# A method for predicting the distribution of harmonic components of the electric energy unbranched parts of the power system

The invention relates to electrical engineering and can be used in the process of designing, commissioning and operation of modern power systems, which have a high degree of presence of nonlinear electrical loads, which is one of the main reasons for the distortion of the shape of the load, which is one of the main causes distortion of the voltage and current, and therefore, are responsible for the presence of harmonic components of electrical energy (all except the main one). Object of the invention is the prediction of the distribution of the harmonic components of the electric energy unbranched parts of the power system. The technical result is achieved by the fact that non-branched sections of the power system are represented as a group of similar lines, electrical energy as a result of the impact of the incident and reflected waves, and forecasting the distribution of harmonic components of electrical energy is based on the solution of the equations with hyperbolic functions on two variables: the length of the predictable plot and frequency. 1 Il. Invented the temporary electrical power systems (EPS), which have a high degree of presence of nonlinear electrical loads, which is one of the main causes distortion of the voltage and current, and therefore, are responsible for the presence of harmonic components of electrical energy (all except main).A known method of estimation of the propagation of harmonics in electric power in AC networks described in [1]. This method assumes that the known impedance current of each harmonic component. And on the basis of this information, according to this method, composed of a matrix of conductances and identifies current and voltage for different frequencies.However, the exact determination of the full resistance of each harmonic component of the electrical component in the analyzed area real EPS is very problematic. But, nevertheless, the flexibility of these resistances, the frequency is one of the main reasons for changing the amplitude of the harmonic components of the voltages on this or another site power system.If to consider in more detail the reason for the appearance is not always desirable harmonic components of electrical energy in electrical power systems, * electrical load to the electrical network frequency series of harmonic components and, as a result, the occurrence of reflected waves of the electromagnetic energy of the appropriate frequency. In other words, a problem of occurrence of harmonic components can be attributed to the rank of the consequences of the so-called "effect of long lines.It is believed that the effect of long lines" is manifested in the power lines, the length of which is not less than 200-300 km But it's for the harmonic component of the frequency is about 50 Hz. For high-frequency components of the same length of the plot lines that show the effect of long lines, is reduced. So with a length of only 10 km, the above effect is already apparent at the frequency of the 9-th harmonic. This fact can be fixed either experimentally or analytically by below method.Therefore, the closest technical solution to the proposed method is the method of analysis of the distribution of electric energy through the power lines of great length (lines with distribution parameters) [2].Object of the invention is the prediction of the distribution of the harmonic components of the electric energy unbranched parts of the power system.The technical result is achieved by the fact that nerazvit the mental energy as a result of the impact of the incident and reflected waves, and forecasting the distribution of harmonic components of electrical energy is based on the solution of the equations with hyperbolic functions on two variables: the length of the predictable plot and frequency.The drawing shows a block diagram of the algorithm implementing the method for predicting the distribution of harmonic components of the electric energy unbranched sections EPS.It is necessary to divide the studied unbranched part of the power system on at least relatively homogeneous areas.To implement the distribution of harmonic components of the electric energy unbranched parts of the power system it is enough to know the spectral compositions of the voltage and current at any point of the investigated area of the system. In addition, it is necessary with sufficient accuracy to represent the location of the sources of each harmonic component of the electrical energy that will allow us to determine the direction of propagation of the incident wave of electromagnetic energy of a particular frequency on this site Naibolee from powerful sources of harmonic components of electrical energythe equations to determine (predict) the voltage and current at the corresponding frequencies at a distance l from the above places, look like this:wherewave resistance consider a uniform area EPS at the frequency f;- coefficient of the electromagnetic wave of frequency f.Equation (1) allows to determine (predict) the numerical values and the nature of the voltage and current of frequency f at any distance from the place (point) EPC with known spectral compositionwithin the uniform area power system. Equations of this type will allow us to determine (predict) the spectral content of the voltage and current and changes the homogeneity of the considered part of the power system, located at a distance n from a place with a known spectral compositionThen, taking this place (point) source, using formulas similar to equations (1), we can determine (predict) the spectral content of the voltage and current at various points in sidelite (predict) the spectral content of the voltage and current at the end of the already mentioned following a uniform area EPS. And so on for all lines of a single class of voltage, connecting a homogeneous areas considered unbranched part of the power system. But in these cases, for each homogeneous area is necessary to determine the coefficients of the propagation of electromagnetic wavesthe wave resistance of the respective plotsIf there is a known spectral composition in place (point) closest to powerful sources of harmonic components of electrical energythe equations to determine (predict) the voltage and current of the respective frequencies at a distance l from the above places, look like this:These equations as equations (1), allow to determine (predict) the spectral content of the voltage and current in any place of this uniform area EPS.The spectral content of the voltage and current at the opposite end of this section, the length of which is determined by the value of n can be determined from the solution of the equationsTaking the end of this section as a starting point, formula, similar Urvaste the studied power system of the same voltage class. Using formulas similar to equations (4), we can determine (predict) the spectral content of the voltage and current at the end mentioned the following uniform area EPS. And so on. But the coefficients of the propagation of electromagnetic waves and wave resistance for each homogeneous area EPS are defined separately.The coefficient of the electromagnetic wave for each frequency is defined as a complex number, which in symbolic form looks like this:

where(f) is the attenuation coefficient of the electromagnetic wave at the frequency f;(f) - factor phase for each frequency oscillations of electromagnetic energy.In this case, the coefficient of the electromagnetic wave is recommended to determine the following:

where

R

_{0}and L

_{0}- specific longitudinal parameters (resistance and inductance) circuit, a uniform area EPS (electric power lines); G

_{0}and C

_{0}- specific cross-parameters (active conductance and capacitance) schematic is operadic can be identified from the relevant literature.Impedance is considered part of the EPC should be determined by the formula

The sequence of actions when implementing the method for predicting the distribution of harmonic components of the electric energy unbranched portions of the EPS can be represented in the form of a structural diagram in the drawing.The forecasting process must be preceded by a determination of the spectral content of the voltage and current at any fixed point EPC (block 1). This operation can be performed either using specialized measuring devices (measuring harmonics, spectrum analyzers, measuring systems, and so on), or due to analytical understanding of the impact of nonlinear loads on the electricity network. In the same block 1, where going to the source for the forecasting process information, the area EPS, subject to survey, identify homogeneous areas and gather information about the respective transmission lines (the specific parameters of the equivalent circuits).In unit 2 according to the formula (6) are determined by the specific longitudinal resistanceand in block 3 by the formula (7) - odelin the two operations can be executed in parallel and independently from each other.Next, in blocks 4 and 5 are two independent from each other surgery: in unit 4 by the formula (5) are the coefficients of the electromagnetic wave, and in block 5 of the formula (8) is the wave resistance of the examined plots of the electricity system.After implementation in the first five units of preparatory operations in the block 6 is determined (predicted) spectral structures of voltage and current in a particular location analyzed EPS or by formulas (1) and (2) or formula (3) and (4) depending on the nature of the source data, versions of which are provided above.Equation(1), (2), (3) and (4) suggest the presence of spectral line voltage at the end or at the beginning of the considered area EPS three-phase execution. And it is quite justified for cases when the level of voltage unbalance in the areas of electrical power does not exceed the normative values.In the event of a significant voltage unbalance in this EPS is better for the original data to make the spectral composition of the phase voltages(block 1), and in section 6 to determine (predict) the spectral phase compositions on the (1), (2), (3) and (4) will appear in a different form: in case of known spectral composition of the voltages and currents in the place (point) EPC, the most remote from powerful sources of harmonic components of electrical energy

or

and at a known spectral composition of phase voltages and currents in the place (point) EPC, as close to powerful sources of harmonic components of electrical energy

or

Thus, the described method allows you to get an idea of the spectral compositions of the voltage and current anywhere analyzed unbranched area power system, and hence to estimate the distribution of the harmonic components of electric energy on the site.Sources of information

1. Harmonics in power systems: Lane. from English./J. Arrillaga, D. Bradley, P. Boger. - M.: Energoatomizdat, 1990. - 320 S.2. Brooms Century A. Ryzhov, Y. P. Distant transmission lines AC and DC. - M.: Energoatomizdat, 1985. - 272 S.

I(f, l)I_{n}(f, l) and current in accordance with the mathematical expressions (1)x electric energy, and in accordance with the mathematical expressions (3) and (4) for homogeneous sections, the source points that are close to powerful sources of harmonic components of electrical energy, mathematical expressions mentioned above

where

wherewave resistance consider a uniform area at a frequency f;

- coefficient of the electromagnetic wave of frequency f;

l is the distance from the location of known spectral composition of current and voltage;

n is the distance changes the homogeneity of the considered site from locations with known spectral composition;

R_{0}and L_{0}- specific parameters: resistance and inductance of the circuit, a uniform area;

G_{0}and C_{0}- specific transverse parameters: active conductance and capacitance circuits a uniform area.

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