A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme

In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons.

Chance-Constrained Based Voltage Control Framework to Deal with Model Uncertainties in MV Distribution Systems

In this paper, a chance-constrained (CC) framework is developed to manage the voltage control problem of medium-voltage (MV) distribution systems subject to model uncertainty. Such epistemic uncertainties are inherent in distribution system analyses given that an exact model of the network components is not available. In this context, relying on the simplified deterministic models can lead to insufficient control decisions. The CC-based voltage control framework is proposed to tackle this issue while being able to control the desired protection level against model uncertainties. The voltage control task disregarding the model uncertainties is firstly formulated as a linear optimization problem. Then, model uncertainty impacts on the above linear optimization problem are evaluated. This analysis defines that the voltage control problem subject to model uncertainties should be modelled with a joint CC formulation. The latter is accordingly relaxed to individual CC optimizations using the proposed methods. The performance of proposed CC voltage control methods is finally tested in comparison with that of the robust optimization. Simulation results confirm the accuracy of confidence level expected from the proposed CC voltage control formulations. The proposed technique allows the system operators to tune the confidence level parameter such that a tradeoff between operation costs and conservatism level is attained.

Linear Optimization in Uncertain Environment: Sensitivity of the Solution to the Belief Degree

Uncertainty theory has been initiated in 2007 by Liu, as an axiomatically developed notion, which considers the uncertainty on data as a belief degree on the domain expert’s opinion. Uncertain linear optimization is devised to model linear programs in an uncertain environment. In this paper, we investigate the relation between uncertain linear optimization and parametric programming. It is denoted that the problem can be converted to parametric linear optimization problem, at which belief degrees play the role of parameters, and parametric linear optimization with its rich literature provides insightful interpretations. In a point of view, a strictly complementary optimal solution of problem is known for the belief degree [Formula: see text], as well as the associated optimal partition. One may be interested in knowing the region of belief degrees (parameters) where this optimal partition remains invariant for all parameter values (belief degrees) in this region. We consider the linear optimization problem with uncertain rim data, i.e., the right-hand side and the objective function data. The known results in the literature are translated to the language of uncertainty theory, and managerial interpretations are provided. The methodology is illustrated via concrete examples.

Solving practical economic load dispatch problem using crow search algorithm

The practical economic load dispatch problem is a non-convex, non-smooth, and non-linear optimization problem due to including practical considerations such as valve-point loading effects and multiple fuel options. An optimization algorithm named crow search algorithm is proposed in this paper to solve the practical non-convex economic load dispatch problem. Three cases with different economic load dispatch configurations are studied. The simulation results and statistical analysis show the efficiency of the proposed crow search algorithm. Also, the simulation results are compared to the other reported algorithms. The comparison of results confirm the high-quality solutions and the effectiveness of the proposed method for solving the non-convex practical economic load dispatch problem.

Analytical Reason for Smaller Lateral Sway in Angled-Plane Scissor Linkage

Scissor linkages are widely used with scissor links arranged in two parallel planes. When small misalignment of revolute joint axes are permissible, the linkage can undergo lateral sway. This paper, using rigid-body kinematics and a modeling of misalignment, converts the task of finding lateral sway into a non-linear constrained optimization problem. Through linearization of the optimization problem, this paper analytically proves that (1) maximum lateral sway increases as the number of units in the parallel-plane scissor linkage increases whereas in angled-plane scissor linkage, the lateral sway tends to a finite limit as the number of units is increased and (2) the lateral sway is independent of connector length in parallel-plane scissor linkage whereas it is dependent on the length of the connector in angled-plane scissor linkage. These results are further substantiated with numerical solution of the non-linear optimization problem. The results imply that the angled-plane scissor linkage can substantially limit lateral sway in comparison to parallel-plane scissor linkage under similar conditions of joint misalignment. The analytical expression derived in this paper helps in identifying the influence of design parameters on lateral sway.

A New Pricing Scheme for Intra-Microgrid and Inter-Microgrid Local Energy Trading

In this paper, an optimum pricing scheme has been designed to maximize the profits earned by sellers in microgrids through intra-microgrid and inter-microgrid local energy trading. The pricing function is optimized for different priority groups of participants within the microgrid and it is represented as a linear function of the energy sold/purchased during energy trading. A non-linear optimization problem has been formulated to optimize the amount of energy sold, as well as the coefficients of pricing function with an objective to maximize the profit for the sellers at a certain time instant. The numerical simulation results demonstrate that the proposed approach can reduce energy mismatch at the participants compared to the case when different priority groups are not considered. The findings also illustrate that the optimum pricing function can achieve higher profit for the sellers when compared with existing pricing schemes.