Power Market Participation of Flexible Loads and Reactive Power Providers: Real Power, Reactive Power, and Regulation Reserve Capacity Pricing at T&D Networks DIMACS, Rutgers U January 21, 2013 Michael Caramanis mcaraman@bu.edu
Outline • How can Flexible Loads Provide Fast Reserves • How do Distribution Network Injections Differ From Transmission System Bus Injections? • Current Market Bidding Rules Motivate Flexible Distributed Loads to Exercise Strategic Behavior Resulting in a Hierarchical Game • Conditions for Hierarchical Game to Converge • Revised Bidding Rules Remove Strategic Behavior Incentives and Allow ISO/“DNO” to Clear Market in a Socially Optimal Manner • Detailed Distribution Market Pricing Real and Reactive Power 2
Outline • How can Flexible Loads Provide Fast Reserves • How do Distribution Network Injections Differ From Transmission System Bus Injections? • Current Market Bidding Rules Motivate Flexible Distributed Loads to Exercise Strategic Behavior Resulting in a Hierarchical Game • Conditions for Hierarchical Game to Converge • Revised Bidding Rules Remove Strategic Behavior Incentives and Allow ISO/“DNO” to Clear Market in a Socially Optimal Manner • Detailed Distribution Market Pricing Real and Reactive Power 3
Generation and Demand Share Functional Characteristics that are Key to the Efficient and reliable Operation of the Electricity Grid Characteristic Generation Demand Dispatchability- Wind, Run of Riv /Neuclear, Capacity Loads, dependent on Schedulability L.E.P,/ HydroFossil env. e.g.,Light/ Ind. Energy Low/Med/High Loads Aluminum idle/Schedulable production of electr. energy intensive storable products (gas liquif.) Flexibility No Ramp – steady output Thermal or work inertia (Allum. Low/med/high e.g., nucl, min gen, start up Smelter)/Enegy Demand with cost and delay/ Inertia and small storage to capacity ratio medium storage/high ramp- (HVAC)/ Large storage to low inertia large storage capacity ratio (ice, molten salt, batteries in Evs) Forecastaility Wind, Solar. RoR Inflexible loads (lighting Low/Med/High Hydro/reliable cooking)/Weather fossil/unreliable fossil dependent/scheduled loads Voltage Control Synchronous Generators with Distributed Power Electronics dynamic Var compensators, accompanying EVs. HVAC, 4 DC-AC Converters Roof top PV.
Flexible Loads Require Energy by some deadline => Capable of Regulation Reserves 1 D: 10/1/11 0.8 S: 9/1/10 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 Instance of PJM Regulation Signal, y ( t ). Note Constant Average over relatively 5 short period of Time
Today Generating Units are Only Reserve Providers Example of Generator providing Super Fast Reserves: Frequency control and 40MW of Secondary Reserves Secondary Reserves Frequency Control 320MW 50MW Source: Courtesy of EnThes Inc., March 2007 6
Outline • How can Flexible Loads Provide Reserves • How do Distribution Network Injections Differ From Transmission System Bus Injections? • Current Market Bidding Rules Motivate Flexible Distributed Loads to Exercise Strategic Behavior Resulting in a Hierarchical Game • Conditions for Hierarchical Game to Converge • Revised Bidding Rules Remove Strategic Behavior Incentives and Allow ISO/“DNO” to Clear Market in a Socially Optimal Manner • Detailed Distribution Market Pricing Real and Reactive Power 7
Distribution Network Low Voltage Bus Marginal Cost Based Dynamic Prices (DLMP) Result from Augmenting Transmission System High Voltage Prices (LMP) by Marginal cost of: Line Losses, Reactive Power, Voltage control, Transformer Life Loss LV, n(k) LMP at Bus n HV, Bus n LV, n(i) DLMP at n(i)=m n(i) (LMP at n)+…Where m n(i) =(1+ML at n(i))… 8
Outline • How can Flexible Loads Provide Reserves • How do Distribution Network Injections Differ From Transmission System Bus Injections? • Current Market Bidding Rules Motivate Flexible Distributed Loads to Exercise Strategic Behavior Resulting in a Hierarchical Game • Conditions for Hierarchical Game to Converge • Revised Bidding Rules Remove Strategic Behavior Incentives and Allow ISO/“DNO” to Clear Market in a Socially Optimal Manner • Detailed Distribution Market Pricing Real and Reactive Power 9
Examples of Flexible Loads: State Dynamics Determine Preferences • Distributed PHEV Charging F F F F t t 1 t t ˆ x x d j j j j n i ( ) n i ( ) n i ( ) n i ( ) F deptime x 0 j n i ( ) • Centralized Pumped Storage Hydro Units psh t psh t 1 p t g t r R t x x p g g n p ( ) n p ( ) n ( ) p n p ( ) n p ( ) n p ( ) n ( ) p n p ( ) ps h 0 p s h 2 4 x x n p ( ) n ( ) p 10
Strategic Flexible PHEV Load Behavior F t E t t { E [ m λ d min j n i ( ) n n i ( ) E t R t t λ , λ , m F F , R n n n i ( ) j t j t j t , d , d , j t , n i ( ) n i ( ) F R , t R t t F t F t m λ d ] U ( x )} j j j n i ( ) n n i ( ) n i ( ) n i ( ) s t . . F F F F t t 1 t ˆ t x x d e.g., state dyn of EV dem. j j j j n i ( ) n i ( ) n i ( ) n i ( ) F F , R t t d d up/dn nature of Reg. Res. j j n i ( ) n i ( ) ˆ F F , R t t t [ d d ] C Local Constraint j j n i ( ) n i ( ) n i ( ) j 11
Use of Current Bidding Rules to Self Schedule F F R , t * t * Bid Energy d d at a very high price j j n i ( ) n i ( ) F R , t * t E t Bid Energy 2 d at energy price ~ m λ j n i ( ) n i ( ) n and Regulation Service Rate at 0. 12
Using the Current Bidding Rules. Bids described on the previous slide, induce the ISO/DSO to almost surely Schedule Energy and Reserves to the * values, and thus effectively self dispatch. ) ( t t t t t t max c u c d c g r R g n i ( ) n i ( ) n ( ) n ( ) n ( ) n ( ) c t t R t d , g , g , t t i n i ( ) n ( ) n ( ) , , s t . . F t t * c t g d d j n ( ) n i ( ) n i ( ) n ( ) n i ( ), j n i ( ) F n i ( ) t * 2 ( d c t ) E u , t d 0, t j n i ( ) n i ( ) n 2 j n i ( ) F R , R t t * c t g d Loss R R u , t t j n ( ) n i ( ) n i ( ) n n ( ) j n i , ( ) n i ( ) 13 & other capacity and ramp constr. for conv. gen. and dem.
Outline • How can Flexible Loads Provide Reserves • How do Distribution Network Injections Differ From Transmission System Bus Injections? • Current Market Bidding Rules Motivate Flexible Distributed Loads to Exercise Strategic Behavior Resulting in a Hierarchical Game • Conditions for Hierarchical Game to Converge • Revised Bidding Rules Remove Strategic Behavior Incentives and Allow ISO/“DNO” to Clear Market in a Socially Optimal Manner • Detailed Distribution Market Pricing Real and Reactive Power 14
Hierarchical Game Dynamics • Undamped Oscillations when Flex Load Updates Clearing Price Estimates Myopically to Most Recent ex-post ISO/DMO value • Convergence to stable equilibrium when Flex Load Updates Clearing Price Estimates Factoring in History, for example sets them Equal to their Time Average 15
UPQB LMP Convergence by Iteration (No Congestion) 5.00% Base Case Discrete Smooth Case 4.00% Quadratic Case % Convergence 3.00% 2.00% 1.00% 0.00% 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125 129 133 137 141 145 149 153 157 161 165 169 173 Iteration 16
UPQB LMP Convergence by Iteration (With Congestion) 5.00% Base Case Bus 1 Discrete Smooth Case Bus 1 Quadratic Case Bus 1 4.00% % Convergence 3.00% 2.00% 1.00% 0.00% 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125 129 133 137 141 145 149 153 157 161 165 169 173 Iteration 17
Step Size Impact on UPQB Convergence 3.00% Discrete Smooth Case Bus 1 (Steepest Descent) Discrete Smooth Case Bus 1 (Averaging) 2.50% Quadratic Case Bus 1 (Steepest Descent) Quadratic Case Bus 1 (Averaging) 2.00% % Convergence 1.50% 1.00% 0.50% 0.00% 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101 105 109 113 117 121 125 129 133 137 141 145 149 153 157 161 165 169 173 Iteration 18
(UPQB LMP - TCCB LMP) by Iteration 0.20 0.10 - 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Hour (0.10) $/MWh (0.20) Bus 1 Iterations 148, 151, 154, etc Bus 1 Iterations 149, 152, 155, etc (0.30) Bus 1 Iterations 150, 153, 156, etc (0.40) (0.50) 19
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