A DCOP Approach to the Economic Dispatch with Demand Response - PowerPoint PPT Presentation

A DCOP Approach to the Economic Dispatch with Demand Response Ferdinando Fioretto 1 , William Yeoh 2 , Enrico Pontelli 2 , Ye Ma 3 , Satishkumar J. Ranade 2 1 University of Michigan 2 New Mexico State University 3 Siemens Industry Inc. May, 2017

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Power Grid 1

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Power Grid: Power Generators 2

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Power Grid: Power Loads 3

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Power Grid: Distribution Cables 4

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Power Grid: Representation Such a G = ( V , E ) , transmission 2 3 1 l 2 g 1 g 3 4 5 l 5 l 4 6 g 6 5

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Power Grid: Representation Such a G = ( V , E ) , transmission 2 3 1 l 2 g 1 g 3 4 5 l 5 l 4 6 g 6 6

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Power Grid: Representation Such a G = ( V , E ) , transmission 2 3 1 l 2 g 1 g 3 4 5 l 5 l 4 6 g 6 7

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Smart Grid • Smart Grid: is a vision of the future electricity grid. • It adopts both electricity and information flow, to improve efficiency and reliability of the energy production and distribution. 8

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Smart Grid : EDDR Model • Economic Dispatch (ED) : Power allocation to generators in order to meet the power load with the lowest costs. • Demand Response (DR): How consumer should change their energy usage to reduce peak power consumption. • ED and DR are typically solved in isolation despite the clear inter-dependencies between them. • We propose a ED DR integrated model aimed at maximize the benefits of customers and minimize the generation costs. 9

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion EDDR Model ws: 0 1 H X @X X ↵ t u l ( L t c g ( G t Maximize: l ) − g ) maximize A t =1 l ∈ L g ∈ G is the discount parameter that captures Where: c g ( G t g )= ↵ g G t g + � g ( G t g ) 2 + | ✏ g sin( � g ( G min − G t g )) | g l ) 2 l ≤ β l ( � l L t l − 1 2 ↵ l ( L t if L t α l u l ( L t l ) = ( L t l ) 2 1 otherwise 2 β l Rippling effect on the generator’s power-cost curve caused by opening a sequence of generator steam valves. 10

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion EDDR Model ws: 0 1 H X @X X ↵ t u l ( L t c g ( G t Maximize: l ) − g ) maximize A t =1 l ∈ L g ∈ G Subject to: is the discount parameter that captures Constraints Type Generators and Loads limits unary Load predictions unary Power supply-demand balance n-ary DC power flow n-ary Transmission lines power limits global – non monotonic Generator ramp rate constraints binary Generator prohibited operating zones unary 11

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion DCOP: Model < X , D , F , A>: • X: Set of variables. • D: Set of finite domains for each variable. • F: Set of constraints between variables . • A: Set of agents, controlling the variables in X . l 2 x a x b U g 1 g 3 0 0 3 0 1 ⏊ 1 0 2 4 5 1 1 5 l 5 l 4 6 Constraint g 6 12

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion DCOP: Model < X , D , F , A>: • X: Set of variables. • D: Set of finite domains for each variable. • F: Set of constraints between variables . • A: Set of agents, controlling the variables in X . • GOAL: Find a utility maximal assignment. x ⇤ = arg max F ( x ) x X = arg max f ( x | scope ( f ) ) x f 2 F i i i 13

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion DCOP: Assumptions • Agents coordinate an assignment for their variables. x a • Agents operate distributedly. f ab f ac Communication: • By exchanging messages. x b x c f bc • Restricted to agent’s local neighbors. Knowledge: f bd • Restricted to agent’s sub-problem. x d • Privacy preserving. 14

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion EDDR Model • The EDDR model accommodates dynamic changes in the load predictions. changes in load predictions t 1 t 2 t 3 t 4 2 1 3 l 2 g 1 g 3 4 5 l 5 l 4 6 g 6 15

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Dynamic DCOP • Dynamic DCOP: • Model dynamic changes as sequence of static DCOPs P 1 , …, P H . • Solve each static DCOP individually. • Reactive approach . changes to the DCOP P 1 P 2 1 2 3 l 2 g 1 g 3 4 5 l 5 l 4 6 g 6 16

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion Dynamic DCOP • Dynamic DCOP: • Model dynamic changes as sequence of static DCOPs P 1 , …, P H . • Solve each static DCOP individually. • Proactive approach . H opt = 3 Lookahead P 4 P 3 P 2 P 1 2 1 3 l 2 g 1 g 3 4 5 l 5 l 4 6 g 6 17

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion EDDR Model • Inference-based DCOP approach. • Problem: Transmission lines power limits. • Causes the messages size to increase exponentially at each step. ws: 0 1 H X @X X ↵ t u l ( L t c g ( G t l ) − g ) maximize Maximize: A t =1 l ∈ L g ∈ G is the discount parameter that captures Subject to: Constraints Type Generators and Loads limits unary Load predictions unary Power supply-demand balance n-ary DC power flow n-ary Transmission lines power limits global – non monotonic Generator ramp rate constraints binary Generator prohibited operating zones unary 18

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion EDDR Model • Inference-based DCOP approach. • Problem: Transmission lines power limits. • Discard the global constraint. • Introduce a penalty term for each transmission line. 0 1 H X @X X X ↵ t u l ( L t c g ( G t � t l ) − g ) − Maximize: ij A t =1 l ∈ L g ∈ G ( i,j ) ∈ E Subject to: Constraints Generators and Loads limits Load predictions Power supply-demand balance Iterative approach to DC power flow attempt improving the solution quality. Transmission lines power limits Generator ramp rate constraints Generator prohibited operating zones 19

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion EDDR: Results • Domains (all with non-convex solution spaces): System # generators # loads # transmission lines IEEE 5-Bus 1 5 7 IEEE 14-Bus 5 11 20 IEEE 30-Bus 6 27 41 IEEE 57-Bus 7 42 80 IEEE 118-Bus 54 91 177 • Evaluation Metric: • Simulated Runtime. • Solution Quality (Normalized Social Welfare). • Solution Stability (with Matlab Simulink SimPowerSystem simulator). 20

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion EDDR: Results Settings N ORMALIZED Q UALITY • 0.01PU discretization unit. 4 1 2 3 4 H opt • Domain sizes = 100 – 320. 5 0.8732 0.8760 0.9569 1.00 • We fix H = 12 and vary the H opt . IEEE Buses 14 0.6766 0.8334 1.00 – 0.8156 1.00 – – 30 57 0.8135 1.00 – – 118 1.00 – – – S IMULATED R UNTIME ( SEC ) Main Results GPU Implementation CPU Implementation • All solutions reported were H opt 1 2 3 4 satisfiable within 4 iterations . 5 0.010 0.044 3.44 127.5 • The solution quality increases IEEE Buses 14 0.103 509.7 – – as H opt increases. 30 0.575 9084 – – • The runtime increases as H opt 57 4.301 – – – increases. 118 174.4 – – – 21

Power Grid | EDDR | DCOP | Relaxation | Results | Conclusion EDDR : Exploiting GPU parallelism • Each agent need to compute a large number of combinations of powers injections and withdraws. • Fine granularity in the domain representation (0.01 PU). • Exploit Parallelism from [Fioretto et al., CP’15]. Exploit GPU parallelism G 1 L 1 f 1 f 1 . . . . . . Utility 1 1 12 13 10 23 . . . 21.3 1.3 . . . 70.4 9 23 . . . 20.3 2.2 . . . 71.3 . . . . . . . . . . . . . . . . . . . . . G 1 L 1 f 1 f 1 . . . . . . Utility 1 2 1 2 12 13 (b) Example Initialized Table for Agent + + 15 33 . . . 22.9 3.5 . . . 80.4 G 1 L 1 f 1 f 1 . . . . . . Utility + 2 2 12 13 + 16 33 . . . 24.5 -3.1 . . . 90.4 5 10 . . . 1.6 2.2 . . . 10.0 . . . . . . . . . . . . . . . . . . . . . 6 10 . . . 3.2 -4.4 . . . 20.0 . . . . . . . . . . . . . . . . . . . . . (c) Example Aggregated Table for Agent 22