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## Operation and Control of Modern Power Systems and Power Flow Analysis and Control.

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The objective of this assignment is to investigate the power flow solutions of a general power system for various operating conditions using a standard computational tool. The effects of various control parameters and loads on power flow solutions will also be investigated. The single line diagram of the IEEE 14-bus system is shown in the next page. The power flow data of the system is also given in the next page. This is a group assignment and two students will work in a group. Each group is required to submit a formal report that should include the following. 1. Obtain the base-case power...

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#### Question Preview:

The objective of this assignment is to investigate the power flow solutions of a general power system for various operating conditions using a standard computational tool. The effects of various control parameters and loads on power flow solutions will also be investigated. The single line diagram of the IEEE 14-bus system is shown in the next page. The power flow data of the system is also given in the next page. This is a group assignment and two students will work in a group. Each group is required to submit a formal report that should include the following. 1. Obtain the base-case power flow solution using the Newton-Raphson (NR) method. Show the voltage profile of the system as well as the convergence pattern of the NR method. 2. Using the power flow results (complex bus voltages), calculate the complex power generated by the swing generator. Also determine the complex power at both ends of tap changing transformer connected between buses 5 and 6. Compare the calculated results with the corresponding simulation results (obtained by the NR method) and find the errors in percentage. 3. The reactive power of a voltage-controlled bus (or P-V bus) depends on the specified voltage magnitude. Vary the voltage magnitude of of P-V bus 2 from 0.90 pu to 1.10 pu (with a suitable increment). You may relax the reactive power limits of the bus (say, from -500 to +500 MVAr), if necessary. Run the power flow program and record the corresponding reactive power of the generation. Plot the variation of reactive power against terminal voltage of the generator. 4. The voltage magnitude of a load bus (or P-Q bus) depends on bus load. Select a particular load bus and increase the load of the bus at a constant power factor (0.8 lagging) in steps (start at 5 MVA) and obtain the corresponding voltage from power flow solutions. Continue to increase the load until the voltage drop to 0.8 pu. Plot the load voltage against load MVA. Describe a common method of improving voltage of a load bus with suitable simulation results. 5. Consider the system load is decreased by 50% during off-peak period and increased by 75% during peak period. Investigate the voltage profile of the system during the peak and off-peakperiods. Report The deliverables of the assignment are the results of steps 1-5 with critical analysis and discussions. The assumptions and approximations used in evaluating the results should be clearly stated. The reports should have the following format: title, abstract, brief introduction, main body (with sections and subsections as required), conclusions and references. The report should be submitted via learnonline as a single pdf file.

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## Solution Preview

Power flow analysis is the backbone of power system analysis and design. They are necessary for planning, operation, economic scheduling and exchange of power between utilities.  The principal information of power flow analysis is to find the magnitude and phase angle of voltage at each bus and the real and reactive power flowing in each transmission lines. Power flow analysis is an importance tool involving numerical analysis applied to a power system. In this analysis, iterative techniques are used due to there no known analytical method to solve the problem. To finish this analysis there are methods of mathematical calculations which consist plenty of step depend on the size of system. Load flow studies are used to ensure that electrical power transfer from generators to consumers through the grid system is stable, reliable and economic. Conventional techniques for solving the load flow problem are iterative, using the Newton-Raphson or the Gauss-Seidel methods.

Introduction- Power flow study is a fundamental task of power system operation and planning. various methods developed in commercial package for power flow study, the Newton-Raphson method is the most successful one. It is however well recognized that the NR method may diverge in power flow study. In this paper, we numerically study the convergence regions of power flow solutions using Newton-Raphson(NR) method. This study of convergence region is motivated by the need to determine an initial guess which converges to one of the power flow solution. It will be numerically shown that the convergence region of NR method, if exist, has a fractal boundary and is hence sensitive to initial conditions. Several fractal features will be investigated considering the convergence regions of power flow at the base case and at various loading conditions, and with different load models.

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