An Approach for Assigning Responsibilities of Short-Term Voltage Variations in Electrical Power Systems

Short-term voltage variations (STVVs) are phenomena manifested as voltage sags, voltage swells, or interruptions lasting up to 1 minute. Despite their short duration, they greatly influence the operations of loads. In fact, residential, commercial, and industrial consumers can be strongly affected when facing supply discontinuities, loss of production, physical damages, and other issues. Under such circumstances, conflicts may arise between suppliers and consumers. Thus, a strategy that identifies whether the STVV phenomenon was produced upstream or downstream of a given point of common coupling between two agents interconnected by a transformer is proposed in this paper. The methodology is based on the transference mechanism of imbalance indicators through this connecting transformer. The current process is not about determining the physical location of the disturbance in the network but only about establishing the responsibility for the disturbance. The effectiveness of the process is determined through computational and experimental studies, for which typical electrical systems are employed. To this end, unbalanced STVVs are imposed on these systems, and the voltage and current imbalance levels on the primary and secondary sides of transformers are correlated to validate the proposal.


I. INTRODUCTION
Studies and procedures in the Power Quality area are related to voltage deviations from standards established by the regulatory agencies. In this scenario, several indicators, such as long-term voltage levels, harmonic distortions, and imbalances, are widely known and regulated phenomena [1], [2], [3], [4], [5]. However, most power quality standards still do not consider other anomalous phenomena, such as short-term voltage variations (STVVs). This abnormal operating condition produces significant variations in the RMS voltage amplitudes that last up to one or three minutes [6], [7], [8].
The associate editor coordinating the review of this manuscript and approving it for publication was Nagesh Prabhu .
Following several guidelines, the disturbances herein focused on are typically organized as given in Table 1 [8]. The terms and values presented are established by the power quality standards of electrical distribution agencies, such as [9] and numerous others [10], [11]. Table 1 highlights that voltage occurrences are classified as instantaneous events (between 0.5 and 30 cycles), momentary variations (less than 3 seconds), and temporary variations (up to 1 minute). Although many countries use the time limit of 1 minute [8] for the temporary phenomenon, others have defined this limit as 3 minutes [6].
Although the terminology ''short-term voltage variation'' applies to situations of voltage dips (sag), overvoltages (swell), and interruptions, the vast majority of occurrences and their effects are related to sag occurrences.   The importance of STVVs is evident, given their significant impacts on the operation and production of industrial plants. As exemplified in Fig. 1, according to the survey carried out [12], it is evident that STVVs mostly affect consumers.
The relevance of the effects caused by STVVs is reflected in security, discomfort, and financial losses, among others. Table 2 indicates the typical costs of industrial shutdowns related to voltage sag events [13]. Other relevant information on the relationship between disturbances and economic aspects can be found in [14] and [15].
Given the above, the importance and the need for regulating through normative documents the STVVs are recognized. Some standards define this phenomenon according to its magnitude level and duration, such as the IEEE 1159 [8], IEC 61000-2-8 [16], EN 50160 [17], among others [18]. In addition, other guidelines quantify STVV events to meet power quality supply standards. In this context, the NRS 048 [11] and PRODIST [9] provide numerical indicators focused on establishing quantitative limits for STVV events, taking into account their characteristics (magnitude level, duration, and severity). However, the existing standards and guidelines, either qualitative or quantitatively, do not consider assigning or establishing responsibility for the origin of the STVVs.
It is evident that the responsibility for the origin of STVVs can motivate conflicts between the agents involved. Such questions may be grounds for legal complaints about the physical and financial compensation arising from STVVs. In this sense, as for other power quality indicators, an important question arises about the responsibility of the disturbance. This issue can be understood in Fig. 2, which shows the connection busbar between utility and industrial installations. The figure makes it clear that the search for a strategy focused on the proposal of this paper does not aim to identify the physical location of the disturbance occurrence, such as in [19]. In fact, the proposed methodology is aimed at determining if the phenomenon occurred in the electrical area upstream or downstream of the point of analysis.
Regarding STVV responsibility, few studies can be found compared to other power quality indicators. In [20], a proposal is given based on the measurements carried out on several network buses. The approach is based on the residual voltage being monitored on each busbar (the remaining voltage associated with the STVV), the instant the event occurs, and its duration. After collecting the data, they are analyzed, and each measured quantity relates to others at different busbars. It is important to emphasize that the method needs a well-structured network supported by several meters to guarantee its reliability. A technique using fast Fourier transform is considered in [21]. Voltages and currents are monitored and treated, leading to the identification of the source of the event. The method requires a considerable level of computational processing. An approach to identifying the responsibility of STVVs based on the power flow behavior before and during the voltage sag can be found in [22]. The application of this method requires knowledge of the sequence components of the impedances. In [23], an approach is given based on the current, active power, and harmonic distortion measurements before and during the event. The need for different measurements at different moments causes difficulties in the practical applications of the methodology. Reference [24] uses a procedure based on the negative-sequence voltage and current measurements. From these quantities, the negative-sequence impedances are determined for the given purposes. Reference [25] evaluates existing and new methods, showing the results that reveal the performance improvement of established procedures to choose time windows for each method. The process application in real time is pointed out using the proposed resources. Despite the promising computational results, there is no evidence of its practicability and effectiveness in real installations to identify the origin of STVVs.
Although the above works are focused on sorting out the challenge of identifying the responsibility of STVVs, thus far, there is no evidence of any strategy that has been reported with effective practicability and success to be applied in real installations.
To search for the causes that lead to the responsibility identification of the power quality occurrences discussed herein, a simple and feasible method is proposed in this work.
In line with the established objectives, this article is structured into four sections in addition to the present one. In Section II, a summary of the proposed process fundaments is presented. MATLAB-SIMULINK computational studies aiming to demonstrate the methodology application using a typical electrical arrangement are performed in Section III. In Section IV, experimental studies are included to demonstrate the effectiveness of this method. The simulations and experiments consider different types of STVVs and commercial winding connections for the transformers. In Section V, final considerations on the performance and application perspectives of the proposal are provided.

II. THE STVV ORIGIN IDENTIFICATION FUNDAMENTS
Most STVVs present asymmetrical characteristics. With this in mind, the unbalanced three-phase voltages and currents can be decomposed, among other analysis techniques, into their positive, negative, and zero sequence components [26], [27], [28].
The relationship between the original A, B, and C components and the sequence components is given by (1). In contrast, the inverse of (1) provides the opposite transformation between the quantities.
Once the sequence components of the voltages are obtained, the negative and zero unbalance factors are calculated as given in [29]: where: • UF v2 % is the negative-sequence voltage unbalance factor; • UF v0 % indicates the zero-sequence voltage unbalance factor. Similarly, the corresponding current unbalance factors are: • UF i2 % for the negative-sequence current unbalance factor; • UF i0 % represents the zero-sequence current unbalance factor. Notwithstanding the recognition that obtaining negativesequence unbalance factors for voltages is conceptually established by (2), the literature indicates a straightforward strategy that would lead to the same results [30]. This procedure is widely used for practical situations since the negative-sequence unbalance factor can be obtained throughout the phase-to-phase RMS voltage magnitude, as indicated by (4) and (5). These expressions do not require knowledge of the phase angles of voltages and currents, which are not commonly available.
The proposed approach is based on three-phase voltage and current measurements on the primary and secondary sides of the transformer connecting two electrical systems. This transformer connects the upstream and downstream electrical areas of the point of analysis. This point of analysis may represent the connection busbar between a supplier and a consumer or a transmission network and a distribution system. By obtaining three-phase voltages and currents, their corresponding negative and zero sequence unbalance factors can be promptly calculated. Next, the transference mechanism of these quantities from one side of the transformer to the other is analyzed to identify those applicable to establish the STVV origin identification approach.
It is worth mentioning that the mechanism that governs the transference of the imbalance quantities is directly dependent on the connecting transformer windings. Surveys made in several databases show that, with regards to distribution networks, most transformers have the primary in delta and the secondary in star-grounded. Regardless, to expand the investigations while recognizing that other connections are commercially used, different transformer windings are considered in this work. Typical percentages of the winding connections of transformers employed in the Brazilian national distribution electrical grid for voltages below 138 kV are presented in Table 3 [31].

III. COMPUTATIONAL PERFORMANCE OF THE UNBALANCE FACTORS TRANSFERENCE MECHANISM A. ELECTRICAL SYSTEM ARRANGEMENT
The electrical system implemented for the computational studies is shown in Fig. 3, and its parameters are given in Table 4. The consumer unit is defined by a combination of loads containing constant impedance, constant power, and induction motors. This load combination makes the analysis broader than if passive components were simply consid-  ered in the analysis. This arrangement was implemented in MATLAB-SIMULINK software.

B. CASE STUDIES
To generate the STVVs used for this study, the work is carried out through the application of electrical short circuits on the sides of the transformers for which the events were defined. The use of such faults was merely a strategy for the simulation studies. The disturbances applied led to the final voltage levels of the respective phases that are close to 0.5 pu. However, it is worth noting that the imposed voltage sag levels are only illustrative, as the analysis process applies to other asymmetrical conditions.
The STVV events occurring on the primary sides of the connecting transformer are given below.
• Case 1.1 -Phase-to-ground short-term voltage asymmetry produced on the primary side of the transformer with different transformer winding connections. Therefore, the case study is subdivided into three subcases: 1.  The studies related to the occurrence of the STVV on the secondary side of the connecting transformer are as follows.  Fig. 4 provides the unbalance factors on both the primary and secondary transformer sides for the STVV events occurring on the primary side. Fig. 4(a) shows the voltage unbalance factors, and Fig. 4(b) presents the current unbalance factors. When the STVV phenomenon is produced on the secondary side, the corresponding results for the unbalance factors for voltages and currents are shown in Fig. 5(a) and Fig. 5(b), respectively.

C. RESULTS AND DISCUSSION
The results show the following.
• STVV produced on the primary side of the transformer: If the origin of the events occurs on the primary side of the transformers, the negative-sequence voltage unbalance factors (UF v2 ) on both sides of the transformer are the same, regardless of the STVV nature and the type of transformer connections. For the levels found for the negative unbalance factors of the currents (UF i2 ), these indicators also proved to be the same on both sides of the transformer. Regarding the zero-sequence voltage unbalance factors (UF v0 ), their values were shown to be dependent on the nature of the STVV and the transformer winding connection, that is, whether they involved a ground. Concerning the values of the zero-sequence unbalance factors for the currents (UF i0 ), these have been shown to be very small in magnitude.
• STVV produced on the secondary side of the transformer: The performances obtained with STVV events on the secondary side of the transformer showed a behavior different from that obtained previously. The negative-sequence voltage unbalance factors (UF v2 ) have shown different magnitudes on both sides of the transformer. An exception was identified VOLUME 11, 2023  when the Y-transformer connection was exposed to a phase-to-ground voltage variation. This situation led to a zero level of negative-sequence voltage unbalance factors on both sides. This behavior occurs because the network prevents the flow of negative-sequence currents. The values of the negative-sequence current unbalance factors(UF i2 ) were the same on the primary and secondary sides of the transformer. The zero-sequence voltage unbalance factors exist only on the STVV origin side, except for the Yn-Yn connection. In this case, the (UF v0 ) indicator is presented on both sides. Regarding the zero-sequence current, these only exist when using connections in Yn. Table 5 summarizes the findings of the transference processes of negative and zero sequence unbalance factors, both for voltages and currents. It is shown that UF v2 is a promising indicator that identifies the origin of the STVV. UF i2 did not prove to be an efficient indicator for the required purposes. The quantities UF v0 and UF i0 can be used as crossover information as long as the STVV events involve a ground, and the transformer has only one grounded winding.

IV. EXPERIMENTAL VALIDATION
An experimental procedure for validating the proposed methodology was set up using a laboratory arrangement containing an equivalent supply system, a transformer, and loads. The electrical arrangement is shown in Fig. 6. The supply is provided by a controlled voltage source and reactors representing the system impedance. The connecting transformer is a three-phase unit with three possibilities for the winding connections: -Yn, Y-, and Yn-Yn. Three-phase variable resistors are taken as the supplied loads connected in Y. The switchable inductive components in parallel with the resistors are meant to increase the secondary side unbalances. Table 6 presents the parameters of the individual components.
It is noteworthy that the imbalance levels obtained experimentally were much lower than those used in the computational studies. Such limitations were imposed since higher imbalances would require current levels above the supportability of the equipment used in the laboratory structure. Moreover, the experimental studies were performed for only  two types of events, i.e., phase-to-ground and phase-phaseto-ground short-term events.
In accordance with the above, Case 3 corresponds to the STVV events produced on the primary side of the transformer by unbalancing the three-phase voltage supply. The resistive loads were kept balanced, and the reactors were switched off.
• Case 3.1 -Phase-to-ground short-term voltage asymmetry produced on the primary side of the transformer with three subcases for the connection windings of the transformer: 3.1.1 ( -Yn), 3.1.2 (Y-), and 3.1.3 (Yn-Yn).
• Case 3.2 -Phase-phase to ground short-term voltage asymmetry produced on the primary side of the In line with the findings obtained by the computational results, the quantity that proved to be promising for the objectives of the article was the relationship of the negative-sequence voltage unbalance factors. Thus, the results from the experiments given in the sequence include only this quantity.
The results found for an STVV produced on the primary are shown in Fig. 7(a), whereas Fig. 7(b) presents the results for a corresponding event occurring on the secondary.
In general, the experimental results concerning the UF v2 agree with those found in the computational studies. In fact, the STVV arising on the primary side produces approximately the same UF v2 on both sides of the connecting transformer. However, when the STVV is produced on the secondary side, the value of UF v2 is distinct on each side of the transformer.

V. CONCLUSION
The results and analyses on the STVV responsibility assignment based on the transference mechanism of the negative-sequence voltage unbalance factors (UF v2 ) have been promising. This strategy emerges as a reliable, simple, and feasible way to identify the origin of the STVV phenomenon.
In general, when the STVV is produced upstream of the transformer, the UF v2 and UF i2 quantities present the same values on both the primary and secondary sides, regardless of the transformer winding connection. On the other hand, when the event occurs on the secondary side, UF v2 are different for both sides of the transformer. In this case, it was also found that the UF i2 values are practically the same for both sides of the transformer.
Regarding the zero-sequence unbalance factors, if these quantities are available, they do not modify the above findings but only provide additional information for attributing the STVV responsibility. As expected, the zero-sequence unbalance factors are only present in voltages and currents when the causes of the STVV are events involving a ground. In fact, in the case of transformers with -Yn and Y-connections, the zero-sequence factor can be found only on the side where the phenomenon occurred. This does not apply to the Yn-Yn connection.
It is also worth emphasizing that the use of UF v2 is a straightforward monitoring strategy since its formulation requires only the RMS values of the voltages without the need to know the corresponding phase angles. Thus, the analysis process proposed here can be implemented without modifying the existing measurement framework.
Finally, it must be stressed that this paper is not aimed at identifying the exact physical location of the event in the network but just if the disturbance occurred upstream or downstream of the point of analysis. Therefore, the methodology proposed in this article contributes to advancing the standards for regulating the responsibility over STVVs.