New Models and Algorithms of Optimal Reactive Power Flow and Applications in Voltage Stability Risk Assessment
|Keywords||power system reactive optimal power flow voltage stability risk assessment quadratic optimal model interior point method|
In the past decades, power systems around the world have been continuously experiencing various significant changes, including broad applications and implementations of high voltage direct current (HVDC) and flexible AC transmission systems (FACTS), as well as the development of electric power markets. These changes have produced great effects on security and economy of power systems. This process of changes also brings new challenges and more development directions in the reactive optimal power flow (ORPF) area. In this dissertation, new models and algorithms of ORPF are investigated systematically. In modeling, control modes of HVDC and FACTS, requirements in reactive ancillary service costs due to electric power markets and capability curve limits of generators are incorporated in the newly developed models whereas in the computing techniques, improvements in the interior point method (IPM), immune genetic algorithm (IGA) and sparse technology are addressed. Besides, the proposed ORPF models and algorithms are applied to static voltage stability risk assessment.In rectangular coordinates, a load tap changing (LTC) transformer branch is represented by an ideal transformer and a series impedance with a dummy node located between them. The voltages at the two sides of the ideal transformer are used to replace the turn ratio of the LTC so that the LTC model becomes quadratic. Then, a fully quadratic ORPF model is derived with the quadratic LTC model. Hessian matrices in the ORPF model are therefore constant, and need to be calculated only once in the entire optimazation process using the predictor-corrector primal dual interior point method (PCPDIPM). This speeds up calculations greatly and reduces complexity in programming. Also, calculating nonzero elements and optimal ordering algorithm are used to form and solve the correction equation, which improves effectiveness in calculations of PCPDIPM. The numerical results indicate that the proposed model and algorithms are accurate and have a higher computing speed.On top of the AC quadratic ORPF model, the quadratic models of power flow (PF) and ORPF with HVDC and FACTS are further developed. By using voltage magnitudes at the two sides of an ideal converter transformer as state variables, the quadratic PF equations for AC system and DC system are fisrt established respectively in the rectangular and polar coordinates. Then a quadratic integrated AC-DC PF model with HVDC control modes is developed through equality constraints to the real and imaginary parts of the lower voltage of the converter transformer. Based on the proposed quadratic AC-DC PF model and the quadratic AC ORPF model, the quadratic AC-DC ORPF model is developed, in which the control variables of HVDC systems are optimized variables or some of them can be easily specified as given control conditions. For FACTS components, by using real and imaginary parts of the voltage to substitute its magnitude and phase, a quadratic expression of FATCS system is directly derived. Besides, the algorithm retaining nonlinearity for quadratic homogeneous equations is extended to solve the quadratic equations with linear terms. The quadratic ORPF model with HVDC and FACTS systems requires less computing efforts in using the PCPDIPM. Results obtained from test systems indicate that the proposed model achieves a superior performance to conventional models.In the environment of electric power markets, reactive ancillary service costs and generator capability curve limits are varied when the reactive power outputs change. Based on this fact, a generator operation area is divided into four segments with each one having different reactive ancillary service costs and capability limits. With this expression, the unfixed piecewise mixed-integer quadratic ORPF models for AC and AC-DC power systems are proposed respectively. Numerical results indicate that reactive ancillary service costs will have great effects on the reactive power flow and the HVDC operation mode. The proposed ORPF models are the useful computing tool for AC-DC power systems under the condition of electric power markets.Based on the heuristic approach, IPM and IGA, two hybrid algorithms are developed to solve the unfixed piecewise mixed-integer quadratic ORPF model. The first one is a heuristic mixed-integer interior point method (HEUIPM), in which the heuristic approach is used to search generator operation segments so that the unfixed piecewise model can be converted into a general mixed-integer quadratic model which can be solved using the IPM capable of dealing with the discrete variables. By integrating IGA into IPM, a heuristic hybrid stochastic search method (IPMIGA) is proposed as the second algorithm. Numerical results indicate that HEUIPM can reach the optimal solution faster in cases where there is no convergence problem; otherwise, IPMIGA should be used to ensure quality of the solution, but with a relatively low computing speed.Based on the proposed ORPF models, the quadratic optimal models of minimizing the total load curtailment are established to identify power flow unsolvability for AC and AC-DC power systems, and can be further used to identify system voltage instability with the modal analysis method. In this way, the voltage stability corrective control method are produced. This method need to be calculated only once to identify system voltage instability. It can not only reschedule generations and alleviate constraint violations, but also minimize the total load curtailment to restore the voltage stability from instability.A risk assessment method for static voltage stability is investigated. In this method, the probabilistic behavior of available generators, network configurations and loads is considered. Monte Carlo simulation is used to select different system states. The proposed voltage stability corrective control method is used to identify system voltage instability and perform corrective controls. The system voltage instability risk indices that are obtained using the risk assessment method include the voltage instability probability, expected load curtailment to avoid voltage instability, and the relationship between load curtailments and voltage instability probability. In other words, the method evaluates not only system voltage instability probability but also load curtailments to avoid system collapse that correspond to different voltage instability risk levels. The proposed method provides an effective tool to assess the voltage stability risk.