An Optimal and Distributed Method for Voltage Regulation in Power Distribution Systems

This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric vehicles. We cast the problem as an optimization program, where the objective is to minimize the losses in the network subject to constraints on bus voltage magnitudes, limits on active and reactive power injections, transmission line thermal limits and losses. We provide sufficient conditions under which the optimization problem can be solved via its convex relaxation. Using data from existing networks, we show that these sufficient conditions are expected to be satisfied by most networks. We also provide an efficient distributed algorithm to solve the problem. The algorithm adheres to a communication topology described by a graph that is the same as the graph that describes the electrical network topology. We illustrate the operation of the algorithm, including its robustness against communication link failures, through several case studies involving 5-, 34-, and 123-bus power distribution systems.Comment: To Appear in IEEE Transaction on Power System

Solving multiobjective constrained trajectory optimization problem by an extended evolutionary algorithm

Highly constrained trajectory optimization problems are usually difficult to solve. Due to some real-world requirements, a typical trajectory optimization model may need to be formulated containing several objectives. Because of the discontinuity or nonlinearity in the vehicle dynamics and mission objectives, it is challenging to generate a compromised trajectory that can satisfy constraints and optimize objectives. To address the multiobjective trajectory planning problem, this paper applies a specific multiple-shooting discretization technique with the newest NSGA-III optimization algorithm and constructs a new evolutionary optimal control solver. In addition, three constraint handling algorithms are incorporated in this evolutionary optimal control framework. The performance of using different constraint handling strategies is detailed and analyzed. The proposed approach is compared with other well-developed multiobjective techniques. Experimental studies demonstrate that the present method can outperform other evolutionary-based solvers investigated in this paper with respect to convergence ability and distribution of the Pareto-optimal solutions. Therefore, the present evolutionary optimal control solver is more attractive and can offer an alternative for optimizing multiobjective continuous-time trajectory optimization problems

Sensitivity analysis and evolutionary optimization for building design

In order to achieve global carbon reduction targets, buildings must be designed to be energy efficient. Building performance simulation methods, together with sensitivity analysis and evolutionary optimization methods, can be used to generate design solution and performance information that can be used in identifying energy and cost efficient design solutions. Sensitivity analysis is used to identify the design variables that have the greatest impacts on the design objectives and constraints. Multi-objective evolutionary optimization is used to find a Pareto set of design solutions that optimize the conflicting design objectives while satisfying the design constraints; building design being an inherently multi-objective process. For instance, there is commonly a desire to minimise both the building energy demand and capital cost while maintaining thermal comfort. Sensitivity analysis has previously been coupled with a model-based optimization in order to reduce the computational effort of running a robust optimization and in order to provide an insight into the solution sensitivities in the neighbourhood of each optimum solution. However, there has been little research conducted to explore the extent to which the solutions found from a building design optimization can be used for a global or local sensitivity analysis, or the extent to which the local sensitivities differ from the global sensitivities. It has also been common for the sensitivity analysis to be conducted using continuous variables, whereas building optimization problems are more typically formulated using a mixture of discretized-continuous variables (with physical meaning) and categorical variables (without physical meaning). This thesis investigates three main questions; the form of global sensitivity analysis most appropriate for use with problems having mixed discretised-continuous and categorical variables; the extent to which samples taken from an optimization run can be used in a global sensitivity analysis, the optimization process causing these solutions to be biased; and the extent to which global and local sensitivities are different. The experiments conducted in this research are based on the mid-floor of a commercial office building having 5 zones, and which is located in Birmingham, UK. The optimization and sensitivity analysis problems are formulated with 16 design variables, including orientation, heating and cooling setpoints, window-to-wall ratios, start and stop time, and construction types. The design objectives are the minimisation of both energy demand and capital cost, with solution infeasibility being a function of occupant thermal comfort. It is concluded that a robust global sensitivity analysis can be achieved using stepwise regression with the use of bidirectional elimination, rank transformation of the variables and BIC (Bayesian information criterion). It is concluded that, when the optimization is based on a genetic algorithm, that solutions taken from the start of the optimization process can be reliably used in a global sensitivity analysis, and therefore, there is no need to generate a separate set of random samples for use in the sensitivity analysis. The extent to which the convergence of the variables during the optimization can be used as a proxy for the variable sensitivities has also been investigated. It is concluded that it is not possible to identify the relative importance of variables through the optimization, even though the most important variable exhibited fast and stable convergence. Finally, it is concluded that differences exist in the variable rankings resulting from the global and local sensitivity methods, although the top-ranked solutions from each approach tend to be the same. It also concluded that the sensitivity of the objectives and constraints to all variables is obtainable through a local sensitivity analysis, but that a global sensitivity analysis is only likely to identify the most important variables. The repeatability of these conclusions has been investigated and confirmed by applying the methods to the example design problem with the building being located in four different climates (Birmingham, UK; San Francisco, US; and Chicago, US)

Multiobjective overtaking maneuver planning of autonomous ground vehicles

This paper proposes a computational trajectory optimization framework for solving the problem of multi-objective automatic parking motion planning. Constrained automatic parking maneuver problem is usually difficult to solve because of some practical limitations and requirements. This problem becomes more challenging when multiple objectives are required to be optimized simultaneously. The designed approach employs a swarm intelligent algorithm to produce the trade-off front along the objective space. In order to enhance the local search ability of the algorithm, a gradient operation is utilized to update the solution. In addition, since the evolutionary process tends to be sensitive with respect to the flight control parameters, a novel adaptive parameter controller is designed and incorporated in the algorithm framework such that the proposed method can dynamically balance the exploitation and exploration. The performance of using the designed multi-objective strategy is validated and analyzed by performing a number of simulation and experimental studies. The results indicate that the present approach can provide reliable solutions and it can outperform other existing approaches investigated in this paper

Analysis and management of security constraints in overstressed power systems

Management of operational security constraints is one of the important tasks performed by system operators, which must be addressed properly for secure and economic operation. Constraint management is becoming an increasingly complex and challenging to execute in modern electricity networks for three main reasons. First, insufficient transmission capacity during peak and emergency conditions, which typically result in numerous constraint violations. Second, reduced fault levels, inertia and damping due to power electronic interfaced demand and stochastic renewable generation, which are making network more vulnerable to even small disturbances. Third, re-regulated electricity markets require the networks to operate much closer to their operational security limits, which typically result in stressed and overstressed operating conditions. Operational security constraints can be divided into static security limits (bus voltage and branch thermal limits) and dynamic security limits (voltage and angle stability limits). Security constraint management, in general, is formulated as a constrained, nonlinear, and nonconvex optimization problem. The problem is usually solved by conventional gradient-based nonlinear programming methods to devise optimal non-emergency or emergency corrective actions utilizing minimal system reserves. When the network is in emergency state with reduced/insufficient control capability, the solution space of the corresponding nonlinear optimization problem may be too small, or even infeasible. In such cases, conventional non-linear programming methods may fail to compute a feasible (corrective) control solution that mitigate all constraint violations or might fail to rationalize a large number of immediate post-contingency constraint violations into a smaller number of critical constraints. Although there exists some work on devising corrective actions for voltage and thermal congestion management, this has mostly focused on the alert state of the operation, not on the overstressed and emergency conditions, where, if appropriate control actions are not taken, network may lose its integrity. As it will be difficult for a system operator to manage a large number of constraint violations (e.g. more than ten) at one time, it is very important to rationalize the violated constraints to a minimum subset of critical constraints and then use information on their type and location to implement the right corrective actions at the right locations, requiring minimal system reserves and switching operations. Hence, network operators and network planners should be equipped with intelligent computational tools to “filter out” the most critical constraints when the feasible solution space is empty and to provide a feasible control solution when the solution space is too narrow. With an aim to address these operational difficulties and challenges, this PhD thesis presents three novel interdependent frameworks: Infeasibility Diagnosis and Resolution Framework (IDRF), Constraint Rationalization Framework (CRF) and Remedial Action Selection and Implementation Framework (RASIF). IDRF presents a metaheuristic methodology to localise and resolve infeasibility in constraint management problem formulations (in specific) and nonlinear optimization problem formulations (in general). CRF extends PIDRF and reduces many immediate post-contingency constraint violations into a small number of critical constraints, according to various operational priorities during overstressed operating conditions. Each operational priority is modelled as a separate objective function and the formulation can be easily extended to include other operational aspects. Based on the developed CRF, RASIF presents a methodology for optimal selection and implementation of the most effective remedial actions utilizing various ancillary services, such as distributed generation control, reactive power compensation, demand side management, load shedding strategies. The target buses for the implementation of the selected remedial actions are identified using bus active and reactive power injection sensitivity factors, corresponding to the overloaded lines and buses with excessive voltage violations (i.e. critical constraints). The RASIF is validated through both static and dynamic simulations to check the satisfiability of dynamic security constraints during the transition and static security constraints after the transition. The obtained results demonstrate that the framework for implementation of remedial actions allows the most secure transition between the pre-contingency and post-contingency stable equilibrium points