Principles of electricity metering in networks with non-liner load

. The existing approach to electricity metering, which underlies the formation of payment for consumed electricity, has a significant drawback. It can be correctly used in systems with a sinusoidal symmetrical mode, but needs to be improved in other network modes. The article defines indicators that numerically reflect the effect of distortions on the modes of distribution electric networks, as well as indicators that take into account consumed inactive power (by analogy with reactive power in a sinusoidal mode) when paying electricity bills to an electricity supplier. The proposed principles of electricity consumption metering includes the influence of such indicators as the spectral composition of voltage and current, the ratio of linear and nonlinear loads of consumers, as well as the influence of the topology of the electric network.

Non-sinusoidal network operation occurs when there is a non-linear load, which is represented by a variety of technical means and equipment [6][7][8]. As a result, higher harmonics of current and voltage appear in the electric network of the electrical complex [9][10][11], the influence of which must be taken into account in non-sinusoidal network operation modes [12][13][14][15]. This leads to attempts to replace the concept of "reactive power" with others, which could reflect the influence of higher harmonics on power consumption modes and its accounting [16][17][18]. At the same time, counters with built-in microprocessors are still used to pay for reactive energy, into which various "measuring" equations are embedded [19,20]. Among these equations, the following are most widely used: where U 1 , I 1 , sinφ 1 -voltage, current and phase difference between them at the first harmonic, resp.
where S=UI -apparent power; U,I -effective values of voltage and current, resp.; P -active power.
Only the fact that the consumer is offered various expressions for determining reactive power, speaks of the incorrectness of accounting for reactive energy.
It follows from the above that at least two problems have not yet been solved: 1) Not defined indicators that reflect numerically the effect of distortion on the modes of distribution of electrical networks; 2) The indicators taking into account the consumed inactive power (by analogy with the reactive in sinusoidal mode) when calculating for electricity with the electricity supplier are not defined. From here follows the relevance of the topic raised in the article.

Methods
Before presenting a solution to the first problem, we analyze the most correct indicator, the value of which should be equal to unity.
where P  -total active power including higher harmonics.
where P(i)active power of i-es harmonic including fundamental harmonic. Solving the second problem, first of all, it is necessary to analyze the following situation: why and what for energy supplying organizations are interested in paying for reactive power?
When generating electricity for the consumption of reactive power of the load, no primary energy is spent. It follows that reactive power causes only an increase in current in the line and windings of the generator. Thus, with a high degree of probability it can be argued that reactive power was and remains an indirect sign of the presence of an inactive current (or reactive current at each higher harmonic), which reduces the line throughput, the load of the active power generator and the cost of examining the transmission line.
The model of the studied distribution network is presented in Figure 1.
The model includes a voltage source U, active and inductive resistance of the lines Rl1, Rl2, Xl1, Xl2. The load is represented by a parallel connection of active and inductive resistances, including sources of fundamental and higher harmonics (1, 5.7). If necessary, model parameters can be adjusted. The number of harmonics generated by the current sources at each load can also vary.
On each line, a set of measuring instruments is installed that record the THD values for current and voltage, their RMS values. In addition, for detailed detailing of distortions, there is a block that reflects the phase and amplitude values of each harmonic separately.

Results and Discussion
The solution to the first problem.
As the conducted research showed, the value of KM = 1 is not the only and sufficient condition for the optimality of the transmission of electricity. This is explained by an increase in active power losses with an increase in the order of harmonics (Fig. 1), which are determined by the formula: From the graph it follows that the effective value of the total current can be expressed through a harmonic series as follows: (6) where Ia (1) -active current of fundamental harmonic; Ia (i) , Ip (i) -active and reactive current of i-es harmonic.
The value of KM = 1 can be obtained under conditions: or Based on the real situation of reactive power compensation, condition (6) is possible only if a rather complicated active filter configuration is used. In other cases, the fulfillment of this condition is impossible.
From this condition, the developed condition follows, which can be represented as follows: The solution to the second problem.
For the correct accounting of electricity, it is necessary to take into account the influence of distortions as follows: Let's I=100 A, Ia (1) =0-1, then the curves of changes in V1 and V2 presented in Figure 4.2 determine the costs of inactive energy. Graphs are presented in relative units. Thus, the choice of calculating electricity consumption for V1 and V2 should be made by the tariff committee.

Conclusions
Payment for active energy is not in doubt and complies with generally accepted practice and physics of generation, as well as transmission of electricity. Based on the foregoing, payment for reactive energy by meters seems incorrect. Payment for the full current (or a component of power directly proportional to it) can be correct, which can be realized, For instance, by an integrated current meter. In this case, two options are proposed for calculating the indicator that determines the costs in the process of "generation-transmission-consumption" of electricity, which reflects the essence of energy accounting in the presence of distortions and directly includes the effect of harmonics on active power consumption.