Presentation on theme: "Electrical and Computer Engineering Mississippi State University"— Presentation transcript:
1Electrical and Computer Engineering Mississippi State University 5th Southeast Symposium on Contemporary Engineering Topics (SSCET), 2014A Parallel Solution to Stochastic Power System Operation with Renewable EnergyYong Fu, Ph.D.Associate ProfessorElectrical and Computer EngineeringMississippi State UniversityNew Orleans, LASeptember 19th, 2014
2Parallel ComputingWith development of high performance computing technique, parallel computing technique can significantly improve computational efficiency of optimization problem with utilization of multi-processors and multi-threads.These improvements cannot be achieved by the architectures of the machines alone, it is equally important to develop suitable mathematical algorithms and proper decomposition & coordination technique in order to effectively utilize parallel architectures
3Large Scale, Non-Convex, Mixed Integer Nonlinear Problem A Typical Power System Operation Problem– Security Constrained Unit CommitmentObjective Function – MinimizeGeneration and startup/shutdown costsGenerating Unit ConstraintsUnit 1Unit 2Unit 3Generation capacityMinimum ON/OFF time limitsRamping UP/DOWN limitsMust-on and area protection constraintsForbidden operating region of generating unitsSystem Operation ConstraintsPower balanceSystem reserve requirementsPower flow equationsTransmission flow and bus voltage limitsLimits on control variablesLimits on corrective controls for contingenciesLarge Scale, Non-Convex, Mixed Integer Nonlinear Problem
4Security-Constrained Who Use SCUC and How?ISOs: PJM, MISO, ISO New England, California ISO, New York ISO and ERCOTDay Ahead Market (DAM) determines the 24-hourly status of the generating units for the following day based on financial bidding information such as generation offers and demand bids.Day Ahead UC for Reliability (RUC), which focuses on physical system security based on forecasted system load, is implemented daily to ensure sufficient hourly generation capacity at the proper locations.Look-Ahead UC (LAUC), as a bridge between day-ahead and real-time scheduling, constantly adjusts the hourly status of fast start generating units to be ready to meet the system changes usually within the coming 3-6 hours.Real-Time Market (RTM) further recommits the very fast start generating units based on actual system operating conditions usually within the coming two hours in 15-minute intervals.GENCOsTRANSCOsISOSecurity-ConstrainedUnit CommitmentDISTCOsISO (SCUC) and Market Participants
5Stochastic SCUCIn stochastic programming, the decision on certain variables has to be made before the stochastic solution is disclosed, whereas others could be made after.The set of decisions is then divided into two groups:A number of decisions are made before performing experiments. Such decisions are called first-stage decisions and the period when these decisions are made is called the first stage.A number of second-stage decisions are made after the experiments in the second stage.Stochastic models containing above two groups of variables, first-stage and second-stage decision variables, are called two-stage stochastic programming.
6Stochastic SCUC --- Example CasesEquipment OutageWind(WM)Load (MW)Base case-20100Scenario 1G315105Scenario 2L22395G113 $/MWh40MW~80MW12G316 $/MWh10MW~40MWL1 75MWG242 $/MWh15MW~ 40MWL2 75MWLoadG3 can adjust dispatches by 5 MWG2 is quick-start unit with 30 MW QSCWSystemBase Case Scenario Scenario 280 MW75 MW? MW0 MW0 MW0 MWSolution 150 MW52.5 MW75 MW0 MW15 MW? MW50 MW100 MW52.5 MW105 MW95 MW20 MW15 MW23 MWBase Case Scenario Scenario 265 MW60 MW52 MW20 MW15 MW0 MW42.5 MW52.5 MW75 MWSolution 20 MW30 MW0 MW42.5 MW100 MW52.5 MW105 MW95 MW20 MW15 MW23 MW
7Current WorkAmdahl’s law: an upper bound on the relative speedup achieved on a system with multi-processors is decided by the execution time of the application operating sequentially.
8Proposed ApproachStructure of Algorithm: Scenario-based stochastic model is adopted to analyze the uncertainties of load and wind energy in this paper. Instead of master-and-slave structure, UC and OPF subproblems are solved simultaneously in the proposed parallel calculation method.Convergence performance: In an iterative solution process, the number of iterations affects the overall computational time. Several convergence acceleration options, including initialization and update of penalty multipliers, truncated auxiliary problem principle and trust region technique, are used to improve the convergence performance and efficiency in a scenario-based study.
9Decomposition Strategy Mathematically, the stochastic SCUC can be formulated as a mixed integer programming (MIP) problem as shown inVariable Duplication TechniqueAugmented Lagrangian Method
10Algorithms for Parallel Solutions Auxiliary Problem Principle (APP) MethodDiagonal Quadratic Approximation (DQA) MethodAlternating Direction Method of Multipliers (ADMM)Analytical Target Cascading (ATC) Method
11Iterative Solution Procedure Decomposition structure:Two separated auxiliary problem:Given valuesfrom the previous iterationDecision variables for the current iteration
12Case Study – IEEE 118-bus Testing System Case 1: Deterministic caseCase 2: Stochastic case with 3 scenarios54 thermal units3 wind farms118 buses186 branches
13Deterministic Case Study The converged result is obtained after 39 iterations.Unit 36 at Hour 5Unit 45 at Hour 5Unit 36 at Hour 21Unit 45 at Hour 21
14Deterministic Case Study ItemsCentralizedSCUCParallelChangesTotal Cost ($)1,583,7001,584,997+0.08%Time (Seconds)198-58%
15Stochastic Case Study (3 scenarios) ItemsCentralized SCUCParallel SCUCChangesCost ($)1,582,8401,583,565+0.046%Time (Seconds)1,08320-96%
16Case Study – A 1168-bus Power System A practical 1168-bus power system with 169 thermal units, 10 wind farms, 1474 branches, and 568 demand sides.It could be nearly impossible to get a near-optimal stochastic SCUC solution for this system by applying a traditional centralized SCUC algorithm.However, the proposed parallel stochastic SCUC algorithm provides solutions.Unit 8 at Hour 1
17Case Study – A 1168-bus Power System # of Scenarios# of IterationTotal Time (sec.)315109.551330146.062299139.313327163.474277142.285278140.286248139.527243130.948242133.259237148.3310231131.95
18ConclusionsThe proposed stochastic SCUC approach minimizes the operation cost of system by possibility expectation of each scenarios, which can adaptively and robustly adjust generation dispatch in response to constraints in different scenarios.In comparison with traditional stochastic SCUC, optimal power flow problem does not have to wait for unit commitment decision, both problems can be solved simultaneously, which is more computational efficient in both day-head and real-time power markets.The ideas can be applied to various power system applications: state estimation, economic dispatch, and planning.