SuperOPF and Global-OPF : Design, Development, and Applications

Transcription

1 SuperOPF and Global-OPF : Design, Development, and Applications Dr. Hsiao-Dong Chiang Professor, School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA School of electrical Engineering and Automation, Tianjin University, Tianjin, PRC President, Bigwood Systems Inc. Ithaca, NY 14850, USA

2 One key Goal SuperOPF commercialization project has been supported by Department of Energy, USA since Develop a n OPF solver which can handle practical large power systems (>100,000 buses); To develop a robust and efficient OPF solver which can converge well under all loading conditions; To develop an OPF solver which can determine optimal values for discrete control variables. Evaluate on the PJM s 15,000-bus system and CAISO s 6,500-bus for Co-optimization models with more than 3 million matrix dimensions (considering renewable and contingency) 2

3 Network Models and Data Management Project objective: create a productiongrade SuperOPF software package Support utility industry OPF network models Handle utility industry standard data formats (CIM 10.0 (CAISO) and PSSE 30 (PJM) or above) Bigwood Systems Inc.,

4 Practical OPF Solvers Modeling capability (support PSS/E model, and CIM-compliance model) Speed Robust Large-scale OPF problems Quality of OPF solutions (local or global OPF solutions) Contingencies Stability constraints 4

5 Conventional formulation of AC Optimal Power Flow The Conventional formulation n B : # of buses n G : # of generators L: the set of lines n T : # of transformers n P : # of phase shifter n S : # of switchable shunts 5

6 Multi-Stage, Multi-level adaptive Homotopyenhanced Interior-Point-based Method A multi-stage and Multi-level solver is developed: Stage 1: Constraint analysis for improving convergence and detecting infeasibility. Stage 2: OPF without thermal constraints and identify active thermal constraints. Stage 3: OPF with active set of thermal constraints to eliminate all thermal violations (multi-level and homotopy-enhaced Stage). Stage 4: Determine discrete control variables 6 Bigwood Systems Inc., 2011

7 Stage 1: OPF Constraint Analysis and Feasibiity Detection 1. Improper generation upper bounds Issue: The upper generation bound is larger than the thermal limit of Line 1 or Line 2. Bus 1 Bus 2 Line 1 Generator 1 10MW Pg 100MW S 80MVA -20MVar Qg 20MVar Bus 1 Bus 2 Bus 23 Generator 1 10MW Pg 100MW -20MVar Qg 20MVar Line 1 S 150MVA Line 2 S 80MVA 7

8 Stage 1: OPF Constraint Analysis 2. Infeasible generation/thermal limits Correction: Lower the generation s upper and bounds. Effects: Such correction will restore the feasibility of the OPF computation. 8

9 Stage 1: detection of feasibility regions How to detect over-constrained OPF solutions (i.e. no solution exists due to over-constrained requirement) How to restore feasible regions 9

10 Stage 2: OPF w/o Thermal Limits The formulation: no thermal constraints 10

11 Stage 3: OPF with Thermal Constraints Only active thermal constraints are involved in stage 3 optimization. Active thermal constraints in the OPF solution at each iteration are added to the constraint set and solved by our proposed homotopy-enhanced Interior Point Method. 11

12 The Test System- PJM on-line test system Total buses loads 9691 generators 2304 Transmission branches transformers 1410 Switchable shunts 1404 Bigwood Systems Inc.,

13 Results: Real Power Loss

14 Results: Efficiency and Robustness (Automatic Differentiation method) Effects of constraint analysis Base case Without constraint analysis Converged in 256 iterations CPU time: ~ 600 seconds OPF loss: MW With constraint analysis Converged in 196 iterations CPU time: ~ 400 seconds OPF loss: MW Robustness of our method Loading Condition One-Staged Scheme Multi-Staged Scheme 1 Succeeded Succeeded 2 Succeeded Succeeded 3 Failed Succeeded 4 Failed Succeeded 5 Failed Succeeded 6 Failed Succeeded 7 Failed Succeeded 8 Failed Succeeded 9 Failed Succeeded 10 Failed Succeeded 14

15 Results: Efficiency and Robustness (Analytical Jacobian matrices) Effects of constraint analysis Base case Without constraint analysis Converged in 217 iterations CPU time: 177 seconds OPF loss: MW With constraint analysis Converged in 191 iterations CPU time: 143 seconds OPF loss: MW Robustness of our method Loading Condition One-Staged Scheme Multi-Staged Scheme 1 Succeeded Succeeded 2 Succeeded Succeeded 3 Succeeded Succeeded 4 Succeeded Succeeded 5 Failed Succeeded 6 Failed Succeeded 7 Failed Succeeded 8 Failed Succeeded 9 Failed Succeeded 10 Failed Succeeded 15

16 Results: Efficiency and Robustness The constraint analysis of Stage one can effectively speed-up OPF computation. The proposed multi-staged adaptive IPM-based method can robustly compute OPF solutions under all loading conditions. 16

17 Results: Thermal Violation

18 On the Global Convergence of a Class of Homotopy Methods for Nonlinear Circuits and Systems Tao Wang,Member, IEEE, and Hsiao-Dong Chiang,Fellow, IEEE IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 61, NO. 11, NOVEMBER 2014 Abstract Homotopy methods are developed for robustly computing solutions of nonlinear equations, which is of fundamental importance in nonlinear circuit and system simulations. This brief develops theoretical results on the global convergence of a class of homotopy methods for solving nonlinear circuits and systems. A set of sufficient conditions that guarantee the global convergence of homotopy methods is derived. These analytical results are then illustrated on a small nonlinear circuit and a large (about dimension) power grid.

19 Result 2: Generation Cost Minimization Randomly assigned generator types and costs Type # of Generators Min Cost ($/MWHr) Max Cost ($/MWHr) Mean Cost ($/MWHr) Coal 40 % Oil 15 % Nat. Gas 15 % Hydro 26 % Nuclear 2 % Wind 2 %

20 Result 2: Generation Costs 20

21 Result 2: Marginal Prices 21

22 CAISO 6534-Bus System Super-OPF Stage I: OPF Constraint Analyzer Stage II: Simple OPF without Thermal Limits Stage III: Homotopy OPF w/ Active Thermal Limits Stage IV: Sensitivity Analyzer for Discretization Input Data OPF Result CAISO System: Buses: 6534 Loads: 2901 Generators: 1903 Branches: 8295 Transformers: 294 Switched shunts: 520 OPF Dimensions: Dimension of x: Nonlinear equality constraints: Nonlinear inequality constraints: varying (<100) Total equality constraints: Total inequality constraints: >13652(varying) OPF Dimensions: Dimension of x: Nonlinear equality constraints: Nonlinear inequality constraints: 0 Total equality constraints: Total inequality constraints: CAISO System: Continuous variables: Discrete variables: 814

23 Super-OPF Contingency Analysis CAISO 6534-Bus System Initial Power Flow Super-OPF Solution BSI VSA Preventive Control CAISO System 1062 N-1 Contingencies Load margin: 3010MW Objective (loss): MW 7 insecure contingencies Load margin: 4840MW Objective (loss): MW 5 insecure contingencies Load margin: 4840MW Objective (loss): MW No insecure contingency

24 Challenges min Cx ( ) Subject to: hx ( ) 0 gx ( ) 0 However, security-constrained OPF can not be expressed as the above analytical form: i. Power balance equations: ii. iii. iv. Voltage limit constraints: Thermal limit constraints: Transient-stability constraints: v. Voltage stability constraints: hx ( ) 0 x x x gx ( ) 0?????? 2015/5/20

25 Super-OPF-VS (Voltage Stability) 1. Input 2. Feasibility Check 3. Ensuring Feasibility 4. Computation Engine S.E. Snapshot (CIM, PSSE, PSLF) Generation Cost Data Contingency List Base-case OPF Feasibility Analysis Base-case (Optimal) Adjustment for Restoring Feasibility N Feasible? Y Base-case Simulation Base-case Optimal Power Flow Computation (Super OPF Engine) Contingency List 3000 Detailed Output Report VSA Optimal Preventive Control VSA Optimal Enhancement Control Insecure Contingencies Critical Contingencies N Secure? Y Base-case OPF Voltage Security Analysis (BSI VSA Engine) 7. Output Report 6. VSA Enhancement 5. VSA Check

26 Automatic Voltage Control for Optimal Available Transfer Capability Project Dr. Hisao-dong Chiang (BSI) Principal Researcher Dr. Robert Entriken (EPRI) Project Manager

27 AVC project for Taiwan Power Company (TPC) Objective Design a real-time, closed-loop automatic voltage control system for TPC Assess its feasibility for implementation at TPC Metrics Power transfer capability increase Power losses reduction Voltage profile improvement

28 Every 1 5 minutes Every minutes Every 30 minutes - 1 hour BSI-AVC Design Objectives Architecture Time Voltage Stability Transfer Capability Central Control Center Regional optimization objectives Regional Control Center Regional Control Center Plant Controller Substation Controller Plant Controller Substation Controller

29 BSI AVC Key Benefits Central Control Center Regional Control Center System Wide Enhanced transfer capability Ensured static security including voltage stability Improved system wide voltage profile Reduced power losses Minimal system investment due to simple hierarchy

30 Three-layer Architecture Central Control Center Regional Control Center Plant & Substation Controller Plant & Substation Controller Plant & Substation Controller Source: 2012 Sustainability Report, TPC, August 2012

31 Architecture 1 Third Tier: On-line VSA Engine Taiwan Power Network Second Tier: On-line OPF Engine Control Center First Tier: Controllers Plant & Substation Controller Plant & Substation Controller Plant & Substation Controller

32 Transfer Capability Power Transfer Capability Definition Load margin (to the constraint violation point or to the voltage collapse point) is calculated as transfer capability in this test Power Transfer Pattern Load increase in area 1 (north), and is picked up by generators in area 2 and 3 (central and south)

33 System Information: 4 Areas North, Central, South, East System Information Buses 1713 (number of Loads 528 components) Generators 294 Branches 1331 Transformers 1333 Shunts 503

34 VSA/E Result Limiting contingency-no Pilot buses selected BUS Name vset BUS 210 林口 E BUS 1700 板橋 E 1.026

35 Transfer Capability (MW) Transfer Capability Improvement % 2334 Compared to results before AVC % Base Case Limiting Ctg

36 Power Losses (MW) Power Losses Reduction Base Case - 5.9% Compared to results before AVC Before AVC After AVC

37 Voltage Profile Improvement Before AVC (p.u.) After AVC (p.u.)

38 Issues with Current Generation of Optimal Power Flow Optimal power flow solution is NOT a global optimal solution Solvers only compute one (local) optimal solution while there are multiple local optimal solutions Each OPF solution corresponds to one location marginal pricing (which OPF solution is the right one?) Current AC OPF solvers are still not robust (one key reason for the adoption of simplified OPF solvers used in power market). 38