EXPERIMENTAL RESULTS AND ANALYSIS ON UNBALANCED REGIMES ON A WYE-DELTA TRANSFORMER

EMERG, Volume X, Issue /2025 ISSN 2668-7003, ISSN-L 2457-5011 EXPERIMENTAL RESULTS AND ANALYSIS ON UNBALANCED REGIMES ON A WYE-DELTA TRANSFORMER REZULTATE EXPERIMENTALE ȘI ANALIZA LOR ÎN CADRUL UNOR REGIMURI NESIMETRICE LA UN TRANSFORMATOR STEA-TRIUNGHI Andreea IANȚOC1, Mihai SĂNDULEAC1, Ion TRIȘTIU1, Ioan-Cătălin DAMIAN1, Ionuț POPA2, Paul LĂCĂTUȘ1, Ștefan POPA1, Marian PARASCHIV3, Dorel STĂNESCU4 DOI: 10.37410/EMERG.2025.2.10 Abstract: Low voltage (LV) networks are frequently operating with substantial unbalanced regimes, thus bringing power quality issues which need to be addressed. The present work presents experimental results of non-symmetric regimes on a reduced scale star-wye transformer, by applying principles of similitude, and compares the results versus a theoretical analysis of operation in a non-symmetrical regime of the MV/LV transformers. In this respect, a setup using a reduced scale transformer has been used, with a total power of 8 kVA, which is a reduced scale equipment of an 400 kVA MV/LV transformer, by using adequate similitude factors, such as KSIMIL = 50 for the current and power on the LV side. Measurements have been made with high quality devices, using a precision electronic smart meter of class 0.2S on one side and a power quality analyzer on the other side of the transformer, both being integrated in a small SCADA system which acquired and stored the necessary records. The work presents also specific adaptations of the measurement system in order to allow a detailed analysis of regimes of work on both sides of the star-wye transformer. The aim of the analysis is also to show practical aspects which can make a better link between theory and practice. Keywords: unbalanced regimes, star-wye transformers, similitude, reduced scale, experimental results. 1 University POLITEHNICA of Bucharest, Romania, e-mails: [email protected], mihai.sand[email protected]m, [email protected], [email protected], paul.laca[email protected], [email protected] 2 Eng., Straum S.A, e-mail: [email protected] 3 Eng., Transelectrica S.A, e-mail: [email protected] 4 Dr.Eng., Electrica S.A, e-mail: [email protected] Experimental Results and Analysis on Unbalanced Regimes … 151 Rezumat: Rețelele electrice de joasa tensiune (JT) se caracterizează prin regimuri care sunt adeseori puternic nesimetrice, producând probleme legate de calitatea energiei electrice. Lucrarea prezintă rezultatele experimentale ale măsurării regimurilor nesimetrice pe un transformator stea-triunghi realizat la scara redusa, pe baza aplicării unor principii de similitudine si le compara cu analiza teoretică a funcționării in regim de nesimetrie a unor transformatoare de medie pe joasa tensiune (MT/JT). In acest scop se folosește un ansamblu trifazat de transformatoare la scara redusa, cu o putere totala de 8 kVA, care reprezintă un transformator MT/JT de 400 kVA, utilizând factori de similitudine adecvați, cum ar fi KSIMIL = 50 pe partea de joasă tensiune. Măsurătorile sunt realizate cu aparate de măsurare de înaltă calitate, respectiv cu un contor de energie electrica de precizie și cu un analizor de calitate, ambele fiind integrate într-un mic sistem SCADA cu care s-au realizat înregistrările. In lucrare se prezinta si adaptări specifice ale sistemului de măsurare, care sa permită o analiză in detaliu a regimurilor de funcționare pe ambele părți ale transformatorului steatriunghi. Scopul analizei este sa pună în evidență aspecte practice care sa facă o mai buna legătura intre modelul teoretic si experiența practică. Cuvinte cheie: regimuri nesimetrice, transformator stea-triunghi, rezultate experimentale 1. Introduction Low voltage (LV) networks are frequently operating with substantial non-symmetric regimes, thus bringing power quality issues which need to be addressed. The present work presents experimental results of non-symmetric regimes on a reduced scale star-wye transformer, by applying principles of similitude, and compares the results versus a theoretical analysis of operation in a non-symmetrical regime of the MV/LV transformers. To allow flexibility in performing tests, a reduced scale low-voltage (LV) electrical network has been used. The measurements presented in this work use high quality measurement equipment, respectively a 0.2S high accuracy digital meter and a power quality analyzer, both being integrated in a SCADA system which was able to make records of relevant measurements. Moreover, the paper presents some of the specific adaptations which have been chosen to allow a detailed analysis of the operational regimes on both sides of the wye-delta transformer of the reduced scale model. The analysis highlights also practical aspects which can make a better connection between theoretical model and practical experience. Measurements have been realized on a laboratory-based reduced scale network which uses principles of similitude to obtain similar results with the ones to be obtained in a real system with a 400 kVA MV/LV transformer. 152 Ianțoc, M. Sanduleac, I. Triștiu, I.C. Damian, I. Popa, P. Lăcătuș, S. Popa …. 2. Using principles of similitude and reduced scale models John Strutt, known also as Lord Rayleigh, introduced in 1915 the paper “The principle of similitude” [1], saying that he has “often been impressed by the scanty attention paid even by original workers in physics to the great principle of similitude”. In [2] it is stated that for power systems engineers, models are critical to the planning and economic design of this massive infrastructure, pointing that physical modeling has always had a role as well, stretching to use the laws of similitude to use more convenient frequency, impedance base, and physical size. The method presented in the paper [3] aims to establish in laboratory conditions, using the similitude criteria, the real value and the duration of a three phase short-circuit current acting in wind farms connected to the electric grids, while paper [4] gives some prerequisites of using similitude for studying distribution networks with a laboratory-scaled grid. In the paper [5], experimental determinations have been obtained, for medium voltage faults on the lines radially connected to the main line emerging from a wind farm, using the similarity relations, allowing the determination of the electrical quantities from the real network. Similarity is used in many fields. For instance, the study from [6] explores the vulnerability of Internet-exposed services and the prevalence of Brute Force Attacks (BFAs) as an intrusion method. Within this study, are also evaluated similarity metrics based on Bloom Filters (BFs). In the paper [7] are described different prototypical labs and their application are described, where users can exploratively learn the method of differential balancing, including similitude mechanics and visualization types in fluid mechanics, while in [8], based on the similarity theory, a reduced-scale model is proposed to study the voltage distribution characteristics in ultra-high voltage direct current converter transformer windings under the impulse voltage. The paper [9] presents a reduced scale model for grounding resistance calculation using finite element method FEM method. In the paper [10], by using the finite element simulation platform, a reduced-scale model of two-span transmission line and its prototype finite element simulation model are established. The basic principle which has been used is that the main test data measured by the model and prototype in the test are similar or meet a certain proportion. In [11] it is presented an original smart-grids test bed aimed at teaching novel feeder automation functions to students from both university and industry origins, by using reduced-scale loads, generators, and a supervisory control and data acquisition system and paper [12] compares steady state and dynamic behavior of a large 117-inverter based, 147-MW solar PV plant Experimental Results and Analysis on Unbalanced Regimes … 153 connected to IEEE 39-bus system, considering also reduced scale solar PV plant models. In the paper [13], the operation of an MMC converter in an MTDC network containing three converter is verified experimentally in a reducedscale pilot. In the tests, the energy buffering of the MMC converter was considered to sustain either AC or DC grids’, by using the framework of the Multi Terminal DC pilot. In paper [14], the authors present a reduced-scale reconfigurable dc distribution testbed that contains a number of converters, inverters and adjustable link impedances. In [15] it is made a real-time grid-impedance measurement, and experiments are conducted on a reduced scale 3 kVA laboratory testbed. All these works show the broad spectrum of applications and how promising are the principles of similitude in various domains as well for studying various aspects of the power grid in the energy domain. 3. A reduced scale network, based on similitude factors A reduced scale network (RSN) has been constructed and used for making various tests and by using principles of similitude. It is a low voltage network using five LV nodes (N1 – N5) which is supplied through a delta-wye three-phase transformer. While the delta part of the transformer is intended to represent a medium voltage connection in node N0, this node and the delta part of the transformer are still implemented in LV, for laboratory purposes. The applied principles of similitude are targeting: – A much lower power and current in the LV part of the scaled network – A much lower voltage implemented for the primary of a real MV/LV transformer. The following sections give the main formulas used in order to study such a reduced scale network and to obtain results regarding the operational status of the grid which can apply on a real and powerful network. 3.1. Similitude between currents of a real electrical network versus currents of a reduced scale network at the same voltage level For the reduced scale model having a different current level than for the real system, it is needed to introduce a current similitude factor. For this, we apply the following rule: the current of the real system and the current of the reduced scale model need to produce the same voltage 154 Ianțoc, M. Sanduleac, I. Triștiu, I.C. Damian, I. Popa, P. Lăcătuș, S. Popa …. drop on an impedance Z, if the reduced scale model is at the same voltage level as voltage level of the real system: 𝑍 𝑅𝑒𝑎𝑙 × 𝐼 𝑅𝑒𝑎𝑙 = ∆𝑈 𝑅𝑒𝑎𝑙 = 𝑍 𝑆𝑖𝑚𝑖𝑙 × 𝐼 𝑆𝑖𝑚𝑖𝑙 = ∆𝑈 𝑆𝑖𝑚𝑖𝑙 (1) for: 𝐾 𝑆𝑖𝑚𝑖𝑙 𝐼 = 𝐼 𝑟𝑒𝑎𝑙 𝐼 𝑆𝑐_𝑅𝑒𝑑 where 𝐼𝑟𝑒𝑎𝑙 is the current in the real network, while 𝐼𝑆𝑐_𝑅𝑒𝑑 is the current in the reduced scale network. It results the relation: 𝐼 𝑅𝑒𝑎𝑙 = 𝐾 𝑆𝑖𝑚𝑖𝑙 𝐼 × 𝐼 𝑆𝑖𝑚𝑖𝑙 (2) And we can write that: 𝑍𝑅𝑒𝑎𝑙 × 𝐾𝑆𝑖𝑚𝑖𝑙𝐼 × 𝐼𝑆𝑖𝑚𝑖𝑙 = 𝑍𝑆𝑖𝑚𝑖𝑙 × 𝐼𝑆𝑖𝑚𝑖𝑙 (3) Which brings the relation between the two impedances as being: 𝑍 𝑅𝑒𝑎𝑙 × 𝐾 𝑆𝑖𝑚𝑖𝑙 𝐼 = 𝑍 𝑆𝑖𝑚𝑖𝑙 (4) 𝐾 𝑆𝑖𝑚𝑖𝑙 𝑈 = 𝑈 𝑟𝑒𝑎𝑙 𝑈 𝑆𝑐_𝑅𝑒𝑑 (5) For a real current 𝐼𝑟𝑒𝑎𝑙 = 50 𝐴, which corresponds to a current in the reduced scale model 𝐼𝑆𝑐_𝑅𝑒𝑑 = 1 𝐴, we have: 𝐾 = 𝐼 𝑟𝑒𝑎𝑙 = 𝐼 𝑟𝑒𝑎𝑙 = 50 = 50 (6) 𝑆𝑖𝑚𝑖𝑙 𝐼 𝐼 𝑆𝑐_𝑅𝑒𝑑 𝐼 𝑆𝑖𝑚𝑖𝑙 1 This is the current similarity factor which has been chosen for the reduced scale grid. 3.2. Similitude between voltages of a real electrical network versus voltages of a reduced scale network For the reduced scale model having a different voltage level than for the real system, it is needed to introduce a voltage similitude factor, as follows: 𝐾 𝑆𝑖𝑚𝑖𝑙 𝑈 = 𝑈 𝑟𝑒𝑎𝑙 𝑈 𝑆𝑐_𝑅𝑒𝑑 (7) For 𝑈𝑟𝑒𝑎𝑙 = 20 𝑘𝑉 and 𝑈𝑆𝑐_𝑅𝑒𝑑 = 𝑈𝑆𝑖𝑚𝑖𝑙 = 0,4 𝑘𝑉, we have the following voltage similitude factor: 𝐾 = 𝑈 𝑟𝑒𝑎𝑙 = 20000 = 50 (8) 𝑆𝑖𝑚𝑖𝑙 𝑈 𝑈 𝑆𝑐_𝑅𝑒𝑑 400 Experimental Results and Analysis on Unbalanced Regimes … 155 This is the volage similarity factor which has been chosen for the medium voltage part of the reduced scale grid. The 𝐾𝑆𝑖𝑚𝑖𝑙𝑈 = 50 allows to have a 400 V AC three-phase system on the transformer side which represent the real system phase to phase voltage of 20 kV. 4. Tests and results The reduced scale network used for the tests is presented in Figure 1. It is a three-phase LV network which is supplied by a three-phase transformer. The transformer has been constructed by using three single-phase transformers having on the primary winding 𝑈𝑁𝑃𝑟𝑖𝑚 = 400 𝑉 and on secondary 𝑈𝑁𝑆𝑒𝑐 = 230 𝑉. The three single-phase transformers are connected on primary side in delta, while on the secondary side they are connected in wye. Figure 1. Reduced scale network used in the tests. In order to test the behavior a MV/LV transformer with delta connection on MV and wye connection on LV side, tests have been made by connecting on the LV part of the transformer only single-phase loads. This brought three different scenarios, which are presented below. Test 4.1 – Single-phase load between phase “a” and the neutral of the wye connection on the LV side. The situation is depicted in Figure 2. It has been used a pure resistive load (X=0). 156 Ianțoc, M. Sanduleac, I. Triștiu, I.C. Damian, I. Popa, P. Lăcătuș, S. Popa …. Figure 2. The voltage drops on an electrical line It can be seen that the current 𝐼𝑎 is obtained based on the magnetic coupling of the secondary between a and null (a-n) and the primary connected between phases A and B. Moreover, as for each reduced scale single-phase transformer of the three-phase transformer the primary winding has a nominal voltage of 230 × √3 ≅ 400 𝑉, while the secondary has a nominal voltage of 230 V per phase, the relation between the currents is given by: 𝐼𝐴𝐵 = 𝐼 𝑎 𝑁 𝑇𝑟𝑎𝑓𝑜 (9) where the ratio 𝑁𝑇𝑟𝑎𝑓𝑜 is given by: 𝑁 = 𝑈 𝑃𝑟𝑖𝑚𝑎𝑟𝑦 = 400 = 1.73 (10) Then: 𝑇𝑟𝑎𝑓𝑜 𝑈 𝑆𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 230 𝐼 = 𝐼 𝑎 = 𝐼 𝑎 (11) 𝐴𝐵 𝑁 𝑇𝑟𝑎𝑓𝑜 1.73 The currents on phases A and B are: 𝐼𝐴 = 𝐼𝐵 = 𝐼𝐴𝐵 (12) Moreover, there is no current 𝐼𝐶, thus it can be considered 𝐼𝐶 = 0. Experimental Results and Analysis on Unbalanced Regimes … 157 This situation on the primary side of the transformer occurs when the single-phase load is connected on the secondary side between phase “a” and the neutral “n” of the wye. The secondary currents are 𝐼𝑎 = 𝑈𝑎−𝑛/𝑍𝐿𝑜𝑎𝑑, 𝐼𝑏 = 0 and 𝐼𝑐 = 0. Test 4.2 – Single-phase load between phase “b” and the neutral of the wye connection on the LV side. The situation is depicted in Figure 3. It has been used a pure resistive load (X=0). Figure 3. The voltage drops on an electrical line In this second test it can be seen that the current 𝐼𝑏 is obtained based on the magnetic coupling of the secondary between phase b and null (b-n) and the primary connected between phases B and C of the transformer’s primary windings. Test 4.3 – Single-phase load between phase “c” and the neutral of the wye connection on the LV side. The situation is depicted in Figure 4. . It has been used a pure resistive load (X=0). 158 Ianțoc, M. Sanduleac, I. Triștiu, I.C. Damian, I. Popa, P. Lăcătuș, S. Popa …. Figure 4. The voltage drops on an electrical line In the third test it can be seen that the current 𝐼𝑐 is obtained based on the magnetic coupling of the secondary between phase c and null (c-n) and the primary connected between phases C and A of the transformer’s primary windings. 4.4 – Results and assessment The currents and phases of currents related to their phase voltages have been measured and recorded each 2 seconds, for a period of at least 30 seconds. Tables 1 and 2 show average values of currents (in Amperes, [A]) and of angles (in degrees, [º]) during stable load-flows in no-load status and with single-phase loads on each secondary phase of the transformer. The ∆I [%] errors are calculated with the formulas: ∆𝐼𝐴% = (𝐼𝐴 − 𝐼𝐵)/𝐼𝐴 × 100 (13) ∆𝐼𝐵% = (𝐼𝐵 − 𝐼𝐶)/𝐼𝐵 × 100 (14) ∆𝐼𝐶% = (𝐼𝐶 − 𝐼𝐴)/𝐼𝐶 × 100 (15) According to Figures 2, 3 and 4, the following relation should apply in theory for the primary currents: – In Test 4.1 we should have 𝐼𝐴 = 𝐼𝐵 and 𝐼𝐶 = 0 – In Test 4.2 we should have 𝐼𝐵 = 𝐼𝐶 and 𝐼𝐴 = 0 – In Test 4.3 we should have 𝐼𝐶 = 𝐼𝐴 and 𝐼𝐵 = 0 Experimental Results and Analysis on Unbalanced Regimes … 165 Dorel STĂNESCU holds a Ph.D. in Electrotechnics Engineering and from Technical University of Timisoara in 2024 in Distribution Management Systems. He took part in several projects concerning metering systems, power quality monitoring systems and distribution automation. He is now coordinating the Meter Data Management System at DEER, largest distribution operator in Romania. Email: [email protected]