TAILIEUCHUNG - Lecture Methods of Electric power systems analysis - Lesson 8: Sparse systems

Lecture Methods of Electric power systems analysis - Lesson 8: Sparse systems provide students with knowledge about general sparse matrix storage; a general approach for storing a sparse matrix would be using three vectors, each dimensioned to number of elements; unordered approach doesn’t make for good computation since elements used next computationally aren’t necessarily nearby; . | ECEN 615 Methods of Electric Power Systems Analysis Lecture 8 Sparse Systems Prof. Tom Overbye Dept. of Electrical and Computer Engineering Texas A amp M University overbye@ Announcements Homework 2 is due on Thursday September 17 Optionally you can setup your code to ignore the resistance terms this eliminates the G elements from the bus admittance matrix For homework 2 you ll need to commercial version of PowerWorld Simulator. 1 General Sparse Matrix Storage A general approach for storing a sparse matrix would be using three vectors each dimensioned to number of elements AA Stores the values usually in power system analysis as double precision values 8 bytes JR Stores the row number for power problems usually as an integer 4 bytes JC Stores the column number again as an integer If unsorted then both row and column are needed New elements could easily be added but costly to delete Unordered approach doesn t make for good computation since elements used next computationally aren t necessarily nearby Usually ordered either by row or column 2 Sparse Storage Example Assume 5 0 0 4 0 4 0 3 A 0 0 3 2 4 3 2 10 AA 5 4 4 3 3 2 4 3 2 10 Then JR 1 1 2 2 3 3 4 4 4 4 JC 1 4 2 4 3 4 1 2 3 4 Note this example is a symmetric matrix but the technique is general 3 Compressed Sparse Row Storage If elements are ordered as was case for previous example storage can be further reduced by noting we do not need to continually store each row number A common method for storing sparse matrices is known as the Compressed Sparse Row CSR format Values are stored row by row Has three vector arrays AA Stores the values as before JA Stores the column index done by JC in previous example IA Stores the pointer to the index of the beginning of each row 4 CSR Format Example Assume as before 5 0 0 4 0 4 0 3 A 0 0 3 2 4 3 2 10 Then AA 5 4 4 3 3 2 4 3 2 10 JA 1 4 2 4 3 4 1 2 3 4 IA 1 3 5 7 5 CSR Comments The CSR format reduces the storage requirements by taking advantage of needing only one .

• Điện - Điện tử
• Lecture Methods of Electric Power Systems
• Bài giảng Phương pháp phân tích hệ thống điện
• Methods of electric power systems
• Sparse systems
• Compressed sparse row
• Graph theoretic interpretation
• Power systems overview
• Consumes electric energy
• Electric grid time frames
• Inertia power flow
• Black start
• Electric grid visualization
• Synthetic electric grids
• Voltage stability
• High quality synthetic electric grids
• Geomagnetic disturbances
• Electric grid risks
• Electric power dashboard
• Advanced power flow
• Sparse vector methods
• Power operations
• Power flow
• Automatic generation control
• Residential distribution transformers
• Synchronous machines generate electricity
• DC power flow
• Gaussian elimination
• Power flow analysis
• Power system analysis tools
• Steady state analysis tool
• Power balance equations
• Newton Raphson algorithm
• Newton Raphson power flow
• Modeling voltage dependent load
• Circulating reactive power
• Coordinated reactive control
• Power flow sensitivities
• Power llow sensitivity analysis
• Post contingency system
• Power transfer distribution factor
• Line outage distribution factor
• Economic dispatch
• Optimal power flow
• Mixed integer programming
• Linear programming (LP)
• OPF problem formulation
• State estimation
• Electric grid measurements
• Potential transformers (PTs)
• Power flow topology processing
• Topology processing agorithm
• Substation configurations
• Electricity markets
• Horizontal market power
• Simultaneous auctions
• Pseudo inverse
• Energy management systems
• Matrix singular value decomposition
• Dynamic pricing
• Low frequency events
• Avoidable transmission level
• Least squares
• Nonlinear formulation
• Nutrition problem marginal costs
• Nonlinear cost functions