A Dynamic Framework for Real time and Regulation Markets for Smart Grids Anuradha Annaswamy Active adaptive Control Laboratory Department of Mechanical Engineering Massachusetts Institute of Technology * Joint work with A. Kiani, J. Knudsen, J. Hansen, D. Shiltz, M. Cvetkovic, T. Nudell, N. Nandakumar IMA Workshop on Control at Large Scales: Energy Markets and Responsive Grids
Paradigm Shift in Power Grids Generation Network Operations Transmission Increasing supply demand gap Environmental concerns Aging infrastructures Industrial Consumers Distribution Demand Response Smart Meters Smart Devices Distribution Consumers Industrial Consumers Distribution Consumers Conventional Grid Two major changes: Renewable energy resources Demand Response Both necessitate a dynamic framework Dynamic Market Mechanisms Utilities Energy providers DERs Microgrid Generation Facilities Network Operations Transmission Distribution Distributed Community Storage
Outline of my talk What is a Dynamic Market Mechanism? DMM and Frequency Regulation Dynamic Regulation Market Mechanisms Case study 1: 118 bus Case study 2: 3120 bus Case study 2: 3 interconnected 900 bus Focus is on wholesale markets
Economic Dispatch Today Collect cost curves Find optimal dispatch Communicate set points Generation ISO Flexible demand Periodic with a regular interval. Single iteration process. Centralized computation. Inflexible load Automatic generation control Generation set points Economic dispatch interval Time
Dynamic Market Mechanism Optimize social welfare Subject to constraints Lagrangian: S U P C P C P W D D Gc Gc Gw Gw j i l j j i i l l P P P B Gci Gwl wl D j nm n m i l j ( n, m) x: power generation/consumption : LMPs h: equality constraints : congestion prices g: inequality constraints B 0 max P nm n m nm T T,, L x f x h x g x k k k k x L x,, DMM: an iterative solution for economic dispatch x
Dynamic Market Mechanism (DMM): An iterative solution Start negotiations Negotiate and converge to an optimal solution Sufficiently long period for convergence Implement set points T T,, L x f x h x g x Δ,, Δ,, : Power generation/consumption : Marginal price : Social Welfare incl. Marginal Cost : Equality constraints : Inequality constraints Inflexible load Automatic generation control Use recent information,, Cost curves remain private Generation set points Economic dispatch interval Time
DMM and Demand Response* Generation (with Renewable Energy Resources) Consumption ISO, : Suggested generation/consumption at time : Suggested price at time
Dynamic Market Mechanism (contd.)* * Kiani and Annaswamy, IEEE TSG, 2014 Efficient Unique Equilibrium under KKT conditions Quantifies effect of volatility and stability Can help reduce reserve costs with uncertainty Δ in renewables Can incorporate adjustable DR
Simulation Results Wind Properties: : Actual Wind Power : Mean value of the projected wind. Current Market Practice : ARMA model of the actual wind power. With DMM G G 2 1 Area 2 Area 1 4 3 L 2 P D2 P D1 L 1
Simulation Results: Effect of Wind Uncertainty* All consumption devices were assumed to be adjustable. Less reserve is required. Hierarchical coordination * Kiani, Annaswamy, and Samad, IEEE TSG, 2014.
Demand Response: Bucket, Battery, Bakery Buckets P Dc Most flexible type of demand (can consume or supply power) Example: energy storage units, HVAC Batteries P Dt Have a deadline for achieving a fully charged state Example: Plug-in Hybrid Electric Vehicle Bakeries P Dk Energy must be consumed in an uninterrupted stretch Example: industrial production cycles The BBB Configuration Source: J. Hansen, J. Knudsen, and A.M. Annaswamy, Demand Response in Smart Grids: Participants, Challenges, and a Taxonomy, IEEE CDC, Los Angeles, CA, 2015
Problem Formulation (including BBB)* Note: The index k corresponds with the market clearing instance Nodal Power Balance Line Capacity The index K corresponds with the negotiation iterations Generation/Demand Power Limits Generation Rates of Change Demand Energy Limits * J. Knudsen, J. Hansen, and A.M. Annaswamy A Dynamic Market Mechanism for the Integration of Renewables and Demand Response, IEEE Transactions on Control Systems Technology, vol. 24, No. 3, 2016.
The Overall DMM Conventional generation Renewable generation Demand response Voltage angles Stability and convergence can be guaranteed.
Modified IEEE 118 Bus Test Case* Bus consists of: 45 conventional generators 9 renewable generators (30% penetration) 7consumers (10% penetration) 186 transmission lines * Knudsen, Hansen, Annaswamy, IEEE CST, 2016
Results: IEEE 118 bus
Outline of my talk Dynamic Market Mechanisms for Wholesale Markets an Introduction DMM and Frequency Regulation Dynamic Regulation Market Mechanisms Case study 1: 118 bus Case study 2: 3120 bus Case study 2: 4 interconnected 600 bus
DMM and shorter dispatch interval Negotiate and converge to an optimal solution Implement dispatch on shorter intervals. Start negotiations Inflexible load Sufficiently long period for convergence Implement set points Opportunities for addressing: o Significant and unpredicted penetration of renewables o Non zero mean volatility of renewable generation o High regulation requirements in presence of renewables Automatic generation control Generation set points Economic dispatch interval Time
Time scales Introduced by DMM DMM Negotiations AGC Updates 4 DMM Market Clearing OPF Market Clearing Existing time scales New time scales
Integrated DMM (economic dispatch + AGC) Conventional architecture Proposed approach Energy Market Regulation Market Energy Market Regulation Market Automatic Generation Control Automatic Generation Control Assumption of magnitude and time scale separation between OPF and AGC. Large penetration of intermittent energy represents a challenge. Aggregated feedback from AGC Simultaneous decisions at both markets.
DMM Iterates min f x st.. h' x 0 -S W + Barrier Functions Power Balance + K L B (ACE) m 2 feedback gain ACE from measurement phase disaggregation matrix Augmented Lagrangian: c L f x h x h x 2 T ' ' 2 Update x and using Newton s method k 1 k k x H N xlx, k N 0 k h' x
Feedback from AGC to DMM Measurements Negotiations Operation Frequency measurements averaged over, are used in negotiations during,, which take effect during the operating period,.
DMM Iterates Final Form Approximated Hessian Increases rate of convergence Preserves privacy Distributed gradient updates A single cost/utility bid per iteration Preserves privacy Procedure: 1. ISO sends x k 2. Market players send f 3. ISO computes and h 4. ISO computes x k+1 ) Modified power balance Integrates real time market and AGC Includes disaggregated ACE error as an extra load on the buses Market players can bid to optimally meet this load * Shiltz, Cvetkovic, Annaswamy, IEEE Transactions on Sustainable Energy, vol. 7, No. 2, 2016.
Modified IEEE 118 Bus Test Case Bus consists of: 45 conventional generators 9 renewable generators (30% penetration) 7flexible consumers (10% penetration) 186 transmission lines
DMM Market Clearings (50 clearings) 2600 30 s Generation [MW] 2400 2200 2000 1800 1600 275 270 265 260 255 250 245 Flexible Demand [MW] 1400 0 500 1000 1500 Conventional Generation Time [s] Renewable Generation Flexible Demand
Negotiations over a single 30 second period 36 400 Flexible Consumption [MW] 34 32 30 28 26 24 Conventional Generation [MW] 350 300 250 200 150 100 50 22 1110 1115 1120 1125 1130 1135 1140 Time [s] 0 1110 1115 1120 1125 1130 1135 1140 Time [s] Conventional generation Renewable generation Demand response Voltage angles
Actual Generation and Demand (With AGC feedback) 2600 Generation [MW] 2400 2200 2000 1800 1600 275 270 265 260 255 250 245 Flexible Demand [MW] 1400 0 500 1000 1500 Conventional Generation Time [s] Renewable Generation Flexible Demand
Impact on Area Control Error Peaks less severe using DMM than OPF Adding feedback shifts ACE closer to zero
Summary of DMM (with AGC)* 1. Allows flexible consumers to act as price setters at the real time market (and not only to respond to price) 2. Admits the most recent weather predictions in market clearing (every 30 seconds) 3. Enables feedback from AGC layer into the market layer, reducing regulation requirements 4. Preserves privacy of market players sensitive information e.g. cost curves, generation/consumption bounds Is this scaleable? * Shiltz, Cvetkovic, Annaswamy, IEEE Transactions on Sustainable Energy, vol. 7, No. 2, 2016.
Number of iterations to convergence Matpower test cases Number of iterations does not increase with decision variables The convergence time depends on: Step size Congestion Cost curves
Polish 3120 Bus Test System The system consists of: 3120 buses 3693 transmission lines with line capacities of 250 MW 505 generators with linear cost curves and capacities in the range 10MW 150MW Data source: Matpower Figure source: Paul Hines, Estimating and Mitigating Cascading Failure Risk, JST NSF DFG RCN Workshop, April 2015
Single DMM Clearing Transmission line flows Power generation Line 59 congestion Lines 31,32 congestion =30 s Locational marginal prices 30ms per iteration Generation and price increase at bus 3010 once three transmission lines reach their limits.
Outline of my talk Dynamic Market Mechanisms for Wholesale Markets an Introduction DMM and Frequency Regulation Dynamic Regulation Market Mechanisms Case study 1: 118 bus Case study 2: 3120 bus Case study 2: 4 interconnected 600 bus
Dynamic Regulation Market Mechanism In frequency regulation, set points are communicated every 2 4 seconds DMM takes roughly 30 seconds to converge P G Can we use intermediate negotiations as set points? t = 0 t = 30 s
DRMM as Secondary Control Current practice: Regulation Market Once per hour Real Time Market Wholesale dispatch Every 5 minutes Secondary Control Generator and DR set-point adjustments Every 2-4 seconds Primary Control Area Control Error Proposal: Market Players Real Time Market Price response signals Wholesale dispatch Every 5 minutes DRMM Generator and DR set-point adjustments Every 2-4 seconds Primary Control Area Control Error
Primary Control Dynamics Y PM P C bus frequencies bus voltage angles governor valve positions power generation power consumption P u P G D commanded generation commanded consumption : Buses with at least one generator : Load buses Bus dynamics (swing equation) M D P P P T in i i i i M j Cj Li ij i j G jg jd i, j E i i D P P T in i i Cj Li ij i j L jd i, j E i
Primary Control Dynamics (cont.) Simplified generator model 1 GY i i PG Y i i j ig Ri CH P i M Y i i PM ig i DR aggregator Combined dynamics P P P id D C D C i i i i A Bu EP L droop control inflexible load (exogenous) (governor) (turbine) Wholesale dispatch Market Players DRMM Comes from the DRMM Primary Control ACE
DRMM Dynamics Similar to DMM Decision variables: Update Equations: P G PD commanded voltage angles commanded generation commanded consumption price reply signals k1 k ˆ 1 k ˆk H N h negotiated prices at buses Solves modified OPF: energy neutral requirement of DR min f s.t. h = 0 g 0 E D = 0 error like signal modified power balance (including frequency feedback)
Link between Primary Control and DRMM Primary control: A Bu EP L Assume P L and u vary slowly u P k 1 k k k B E L where A t e t Δ (ex. Δ 1 0 As B e dsb t 0 As E e dse
DRMM Implementation Two way communication with System Operator Real Time Market Price response signals Wholesale dispatch Every 5 minutes Market Players DRMM Generator and DR set-point adjustments Once per second Primary Control ACE Set point vector drives both physics AND market negotiations in real time Conditions for stability and frequency regulation can be derived.* * Shiltz and Annaswamy, American Control Conference, 2016
3 area 900 bus example Extended to multiple interconnected power systems 3 Areas, 900 buses, 1233 transmission lines, 168 generators, 90 DR units
Disturbance Profile Load imbalance occurs at t = 0 Load imbalance assumed to be restored (by RTM dispatch) as shown in the figure
Results Frequency and tie line flows restored in all three areas
Results (cont.) Define regulation service costs as S S c ACE W ACE 2 DR shifts consumption into the future, when the need for power is less
Results (cont.) Regulation costs can be significantly reduced if DR units are able to defer consumption energy payback profiles costs normalized by the cost of primary control alone
Summary Dynamic Market Mechanism A framework for Wind and Solar integration and DR. Two different DMMs outlined. Dispatch DMM Economic dispatch can be made faster (~30s) Aggregated feedback from AGC can be introduced to result in reduced ACE. Improvement in Social Welfare Validation in 118 and 3120 buses Dynamic Regulation Market Mechanism Market and frequency dynamics proceed at the same time scale Validation in a 3 area 900 bus networks
Dynamic Market Mechanism for Dispatch Current Practice Regulation Market Once per hour Real Time Market Wholesale dispatch Every 5 minutes Secondary Control Generator and DR set-point adjustments Every 2-4 seconds Primary Control Area Control Error DMM Market Players Regulation Market DMM Negotiations several per second Wholesale dispatch Every 30 seconds Secondary Control Once per hour Generator and DR set-point adjustments Every 2-4 seconds Primary Control Area Control Error
Dynamic Regulation Market Mechanism for frequency regulation Current practice: Regulation Market Once per hour Real Time Market Wholesale dispatch Every 5 minutes Secondary Control Generator and DR set-point adjustments Every 2-4 seconds Primary Control Area Control Error DRMM Market Players Real Time Market Price response signals Wholesale dispatch Every 5 minutes DRMM Generator and DR set-point adjustments Every 2-4 seconds Primary Control Area Control Error
References A. Kiani, A.M. Annaswamy, and T. Samad, A Hierarchical Transactive Control Architecture for Renewables Integration in Smart Grids: Analytical modeling and stability, IEEE Transactions on Smart Grid, Special Issue on Control Theory and Technology, 5(4):2054 2065, July 2014. A. Kiani and A.M. Annaswamy. A Dynamic Mechanism for Wholesale Energy Market: Stability and Robustness, IEEE Transactions on Smart Grid, 5(6):2877 2888, November 2014. A. Kiani and A. M. Annaswamy. Equilibrium in Wholesale Energy Markets: Perturbation Analysis in the Presence of Renewables, IEEE Transactions on Smart Grid, 5(1):177 187, Jan 2014. Y. Sharon, A. M. Annaswamy, A. Motto, and A. Chakraborty, Adaptive Control for Regulation of a Quadratic Function of the State, IEEE Transactions on Automatic Control, 59(10):2831 2836, October 2014. J. Hansen, J. Knudsen and A. M. Annaswamy. "A Dynamic Market Mechanism for Integration of Renewables and Demand Response,, IEEE Transactions on Control Systems Technology, 2016. D. Shiltz, M. Cvetkovic, and A.M. Annaswamy, An Integrated Dynamic Market Mechanism for Real time Markets and Frequency Regulation,, IEEE Transactions on Sustainable Energy, vol. 7, No. 2, 2016. D. Shiltz and A.M. Annaswamy, A Practical Integration of Automatic Generation Control and Demand Response, American Control Conference, July 2016.
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