Multifactor-based analysis of digital energy metering errors and online detection techniques

In light of the lack of online detection techniques in digital energy metering systems and the ambiguity surrounding factors that contribute to metering errors, this study introduces a multifactor-based approach to comprehensively analyse and detect digital energy metering errors. Through a systematic exploration, the research not only identifies the factors that significantly influence metering errors within digital energy metering systems but also quantifies their individual impacts. A dedicated testing apparatus for digital energy metering systems is devised and the impact of error-inducing factors in the on-site testing is validated. The outcomes serve to validate the precision of theoretical analyses.


Introduction
In the wake of the advancement in intelligent substation construction [1][2], the shift towards intelligent substations is reshaping the landscape of newly constructed or renovated substations in China.A notable divergence in the architecture and functionality of energy metering systems emerges between intelligent substations and their conventional counterparts.In an intelligent substation, the digital energy metering system replaces the conventional alternating current energy meters and consists of voltage merging units, current merging units, and digital energy meters.Due to concerns about stability and reliability related to electronic instrument transformers [3], many intelligent substations opt for conventional instrument transformers coupled with analog input merging units.These units transform analog voltage and current values into digital signals for transmission via optical fibres to the energy meters for energy calculation.In practical operations, the digital energy metering system grapples with challenges like elevated fault rates and reduced accuracy, potentially leading to energy settlement discrepancies.Thus, the imperative lies in subjecting digital energy metering systems to meticulous testing to secure energy measurement accuracy.
Cited work [4] introduced a dual-redundant power supply approach for meters, elevating the operational reliability of digital energy meters.Meanwhile, reference [5] proposed a strategy for event recording and accuracy testing of digital energy meters amid abnormal conditions in the analog field merging unit network.Reference [6] established a testing platform for digital energy metering devices using authentic power sources; however, precise calibration of the analog-to-digital conversion module remains an outstanding requirement.Notably, references [7][8][9][10] delineated laboratory and field-testing methodologies for merging units and devised pertinent standard testing tools.Despite the individual validation of merging units and digital energy meters, an issue endures that energy metering errors in digital energy metering systems exceed the limits of accuracy.Consequently, the pressing need arises to dissect the sources behind these errors, providing a meticulous foundation for calibration and maintenance endeavours in digital energy metering.
In this paper, founded on the intelligent substation framework, a comprehensive test platform for identifying digital energy metering system errors was established.A rigorous scrutiny of factors influencing metering errors within digital energy metering systems ensued, and a field-testing methodology for evaluating secondary side energy metering systems was introduced.This approach ensures the alignment of energy metering errors with pertinent specification standards.

Analysis of sources of metering errors in digital energy metering systems
Drawing insights from the on-site wiring configuration of intelligent substations [11], the direct sampling of voltage and current signals from merging units becomes apparent.The connection mode between the voltage and current merging units follows a cascading arrangement.Specifically, the voltage signal is transmitted from the voltage merging unit to the current merging unit.Inside the current merging unit, voltage and current signals undergo framing before being transmitted to the digital energy meter.This framing process is visually elucidated in the diagram in Figure1.In light of the individual testing qualification for both voltage and current merging units, the measurement error within the digital energy metering system encompasses three key components: (1) Phase error in the voltage and current merging units.
(2) Amplitude error in the voltage and current merging units.
(3) Calculation error within the digital energy meter.Of these, the digital energy meter leverages the IEC 61850 digital signal derived from the current merging unit for real-time power accumulation and averaging.This facilitates the determination of active power, subsequently multiplied by time for energy value calculation.The digital energy meter, devoid of sensory or transformative apparatus and lacking an analog-to-digital conversion stage, is not traditionally classified as a genuine instrument.Instead, it primarily serves as an energy calculator, engaging in mathematical computations.This inherent characteristic eliminates the possibility of errors in its functioning [12].However, in practice, two potential error sources should be considered.Firstly, algorithm-induced errors arise due to signal frequency fluctuations, waveform variations, and asynchronous sampling.Secondly, precision errors occur during floating-point arithmetic, commonly known as truncation errors, intrinsic to computer systems [13][14].The errors inherent in the digital energy meter remain remarkably stable, holding little significance as long as the components remain uncompromised.This stability effectively diminishes the change in metering errors.Notably, extensive laboratory assessments involving thousands of digital energy meters have shown that, apart from potential issues linked to parameters like channel configuration, the metering errors of digital energy meters remain below a threshold of 0.06%.Consequently, the influence of these errors on the precision of the energy metering system in intelligent substations can be deemed negligible.

Test platform for errors
The present study establishes a test platform for the digital energy metering system, comprising the voltage merging unit, current merging unit, digital energy meter, clock synchronization system, and DC power supply.Leveraging the validated detection outcomes of the digital energy meter, merging units, and time synchronization system, an analysis of metering errors inherent to the digital energy metering system is systematically undertaken.Initially, the laboratory testing of the secondary-side energy metering system in the intelligent substation follows an approach: Drawing from actual metering data, a comprehensive analysis delves into the influences of precision in static signal measurements and dynamic signal measurements, the sampling point count on energy metering accuracy.Furthermore, meticulous scrutiny is devoted to the merging unit's impact on the energy metering system.The test plan for the merging unit's impact on the energy metering system is visually presented in Figure 2. Some test devices are shown in Figure 3.In line with the stipulations articulated in Q/GDW11015-2013 "Specification for Testing Analog Input Merging Units" and DL/T282-2012 "Technical Conditions for Merging Units" [7][8], the assessment of voltage and current merging units is meticulously carried out.Reference [10] highlights that when the input signal of the current merging unit diminishes, the occurrence of phase and ratio errors exceeding the limits of accuracy becomes more significant.Consequently, laboratory assessments are conducted on the merging units, utilizing a 100V and 5A range, encompassing measurements at all measurement points within this range and closely aligned with maximal error margins.By subjecting the system to diverse power factors, ratio errors and deviations in the angle between voltage and current are combined separately, yielding insights into the errors within the energy metering simulation system.

Causes of phase errors in merging units
The phase errors, often referred to as the power factor error, originating from the voltage and current merging units, can be attributed to various influencing factors: (1) The inherent phase errors in the sampling transformers of voltage and current merging units contributes significantly to the phase errors.
(2) Throughout the transmission process, voltage sampling values undergo quadratic interpolation within the current merging unit.This may lead to asynchronous voltage and current sampling values, thereby inducing phase errors.
(3) Inconsistencies between the fixed and actual time delays in the voltage and current merging units can result in unsynchronized voltage and current sampling values, consequently engendering phase errors.

Fixed time delays.
Due to the fact that the fixed time delays in the voltage merging unit and current merging unit are determined during type testing, and the on-site installed units have not undergone type testing, along with variations in the components and parameters used in on-site installations, there inevitably exists a certain deviation between the fixed and actual time delays of the voltage and current merging units.Industry regulations deem deviations within 10 microseconds as permissible.In testing, while keeping phase and ratio errors in normal state, adjustments are introduced to the fixed time delay of the current merging unit.This refinement induces asynchronous voltage and current sampling.In this context, both the voltage and current merging units are subjected to assessment for phase and ratio errors, coupled with the energy metering error.The test outcomes are shown in Table 1 and Table 2 Upon scrutinizing the test outcomes, it becomes evident that the fixed time delay in the current merging unit has an insubstantial impact on the phase error in the voltage merging unit.Nonetheless, it directly influences the phase error in voltage sampling values.A mere 1 μs time delay deviation corresponds to an approximate phase error of 1'.In conditions featuring a unity power factor (1.0), this error culminates in an energy metering error of less than 0.05%.Consequently, the impact of fixed time delay errors in the merging unit on energy metering errors is traceable to the repercussions of phase errors in the merging unit.Furthermore, the analysis underscores that the fixed time delay error in the current merging unit distinctly influences the outcome of voltage quadratic interpolation.When scrutinizing the voltage merging unit within a cascaded configuration, the phase error amplifies, subsequently engendering a conspicuous escalation in energy metering errors.

Quadratic interpolation.
When the voltage merging unit is integrated with the current merging unit in a cascading manner, the current merging unit undertakes an interpolation process on the voltage sampling values.These interpolated voltage values are then amalgamated with the current sampling values to form a comprehensive Sampled Value (SV) message signal.Subsequently, this amalgamated signal is transmitted to the digital energy meter.In this context, the frequently employed interpolation algorithm is the Lagrange quadratic interpolation method [14][15][16][17].
In both laboratory and on-site environments, we conduct simultaneous data acquisition of IEC61850 signals from the voltage merging unit and the current merging unit.Voltage sampling values generated by the voltage merging unit and the interpolated voltage sampling values generated by the current merging unit are subjected to a comparative analysis using a network analyser.The data are shown in Figure 4 and Figure 5.Following multiple measurement, the data indicate that upon cascading the voltage merging unit with the current merging unit, the time delay introduced during the data transmission from voltage merging unit to the current merging unit, for alignment and framing purposes, is exceedingly minimal.The phase error arising from the quadratic interpolation of voltage sampling values within the current merging unit is under 10 microseconds and remains predominantly stable, unswayed by load fluctuations.This effect can be mitigated through delay compensation methods [18].

Single-factor analysis of energy metering errors
Without considering the impact of calculation errors, the energy in the secondary-side energy metering system of an intelligent substation can be computed as follows: =  =  (1) Energy metering errors can be defined as follows: is the actual measured energy and   is the standard energy.

Impact of amplitude errors in merging units.
When the phase errors of both the current and voltage merging units are within ±10 degrees, and their error directions remain consistent, these phase errors counterbalance each other, effectively minimizing their impact on energy metering errors.In such scenarios, the overall error stemming from the merging units predominantly arises from amplitude errors.
(1) When the amplitude errors of both the current and voltage merging units lie within the ±0.2% range, yet their error directions diverge, the resultant energy metering error can be computed as follows: ∆ ≤ (1±0.2%)(1∓0.2%)− (2) In situations where the amplitude errors of both the current and voltage merging units are within the ±0.2% range, and their error directions coincide, the energy metering error scope can be defined as follows: So, -0.3996%≤∆E≤0.4004%.
During the practical measurement phase, systematic adjustments were made to the amplitude and phase angle errors of the voltage and current merging units.This meticulous procedure aimed to precisely determine the extent of their impact on energy metering errors.The testing outcomes are detailed in Table 3. From the data presented in the table above, it becomes apparent that when the phase errors of both the voltage and current merging units change in the same direction, the resultant energy metering error can peak at ±0.4%.The error's polarity aligns with the phase error values' direction.Conversely, if the phase errors of the voltage and current merging units change in opposite directions, the influences of these two error types partially negate each other, leading to a reduction in energy metering error to ±0.02%.

Impact of phase error in merging units.
Owing to phase errors stemming from the voltage and current merging units' sampling transformers, a phase error arises between the voltage and current merging units, consequently inducing phase errors between voltage and current.Hence, a comprehensive assessment of phase errors' influence on energy metering errors across different power factors becomes imperative.In order to delve into their impact on energy metering errors, we initially adjust the amplitude errors of the voltage merging unit and current merging unit to lower values.Subsequently, while adhering to acceptable phase error limits, we separately adjust the phase angle errors of the voltage and current merging units to examine their respective impacts on energy metering errors.
(1) Under a power factor of 1, the outcomes of on-site testing are presented in Table 4.The aforementioned test results offer insights that, in the presence of an acceptable phase error and a power factor of 1.0L, the energy metering error attributable to phase errors remains below 0.07%.
(2) For power factors other than 1, the results of on-site testing are depicted in Table 5 and Table 6.The analysis of the abovementioned test results reveals that when the phase errors of the voltage and current merging units change in opposite directions, the energy metering error is approximately ±0.9% at a power factor of 0.5L, and around ±0.4% at a power factor of 0.8L.This demonstrates that as the power factor diminishes, concurrently enlarging the phase error between voltage and current, the ensuing energy metering error assumes greater significance.

Analysis of Multi-Factor Energy Metering Errors
Drawing from the comprehensive analysis above, the impact of the current and voltage merging units on digital energy metering errors can be attributed to two key factors: the amplitude and phase errors of voltage and current.The individual contributions of these elements to energy metering errors have been meticulously examined and evaluated.Nevertheless, real-world scenarios frequently involve the simultaneous influence of multiple factors on energy metering errors.Thus, it is imperative to assess the cumulative effects of these various factors on energy metering errors.
The testing procedure encompasses configuring the amplitude error range of both the current and voltage merging units to ±0.2%, coupled with a phase error range of ±10'.Varied combinations of the amplitude and phase errors are explored across diverse power factors.The ensuing on-site testing outcomes are outlined in Table 7, where a subset of results is provided for the sake of illustration, given the extensive dataset.The test outcomes highlighted above underscore that the impact of ratio errors on energy metering errors is most pronounced under a power factor of 1.0.When the magnitudes of the current and voltage merging units share the same polarity and hover around 0.2%, the resultant energy metering error approximates ±0.4%.Conversely, the influence of phase errors on energy metering error is highly negligible.
Applying this approach to cases where the power factor deviates from 1, the testing outcomes divulge that at a power factor of 0.8L, where the current merging unit has a negative ratio error and the voltage merging unit has a positive ratio error, with both having positive phase errors, the energy metering error is minimized, measuring below 0.004%.Conversely, when the current merging unit has a positive ratio error and the voltage merging unit has a negative ratio error, both accompanied by positive phase errors, at a power factor of 0.5L, the induced energy metering error exceeds 1.4%.

Response and recommendations
In response to the challenge that errors exceed the limits of accuracy within the digital energy metering system, a dual-pronged strategy is adopted, comprising a laboratory modelling analysis and a practical on-site assessment.This approach is strategically designed to unravel the underlying sources of the errors that exceed the limits of accuracy in energy metering and subsequently formulate precise interventions for their mitigation.

On-site testing system
Given the distributed nature of the current and voltage merging units, digital energy meters, this paper introduces a comprehensive testing system in Figure 6.Drawing inspiration from the synchronous simulation control system designed around PMU detection devices, our comprehensive testing system comprises multiple comprehensive testing devices, all orchestrated under the control center.This control center dispatches instructions through wireless channels, coordinating the synchronized activation of distributed testing devices positioned across various locations.Adhering to predetermined timelines, these devices emit three-phase alternating current power signals to the merging units.This process enables an on-site inspection of the energy metering system within intelligent substation.The on-site testing methodology for the digital energy metering system is outlined as follows: (1) The testing system is established.The on-site comprehensive testing system is orchestrated through wireless communication, encompassing two comprehensive testing devices and a control center.Functioning as the system's server, the control center governs the orchestration of the two testing devices.Both devices are connected to the center, establishing an information conduit between the center and them.
(2) The control center meticulously designs the on-site testing protocol, encompassing crucial aspects such as activation timing, parameters of the merging unit under examination, digital energy meter parameters, and the content of assessment.
(3) Facilitated by wireless networking, the control center transmits the meticulously developed testing protocol to the comprehensive testing devices.
(4) Aligned with UTC time as the reference, two comprehensive testing devices meticulously synchronize their testing initiation with the predetermined schedule.At the designated moment, they emit three-phase alternating current and voltage signals.In parallel, they ensure that these voltage and current signals meet the specified frequency and power factor requirements, thus instigating an on-site evaluation of energy metering accuracy.This comprehensive evaluation includes latent test; starting test; constant test; under balanced load, the basic error test of electric energy with different power factors and current values; under unbalanced load, the basic error test of forward active, reverse active, forward reactive and reverse reactive electric energy with different power factors and current values.
(5) Utilizing the data output from the comprehensive testing devices and the energy pulses of the digital energy meter, the control center rigorously compares the errors between the two datasets.This process leads to a comprehensive evaluation of the testing outcomes.

On-site testing effectiveness
The on-site testing system is applied to two subsidiary substations, A and B. Through timed data collection, the system obtained real-time parameters such as current, voltage, power, and power factor from both digital and analog energy meters.A fault that errors exceed the limits of accuracy was identified within the digital energy metering system of Substation A. Subsequent on-site testing and analysis unveiled the following root causes for this fault: (1) A phase reversal fault in the A-phase current circuit of the 10kV busbar merging unit's metering winding was detected.
(2) An incorrect channel configuration was identified in the voltage metering setup of the merging unit.
Regarding the fault observed in the digital energy metering system of Line 2 in Substation B, an approach was adopted.By configuring the voltage merging unit and current merging unit with disparate directions of the ratio error, while simultaneously aligning the phase error directions of the voltage and current merging units, a harmonization of errors was achieved.Through on-site testing, the cumulative metering error of the energy system was found to be within the range of 0.06%, adhering to the accuracy requisites of Class 0.2S.These findings underscore the precision and validity of the testing outcomes presented in this paper.

Recommendations
(1) Before launching intelligent substations, it is crucial to intensify inspections of wiring of voltage merging units, current merging units, and digital energy meters.This proactive approach will prevent wiring errors stemming from insufficient detection or attention to detail during installation.
(2) Strengthen the management of configuration information for voltage merging units, current merging units, and digital energy meters.
(3) Strengthen the pre-installation metrological performance assessment of digital energy meters and merging units.
(4) Conduct comprehensive on-site testing of the energy metering system within intelligent substations.By configuring the voltage and current merging units with divergent directions and aligning the phase error directions of voltage and current merging units, the overall accuracy of the digital metering system can be elevated.This strategic alignment ensures that errors adhere to the accuracy requirements of Class 0.2S or Class 0.5S.
(5) Strengthen the development of technical personnel in municipal companies engaged in digital metering testing through training and practical experiment.This approach aims to elevate the technical proficiency of metering inspection personnel.

Conclusions
In response to the issue that errors exceed the limits of accuracy in digital energy metering systems, this study analyses digital energy metering errors by considering multiple factors and employing online verification techniques.Initially, influential factors affecting energy metering errors were categorized into merging units and digital energy meters.The potential impact of digital energy meter performance on energy metering errors was theoretically ruled out.Subsequently, in a laboratory setting, single and multiple factor simulations were conducted to reveal how the operational state of merging units affects the energy meter performance of the digital energy metering system.Finally, an on-site testing system was established to monitor instances of substandard performance in the digital energy metering system within substations and provide corresponding solutions.The on-site testing results have validated the accuracy of the simulation testing outcomes.The primary conclusions of this study are as follows: (1) The errors associated with digital energy meters are essentially stable, measuring below 0.06%.Their impact on the digital energy metering system's errors can be negligible.
(2) The impact of merging units on the energy metering errors of intelligent substations can be attributed to two factors: amplitude errors and phase errors.
(3) When the ratio error directions of voltage and current merging units are discordant, yet the phase error directions of voltage and current merging units align, the influence of merging units on the incurred errors in energy metering can be minimized.

Figure 1 .
Figure 1.Flowchart of Merging Unit Sampling Process.

Figure 2 .Figure 3 .
Figure 2. Test Plan for the Merging Unit's Effects on the Energy Metering System.

Figure 4 .Figure 5 .
Figure 4. Measurement Results in the Laboratory Environment.

Table 1 .
. Fixed Time Delay of Current Merging Unit is 50 μs (Power Factor 1.0 L).

Table 2 .
Fixed Time Delay of Current Merging Unit is -50 μs (Power Factor 1.0 L).

Table 3 .
Impact of Ratio Error Change Direction on Energy Metering Error.

Table 4 .
Impact of Phase Error Change Direction on Energy Metering Error (Power Factor 1).

Table 5 .
Impact of Phase Error Change Direction on Energy Metering Error (Power Factor 0.5L).

Table 6 .
Impact of Phase Error Change Direction on Energy Metering Error (Power Factor 0.8L).

Table 7 .
Experimental Results Considering Multiple Factors of Errors.