Assessment of the Performance of Active Energy Meters Under Unbalanced Conditions

Over recent decades, electrical power concepts under nonsinusoidal and unbalanced conditions have been continually researched by several academics around the world. The results from these studies present a direct relationship between the performance of electric energy meters and the physical reality of the power balance between loads and sources. As such, this study presents a wide-ranging subject analysis that contemplates analytical, computer, and laboratory developments. This, in turn, opens the possibility of the physical representation of active power under unbalanced conditions, directly impacting the amount of active energy measured by the polyphase meters for billing purposes (from different manufacturers and models) and the composition of technical losses on distribution systems. The results showed that when using the fundamental active power of positive sequence as a reference, as suggested by IEEE Std. 1459/2010, none of the meters available worldwide correctly accounts for active energy. In this context, the study also presents the results from a power measurement campaign performed with 162 different low-voltage three-phase residential consumers located on five different electric energy utilities to understand the actual levels of current unbalance on this specific type of load. In this context, the main contributions of this work are related to (i) the quantification of measurement differences between active energy meters, highlighting the lack of equity in the measurement process of active energy under unbalanced conditions and (ii) the demonstration that the components of zero and negative sequence currents, produced by unbalanced loads, increase the technical losses of distribution systems. Furthermore, the results indicate the urgency of reviewing active energy measurement protocols for billing electricity consumers.

ABSTRACT Over recent decades, electrical power concepts under nonsinusoidal and unbalanced conditions have been continually researched by several academics around the world. The results from these studies present a direct relationship between the performance of electric energy meters and the physical reality of the power balance between loads and sources. As such, this study presents a wide-ranging subject analysis that contemplates analytical, computer, and laboratory developments. This, in turn, opens the possibility of the physical representation of active power under unbalanced conditions, directly impacting the amount of active energy measured by the polyphase meters for billing purposes (from different manufacturers and models) and the composition of technical losses on distribution systems. The results showed that when using the fundamental active power of positive sequence as a reference, as suggested by IEEE Std. 1459/2010, none of the meters available worldwide correctly accounts for active energy. In this context, the study also presents the results from a power measurement campaign performed with 162 different low-voltage threephase residential consumers located on five different electric energy utilities to understand the actual levels of current unbalance on this specific type of load. In this context, the main contributions of this work are related to (i) the quantification of measurement differences between active energy meters, highlighting the lack of equity in the measurement process of active energy under unbalanced conditions and (ii) the demonstration that the components of zero and negative sequence currents, produced by unbalanced loads, increase the technical losses of distribution systems. Furthermore, the results indicate the urgency of reviewing active energy measurement protocols for billing electricity consumers.
INDEX TERMS Load unbalance, electrical losses, measurement errors, active power meters. NOMENCLATURE P (source) Active power on the source side. P Measured Active power measured by conventional active energy meters. P (load) Active power on the load side. P (load)+ Positive sequence active power on the load side. P (load)− Negative sequence active power on the load side. P (load)h Harmonic active power on the load side. P (loss) Total losses in the electrical system.
The associate editor coordinating the review of this manuscript and approving it for publication was Diego Bellan .

I. INTRODUCTION A. MOTIVATION
In their almost absolute entirety, electric energy generators deliver voltages and currents of positive sequence to the power system in the fundamental frequency. On the other hand, after an internal process of electric power conversion, most loads return an important portion of energy with features different from those delivered by generators. This portion of energy returned to the system comprises harmonic components or fundamental frequency components with negative and zero sequences, which solely and exclusively contribute to increased losses in the power systems.  Figure 1 illustrates the energy balance under these conditions, evidencing the intrinsic losses related to the positive sequence power flow at the fundamental frequency, P (loss)+ , the losses due to harmonic power flow, P (loss)h , and the fundamental frequency losses of negative and zero sequences, P (loss)− and P (loss)0 , due to current unbalance.
Faced with this physical scenario, the performance of energy meters (with the intent of billing) has gradually become the object of discussion since the conception of alternating current systems. Thus, considering the specific case of measuring unbalanced loads (resulting in the circulation of zero and negative sequence currents), what do these meters measure?
In addition to providing an answer to this question, the main motivation behind this work is to demonstrate that active electricity meters (from different manufacturers and models) used worldwide cannot accurately measure the amounts of kWh consumed by unbalanced loads. Additionally, this article aims to demonstrate that the zero and negative sequence current components produced by these loads increase the technical losses of the distribution systems as their only destination.

B. LITERATURE REVIEW
The study published by Hollister [1] in 1915 was one of the first studies to conduct research on the performance of active energy meters under non-ideal conditions in which an analytical approach reflected the essence of the physical meaning of active power under nonsinusoidal conditions and emphasized the impact of the presence of harmonic components on electric energy measurement systems. Since then, several other studies [2], [3], [4], [5], [6], [7], [8] have been published contemplating analytical, computational, or practical studies that cover the performance of active or reactive energy meters under nonsinusoidal conditions.
Simultaneously, concerns about the performance of electrical energy meters under unbalanced conditions have been researched. In 1991, the study in [9] demonstrated that unbalanced three-phase systems cause increased technical losses on power grids and indicate possible consequences on the billing for different three-phase consumers.
In 1996, more extensively, the study indicated in [10], besides demonstrating that unbalanced currents cause an increase in active power loss on the distribution system, proposes that meters for the billing of electric energy should solely and exclusively consider the active power of positive sequence on the fundamental frequency. This proposition has been corroborated by the lifelong work developed by Prof. Alexander E. Emanuel [11], which resulted in the elaboration and publication of the IEEE Standard 1459 [12].
The studies developed in [13], [14], and [15] return to the question of problems associated with the measuring of electric energy under unbalanced conditions, considering, for this purpose, only the effects of voltage unbalance in the composition of active and reactive electrical energy. However, in practical terms, due to voltage regulation resources that exist on distribution systems, voltage unbalances present very low amplitudes, in general, less than 3%, when compared to the amplitudes of current unbalances caused by unbalanced loads, which can easily reach more than 50% in low voltage three-phase circuits. Therefore, all the developments and results presented in this study only consider the load unbalances, quantified by the ratio between the negative and positive sequence currents.
In 2012, the study presented in [16] put forward, for the first time, the application of laboratory tests on different electric energy meters, where these had their accuracy tested under different load unbalance conditions while respectively considering the measurement of reactive and active electric energy. The results demonstrate, in a practical way, the findings already presented by other researchers. However, a broader approach to the issue demands a joint analysis that contemplates the performance of different electric energy meters under unbalanced conditions and the impacts of technical losses on distribution systems, as approached in [17] and [18].
The dissemination of single-phase distributed generation units [19], [20] and electric car chargers [21] directly connected to low-voltage circuits raised new concerns, highlighting greater urgency to review criteria and methodologies for measuring electric energy. The analysis of the literature available on the subject highlights the absence of information related to the analysis of what the various active energy meters effectively measure and the differences in the measurements resulting from these meters when supplying unbalanced loads.

C. CONTRIBUTIONS AND PAPER ORGANIZATION
This work's main contribution is quantifying measurement differences between active energy meters under unbalanced VOLUME 11, 2023 load conditions, filling an important literature gap. Additionally, this work highlights the lack of equity in the measurement process of active electrical energy under unbalanced conditions and demonstrates that the differences between the amount of positive sequence active energy and the amount of negative and zero sequence active energy result in increased technical losses in electrical distribution systems. To achieve this goal, this paper is organized as follows: Section II describes the results from a measuring campaign to determine present levels of load unbalance on low voltage three-phase residential consumers. Section III presents the background associated with the energy balance under load-unbalanced conditions. Section IV presents the results from the computational modeling and laboratory tests, facilitating the qualification and quantification of impacts related to load unbalances in the measuring process of electric energy and the composition of technical losses on distribution systems. Section V presents the results from laboratory tests to quantify the performance of different commercially available active energy meters, taking into consideration their use in unbalanced load conditions. The conclusions have been detailed in Section VI.

II. MEASUREMENT CAMPAIGNS
Before developing the proposed studies, a short measurement campaign was conducted by considering a group of 162 lowvoltage three-phase residential consumers across five different distribution energy utilities. Figure 2 illustrates the setup for the measurements performed. The AIW-PEX meter, manufactured by Sigmasys Engineering Ltd., was used in the measurement campaign. The result from the measurement campaign showed that the current unbalance factor (CUF%), quantified through the relationship between the negative and the positive sequence currents, along with the low voltage three-phase consumers, compose a broad range of values, which start from very low values at some moments during the day until they reach values close to 100%. All measurements were recorded over seven consecutive days, with 10-minute aggregation intervals, resulting in 1008 CUF% records for each measurement. Figure 3 shows the extensive range of amplitudes obtained in the measurements, albeit only visually and qualitatively. To facilitate quantitative analysis of the results, Figs. 4(a) and 4(b) present the statistics of the results obtained in the measurement campaign.
The histogram analysis in Fig. 4(a) shows that most 10-minute readings for CUF% are found on the amplitude ranges lower than 20%. However, several recordings have still been noted for CUF% with magnitudes above 50% and a few measurements with amplitudes of current unbalance of over 90%. The cumulative probability curve, presented in Fig. 4(b), shows, for example, that approximately half of the 56528 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. recordings for CUF% present amplitudes lower than 20%. Simultaneously, approximately 90% of CUF% recordings present values lower than 50%. The results show that, depending on the current unbalance's impact on measuring active electric energy and the composition of technical losses, the amplitudes of CUF% verified with low voltage threephase consumers can represent an aspect of significant relevance in these processes. To better understand the impact of unbalanced current in the measuring processes of active energy and composition of technical losses, the following topic presents the complete theoretical foundation related to the subject.

III. BACKGROUND
Under hypothetical operating conditions, considering perfectly balanced linear loads, the electrical circuits would essentially consist of fundamental voltage and current components in a positive sequence. However, the unbalanced load, even considering only linear loads, converts a part of the active, positive sequence energy received from the source into portions of negative and zero sequence energy [11], which are returned to the system with the sole purpose of increasing technical losses. To exemplify this process, the elementary electric system shown in Fig. 5 represents a three-phase fourwire circuit with a balanced voltage source, a line with equal impedances on all phases, a neutral, and a star-connected unbalanced linear load with a grounded neutral. If one considers that R g ≫ r n → I g ≈ 0, based on the classical theory of electric circuits in the frequency domain, then the circuit indicated in Fig. 5 can be divided into three distinct meshes in such a way that.
For Mesh # 1, one has the following: In the same way, for Mesh #2, the result is as follows: Finally, for Mesh #3, one has the following: Considering that the currentsİ 1 ,İ 2 , andİ 3 are the circuit mesh currents, one has the matrix equation in (7).
The line and neutral currents on the generic circuit shown in Fig. 2 can be easily calculated using equation (7). This has been highlighted as follows: At this point, it is important to highlight that the phase voltages used by the active electric energy meter for lowvoltage consumers are always taken into consideration in regard to point n of the circuit in Fig. 5. In other words, point n is the voltage reference for these meters regardless of the equivalent neutral and earth impedance between load and source, as noted from Fig. 6, which illustrates the internal connection diagram of the electric energy meters. Notably, the current I n and the voltage V Nn (as shown in Fig. 5) are not equal to zero under unbalanced conditions, resulting in the obvious P neutral difference to zero. This result shows that the neutral conductor plays an important role in the power balance of the system. However, for practical purposes, as the voltage reference for the meters will always be point n, and there are no current sensors for the neutral conductor, P neutral will always be equal to zero, which means that the values measured by these meters cannot be used for power balance analysis considering the electrical system as a whole. Therefore, once the line currents of the circuit are known,  the phase voltages on the load (voltages considered by the meters) can be easily calculated as follows: Likewise, with the line currents and voltages recorded by the meters at hand, the active powers (and consequently the active energies) can be calculated as the algebraic sum of the active powers measured during each phase of the circuit. Therefore, Circuit losses, in turn, can be calculated as the difference between the total power delivered by the source and the power measured on the load. Accordingly, the power delivered by the source of the circuit in Fig. 5 will be equal to the following As such, the losses on the circuit will be as follows: Or yet, in another form: Although the classic theory of circuits on the frequency domain enables the quantification of the magnitudes involved, the physical analysis that permits the correct identification of the portions of power that constitute the load, and principally, the losses on electric systems, is only possible by considering components of positive, negative, and zero sequences of the circuit under analysis. As electrical power distribution systems naturally comprise unbalanced loads, negative and zero-sequence currents occur, as shown in Fig. 7. Accordingly, after calculating the sequence components of the phase voltages on the load and the line currents, the total power on the load can also be calculated as follows: where, In the same manner, the total power at the source will be as follows: Technical losses on the system can also be expressed in terms of symmetrical components. Thus, based on Fig. 5, for the sake of simplification, the following has been assumed: In such a form that: where, The analysis of (19) shows that the zero sequence losses possess two portions. One is conducted on the phase conductors and the other on the neutral. 56530 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
To better understand the power balance of the hypothetical circuit shown in Fig. 5, a numerical analysis of the above circuit becomes interesting under unbalanced load conditions. As such, by considering phase voltages at the source perfectly balanced and equal to: and line impedances: r a = r b = r c = r n = 1.0 and R g ≫ r n and load impedances: It follows that, based on (2), (4), (6), and (7), the mesh currents will be as follows: The line currents and the neutral current of the circuit can be calculated based on (8), resulting in the following: The positive and zero sequence currents of the circuit will be equal to the following: The phase voltages obtained by way of the symmetric components are as follows: The active power seen by the source, according to (11), will be as follows: P (source) = P A + P B + P C P (source) = 311.7592 + 64.8040 + 96.7251 = 473.31 W The active power on the load, theoretically seen by the energy meter allocated at the consumer installation, according to (10), will be as follows: P (load) = P a + P b + P c P (load) = 301.3022 + 65.1015 + 96.7251 = 463.14 W In terms of symmetrical components, according to (16), the source is represented by perfectly balanced three-phase voltages, resulting in the following: Thus, resulting, according to (16), in the following: Similarly, according to (15), the active power on the load, also in terms of symmetrical components, will be as follows: In other words, these portions of power not used by the load are returned to the system. In the case of the numeric example, the load requests P (load)+ = 468.6763W from the system but uses only 463.14 W to perform its necessary functions. The difference between these values comprises the sum of the portions P (load)− and P (load)0 . Consequently, these two portions' contributions to the system's power balance must be observed. The answer to this question can be obtained by calculating the technical losses of the system, which can be calculated in three different ways, as follows: Resulting, therefore, in the following: The amount of power returned to the system by the load, comprising the sum of the negative and zero sequence portion of power on the load, is fully converted into technical losses in the distribution grid. Starting from the premise that the various sources deliver mostly (and almost entirely) balanced positive sequence voltages with fundamental frequency, this reality could not be different. Apparently, given the results obtained through the numerical example, for the same magnitude of total power, the greater the load unbalances, the greater the technical losses of the system. In line with those mentioned above, the difference between the power effectively used by the load and the total power delivered by the source will also be greater. The following topic will confirm this understanding through computer simulations and laboratory tests.

IV. COMPUTER SIMULATION AND LABORATORY TESTS
Computer simulations and laboratory tests were conducted for a more comprehensive analysis of the impact of load unbalances on the electrical system, whether in terms of the performance of electrical energy meters or the number of technical losses on the distribution system. Thereafter, these two parameters were analyzed for different magnitudes of load current unbalance.

A. COMPUTER SIMULATION
The elementary three-phase four-wire electric circuit, shown in Fig. 8, was modeled on Matlab-Simulink software so that different compositions of the load impedance (Z a , Z b , and Z c ) could be used to obtain different magnitudes of current unbalance. Therefore, line and neutral impedances equal to 1 were considered for the circuit in question, along with a voltage perfectly balanced and phase magnitude equal to 127 V rms . Ground resistance (R g ) was considered equal to 50 . The load impedances were varied to obtain current unbalance levels of 10 in 10%, from a perfectly balanced operation condition up to an extreme operation condition, with a current unbalance level (CUF%) equal to 100%.
The current unbalance (CUF%) for all the proposals in this study was calculated using the ratio between the negative sequence current and the positive sequence current (I − /I + ).  In addition, active power meters were also modeled on the side of the source (Meter #1) and the side of the load (Meter #2). Fig. 9 illustrates the block diagram used for modeling the meters, as verified on the various electronic and electric energy meters available on the market, which consider the total active power as the sum of the averages of the instantaneous total power in each phase of the circuit.

B. LABORATORY TESTS
In addition to the computer simulations, laboratory tests were also performed. These tests aimed to validate the results of the computer modeling. The test setup used, as presented in Fig. 10, comprises a programmable voltage source, Model CSW5500, manufactured by California Instruments, two 56532 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  power quality parameters meters with IEC class A standard, model ION9000, manufactured by Schneider Electric, which was used in the monitoring of power delivered by the source, and the power used by the load. In addition, the test setup comprises a set of four resistors of 1 × 100W for representing the phase of the neutral conductors, a resistor of 50 × 100W for representing the earth path, and a set of 15 switchable resistors of 500 × 100W, for each phase of the circuit for representing the load. The different possible status for each of the 45 (3 × 15) switches on the circuit facilitate the obtainment of different levels of current unbalance, as shown in Table 1, while maintaining the active power of positive sequence constant on the load side.
The tests related to the computer simulations consider the same topologies as the resistive loads shown in Table 1. Finally, it is noteworthy that the test setup used in the laboratory, as shown in Fig. 10, also comprises a set of seven different active energy meters that are commercially available. These were submitted to specific calibration tests under unbalanced load conditions aimed at the compliance analysis concerning the IEEE 1459 [12] standard, which will be further discussed herein. Figure 11 shows the results obtained through the computer simulations and the laboratory tests on the composition of the load registered in terms of its sequence components while maintaining the active power of the positive sequence constant. The positive, negative, and zero sequence power components were separately recorded by the ION9000 meters on the load and the source sides, using specific resources made available by these meters. In this way, the power P (load) will be equal to the sum of the positive, negative and zero sequence powers. Additionally, based on power recordings, with regard to symmetrical components, it was also possible from the differences between the two meters used the calculation of the technical losses on the circuit in terms of its sequence components, as shown in Fig. 12.

C. OBTAINED RESULTS
The results in Fig. 11 demonstrate that a linear increase in current unbalance (or load) causes an exponential reduction in the total active power (or net) registered on the load.   Simultaneously, the results shown in Fig. 12 demonstrate that the same linear increase in the levels of current unbalances cause an exponential increase in the technical losses on the circuit, increasing the technical losses registered/simulated regarding the hypothetical situation of the perfectly balanced load (CUF% = 0) by up to five times.
The results obtained through computer simulations or laboratory tests do not leave any doubt regarding the relevant impact that the unbalanced currents present on the power registered on the three-phase loads and the technical losses of electric systems.
Therefore, the pertinent question must be answered: What do the different active electrical energy meters measure under unbalanced conditions? If these meters measure, for billing purposes, positive sequence fundamental active power, as suggested by the IEEE 1459 standard [12], then technical losses will be billed at the origin (in this case, the load) and will not need to have their costs passed on to the different consumers in each distribution concession area through tariff increases. Otherwise, the technical losses associated with the negative and zero sequence loss components resulting from the load unbalances caused by the consumers must be completely passed on to consumers through adjustments in their electric energy tariffs. The next topic has been exclusively dedicated to answering this fundamental issue.

V. PERFORMANCE OF ACTIVE ENERGY METERS UNDER UNBALANCED CONDITIONS
To analyze the performance of different active energy meters under unbalanced conditions, the laboratory setup shown in Fig. 10 was used. The standard of comparison has been represented by an IEC Class A meter located at the load side and the meter to be tested. Seven different meters available on the market for the billing of active electric energy were tested to achieve this goal. Each meter was subjected to eleven different unbalanced load conditions, considering CUF% values ranging from 0.0% to 100%, with steps of 10%. The load composition for obtaining these unbalanced current values was the same as indicated in Table 1. Taking as a comparison reference for the positive sequence fundamental power, as suggested by the IEEE 1459 standard [12], one notes that, as shown in Fig. 13, the tested meters present errors greater than their respective accuracy class (in this case equal to ± 1.0%) for levels of current unbalanced above 40% [which represent around 20% of the measurements registered, as shown in Fig. 4(b)]. Figure 13 presents the result of the relationship between the active power effectively registered for each meter (P Measured ) and the positive sequence fundamental power registered by the standard meter (P (load)+ ). The meters are represented in letters and numbers, where the letters represent the manufacturer and the meter model numbers.   The results obtained, as shown in Figures 13 and 14, leave no doubt concerning the fact that three-phase meters currently available on the market and used in the billing of energy consumers measure (under unbalanced load conditions) the difference between the fundamental active energy of positive sequence and the sum of the active energies of negative and zero sequences. The analysis of Fig. 13(b) highlights that the differences obtained for current unbalance levels of only 10% result in errors greater than the accuracy class of one of the tested meters (Meter A.3). Additionally, the differences obtained for current unbalance levels starting at 40% represent measurement errors higher than the accuracy classes of all tested meters. Finally, it is also important to highlight the maximum reading differences registered between the different meters for each level of current unbalance considered. In this sense, Fig. 15 shows that the maximum deviations verified were up to seven times higher than the accuracy class of the meters (1%). The deviations between the values recorded by the different meters were smaller than their respective accuracy classes only under the perfectly balanced load condition (CUF = 0.0%). These results show that, under unbalanced load conditions, there is a lack of equity in measuring electricity between different consumers.
In addition to the results presented so far, Fig. 16 shows the results obtained for each of the tested meters, considering the active power values measured by the meters and the positive, negative, and zero sequence active power values recorded by the standard meter installed on the load side, as shown in Fig. 10. The analysis of Fig. 16 highlights that, for each level of CUF% considered, the power effectively measured by the different meters tested (P Measured ) is equal to the difference between the positive sequence active power and the negative and zero sequence active power produced by the load (P (load)− and P (load)0 ), in such a way that: In P Measured ≤ P (load)+ , the components P (load)− and P (load)0 have a negative sign, as they are generated by the load and returned to the system.

VI. DISCUSSIONS ON THE RESULTS OBTAINED AND MAIN ACHIEVEMENTS
The results obtained from the simulations and the various laboratory tests, which consider different levels of load unbalance, lead to the same conclusions indicated in various works when analyzing the active power components resulting from the injection of harmonic currents into electrical systems. In other words, the active energy measured by the active energy meters reflects the difference between the total energy delivered to the loads by the source (represented by the positive sequence active energy at the fundamental frequency) and the energy components returned to the electrical system. These energy components returned to the system are related to any disturbance generated by the load, such as harmonic distortions or, as addressed in the present study, negative and zero sequences of active energy resulting from load unbalance. In such a context, the main achievements of this work are as follows: (i) implementing computer modeling and simulations, conducting laboratory tests, and demonstrating that active energy meters (from different manufacturers and models) are not capable of equitably measuring the quantities of kWh consumed by unbalanced loads; (ii) demonstrating that the components of zero and negative sequence currents, produced by unbalanced loads, increase the technical losses of distribution systems.
These findings highlight the urgency for the various metrological regulatory entities worldwide to promote the revision of three-phase active energy measurement protocols for billing electricity consumers.

VII. CONCLUSION
The present study reported on the fundamental theories relative to active energy under unbalanced conditions, making it evident that three-phase loads use active energy of positive sequence for their different energy conversion processes. Subsequently, these loads return to the system the portion of energy associated with the sum of the negative and zero sequence active energies, which, in turn, possess the increase of technical losses on electric systems as their sole purpose. The same conclusions were drawn from laboratory tests. Additionally, a limited measurement campaign covering 162 three-phase low voltage consumers showed that the existing unbalanced current levels are expressive, highlighting that the performance analysis of three-phase active energy meters is an important endeavor in these operating conditions. The results obtained in the performance tests of the meters show that, as a rule, this device measures the difference between the fundamental active energy of the positive sequence and the sum of negative and zero sequence active energies in terms of kWh. As such, using the positive sequence fundamental power as a comparison reference, as suggested by the IEEE 1459 standard [12], the verified errors were greater than the precision class of the meters (± 1.0%) when magnitudes of the current unbalanced factor of only 10% are considered. These results suggest a degree of urgency in revising active energy measurement protocols worldwide. This is understood not only due to the effects of harmonic components, as shown in several different studies already published in various scientific magazines and journals of great importance, but also due to the impact of load unbalance on the measurement of active energy and in the composition of technical losses, noteworthy in electrical energy distribution systems.
Finally, based on the results obtained in this work, future research directions should include new active energy measurement protocols. Additionally, the studies conducted in this work should be extended to the measurement of reactive energy and other analyses, taking into consideration, for example, the participation of the impedance resulting from the ground/neutral path in the power balance of the system and, more directly, in the active and reactive electric energy measured (and billed) by the meters currently available to the most diverse consumers of electric energy.