Optimization and modeling of electric generators elements of wind power plants

. The issues of improving the exploitation properties of renewable energy equipment are considered. The concept of improving power electronics and the design of a wind farm is defined. A model and algorithms for controlling the power of an electric generator have been developed. The results of computer modeling are presented.


Introduction
The modern economics, for the most part, is based on the use of energy from carbon minerals.Energy consumption is directly related to economic growth.Consequently, all developed countries are interested in cheap energy resources.Along with that, energy resources tend to rise in price, which directly contradicts the interests of industrialized countries.
If we proceed from the assumption that the supply of energy resources will be reduced, then consumption will be forced to become more rational, which means that demand will decrease in quantitative terms.This, in turn, will lead to a reduction in production, and as a result, to an increase in unemployment and an increase in social tension.The solution of these questions lies in the plane of the new economic paradigm and the transition to its realization.Obviously, this will lead to a new round of economic development.The main task of such development is the struggle for energy efficiency and product quality.Due to the energy shortage, new jobs will need to be created in those areas of social activity that require a minimum amount of energy and, if possible, in one way or another contribute to the development of community -first of all, science, education, culture.
Recently, renewable energy projects have been increasingly promoted.Global trends are directed at forming programs for the development of wind and solar energy.The undoubted leaders in the development of renewable energy are the United States, China and the European Union.The official explanation for the development of renewable energy is formulated by reducing the anthropogenic impact on the climate and reducing carbon dioxide emissions into the atmosphere.According to the World Wind Energy Association, in 2021, the total amount of electricity generated by a wind generators in the world exceeded 84010 9 watts, which was approximately 7% of the total amount of electricity generated [1].
In the process of coal mining, especially in the open way, the fertile layer of soil is destroyed, the level of groundwater changes, soil, water, and atmosphere are contaminate.These processes have a negative impact on the ecological situation.To some extent, the negative consequences associated with the extraction and combustion of fossil fuels can be compensation by reclamation.At the same time, in some areas, the consequence of the extraction and burning of minerals is a significant degradation in the ecological situation.This significantly deteriorate the living conditions of the population and causes forced mass migration.
The competitive advantages of renewable energy are mainly associated with an increase in oil and gas prices and a decrease in the production of these resources.At the same time, the development of new energy sources, energy efficiency and environmental management issues give impetus to the development of science and technology.One of the most promising directions in the development of alternative energy is wind energy [2].
The apparent advantage of wind power is the actual infinity of resources: as long as there is an atmosphere on the planet and the Sun is shining, there will also be movement of air masses that can be used to generate energy.Another undoubted plus is environmental ecological compatibility [3][4][5].Wind power plants do not emit harmful substances, do not pollute the environment, and at the same time are subjected to serious mechanical loads.
Turbine blades, transmission, rotary mechanism, mast structure should be made by special methods from innovative steel and composite materials [6][7][8][9], capable of withstanding significant loads with minimal consumption of the material itself.Processing and obtaining of such materials is implemented in various ways [10][11][12][13][14][15].As a result of processing and selection of optimal geometry, constructional elements and parts are able to withstand cyclic, constant loads under various operating conditions.

Theoretical foundations
At present, much attention is paid to digital control systems.But at the same time, they do not forget about the development of such development and analysis tools as software for mathematical modeling and numerical analysis, high-level programming languages, as well as hardware capabilities of computer technology.
The use of simulation modeling at the design stage of complex systems can significantly reduce the cost of research, prototype development and testing, and reduce the cost of product development.
The authors developed the computer model using the MATLAB/Simulink package for mathematical calculations from Mathworks Inc.The MATLAB/Simulink software package is based on the MATLAB mathematical calculator.
Supplemented with the Simulink extension package, it allows solving a complex range of tasks:  Development of the concept of the model;  Testing;  Examination;  Hardware implementation.
The purpose of the simulation is to study the effectiveness of the selected wind turbine.Automatic switching between sources of electrical energy and automatic input of the reserve ensures the reliability and uninterrupted power supply.
Structural diagram of a wind power plant (WPP) when working for a consumer is shown in Figure 1.
The wind wheel (1) converts the oncoming flow of wind energy into mechanical energy of rotation of the electric generator shaft (2).An electrical machine converts the mechanical energy of a shaft rotation into electrical energy, a three-phase alternating current voltage.
An active three-phase rectifier converts alternating current voltage to direct current voltage.The controller (4) controls the charge of the batteries and redistributes the energy among the batteries, the generator and the inverter (3).Batteries are designed to store unclaimed electricity with its subsequent return to the network at the time of peak loads.The inverter converts the direct current voltage into a sinusoidal three-phase voltage of 380 V with a frequency of 50 Hz.To transfer energy to the consumer, the voltage is increased by a transformer, for example, up to 10 kV.Electricity is transported via a high-voltage transmission line.Consumers ( 5) are connected through step-down transformers.
The scheme considered in Figure 1 is an autonomous generation.If wind farms are to be integrated into the United Energy Sistem (UES) with their connection to the 35-220 kV distribution grid, then certain conditions must be met.There are two obvious integration scenarios.
The first scenario is to adapt the equipment of wind farms in accordance with the technical specifications prepared by the System Operator of the UES.In this case, the connection of the generating equipment of the power plant is carried out to a predetermined place in the electrical network.Setting the ranges of change of coordinates of the characteristic points of the LVRT-characteristic is carried out by designers based on the modeling of regulatory disturbances in accordance with the "Methodological guidelines for the stability of power systems" in accordance with the actual response times of the relay protection of the adjacent power grid.The characteristic is built in such a way that the stability of the generating equipment is not violated during standard disturbances in the power grid.These conditions become mandatory for the manufacturer of wind turbine equipment.
The second scenario is to upgrade the existing relay protection.At the point of the adjacent power grid, it is mandatory to use basic protection, and in some cases, the replacement of long-range redundancy with short-range redundancy for the required number of elements of the power grid adjacent to the wind farm.
The main line protections are differential, differential-phase or high-frequency blocking protection.
At the point of the adjacent power grid to the wind farm, to ensure the LVRTcharacteristic, the relay protection is being upgraded.
It should be taken into account that with the mass use of low-capacity generating sources with a poorly predictable power output schedule, additional technological difficulties arise in ensuring a reliable power supply.The concept of an intelligent power grid (Smart Grid), which includes passive and active objects of the electric grid economy, is based on the use of a control system that regulates the power balance between controlled power plants and consumers technologically connected to it in real time.The application of Smart Grid makes wind power plants economically very attractive.
Currently, five types of generators are allowed in wind turbines: asynchronous generators with a squirrel-cage rotor (squirrel cage), asynchronous generators with a phase rotor and additional resistance in the rotor circuit, dual-fed asynchronous generators, in which the current to the rotor winding is supplied through a semiconductor converter, generators working for the network through a thyristor converter, a synchronous generator connected to a wind turbine through a multiplier with a variable gear ratio necessary to maintain a constant rotor speed.
Machines of the first and second types cannot independently produce reactive power, which is why capacitor banks are installed on their tires.Generators of the third and fourth types are capable of generating active and reactive power using controlled converters.
Let us study the way to improve the effectiveness of a wind power plant.Assume that the most effective result of R will be in case when all local tasks Ri are also effective.Taking into account the structure of wind power plant we have 7 local tasks.The R1 characterized the effectiveness of the wind wheel, and R2-R7 criteria characterized the effectiveness of electric generator, three-phase rectifier, inverter, controller, rechargeable battery and transformer, correspondingly.Thus, the equation will have the form: Criterion  1 depends on the technical characteristics of element of structure   = (  ).It should be noted that the solution could be inferred in case of similar characteristics for all criteria.
Globally the task is formalized as follows: If the   criteria are similar, for example the efficiency of the element, the optimal result take place when each element has maximum efficiency or maximum reliability: Similarly, formalization takes place when cost C is chosen as a criterion: However, the actual tasks demand to fulfill several criteria.For example, we have to obtain inexpensive but reliable wind power plant with high efficiency.In this case every   E3S Web of Conferences 431, 02023 (2023) ITSE-2023 https://doi.org/10.1051/e3sconf/202343102023criterion becomes multidimensional.Let us introduce the j index of multidimensionality into the element of optimality R i opt j .For this case the task is formulated as follows: or in expanded form: Such tasks are the multicriteria ones, and usually search for solutions take place in Pareto area (Figure 2).Consider the solution of local problem of increasing the efficiency of three-phase rectifier.
To convert the mechanical energy of shaft rotation into electrical energy in wind power plants (WPP), electric generators are used.Special requirements are imposed on electric generators used in wind power plants, taking into account the peculiarity of their operation.One of the most important features is that the generator is driven by a wind wheel, the speed mode of which depends on the wind speed and is unstable.For variable loads, it is better to use materials with high fracture toughness [8][9][10][15][16][17][18].
Modeling of an electric generator of a wind power plant is carried out on the basis of studying a number of features of an electric machine.The electric generator in question is a synchronous electric machine with excitation on permanent magnets with an axial direction of the magnetic flow.
When modeling algorithms for controlling the power of wind power plants in purpose to optimize the use of computing resources within the framework of the task, the following model of an electric generator is used.Based on the substitution scheme, the voltage of the phase winding of the generator is Eq. 1 to: where:  is the electromotive force (EMF),   is the active resistance of the phase winding,  is the current in the phase winding,  is the inductance of the phase winding.
In purpose to minimize the influence of the electric machine on the results of the study.We take  = 0;  = 0; the EMF in the windings of the electric generator is given by the following Eq.2: where:   ,   ,   is the EMF the phase windings of the electric generator, 2 is the number of pairs of poles,  is the angular velocity of the generator rotor,  is the time.
Figure 3 shows a block diagram of an electric generator model in an environment MATLAB/Simulink.
The generator simulation assumes RPM=180 RPM at idle and under load.The generator has 25 pairs of poles, the active resistance of the phase winding is 3.5 ohms.The angular velocity of the generator rotor ω is determined by the RPM value.User blocks f(u) form a three-phase voltage, denoted as Phase A, B, C. The "Multiplexer" block combines the A, B, C signals into a vector for further display by the oscilloscope block.The phase voltage is supplied to the three-phase rectifier unit.Straightened pulsed voltage is displayed by the oscilloscope unit.The power of the generator is determined by the "Dot product 1" block, which calculates the dot product of the voltage and current vectors.The torque is calculated by the Divide 2 block.The "Subtract" block allows you to create a simple subsystem with the required number of input and output ports (In and Out).The generator model uses two subroutines: delta-star winding switching and three-phase rectifier bridge.
Figure 4 shows a block diagram of the connection model of the generator windings according to the "Star" scheme.

Results
The result of modeling the operation of an electric generator at a nominal shaft speed of 180 rpm at no load is shown in Figure 6.The upper part of the graph shows the behavior of the EMF of the phase windings of the generator at the input of the rectifier and the lower part shows us the voltage values at the output of the rectifier.In accordance to the results of the simulation of the electric generator it is clearly seen that the use of a three-phase rectifier bridge leads to significant pulsations of the electromagnetic moment of the electric generator.So that smooth out the pulsations of the electromagnetic moment an active three-phase voltage rectifier should be used as the load of the wind turbine which allows us to assume that the phase windings of the generator are loaded with active resistances.In this case the current in the windings of the electric generator is sinusoidal and accordingly in-phase with the voltage in the corresponding winding, and the electromagnetic moment of the generator.

𝑀 𝐸𝑙 = 3 • 𝑘 • 𝐼 𝑝
where:   is the amplitude of the phase current of the generator.
Raising the efficiency of wind power plants is a complex task not only of electromechanics.A comprehensive approach is needed in the field of mechanical engineering, metallurgy and modern nanotechnologies for obtaining and processing materials [13][14][15][16][17][18].The use of new alloys [6][7][8][9][10][18][19] is important not only in the design, but also in the electrical part, for example, in generators.Comparative analysis showed that due to low dynamic losses in an active three-phase voltage rectifier, the efficiency increases up to 98%, an overall dimensions of the inductive storage and output capacitors are reduced.

Conclusions
The main results of work carried out have obviously ecological and practical significance in the reconstruction of industrial enterprises.
Energy based on renewable energy sources will be actively developed in all countries, especially for large cities with a large population and industrial regions.The construction of small and large hydroelectric power plants, complexes of solar power plants, geothermal power plants and heat supply plants, bioenergy and wind installations, incineration and waste-processing power complexes is a promising and politically justified solution for the United States, China and the European Union.It is possible to use the energy of tides.
A defined prospect of using wind energy is that it is environmentally friendly energy.It does not have a significant negative impact on the environment.Accordingly, the production of electricity using wind energy does not lead to negative result in the social sphere.
In addition, the advantages of renewable energy are also associated with higher prices for oil, natural gas, coal and a decrease in the extraction of these resources.At the same time, the development of new energy sources, energy efficiency and environmental management issues give impetus to the development of innovative engineering, science and technology.
The effective use of wind energy integrated into a UES is especially important in such power supply modes, in which additional backup thermal power plants are involved.As a rule, such modes occur periodically due to peak load.Consequently, it is possible to balance energy demand and reduce environmental load on the environment from energy enterprises.Only such energy can be considered green and safe for the environment.
First of all, a practical example shows the possibility of effectively using the conversion of mechanical energy of a wind generator machine using optimal energy conversion schemes without introducing significant imbalances into a UES.
Solving the problem of increasing the efficiency of technically, in particular wind turbines, we have shown the complexity and multivariance of solution.The difficulty is that in order to obtain one solution for one criterion, processing of large data arrays and preliminary computer modeling are required.Having received these solutions, we need to solve the multicriteria optimization problem.On the example of the wind turbine, as a technically complex device, we have shown that the optimization problem applies to all components of the system.One of the obtained solutions illustrates the choice of an active three-phase voltage rectifier and efficiency increase up to 98%, while reducing an overall dimensions of the inductive storage and output capacitors.

Figure 5
Figure 5 shows a block diagram of a three-phase rectifier bridge model to simulate the operation of an alternating sinusoidal current generator on direct current (DC) loads.

Fig. 6 .Figure 7
Fig. 6.Voltage at the and output of the rectifier

Fig. 7 .
Fig. 7. Operation of a generator with a three-phase rectifier bridge.