maximum capacity factor [ ] for unit i LOADt = MW demand to be met in period t

  17. Operations LP MIN Variable Cost = Si,f,t Ht CYiftyift subject to: Si,fyift=LOADt t Sfyift<(1- FORi)Xi i,t Sf,tHtyift<CFi 8760Xi i yift> 0 i,f,t

  18. Using Operating Models to Assess NOx Regulation:The Inefficiency of Rate-Based Regulation(Leppitsch & Hobbs, IEEE Trans. Power Systems, 1996) • NOx: an ozone precursor N2 + O2 + heat  NOx NOx + VOC + O O3 • Power plants emit ~1/3 of anthropogenic NOx in USA

  19. Policy Question Addressed • How effectively can NOx limits be met by changed operations (“emissions dispatch”)? • What is the relative efficiency of: • Regulation based on tonnage caps Total emissions [tons] < Tonnage cap • Regulation based on emission rate limits (tons/GJ)? (Total Emissions[tons]/Total Fuel Use [GJ]) < Rate Limit

  20. Framework We want less cost and less NOx Cost Inefficient Efficient NOx Why might rate-based policies be inefficient? • Dilution effect: Increase denominator rather than decrease numerator of (NOx/Fuel Input) • Discourage imports of clean energy (since they would lower both numerator & denominator--even though they lower total emissions) =Alternative dispatch order

  21. How To Generate Alternatives Solve the following model for alternative levels of the regulatory constraint: MINSi CYiyi s.t. 1. MRi<yi< Xi(note nonzero LB) 2. Siyi> LOAD (MW) 3. Regulatory caps: either Si Eiyi< MASS CAP (tons)or (Si Eiyi)/(Si HRiyi)< RATE CAP (tons/GJ) Notes: 1. MR, X, LOAD vary (used a stochastic programming method: probabilistic production costing with side constraints) 2. Separate caps can apply to subsets of units

  22. Results • 11,400 MW peak and 12,050 MW of capacity, mostly gas and some coal. Most of capacity has same fuel cost/MBTU. Plant emission rates vary by order of magnitude (0.06 - 0.50 lb/MBTU) • With single tonnage cap, the cost of reducing emissions by 20% is $60M (a 5% increase in fuel cost). • Emissions rate cap raises control cost by $1M due to “dilution” effect (increase BTU rather than decrease NOx). More diverse system results in larger penalty.

  23. Cost of Inefficient Energy Trading Higher than Dilution Effect Two area analysis: energy trading for compliance purposes discouraged by rate limits

  24. Operating Model Formulation, Continued: Complications • Other objectives (Max Profit? Min Health Effect of Emissions?) • Energy storage (pumped storage, batteries), hydropower • Explicitly stochastic (usual assumption: forced outages are random and independent) • Including transmission constraints • Including commitment variables (with fixed commitment costs, minimum MW run levels, ramp rates) • Cogeneration (combined heat-power)

  25. Including Transmission:or Why Power Transport is Not Like Hauling Apples in a Cart Node or “bus” m Current Imn • Ohm`s law • Voltage drop m to n = DVmn = Vm-Vn= ImnZmn • DC: Imn = current from m to n, Zmn = resistance r • AC: Imn = complex current, Zmn = reactance = r + -1x • Power loss = I2R = IDV • Kirchhoff`s Laws: • Net inflow of current at any bus = 0 • S voltage drops around any loop in a circuit = 0 Bus n Voltage Vn

  26. Some Consequences of Transmission Laws • Power from different sources intermingled: moves from seller to buyer by “displacement” • Can`t direct power flow: “unvalved network.” Power follows many paths (“parallel flow”) • Flows are determined by all buyers/sellers simultaneously. One`s actions affect everyone, implying externalities: • 1 sells to 2 -- but this transaction congests 3`s transmission lines and increases 3`s costs • One line owner can restrict capacity & affect entire system • Adding transmission line can worsen transmission capability of system

  27. Modeling Transmission Flows(See Wood & Wollenburg or F. Schweppe et al., Spot Pricing of Electricity, Kluwer, 1988) • Linearized DC approximation assumes: • r << x (capacitance/inductance dominates) • Voltage angle differences between nodes small • Voltage magnitude Vm same all busses  an injection yifmt or withdrawal LOADmt at a node m has a linear effect on power ( I) flowing through “interface” k • Let “Power Transmission Distribution Factor” PTDFmk = MW flow through k induced by a 1 MW injection at m • assumes a 1 MW withdrawal at a “hub” bus • Then total flow through k in period t is calculated and constrained as follows: Tk- < [Sm PTDFmk(-LOADmt + Sifyifmt)] < Tk+

  28. Transmission Constraints in Operations LP MIN Variable Cost = Si,f,t Ht CYiftyifmt subject to: Si,f,myifmt=SmLOADtmt Sfyifmt<(1- FORi)Xi mi,m,t Sf,tHtyifmt<CFi 8760Ximi,m Tk-< [Sm PTDFmk(-LOADmt + Sifyifmt)] < Tk+ k,t yifmt> 0 i,f,m,t

  29. Unit Commitment:A Mixed Integer Program • Disregard forced outages & fuels; assume: • uit = 1 if unit i is committed in t (0 o.w.) • CUi = fixed running cost of i if committed • MRi = “must run” (minimum MW) if committed • Periods t =1,..,T are consecutive, and Ht=1 • RRi = Max allowed hourly change in output • MIN Si,t CYityit+ Si,t CUiuit s.t. Siyit=LOADt t MRi uit<yi<Xi uiti,t -RRi < (yit - yi,t-1)<RRi i,t Styit<CFi T Xi i yit> 0 i,t;uit {0,1} i,t

  30. IV. Deterministic Investment Analysis: LP Snap Shot Analysis • Let generation capacity xi now be a variable, with (annualized) cost CRF [1/yr] CXi [$/MW], and upper bound XiMAX. • MIN Si,f,t Ht CYiftyift + Si CRF CXi xi s.t. Si,fyift=LOADt t Sfyift- (1- FORi)xi< 0i,t Sf,tHtyift- CFi 8760xi < 0i Si xi> LOAD1 (1+M) (“reserve margin” constraint) xi<XiMAX (Note: equality for existing plants) i yift> 0 i,f,t; xi > 0 i

  31. Some Complications • Dynamics (timing of investment) • Plants available only in certain sizes • Retrofit of pollution control equipment • Construction of transmission lines • “Demand-side management” investments • Uncertain future (demands, fuel prices) • Other objectives (profit)

  32. Demand-side investments • Let zk= 1 if DSM program k is fully implemented, at cost CZk [$/yr]. • Impact on load in t = SAVkt [MW] • MIN Si,f,t Ht CYiftyift + Si CRF CXi xi+ Sk CZkzk s.t. Si,fyift+ Sk SAVktzk=LOADt t Sfyift- (1- FORi)xi< 0i,t Sf,tHtyift- CFi 8760xi < 0i Si xi+ (1+M) Sk SAVktzk> LOAD1 (1+M) xi<XiMAX i yift> 0 i,f,t; xi > 0 i; zk> 0 k

  33. V. Pure Competition AnalysisSimulating Purely Competitive Commodity Markets: An Equivalency Result • Background: Kuhn-Karesh-Tucker conditions for optimality • Definition of purely competitive market equilibrium: • Each player is maximizing their net benefits, subject to fixed prices (no market power) • Market clears (supply = demand) KKT conditions for players + market clearing yields set of simultaneous equations • Same set of equations are KKTs for a single optimization model (MAX net social welfare) • Widely used in energy policy analysis

  34. KKT Conditions Let an optimization problem be: MAX F(X) {X} s.t.: G(X) # 0 X $ 0 with X = {Xi}, G(X) = {Gj(X)}. Assume F(X) is smooth and concave, G(X) is smooth and convex. A solution {X,λ} to the KKT conditions below is an optimal solution to the above problem, and vice versa. I.e., KKTs are necessary & sufficient for optimality. MF/MXi - Σj λj MGj/MXi# 0; œ Xi: Xi$ 0; Xi(MF/MXi - Σj λj MGj/MXi) = 0 œλj: Gj# 0; λj$ 0; λj Gj = 0 { {

  35. Notation: Each node i is a separate commodity (type, location, timing) Consumer: BuysQDi QDi i j TEij TIij Transporter/Transformer: Uses exportsTEijfrom i to provide importsTIijto j h QSi Supplier: Uses inputsXito produce & sellQSi

  36. Players’ Profit Maximization Problems Consumer at i: MAX Ii(QDi) - Pi QDi {QDi} s.t. QDi$ 0 j Transporter for nodes i,j: MAX Pj TIij - Pi TEij - Cij(TEij,TIij) {TEij,TIij} s.t. Gij(TEij,TIij) # 0 (dual θij) TEij, TIij$ 0 i Supplier at i: MAX PiQSi - Ci(Xi) {QSi,Xi} s.t. Gi(QSi,Xi) # 0 (μi) Xi , QSi$ 0

  37. Supplier’s Optimization Problem and KKT Conditions Supplier at i: MAX PiQSi - Ci(Xi) {QSi,Xi} s.t. Gi(QSi,Xi) # 0 (dual mi) Xi , QSi$ 0 KKTs: QSi: (Pi - μi MGi/MQSi)# 0; QSi$ 0; QSi (Pi - μi MGi/MQsi) = 0 Xi: (-MCi/MXi - μi MGi/MXi) # 0; Xi$ 0; Xi (-MCi/MXi - μi MGi/MXi) = 0 μi: Gi # 0; μi$ 0; μi Gi = 0

  38. KKTs for All Players in Market Game + Market Clearing Condition Consumer KKTs,œ i: QDi: (MB(QDi) - Pi) # 0; QDi$ 0; QDi (MB(QDi) - Pi) = 0 Market Clearing, œ i: Pi: QSi + Σj 0 I(i) TEji - Σj 0 E(i) TIij - QDi = 0 Supplier KKTs,œ i : QSi: (Pi - μi MGi/MQSi)# 0; QSi$ 0; QSi (Pi - μi MGi/MQsi) = 0 Xi: (-MCi/MXi - μi MGi/MXi) # 0; Xi$ 0; Xi (-MCi/MXi - μi MGi/MXi) = 0 μi: Gi # 0; μi$ 0; μi Gi = 0 Transporter/Transformer KKTs,œ ij: TEij: (-Pi - MCij/MTEij - θijMGij/MTEij) # 0; TEij$ 0; TEij(-Pi - MCij/MTEij - θijMGij/MTEij) = 0 TIij: (+Pj - MCij/MTIij - θijMGij/MTIij) # 0; TIij$ 0; TIij(+Pi - MCij/MTIij - θijMGij/MTIij) = 0 θij: Gij# 0; θij$ 0; Gij θij = 0 N conditions & N unknowns!

  39. An Optimization Model for Simulating a Commodity Market • MAX Σi Ii(QDi) - Σi Ci(Xi) - Σij Cij(TEij,TIij) {QDi, QSi, Xi, TEij, TIij} s.t.: QSi + Σj 0 I(i) TIji - Σj 0 E(i) TEij - QDi = 0 (dual Pi)œ i Gi(QSi,Xi) # 0 (μi) œ i Gij(TEij,TIij) # 0 (θij) œ ij QDi, Xi, QSi $ 0 œ i TEij, TIij$ 0 œ ij • Its KKT conditions are precisely the same as the market equilibrium conditions for the purely competitive commodities market! Thus: • a single NLP can be used to simulate a market • a purely competitive market maximizes social surplus

  40. Applications of the Pure Competition Equivalency Principle • MARKAL: Used by Intl. Energy Agency countries for analyzing national energy policy, especially CO2 policies • Similar to EFOM used by VTT Finland (A. Lehtilä & P. Pirilä, “Reducing Energy Related Emissions,” Energy Policy, 24(9), 805+819, 1996) • US Project Independence Evaluation System (PIES) & successors (W. Hogan, "Energy Policy Models for Project Independence," Computers and Operations Research, 2, 251-271, 1975; F. Murphy and S. Shaw, "The Evolution of Energy Modeling at the Federal Energy Administration and the Energy Information Administration," Interfaces, 25, 173-193, 1995.) • 1975: Feasibility of energy independence • Late 1970s: Nuclear power licensing reform • Early 1980s: Natural gas deregulation • US Natl. Energy Modeling System(C. Andrews, ed., Regulating Regional Power Systems, Quorum Press, 1995, Ch. 12, M.J. Hutzler, "Top-Down: The National Energy Modeling System".) • Numerous energy & environmental policies • ICF Coal and Electric Utility Model (http://www.epa.gov/capi/capi/frcst.html) • Acid rain and smog policy • POEMS(http://www.retailenergy.com/articles/cecasum.htm) • Economic & environmental benefits of US restructuring • Some of these modified to model imperfect competition (price regulation, market power)

  41. VI. Analyzing Strategic Behavior of Power GeneratorsPart 1. Overview of Approaches(Utilities Policy, 2000) Benjamin F. Hobbs Dept. Geography & Environmental Engineering The Johns Hopkins University Carolyn A. Berry William A. Meroney Richard P. O’Neill Office of Economic Policy Federal Energy Regulatory Commission William R. Stewart, Jr. School of Business William & Mary College

  42. Questions Addressed by Strategic Modeling • Regulators and Consumer Advocates: • How do particular market structures (#, size, roles of firms) and mechanisms (e.g., bidding rules) affect prices, distribution of benefits? • Will workable competition emerge? If not, what actions if any should be taken? • approval of market-based pricing • approval of access • approval of mergers • vertical or horizontal divestiture • price regulation • Market players: What opportunities might be taken advantage of?

  43. Market Power = The ability to manipulate prices persistently to one’s advantage, independently of the actions of others • Generators: The ability to raise prices above marginal cost by restricting output • Consumers: The ability to decrease prices below marginal benefit by restricting purchases • Generators may be able to exercise market power because of: • economies of scale • large existing firms • transmission costs, constraints • siting constraints, long lead time for generation construction

  44. Projecting Prices & Assessing Market Power: Approaches • Empirical analyses of existing markets • Market concentration (Herfindahl indices) • HHI = Si Si2; Si = % market share of firm i • But market power is not just a f(concentration) • Experimental • Laboratory (live subjects) • Computer simulation of adaptive automata • Can be realistic, but are costly and difficult to replicate, generalize, or do sensitivity analyses

  45. Projecting Prices & Assessing Market Power: Approaches • Equilibrium models. Differ in terms of representation of: • Market mechanisms • Electrical network • Interactions among players “The principal result of theory is to show that nearly anything can happen”, Fisher (1991)

  46. Price Models for Oligopolistic Markets: Elements 1. Market structure • Participants, possible decision variables each controls: • Generators (bid prices; generation) • Grid operator (wheeling prices; network flows, injections & withdrawals) • Consumers (purchases) • Arbitrageurs/marketers (amounts to buy and resell) (Assume that each maximizes profit or follows some other clear rule) • Bilateral transactions vs. POOLCO • Vertical integration

  47. Model Elements (Continued) 2. Market mechanism • bid frequency, updating, confidentiality, acceptance • price determination (congestion, spatial differentiation, price discrimination, residual regulation) 3. Transmission constraint model. Options: • ignore! • transshipment (Kirchhoff’s current law only) • DC linearization (the voltage law too) • full AC load flow

  48. Model Elements (Continued) 4. Types of Games: • Noncooperative Games (Symmetric): Each player has same “strategic variable” • Each player implicitly assumes that other players won’t react. • “Nash Equilibrium”: no player believes it can do better by a unilateral move • No market participant wishes to change its decisions, given those of rivals (“Nash”). Let: Xi = the strategic variables for player i. Xic ={Xj, j  i} Gi = the feasible set of Xi pi(Xi,Xic) = profit of i, given everyone`s strategy {Xj*, i} is a Nash Equilibrium iff: pi(Xi*,Xic*) > pi(Xi,Xic*),  i, XiGi • Price & Quantity at each bus stable

  49. Model Elements (Continued) 4. Types of Games, Continued: • Examples of Nash Games: • Bertrand (Game in Prices). Implicit: You believe that market prices won`t be affected by your actions, so by cutting prices, you gain sales at expense of competitors • Cournot (Game in Quantities): Implicit: You believe that if you change your output, your competitors will maintain sales by cutting or raising their prices. • Supply function (Game in Bid Schedule): Implicit: You believe that competitors won’t alter supply functions they bid Bidi Qi

  50. Model Elements (Continued) 4. Types of Games, Cont.: • Noncooperative Game (Asymmetric/Leader-Follower): Leader knows how followers will react. • E.g.: strategic generators anticipate: • how a passive ISO prices transmission • competitive fringe of small generators, consumers • “Stackelberg Equilibrium” • Cooperative Game (Exchangable Utility/Collusion): Max joint profit. • E.g., competitors match your changes in prices or output