Abstract Reservoir systems are often operated for multiple purposes. This can result conflicting operational goals. To efficiently control these systems and to satisfy the different interests as good as possible, mathematical optimization models can be used to support operational decisions. Common approaches for reservoir optimization apply linear optimization techniques. However, real-world systems often require non-linear functions to describe the relation between water level and volume in a reservoir or to account for the hydropower equation. When the non-linear equations form a non-convex optimization problem, the problem is not necessarily solved to a global optimum. Piecewise-linear or linear formulations of the non-linear equations are a common way to address non-linear non-convex optimization problems. In this paper, the novel homotopy method is compared with two established approaches—the piecewise-linear and the linear approximation—to account for non-linear components in the optimization problem. The analysis is carried out for a cascade of three reservoirs under two scenarios—a flood scenario and a load balance scenario. The optimization software is the open source package RTC-Tools 2.4. Compared to the piecewise-linear and the linear approach the homotopy method shows a better accuracy for the analysed cases, because the method solves the flow equations within the optimization in a non-simplified form. Different to the piecewise-linear and the linear approach, however, the homotopy method does not guarantee a global optimum. The solution is still path-stable, which is a basic pre-requisite for its application in an operational context of hydropwer scheduling. Compared to the piecewise-linear approach, the homotopy method is easier to implement under the condition that the software supports the method.

The efficiency of two numerical methods for solving multidimensional problems of the theory of thermal conductivity ‒ the fractional steps method and the Liebman method - is evaluated. The efficiency of these methods is compared for the operating conditions of industrial furnaces by the example of calculating the symmetrical heating of a two-dimensional cylinder and a three-dimensional plate made of materials with different thermophysical properties (corundum, ceramic brick and carbon steel). A two-dimensional axisymmetric temperature field for a cylinder and a three-dimensional temperature field for a workpiece in the form of a parallelepiped were found by the grid method under boundary conditions of the II and III genera. The difference approximation of differential equations and boundary conditions is performed by the control volume method according to an implicit finite difference scheme. The developed algorithms for solving multidimensional problems of internal heat transfer by fractional steps and the Liebman method are implemented in the form of computer programs in the Object Pascal programming environment. When comparing the effectiveness of solving multidimensional problems with these methods, the criterion of the effectiveness of difference schemes (CERS) proposed by V.V. Bukhmirov and T.E. Sozinova was used as an optimization criterion. Nomograms are constructed to select the optimal parameters of the space-time grid and the best numerical method for solving multidimensional problems for a specific process of heating (cooling) a solid body

Lightning hit a transmission power line outside London, England on 9 August 2019. There followed a loss of power from a cascade of generator outages that exceeded contingency reserves, leading to an exceptional fall in grid frequency causing widespread transport disruptions and the disconnection of over 1 m households. Simulating such events typically involves a system of differential equations representing the overall generation and load present at the time. A standard model based on the swing equation assumes unlimited capacity in aggregated resources, and the availability of these services throughout the duration of the frequency deviation. In simulating the effect of outages on the GB Grid frequency on 2019/8/9, the effect of limiting these services to the capacity of resources engaged during the event is examined. It is shown that by taking these refinements into account the timing and extent of the frequency nadir can be successfully estimated. Insight is gained into the responses of various grid characteristics and how they interact with unplanned generation imbalances. Using this adapted model, further events on the GB grid are examined to validate the influence of these features. With the model’s effectiveness validated, novel mitigating measures to preserve the stability of a low-inertia grid can be evaluated.

The study is devoted to mathematical models of mass transfer during diffusion combustion of gaseous fuel. A numerical approach is presented that makes it possible to estimate the effect of combustion conditions on the length of a direct-flow diffusion flame. A simplified method for calculating the heat release in a diffusion flame is applied, taking into account the fact that the chemical reactions of combustion are concentrated in it at the flame front. Some results of numerical simulation of diffusion combustion processes and complex radiative-convective heat transfer in industrial furnaces in the production of cement clinker are presented.

Diagnostics of electrical equipment at industrial enterprises is an urgent task, since the failure of the main and auxiliary electric drives can lead to significant economic losses for the enterprise. The main share of failures of asynchronous motors is caused by their overload and, accordingly, overheating of the stator winding. Such overheating leads either to an interturn circuit and engine failure, or to a significant reduction in its resource. Therefore, winding temperature control is an important task. In this paper, we propose an algorithm for calculating the temperature of an induction motor with a squirrel-cage rotor with a changing load on the shaft using an equivalent thermal circuit consisting of 10 main nodes. In the work, methods of mathematical modeling were applied using previously developed software, as well as Excel. The task was set to check the possibility of using an equivalent thermal circuit for dynamic modes of operation of electrical equipment. The results of the work allow us to conclude that the developed algorithm can be used for further modeling of both stationary and non-stationary thermal models of asynchronous motors with a squirrel-cage rotor.

A high-speed highway in the design encounters many problems, for the solution of which it is necessary to find the best ways. One of these problems is the overheating of the wire of the contact network (CN) when passing through the neutral insert. The authors propose an insulating connection device (ICD) of the CN, which will allow to avoid the occurrence of an electric arc, and, consequently, the overheating and subsequent failure of the contact wire. ICD CN is a set of resistances that change towards the end of the section in front of the neutral insert. The greatest danger will be the current that occurs when entering the neutral insert than when leaving it to the contact wire (CW). In this case, the overheating of the CW is possible for two reasons. Firstly, the melting of the wire is possible for a classical reason - the heating of the CW that has arisen as a result of a short circuit by an electric arc, and its subsequent rupture. Secondly, after the introduction of additional resistances, a new electrical circuit is formed. Under the influence of current, new elements of this circuit - stepped resistances - will be subjected to heating, which is directly dependent on the time of current action on a certain section of the ICD CN. As a result, the CN proposed by the authors of the ICD should solve the problem of overheating of the CW on the AC railway. In the course of the study, the dependence of the voltage on a specific section of the ICD CN was also obtained at the time the rolling stock was in the same section.