Presentation on theme: "EE 369 POWER SYSTEM ANALYSIS"— Presentation transcript:
1EE 369 POWER SYSTEM ANALYSIS Lecture 12 Power FlowTom Overbye and Ross Baldick
2AnnouncementsHomework 9 is: 3.47, 3.49, 3.53, 3.57, 3.61, 6.2, 6.9, 6.13, 6.14, 6.18, 6.19, 6.20; due November 7. (Use infinity norm and epsilon = 0.01 for any problems where norm or stopping criterion not specified.)Read Chapter 12, concentrating on sections 12.4 and 12.5.Homework 10 is 6.23, 6,25, 6.26, 6.28, 6.29, 6.30 (see figure 6.18 and table 6.9 for system), 6.31, 6.38, 6.42, 6.46, 6.52, 6.54; due November 14.Homework 11 is 6.43, 6.48, 6.59, 6.61, 12.19, 12.22, 12.20, 12.24, 12.26, 12.28, 12.29; due Nov. 21.
3Power System PlanningSource: Midwest ISO MTEP08 Report
4MISO Generation QueueSource: Midwest ISO MTEP08 Report
5MISO Conceptual EHV Overlay Black lines are DC, blue lines are 765kV, red are 500 kVSource: Midwest ISO MTEP08 Report
6ERCOT Also has considerable wind and expecting considerable more! “Competitive Renewable Energy Zones” study identified most promising wind sites,Building around $5 billion (original estimate, now closer to $7 billion) of transmission to support an additional 11 GW of wind.Will be completed in 2014.
16Two Bus Newton-Raphson Example For the two bus power system shown below, use theNewton-Raphson power flow to determine thevoltage magnitude and angle at bus two. Assumethat bus one is the slack and SBase = 100 MVA.
24Two Bus Region of Convergence Graph shows the region of convergence for different initialguesses of bus 2 angle (horizontal axis) and magnitude (vertical axis).Red regionconvergesto the highvoltagesolution,while theyellow regionto the lowsolutionMaximum of 15iterations
25PV BusesSince the voltage magnitude at PV buses is fixed there is no need to explicitly include these voltages in x nor write the reactive power balance equations:the reactive power output of the generator varies to maintain the fixed terminal voltage (within limits), so we can just set the reactive power product to whatever is needed.An alternative is these variations/equations can be included by just writing the explicit voltage constraint for the generator bus: |Vi | – Vi setpoint = 0
27PV BusesWith Newton-Raphson, PV buses means that there are less unknown variables we need to calculate explicitly and less equations we need to satisfy explicitly.Reactive power balance is satisfied implicitly by choosing reactive power production to be whatever is needed, once we have a solved case (like real power at the slack bus).Contrast to Gauss iterations where PV buses complicated the algorithm.
31Voltage Dependent Load, cont'd With constant impedance load the MW/MVAr load atbus 2 varies with the square of the bus 2 voltagemagnitude. This if the voltage level is less than 1.0,the load is lower than 200/100 MW/MVAr.In practice, load is the sum of constant power,constant impedance, and, in some cases,constant current load terms: “ZIP” load.
32Solving Large Power Systems Most difficult computational task is inverting the Jacobian matrix (or solving the update equation):factorizing a full matrix is an order n3 operation, meaning the amount of computation increases with the cube of the size of the problem.this amount of computation can be decreased substantially by recognizing that since Ybus is a sparse matrix, the Jacobian is also a sparse matrix.using sparse matrix methods results in a computational order of about n1.5.this is a substantial savings when solving systems with tens of thousands of buses.
33Newton-Raphson Power Flow Advantagesfast convergence as long as initial guess is close to solutionlarge region of convergenceDisadvantageseach iteration takes much longer than a Gauss-Seidel iterationmore complicated to code, particularly when implementing sparse matrix algorithmsNewton-Raphson algorithm is very common in power flow analysis.