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The work contains selected research results regarding the identification modeling of the Polish Electric Power Exchange on the example of numerical data listed on the Day-Ahead Market of TGE S.A. in Poland. In order to obtain the model of Day-Ahead Market System, first identification for numerical data from the period 01.01.2013-31.04.2016 has been downloaded from TGE S.A., obtaining discrete arx parametric models in MATLAB and Simulink using the System Identification Toolbox. The resulting model was then converted to continuous parametric models, and those to continuous models in the state space for 35 conventional semi-annual measurement periods. On the basis of the obtained test results, state variables and selected model parameters were interpreted, i.e. all non-zero elements of matrix A and nine selected elements of matrix B and one parameter of matrix C.

The publication concerns the important contemporary issues of searching for the Day-Ahead Market system models, including identification and simulation models. The models were obtained as a result of the identification process based on the data listed on TGE S.A. and as a result of building the obtained identification model in Simulink in the form of a simulation model. As a result of the identification, a model of the Day-Ahead Market system was obtained, i.e. relationships were found between 24 input quantities concerning the volume of electricity supplied and sold in each hour of a day and individual output quantities for each hour of a day, i.e. the obtained volume-weighted average electricity price. On the basis of the obtained system identification model, a simulation model was built in Simulink, thanks to which it was possible to conduct, apart from simulation tests, also sensitivity tests and comparative tests. Both models, i.e. the identification model and the simulation model, were further subjected to an evaluation of the efficiency, effectiveness and robustness of the model against the system. Research in this area belongs to the original research.

The paper presents results of research on the improvement of parameters of the neural model of system of the Polish Electricity Stock Exchange in the MATLAB and Simulink environment using methods inspired by quantum computer science. The models of the Artificial Neural Network of the taught Electricity Stock Exchange System, including selected elements of quantum computing used to improve the neural model of this system, and the Electricity Stock Exchange System quantum-neural model were also shown. Particular attention has been paid to neural modeling using Neural Network Toolbox and quantum-neural modeling using Simulink. The research experiments were carried out on the basis of quotations on the Polish Electricity Stock Exchange for quotes on the Day Ahead Market. As input quantities in the learning process of the Artificial Neural Network, the volume of electricity supplied and sold at particular times of the day was used, and the average prices received at each of the 24 hours as a starting point. As a result of the learning, a neural model of Electricity Stock Exchange System in the form of an Artificial Neural Network was obtained, and on its quantum-neuronal model of Electricity Stock Exchange system, which used the quantum calculations simulated in Simulink.

The following paper contains selected results of research on modeling identification of Polish Electricity Exchange on the example of the dates quoted on the Day Ahead Market. In order to obtain a model of the Polish Electricity Exchange System in the beginning it was conducted to identify data for the period from January, 1 (2013) to December, 31 (2015). In the result discrete parametric model using arx method in MATLAB and Simulink environments with System Identification Toolbox was obtaining. The resulting model was converted to a continuous parametric model, and that one in turn into the state space model. On the basis of obtained equations of state and outputs, state variables and parameters of the selected model were interpreted, i.e. selected elements of the matrix' of the state space model. A block diagram was then constructed in Simulink, which was used for simulations and sensitivity studies using: sine, Dirac impulse and step function. Numerous interesting research results have been obtained, including the correctness of the development of the Polish Electricity Exchange.

The work contains selected results of research related to identification modelling of the Polish Power Exchange (Towarowa Gielda Energii Elektrycznej S.A. — TGEE) obtained in MATLAB and Simulink using the System Identification Toolbox and Control System Toolbox. In order to obtain a parametric arx model of the Polish Power Exchange identification was performed using data for the first half year of 2015 (184 days), i.e. for 24 input quantities related to the volume of supplied and sold electrical energy (ee) in each hour of the 24-hour day as well as for individual output quantities related to average prices of supplied and sold ee in consecutive hours of the 24-hour day. 24 discrete parametric models of MISO type were obtained, followed by their transformation into continuous parametric models, and, further, into continuous models in state space. The research was conducted in order to find out whether it was possible to generate a model of the Polish Power Exchange (TGEE) and a metamodel based on the changes of the values of the elements of the model in consecutive hours of the 24-hour day. As a result, changes of elements of matrix A related to changes in the internal organization of the system and selected elements of matrix B related to the change of the control level were analysed. Also, an attempt to analyse the obtained results including state variables was made.

The paper contains selected results of research related to neural modeling of electrical power system development (EPS or EP System). Numerical data presented in paper [1, 8] were used to teach the artificial neural network (ANN) a model of EP system development. The ANN was designed in the MATLAB and Simulink environment using the Neural Network Toolbox. The generated model was used to perform simulation to examine sensitivity in Simulink. On the basis of the simulation model a comparative study was performed to compare responses of the model and the IEEE RTS test system. Sensitivity of the model was also examined by measuring the response of the model to the following input functions: sinusoid, unit step, Dirac impulse (Dirac delta function), etc. The results obtained were interpreted on the basis of the control and systems theory.

This paper presents the first observations on modern genetic algorithms, and then proposed a new algorithm called Systemic Evolution Algorithm (SEA). In the definition of the algorithm uses the concept of SEA electricity market, defined on the basis of control theory and systems. As a result of the identification system received electricity market model in MATLAB and Simulink environment, taking into account the input data such as the number of different types of transmission lines, the number of power stations, the number of transformers, and the amount of energy devoted to the transmission network, or purchased of the Transmission System Operator (TSO), etc. Obtained in this way, using the System Identification Toolbox, appropriate models of type arx, for all inputs and for each individual output and the corresponding models in the state space. Built the model of the development of the electricity market in Simulink, which in addition to simulation studies can also be used in clinical prediction. The present study used figures taken from the Polish Electricity Statistics yearbooks for the years 1946 to 2007 [17].

The paper contains the concept and the results of research concerning the evolutionary algorithm, identified based on the systems control theory, which was called the Systemic Evolutionary Algorithm (SAE). Special attention was paid to two elements of evolutionary algorithms, which have not been fully solved yet, i.e. to the methods used to create the initial population and the method of creating the robustness (fitness) function. Other elements of the SEA algorithm, i.a. cross-over, mutation, selection, etc. were also defined from a systemic point of view. Computational experiments were conducted using a selected subsystem of the Polish Electrical Power System and three programming languages: Java, C++ and Matlab. Selected comparative results for the SAE algorithm in different implementations were also presented.

The paper contains results of research concerning the search for models of Polish electrical energy stock exchange development. The research was conducted using MATLAB environment, and such toolboxes as a System Identification Toolbox and Neural Network Toolbox. Static models of Polish electrical energy stock exchange development as well as a dynamic model allowing to obtain information concerning static models of development for predicting further states of development were presented. Moreover, knowledge maps containing information on the development of GEE (Electrical Energy Stock Exchange), which were obtained by means of designing proper artificial neural networks, were also presented.