Workshop COOPS 2017 in Milano. Bidding System Design for Multiperiod Electricity Markets. Takayuki Ishizaki (Tokyo Institute of Technology)

Transcription

1 Workshop COOPS 2017 in Milano Bidding System Design for Multiperiod Electricity Markets Takayuki Ishizaki (Tokyo Institute of Technology) M. Koike (Tokyo Uni of MST) N. Yamaguchi (Tokyo Uni of Sci) J. Imura (Tokyo Tech)

2 Contents Part I: What is bidding system design? Problem formulation relation between market clearing problem and convex optimization relation between bidding curves and cost functions difficulty in bidding system design for multiperiod markets Part II: How to design a bidding system for multiperiod markets? basis transformation compatible with energy shift market sequential market clearing scheme numerical examples An approximate solution method 2/28

3 Day-Ahead Energy Markets Energy Market (ISO) bidding curves Agg 1 Agg 2 Agg 3 total bidding curves energy price Example 2 time spots, 3 aggregators multiple spots Market Results Aggregator 1 (producer) Aggregator 2 (consumer) Aggregator 3 (prosumer) Clearing Price Spot 1 (AM) [yen/kwh] Spot 2 (PM) [yen/kwh] Decision variables: Balanced Market clearing: Find desirable & such that.

4 Market Clearing as Optimization Market Results Aggregator 1 (producer) Aggregator 2 (consumer) Aggregator 3 (prosumer) Clearing Price Spot 1 (AM) [yen/kwh] Spot 2 (PM) [yen/kwh] Profit of Agg α: (selfish objective function) income cost See later how to determine (especially for prosumer!) Social profit: (social objective function) social cost Social profit maximization = Social cost minimization primal: dual: 4/28

5 Bidding Curves for Market Clearing Suppose that bidding curves for each spot are submitted to ISO Aggregator 1 Aggregator 2 Aggregator 3 Total Spot 1 (AM) energy price Spot 2 (PM) ISO can find each clearing price and balancing amounts as crossing points of (total) bidding curves But Are such crossing points really solutions of social cost minimization:?? 5/28

6 Brief Summary: Bidding System Design Socially optimal market clearing problem: Find primal: dual: Q1: What is a reasonable cost function?? Prosumption solving should be a mixture of generators, batteries, renewables etc Q2: Is it possible to construct bidding curves from?? Social cost should be minimized with and found as crossing-points Energy Market (ISO) total bidding curves bidding curves Agg 1 Agg 2 Agg 3 n spots Bidding system design = Distributed algorithm design under pre-specified ISO operation

7 Contents Part I: What is bidding system design? relation between market clearing problem and convex optimization relation between bidding curves and cost functions difficulty in bidding system design for multiperiod markets Part II: How to design a bidding system for multiperiod markets? basis transformation compatible with energy shift sequential clearing scheme for energy shift markets numerical examples 7/28

8 Prosumption Cost function Agg Internal decision variables generated power battery charge/discharge Constraints: (e.g. ) Generation cost Battery usage cost Given Theorem If and are both convex, then where is convex with respect to Example 2 time spots (AM/PM) Constants: s.t. : supply-demand balance inside aggregator not unique! Optimal strategy for energy resources ensures convexity of. 8/28

9 Prosumption Cost function Agg Internal decision variables generated power battery charge/discharge Constraints: (e.g. ) Generation cost Battery usage cost Given Theorem If and are both convex, then is convex with respect to where Uncertain renewables can be handled as robust optimization like: where is a scenario set of renewable generation on-going work (More interesting to see how magnitude of uncertainty affects economics!) 9/28

10 Derivation of Bid Functions Example 2 time spots [yen] Generators & loads: (A) (A+B) Spec of generators: (A) 0~50 5 [yen/kwh] (B) 0~50 10 [yen/kwh] Generation cost: Feasible generator outputs: additively decomposable disjoint decomposable! Bid functions 10/28

11 Mathematics behind Bid Functions Bid functions (period-specific) [yen] convex Bidding curve monotone increasing Maximum profit [yen] convex [yen/kwh] [yen/kwh] Legendre transform of cost function Legendre transformation (convex conjugation) : convex 11/28

12 Multiperiod Bid Function Generation cost: Feasible generator outputs: Ramp rate limit (Added): temporally correlated! Multiperiod bid function indecomposable! : monotone increasing bidding curves bidding hyperplanes Multiperiod bid function is not compatible with current bidding system

13 Separability of Multiperiod Bid Function Example Battery aggregator SOC constraints: not disjoint! Cost function based on utility of final SOC: [yen] 10 [yen/kwh] 5 [yen/kwh] Lemma The multiperiod bid function is separate iff not additively decomposable! the cost function is additively decomposable and its domain is disjoint i.e. Negative fact!! Traditional bidding curves available just in very special cases

14 Brief Summary: Bidding System Design Socially optimal market clearing : Bidding system design = Distributed algorithm design under pre-specified ISO operation Theorem is convex where Multiperiod bid function: monotone increasing Lemma additively decomposable bidding hyperplanes separate disjoint Bidding system design for multiperiod markets is not so simple!! 14/28

15 Contents Part I: What is bidding system design? relation between market clearing problem and convex optimization relation between bidding curves and cost functions difficulty in bidding system design for multiperiod markets Part II: How to design a bidding system for multiperiod markets? basis transformation compatible with energy shift sequential clearing scheme for energy shift markets numerical examples 15/28

16 Ideas in Proposed Approach A) Basis transformation towards better approximation B) Approximation of bidding hyperplanes to bidding curves high Approximate bidding curve low large variance temporal correlation reduced! smaller variance C) Sequential market clearing scheme From optimization view: (A) preconditioning (B)-(C) updates of primal/dual variables 16/28

17 Energy Shift: A Key Property of Batteries Agg 1 (generators): (A) 0~50 5 [yen/kwh] Spec of gens: (B) 0~50 10 [yen/kwh] Agg 2 (loads): Optimal price: (B) 10 [yen/kwh] (A) 5 [yen/kwh] Agg 3 (batteries): PM: discharge (sell) AM: charge (buy) shift social cost minimum (B) 10 [yen/kwh] (A) 5 [yen/kwh] New optimal price: Battery leads to price levelling-off! Energy market with explicit consideration of energy shift?? 17/28

18 Fourier-Like Basis Transformation Example 2 time spots AM PM AM PM average (total) energy shift energy (PM to AM) : average (levelling-off) price : energy shift price Explicit consideration of levelling-off price & energy shift price Energy shift market: primal: dual: 18/28

19 Sequential Market Clearing Step 1) Market clearing of average energy amounts Multiperiod bid function: Approximate bid function: assumption (premise) of price levelling-off ISO determines & by approximate bidding curves Step 2) Market clearing of shift energy amounts Approximate bid function: cleared amount ISO determines & by approximate bidding curves 19/28

20 Example: Sequential Market Clearing Agg 1 (generators): Agg 2 (loads): Agg 3 (batteries): (A) 0~50 5 [yen/kwh] (B) 0~50 10 [yen/kwh] Utility [yen] 7 [yen/kwh] 3 [yen/kwh] Final SOC Socially optimal market results (only god knows!!) (B) 10 [yen/kwh] Optimal clearing price: (A) 5 [yen/kwh] Agg 1 Agg 3 optimal price levels off (i.e. ) 20/28

21 Example: Sequential Market Clearing Agg 1 (generators): (A) 0~50 5 [yen/kwh] (B) 0~50 10 [yen/kwh] Agg 2 (loads): Agg 3 (batteries): 1) Market clearing of average energy amounts Approximate bid function: Utility [yen] 7 [yen/kwh] 3 [yen/kwh] Final SOC discharge (sell) [yen/kwh] charge (buy) 21/28

22 Example: Sequential Market Clearing Agg 1 (generators): (A) 0~50 5 [yen/kwh] (B) 0~50 10 [yen/kwh] Agg 2 (loads): Agg 3 (batteries): 1) Market clearing of average energy amounts Balancing amounts: 2) Market clearing of shift energy amounts Approximate bid function: Utility [yen] 7 [yen/kwh] Average price: 3 [yen/kwh] Final SOC [yen/kwh] 22/28

23 Example: Sequential Market Clearing Agg 1 (generators): (A) 0~50 5 [yen/kwh] (B) 0~50 10 [yen/kwh] Agg 2 (loads): Agg 3 (batteries): 1) Market clearing of average energy amounts Balancing amounts: 2) Market clearing of shift energy amounts Balancing amounts: Utility [yen] 7 [yen/kwh] Average price: 3 [yen/kwh] Shift energy price: Final SOC Theorem Socially optimal market clearing iff optimal price levels off i.e. 23/28

24 Example: Sequential Market Clearing Agg 1 (generators): Agg 2 (loads): (A) 0~50 5 [yen/kwh] (B) 0~50 10 [yen/kwh] Optimal clearing price: Agg 3 (batteries): (without battery aggregator) 1) Market clearing of average energy amounts Balancing amounts: 2) Market clearing of shift energy amounts (w/o) Average price: Clearing price: [yen/kwh] At least approximate clearing even if optimal price does not level off 24/28

25 Numerical Example Agg 1, Agg 2 (loads & batteries) Charge/discharge efficiencies: SOC/inverter constraints: parameters Agg 3 (9 types of generators) 95% (Agg 1) 94% (Agg 2) Load Generation costs: 3, 6,, 27 [yen/kwh] Time [h] Resultant social costs when varying battery penetration levels (16 time spots) Social cost [yen] comparison (next slides) Battery penetration level : time domain (sequential clearing) : Fourier-like domain (sequential clearing) : socially optimal (only god knows) Almost optimal market clearing when high battery penetration! price levelling-off 25/28

26 Sequential Clearing in Time Domain Clearing price Generators (9 types) Price [yen/kwh] : socially optimal : approx clearing large gap from optimal! Generation Time [h] Time [h] Charge/discharge Charge/discharge of batteries Time [h] Stored energy SOC of batteries Time [h] 26/28

27 Sequential Clearing in Fourier-Like Domain Clearing price Generators (9 types) Price [yen/kwh] : socially optimal : approx clearing smaller gap from optimal Generation Time [h] Time [h] Charge/discharge Charge/discharge of batteries Time [h] Stored energy SOC of batteries Time [h] 27/28

28 Concluding Remarks Bidding system design for multiperiod electricity markets Distributed algorithm design for convex optimization Each aggregator submits bidding curves to ISO ISO finds clearing price and balancing amounts by bidding curves Proposed approach to bidding system design Basis transformation compatible with energy shift markets Sequential clearing scheme based on approximate bidding curves A Distributed Scheme for Power Profile Market Clearing under High Battery Penetration, IFAC WC 2017 Bidding System Design for Multiperiod Electricity Markets: Pricing of Stored Energy Shiftability, CDC 2017 (to appear) Thank you for your attention!