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Electrical and Computer Engineering Mississippi State University

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1 Electrical and Computer Engineering Mississippi State University
5th Southeast Symposium on Contemporary Engineering Topics (SSCET), 2014 A Parallel Solution to Stochastic Power System Operation with Renewable Energy Yong Fu, Ph.D. Associate Professor Electrical and Computer Engineering Mississippi State University New Orleans, LA September 19th, 2014

2 Parallel Computing With 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

3 Large Scale, Non-Convex, Mixed Integer Nonlinear Problem
A Typical Power System Operation Problem – Security Constrained Unit Commitment Objective Function – Minimize Generation and startup/shutdown costs Generating Unit Constraints Unit 1 Unit 2 Unit 3 Generation capacity Minimum ON/OFF time limits Ramping UP/DOWN limits Must-on and area protection constraints Forbidden operating region of generating units System Operation Constraints Power balance System reserve requirements Power flow equations Transmission flow and bus voltage limits Limits on control variables Limits on corrective controls for contingencies Large Scale, Non-Convex, Mixed Integer Nonlinear Problem

4 Security-Constrained
Who Use SCUC and How? ISOs: PJM, MISO, ISO New England, California ISO, New York ISO and ERCOT Day 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. GENCOs TRANSCOs ISO Security-Constrained Unit Commitment DISTCOs ISO (SCUC) and Market Participants

5 Stochastic SCUC In 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.

6 Stochastic SCUC --- Example
Cases Equipment Outage Wind (WM) Load (MW) Base case - 20 100 Scenario 1 G3 15 105 Scenario 2 L2 23 95 G1 13 $/MWh 40MW~80MW 1 2 G3 16 $/MWh 10MW~40MW L1 75MW G2 42 $/MWh 15MW~ 40MW L2 75MW Load G3 can adjust dispatches by 5 MW G2 is quick-start unit with 30 MW QSC W System Base Case Scenario Scenario 2 80 MW 75 MW ? MW 0 MW 0 MW 0 MW Solution 1 50 MW 52.5 MW 75 MW 0 MW 15 MW ? MW 50 MW 100 MW 52.5 MW 105 MW 95 MW 20 MW 15 MW 23 MW Base Case Scenario Scenario 2 65 MW 60 MW 52 MW 20 MW 15 MW 0 MW 42.5 MW 52.5 MW 75 MW Solution 2 0 MW 30 MW 0 MW 42.5 MW 100 MW 52.5 MW 105 MW 95 MW 20 MW 15 MW 23 MW

7 Current Work Amdahl’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.

8 Proposed Approach Structure 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.

9 Decomposition Strategy
Mathematically, the stochastic SCUC can be formulated as a mixed integer programming (MIP) problem as shown in Variable Duplication Technique Augmented Lagrangian Method

10 Algorithms for Parallel Solutions
Auxiliary Problem Principle (APP) Method Diagonal Quadratic Approximation (DQA) Method Alternating Direction Method of Multipliers (ADMM) Analytical Target Cascading (ATC) Method

11 Iterative Solution Procedure
Decomposition structure: Two separated auxiliary problem: Given values from the previous iteration Decision variables for the current iteration

12 Case Study – IEEE 118-bus Testing System
Case 1: Deterministic case Case 2: Stochastic case with 3 scenarios 54 thermal units 3 wind farms 118 buses 186 branches

13 Deterministic Case Study
The converged result is obtained after 39 iterations. Unit 36 at Hour 5 Unit 45 at Hour 5 Unit 36 at Hour 21 Unit 45 at Hour 21

14 Deterministic Case Study
Items Centralized SCUC Parallel Changes Total Cost ($) 1,583,700 1,584,997 +0.08% Time (Seconds) 19 8 -58%

15 Stochastic Case Study (3 scenarios)
Items Centralized SCUC Parallel SCUC Changes Cost ($) 1,582,840 1,583,565 +0.046% Time (Seconds) 1,083 20 -96%

16 Case 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

17 Case Study – A 1168-bus Power System
# of Scenarios # of Iteration Total Time (sec.) 315 109.55 1 330 146.06 2 299 139.31 3 327 163.47 4 277 142.28 5 278 140.28 6 248 139.52 7 243 130.94 8 242 133.25 9 237 148.33 10 231 131.95

18 Conclusions The 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.

19 Thanks !

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