Achieving optimal stochastic dispatch through direct multilateral trades

Prof. Pravin Varaiya (UC Berkeley), Presentation on Day 2 (Nov.4) of Workshop on Architecture and Economics of the Future Grid

Transcript

1. Contingent Coordinated Trading for Electricity Markets Junjie Qin with Ram Rajagopal and Pravin Varaiya Stanford University and University of California, Berkeley Novmber 1, 2016 1 / 20
2. Summary Inflexibility of ISO Coordinated multilateral transactions Basic setup Trading process example Mathematical treatment Discussion 2 / 20
3. ISO Operations ISO objectives of resource adequacy, congestion management and efficiency are achieved through Reserve requirements (reserve margins, LOLP) Day Ahead (DA) and Real Time (RT) markets Centralized dispatch and setting nodal prices (LMPs) of standard energy commodity 3 / 20
4. ISO Operations ISO objectives of resource adequacy, congestion management and efficiency are achieved through Reserve requirements (reserve margins, LOLP) Day Ahead (DA) and Real Time (RT) markets Centralized dispatch and setting nodal prices (LMPs) of standard energy commodity Since standard commodity and prices are too inflexible, ISO permits Bilateral contracts for large agents: GM, Amazon, Mars, Google etc have long-term fixed-price contracts for renewable energy. ISO prices do not affect bilateral contracts (except for congestion prices). New commodities for DR, ramping, · · · 3 / 20
5. ISO Operations ISO objectives of resource adequacy, congestion management and efficiency are achieved through Reserve requirements (reserve margins, LOLP) Day Ahead (DA) and Real Time (RT) markets Centralized dispatch and setting nodal prices (LMPs) of standard energy commodity Since standard commodity and prices are too inflexible, ISO permits Bilateral contracts for large agents: GM, Amazon, Mars, Google etc have long-term fixed-price contracts for renewable energy. ISO prices do not affect bilateral contracts (except for congestion prices). New commodities for DR, ramping, · · · ISO dispatch and prices set in ‘one shot’ by equating aggregate supply function and demand function bids Alternatives suggest price/quantity iterations that converge to ISO prices/quantities 3 / 20
6. A more flexible alternative Proposed alternative (coordinated multilateral transactions) is motivated by these examples: DA consumer demand is uncertain but known 12 hours ahead. This demand cannot be expressed in standard (DA or RT) commodity, although a supplier can meet this 12-hour ahead demand. 4 / 20
7. A more flexible alternative Proposed alternative (coordinated multilateral transactions) is motivated by these examples: DA consumer demand is uncertain but known 12 hours ahead. This demand cannot be expressed in standard (DA or RT) commodity, although a supplier can meet this 12-hour ahead demand. Consumer has a fixed energy demand over 24-hours but does not care when energy is delivered. The least cost way of meeting this demand cannot be expressed with ISO standard prices, although a supplier may meet this demand at cost acceptable to consumer. 4 / 20
8. A more flexible alternative Proposed alternative (coordinated multilateral transactions) is motivated by these examples: DA consumer demand is uncertain but known 12 hours ahead. This demand cannot be expressed in standard (DA or RT) commodity, although a supplier can meet this 12-hour ahead demand. Consumer has a fixed energy demand over 24-hours but does not care when energy is delivered. The least cost way of meeting this demand cannot be expressed with ISO standard prices, although a supplier may meet this demand at cost acceptable to consumer. Generator wants to make six-hour instead of hourly supply contracts, which cannot be expressed in terms of ISO contracts. 4 / 20
9. A more flexible alternative Proposed alternative (coordinated multilateral transactions) is motivated by these examples: DA consumer demand is uncertain but known 12 hours ahead. This demand cannot be expressed in standard (DA or RT) commodity, although a supplier can meet this 12-hour ahead demand. Consumer has a fixed energy demand over 24-hours but does not care when energy is delivered. The least cost way of meeting this demand cannot be expressed with ISO standard prices, although a supplier may meet this demand at cost acceptable to consumer. Generator wants to make six-hour instead of hourly supply contracts, which cannot be expressed in terms of ISO contracts. Consumer has PV, storage, flexible demand that could be advantageously traded with neighbors. Not possible with current markets. 4 / 20
10. A more flexible alternative Proposed alternative (coordinated multilateral transactions) is motivated by these examples: DA consumer demand is uncertain but known 12 hours ahead. This demand cannot be expressed in standard (DA or RT) commodity, although a supplier can meet this 12-hour ahead demand. Consumer has a fixed energy demand over 24-hours but does not care when energy is delivered. The least cost way of meeting this demand cannot be expressed with ISO standard prices, although a supplier may meet this demand at cost acceptable to consumer. Generator wants to make six-hour instead of hourly supply contracts, which cannot be expressed in terms of ISO contracts. Consumer has PV, storage, flexible demand that could be advantageously traded with neighbors. Not possible with current markets. Bilateral contracts do not impose uniform prices or standard commodities. 4 / 20
11. Basic setup Two time periods: DA and RT RT uncertainty expressed as finite set of (agreed-upon) scenarios [S] = {1, · · · , S} Network constraints modeled with DC approximation N buses, L line constraints together with power balance give: Power (net) injection region P = {p ∈ RN | Hp ≤ ¯ f, 1T p = 0} 5 / 20
12. Basic setup Two time periods: DA and RT RT uncertainty expressed as finite set of (agreed-upon) scenarios [S] = {1, · · · , S} Network constraints modeled with DC approximation N buses, L line constraints together with power balance give: Power (net) injection region P = {p ∈ RN | Hp ≤ ¯ f, 1T p = 0} Participants: I = IRT ∪ IDA = ∪n∈[N] In RT participants (e.g. gas, wind, consumers): IRT Contingent power injection plan pi = (pi,s )s∈[S] Local feasibility Pi = Pi,1 × · · · × Pi,S where Pi,s ⊂ R is interval Ex-ante (DA) expected utility Ui (pi ) = Ei [ui,s (pi,s )]. Ei depends on i; Ui assumed concave. DA participants (e.g. coal): IDA RT participants with non-anticipative constraint: Pi = Pi ∩ {pi | pi,s = pi,1 , s ∈ [S]}: pi,s does not depend on s. 5 / 20
13. A benchmark Social welfare maximization under uncertainty: max i∈I Ui(pi) s.t. pi ∈ Pi, i ∈ I xn,s = i∈In pi,s, n ∈ [N], s ∈ [S] xs ∈ P, s ∈ [S] 6 / 20
14. Trading process SO only enforces network constraints and is not concerned with efficiency. 7 / 20
15. Running example Two scenarios, S = 2: High wind output 100 MW w.p. 0.6. Low wind output 50 MW w.p. 0.4. 8 / 20
16. Example continued Trade 1: g3 → L = 150 in both scenarios. Since resulting flow in transmission line is 0, SO approves Trade 1. 9 / 20
17. Example continued Trade 2: g2 → g3 = 100 in S1 and = 50 in S2. Profitable for g2, g3. Flow = 100 in S1 and = 50 in S2 is feasible, SO approves Trade 2. 10 / 20
18. Example continued Trade 3: g1 → g3 = 50 in both scenarios. Flow = 150 in S1 and = 100 in S2 is infeasible. SO curtails trade to g1 → g2 = 20 giving feasible flow = 120 in S1 and = 70 in S2. 11 / 20
19. Example end Since flow = 120 in S1, SO requires future trades to induce no positive flow in S1 Since there is no such profitable trade, trading terminates. 12 / 20
20. Trading process definitions Contingent trade: k-th contingent trade among participants Ik ⊂ I is a collection of power injection plans pk = {(pk i,s ) : i ∈ Ik, s ∈ [S]} that are balanced in every scenario Contingent network nodal injection vector: qk n,s = i∈In pk i,s , n ∈ [N], s ∈ [S] Curtailed trade: γkpk, γk ∈ [0, 1] Trading state: yk i,s = k ξ=1 γξpξ i,s , i ∈ I, s ∈ [S]: accumulated forward positions for delivery at RT Network state: xk n,s = i∈In yk i,s , n ∈ [N], s ∈ [S] Contingent (residual) feasible injection set: Qs(xs) = P − xs 13 / 20
21. Trading process definitions, continued Feasible direction trade: given network state xk, trade pk is FD if its network injection vector qk satisfies hT l qk s ≤ 0, l ∈ Ls(xk s ), s ∈ [S] where Ls(xk s ) is the set of binding constraint in scenario s Ls(xk s ) = {l ∈ [L] : hT l xk s = ¯ fl} Worthwhile trade: trade pk at trading state yk is -worthy if i∈Ik Ui(yk i + pk i ) − Ui(yk i ) > , is -unworthy otherwise, and is profitable if it is -worthy with = 0. 14 / 20
22. Trading process 1 Initialization. SO initializes system state xk corresponding to a proposed feasible trade pk, k = 1. 2 Announcement. SO checks congestion in state xk, identifies Ls(xk s ), s ∈ [S] and announces network loading vectors hl, l ∈ Ls(xk s ), s ∈ [S]. This specifies FD. 3 Trading. If a profitable trade in the feasible direction pk is identified, participants arrange it. If no profitable trade is found, go to Step 6. 4 Curtailment. If pk is not feasible, i.e., the corresponding network injection qk is such that qk ∈ Q(xk), SO curtails trade with γk = max{γ : γqk ∈ Q(xk)} ∈ (0, 1) 5 Update. SO updates network state to xk+1 ← xk + γkqk, k ← k + 1. 6 Termination. 15 / 20
23. Curtailment 16 / 20
24. Efficiency Theorem. Suppose following assumptions hold: for > 0, any -unworthy trade in the feasible direction will not be arranged and any -worthy trade will eventually be identified and arranged, and once a worthy trade is identified, the market participants involved are willing to carry it out. Then the trading process is well-defined and the accumulated trading state yk converges to an -optimal solution pk of the social welfare maximization program. 17 / 20
25. Price discovery and CE Lemma. The trading process discovers the optimal contingent locational marginal prices. In particular, for bus n and contingency s, if there is a participant i ∈ IRT n whose utility function is differentiable and p∗ i,s ∈ P◦ i,s , λ∗ n,s = −π(s) ∂ui,s(p∗ i,s ) ∂pi,s Proposition. The collection of contingent power injection plans and contingent LMPs supports a competitive equilibrium under uncertainty (extended Arrow-Debreu equilibrium). 18 / 20
26. Discussion ISO DAM and RTM imposes particular cost and supply structures; CMT are much more flexible CMT reduces ISO functions to solving load flow CMT will permit many types of transactions that improve efficiency and encourage innovation 19 / 20
27. Discussion ISO DAM and RTM imposes particular cost and supply structures; CMT are much more flexible CMT reduces ISO functions to solving load flow CMT will permit many types of transactions that improve efficiency and encourage innovation Treatment can be extended to multiple delivery periods and multiple forward markets Losses can be incorporated in transactions. For a quadratic loss function, one can explicitly include loss allocation to each trade. DC analysis above can be replaced by nonlinear analysis. 19 / 20
28. Discussion ISO DAM and RTM imposes particular cost and supply structures; CMT are much more flexible CMT reduces ISO functions to solving load flow CMT will permit many types of transactions that improve efficiency and encourage innovation Treatment can be extended to multiple delivery periods and multiple forward markets Losses can be incorporated in transactions. For a quadratic loss function, one can explicitly include loss allocation to each trade. DC analysis above can be replaced by nonlinear analysis. Can CTM be implemented on top of current dispatch as way to manage uncertainty? Generalized convergence bidding? Can CTM, with suitably changed power flow model motivate a transaction based design for new distribution markets? 19 / 20
29. Summary Proposed a contingent trading based design for electricity market under uncertainty In the design, SO ensures reliability using checking and simple feedback (loading vectors announcement) and is unconcerned with efficiency Self-interested participants propose trades driving the system to efficient dispatch matching stochastic dispatch benchmark Trading process also discovers LMPs and supports CE under uncertainty. However, significance of LMPs is much reduced. 20 / 20