Georgi Georgiev

Elimination of nodes with voltage dependent load characteristics in electrical network models

This paper presents a new technique for the reduction of large power system. It is based on Jordan elimination of nodes represented with their static or dynamic load characteristics dependent on voltage. Thus the reduced network models preserve their past behavior with the same final outcomes in problems of steady states, static and dynamic electromechanical transient processes. We report an example of solving a nonlinear problem in Eurostag software

New approaches of static stability research of unified electric power systems

The configuration of the electrical systems should be often changed in terms of market relations. Therefore, an actual necessity of an express evaluation of static stability of power systems appears. Criteria such as “Hurwitz”, “Rauss” are very cumbersome in use. Not only modification of the existing methods are examined and discussed in the paper, but also new ways of getting the evaluation of static stability. The research is aimed to overcome the difficulties while dealing with the characteristic polynomial of a higher degree, as well as to some ideas concerning the reduction of the characteristic matrix dimensionality with the further analysis of its elements without isolation of a polynomial with step-by-step determination of static stability.

Modified givens method for the analysis power system static stability

The current stage of the world energy development is characterized by the creation of powerful territorial and integrated power systems. A gradual unification of the energy markets of different countries is currently going on within a free market: the configuration of networks has been changing, additional relations appear, new energy companies and unions are formed, a sector of renewable sources is rapidly developing with its characteristic distributed generation (decentralization), therefore, the most urgent matter of finding and creating new methods and algorithms for calculation and analysis of complex EPS. In particular, it concerns the issue of problem solving of large-scale power systems with a detailed accounting of basic elements of the system. All ongoing and planned changes both directly and indirectly affect the network configuration, which in its turn leads to the appearance of additional generation and load nodes and, consequently, it requires careful economic and technical computations, in particular, the static stability assessment of the power system.

Algorithmization in the task of optimization of cascade hydro power plants

Our work focuses on the problem of optimizing a cascade of three small hydro power plants. The optimization is based on deciding how much electricity to produce dependent on the day-ahead hourly electricity prices. The problem is reduced to controlling the water volumes in the cascades reservoirs. We examine two approaches — linear programming based on Matlabs Simplex method (the Linprog function) and a Dynamic programming method. Linear programming is used for the limiting case when electricity prices exhibit daily cyclicality and Dynamic programming works for a finite time period. Two numerical examples are considered.

Extra power backup for balancing of power grid with renewables

We introduce a number of mathematical models for the management of an electrical power system in the presence of renewable generation. We also study the impact of power systems of neighbouring countries on the grid.

Factorization of a characteristic polynomial by random search one of its trinomial divisors

In the paper the application of Monte Carlo approach for random search algorithms to finding a pair of conjugated roots of a characteristic polynomial (ChP) is presented. The proposed technique is oriented only to ChPs with real coefficients. The search is produced on the basis of random numbers with uniform distribution in a rather narrow bounded region of the complex plane. Two search methods are considered here: 1) Indirect method to finding a pair of complex conjugate roots; 2) Direct method which results are coefficients of the trinomial divisor of the ChP. Then the conjugated roots can be easily found as roots of the trinomial divisor. If high precision is necessary then the best random hit is used as good initial estimate for further specification of better results by the iterative Newtons method for two equations with two unknowns (the Jacobian is a 2×2 matrix). The specified techniques can be very easily and simply realized in the environment of MS Excel or MATLAB functions at minimum computing resource. The both proposed here methods can be used in the educational process providing good visualization of the study area. Irrespective of the high degree of ChP it is possible to direct the search process so that to find at once only those roots that are of interest in connection with the problem of stability of the corresponding electrical system. The offered algorithms allow creating effective software products.

A study of the change in assessing the stability of the interconnected system when connecting a link (line) between its two subsystems

Under the current conditions of electricity market liberalization, it is often necessary to rapidly perform considerable changes in the power flows of cross-border lines or between isolated subsystems inside the country. For this purpose, in most cases, it is possible to use a simple connection / disconnection of a connection, which leads to a change in the topology of two subsystems. In such a situation it is quite reasonable to consider an issue regarding the change of the stability assessment for the generators on either side of the boundary interconnection before and after switching. In this paper, the authors have studied how the matrix eigenvalues of the coefficients of the two subsystems change after being combined into a single matrix; also, they have derived the conditions at which rapid assessment of the stability of the newly formed interconnected system can be performed according to preliminary estimates of the two subsystems before their interconnection. It has been indicated how and for what purposes this approach can be used when studying the stability of complex electrical systems.

Transformation algorithm of complex power system by means of load nodes elimination, represented as its static and dynamic characteristics

The algorithm proposed in the paper allows easily complete functional reduction of power systems topology under consideration, which is an important moment for the quite a number of researches, including also the analysis of transient process behavior. In the algorithm basis is the methodology of the elimination of optional values of the load nodes represented as static and dynamic characteristics. The transformation completes by the mean of combination of quadratic approximation of nonlinear load and elimination of unknowns by the Jordan method. As a result of completed experiments it was revealed that the behavior of the power system after it topology reduction fully coincides with initial power system in steady state and transient process at the significant declination of analysis labour-intensity and results visualization.