RECTANGULAR HYBRID CURRENT BALANCE POWER FLOW AND SINGLE PHASE INDUCTION MOTOR MODEL FOR DYNAMICS SIMULATION

Power ow calculation in power systems analysis is fundamental to power systems transient stability simulation. The rst part of this thesis focuses on the hybrid current balance power ow calculation in rectangular coordinates. Details about algorithm initialization, bus admittance matrix, complex bus power injections, mismatch functions and Jacobian matrix are provided. The equations of both the mismatch functions and Jacobian matrix are discussed in terms of di erent bus types from swing bus to PV and PQ buses. The standard Newton-Raphson algorithm step, which are the core of power ow calculation, are demonstrated. Furthermore, the hybrid current balance power ow calculation implementation is shown to be an accurate and e cient algorithm by comparing it with the power balance power ow calculation results. Results from the convergence iteration numbers to accuracy, from total execution time to execution time per iteration, are presented for di erent systems in the form of comparison tables. The next part of this thesis focuses on the dynamic variable initialization. Previously, a sophisticated three-phase transient stability simulator required Matlab for the initialization of dynamic variables of the three phase induction motor load, di erent kinds of generators, exciters, turbine governor and network voltages. Now the multimachine dynamic initialization, as well as along the hybrid power ow calcu- lation code, is implemented in C with the assistance of PETSc. For all of the two-axis model machines, a di erential-algebraic model is used. The machine currents are ex- pressed in terms of the state and network variables. Stator algebraic equations are decomposed rst in both the polar form and the rectangular form. While for the net- work equations, they are explained in power-balance form and current-balance form. Finally, the calculation of all dynamic-state initial conditions and xed inputs, based on the base-case load ow solution are shown step by step. x The last portion of this thesis focuses on single-phase induction motor mod- eling. The single phase induction motor forms a large portion of the load in todays power systems load and portrays signi cantly di erent behavior than a three phase motor. A single-phase induction motor model using dynamic phasors is used to rep- resent the compressor portion of the behavior of a typical residential air conditioner load. The initialization and dynamic single-phase induction models are established for a phasor-based transient stability simulator. This model is employed in a voltage ramp test and then validated by a previously published laboratory test. On top of that, the single-phase induction motor is implemented in a three-phase transient sta- bility simulator. Three-phase and single-phase faults are applied on the motor bus in a simple 9-bus system. From the response of the three-phase voltage magnitudes and the rotor speed, the motor stall and delayed voltage recovery phenomena are observed and discussed. The single-phase induction motor model is also compared to the CIM5 three-phase induction motor model.M.S. in Electrical Engineering, December 201