Evaluation of voltage imbalance on low‐voltage distribution networks considering delta‐connected distribution transformers with a symmetrical NGS
2017; Institution of Engineering and Technology; Volume: 12; Issue: 7 Linguagem: Inglês
10.1049/iet-gtd.2017.0631
ISSN1751-8695
Autores Tópico(s)Lightning and Electromagnetic Phenomena
ResumoIET Generation, Transmission & DistributionVolume 12, Issue 7 p. 1644-1654 Research ArticleFree Access Evaluation of voltage imbalance on low-voltage distribution networks considering delta-connected distribution transformers with a symmetrical NGS Rih-Neng Liao, Rih-Neng Liao TC-site Facility Department-1, Taiwan Semiconductor Manufacturing Company Ltd., 6, 1, Keya Road 6, Daya District, Taichung City, 428-82 300-77 TaiwanSearch for more papers by this authorNien-Che Yang, Corresponding Author Nien-Che Yang ncyang@mail.ntust.edu.tw Department of Electrical Engineering, National Taiwan University of Science and Technology, 43, Keelung Road, Section 4, Taipei, 10607 TaiwanSearch for more papers by this author Rih-Neng Liao, Rih-Neng Liao TC-site Facility Department-1, Taiwan Semiconductor Manufacturing Company Ltd., 6, 1, Keya Road 6, Daya District, Taichung City, 428-82 300-77 TaiwanSearch for more papers by this authorNien-Che Yang, Corresponding Author Nien-Che Yang ncyang@mail.ntust.edu.tw Department of Electrical Engineering, National Taiwan University of Science and Technology, 43, Keelung Road, Section 4, Taipei, 10607 TaiwanSearch for more papers by this author First published: 28 February 2018 https://doi.org/10.1049/iet-gtd.2017.0631Citations: 5AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The main purpose of this study is to evaluate the effect of distribution transformers with a delta-connected neutral-grounded structure (NGS) on the voltage imbalance of low-voltage distribution networks. The proposed NGS for delta-connected distribution transformers has a symmetrical structure. That is, the stability and reliability of the operating characteristic of the proposed delta-connected NGS are better than other grounding methods such as corner-grounding, mid-tapped grounding, a zig–zag grounding transformer, and an asymmetrical NGS. In this study, the coupling-free equivalent circuit mathematical models for various methods of grounding a delta-connected structure are first developed. Furthermore, these coupling-free equivalent circuits can be simply implemented in the MATLAB/Simulink platform. Next, the IEEE test feeder system is used as a benchmark for verification. To determine the feasibility of the proposed NGS and evaluate its operational performance, a Monte Carlo simulation-based three-phase power-flow method was proposed to compare the operational characteristics of various grounding structures (i.e. system imbalance resulting from asymmetric load conditions or asymmetric transformer connections) such as phase-to-ground voltages, line currents, power consumption, and voltage unbalance factor. The results provide a valuable reference for distribution engineers and building technologies seeking a suitable method of grounding delta-connected power service systems. 1 Introduction 1.1 Background and literature review In recent years, the progress of society and the rapid development of science and technology had led to an increase in electrical consumption in the residential, industrial, and commercial sectors. The power supply and quality of the smart grid are particularly important, because they can affect people's livelihoods, business operations, and a country's economic development. Therefore, power networks always need to rely on maintenance from relevant personnel involved in power and distribution such as the power construction, system operation, equipment maintenance, and management. The power supply reliability and operating reserve can then be optimised to minimise the integrated cost for the power supply and periods of power shortage [1]. In the advanced countries of the world, the transformer power supply services of distribution networks are commonly classified as three-phase three-wire and three-phase four wire [2]. This is even the case for multi-grounded four-wire [3] and five-wire [4, 5] distribution networks as well as the single-phase three-wire network used in modern home wiring systems [6, 7]. Their differences are based on the methods of system grounding. The purpose of system grounding is to obtain line voltage stability and improve system security, which helps avoid damage to the equipment and reduces personnel accidents [8]. In other words, a system using an appropriate method of system grounding can not only improve the safety and performance of the distribution networks but can also maintain the original system operating performance and power quality. In a typical medium-voltage distribution system (35–6 kV) in Taiwan, a general use medium-voltage three-phase distribution transformer will be converted into a low voltage to supply power to demanding loads. The windings of the three-phase distribution transformer are often connected as a wye (Y) connection or delta (Δ) connection; thus, the primary and secondary side windings may consist of Y–Δ, Y–Y, U–V (open Y–open Δ), and U–U (open Δ–open Δ) connections [9]. For Y–Y and Δ–Δ connections, the voltage displacement between the primary and secondary sides is 0°. For Y–Δ and Δ–Y connections, the voltage displacement between the primary and secondary sides is 30°. However, the windings of the distribution transformers are usually connected to a Δ in medium-voltage distribution networks. If a delta power supply cannot provide the neutral point of the system, the ground potential may not be controllable when faults occur. Even if the delta power supply can ground on the corner or mid-tap of these phase windings [10], this results in the phase-to-ground voltage being inconsistent. The following is a variety of methods for grounding power supply delta transformers. Fig. 1a shows a delta-connected transformer applying the corner-to-grounding method. This method of corner grounding can obtain a zero potential of one phase-to-ground and the other two phase-to-ground voltages are line voltages, i.e. the voltages of the phase-to-ground are inconsistent. This method of corner grounding is mainly used to supply power loads. This method is simple, it can limit the rise of an abnormal potential in networks, and it can block the third harmonic current. Fig. 1b shows a delta-connected transformer applying the mid-tapped-to-grounding method. This method of centre grounding can simultaneously supply power to a three-phase rotating motor and single-phase lighting. This method is called the power supply service system of the three-phase four wire. Two phase-to-ground voltages are 0.5 times the phase-to-phase voltages and another phase-to-ground voltage is 0.866 times the phase-to-phase voltage (high-leg). The phase-to-ground voltages in a delta-connected mid-tapped grounding method are also inconsistent. Fig. 1c shows a zig–zag (Z -type) wiring transformer used for grounding [11]. This grounding transformer can solve the problem of the neutral point being unusable for a Δ- and Y-type wiring. Each phase winding is wound around two magnetic columns, so that the zero-sequence flux generated by the two-phase windings cancel each other. The zero-sequence impedance of the zig–zag wiring transformer is <10 Ω and the no-load loss is low. The useable transformer capacity is higher than 90%. Therefore, among traditional methods, a Z -type wiring transformer used as a ground transformer is a good choice. Fig. 1Open in figure viewerPowerPoint Grounding methods (a) Corner grounding, (b) Mid-tap (centre) grounding, (c) Grounding transformer of zig–zag (Z -type) wiring, (d) Delta-connected structure installed one-grounding winding In recent years, the so-called neutral-grounding method of the delta-connected structure provided a system neutral point by grounding one winding, as proposed in [12, 13]. The delta-connected transformer with one extra grounded winding obtains the neutral point of the system, as shown in Fig. 1d. The first end of the grounded winding is connected to a ground point, which functions as a neutral point of the system. The second end of the grounded winding is connected to a tap of one of the other two-phase windings. The voltage phase displacement between the grounded winding and the corresponding phase winding is 180°. We observed that three phase-to-ground voltages are uniform under distribution network balanced loads. Therefore, the neutral-grounded method can solve the problem of the three-phase voltage inconsistency in traditional methods of grounding the delta-connected structure. Unfortunately, the neutral-ground method with one-grounded winding is an asymmetrical structure. When the distribution networks operate on heavy and unbalanced loads, zero-sequence currents flow through this grounded winding, which can lead to winding overheating and failure. 1.2 Aim and contributions This paper presents a balanced scheme for the neutral-ground method of the delta-connected structure that used three-grounded windings (#g1, #g2, #g3), as shown in Fig. 2. When the distribution networks are operated under unbalanced load conditions, the currents of the grounded windings of the proposed method are less than the methods mentioned above. The stability and reliability of the proposed method are better than those of the one-grounded winding method, because it is a symmetrical neutral-grounded method. The performances (voltages, currents, energy consumption, and voltage imbalance factor) of the distribution systems can be further improved. The proposed transformer can also be used as the multi-voltage solution for distribution networks and buildings [14], e.g. the phase of each 1/2-tap-turn can be drawn out such as m1, m2, and m3 (see Fig. 2). The magnitudes and angles of the voltages are shown in Table 1, in which the phase-to-ground voltage is 1.0 pu system. Fig. 2Open in figure viewerPowerPoint Delta-connected structure installed three-grounding winding (a) Schematic diagram, (b) Voltage phasor diagram Table 1. Relationship of the voltage magnitude and the voltage angle in a symmetrical neutral-grounded method of a delta-connected structure of three-grounding windings a b c m1 m2 m3 n Magnitude a — 1.732a 1.732a 0.866 1.500 0.866 1.000b b 1.732a — 1.732a 0.866 0.866 1.500 1.000b c 1.732a 1.732a — 1.500 0.866 0.866 1.000b m1 0.866 0.866 1.500 — 0.866 0.866 0.500c m2 1.500 0.866 0.866 0.866 — 0.866 0.500c m3 0.866 1.500 0.866 0.866 0.866 — 0.500c n 1.000b 1.000b 1.000b 0.500c 0.500c 0.500c — Angle a — 0d −60 0 −30 −60 −30 b 180 — −120d 180 −120 −150 −150 c 120d 60 — 90 60 120 90 m1 180 0 −90 — −60 −120 −90 m2 150 60 −120 120 — 180 150 m3 120 30 −60 60 0 — 30 n 150 30 −90 90 −30 −150 — a Phase-to-phase voltage. b Phase-to-ground voltage. c Phase-to-ground voltage of the half. d Voltage displacements between Vba, Vcb, and Vca are 120°, in which Vab = 0°. It is necessary to develop an equivalent model for the proposed transformer, because there is currently no commercial software package developed. In this paper, the mathematical models (coupling-free equivalent circuits) of the various methods of grounding the delta-connected structure are developed. This includes corner-grounding, mid-tapped grounding, a zig–zag grounding transformer, the neutral-grounded method of an asymmetrical structure, and the neutral-grounded method of the proposed symmetrical structure. Coupling-free equivalent circuits are implemented by using the MATLAB/Simulink software platform. The operational characteristics of various grounding structures are compared to verify the feasibility of the proposed neutral-grounded structure (NGS) and evaluate its operational performance. The results provide a valuable reference for distribution engineers and building technologies seeking a suitable method of grounding delta-connected power service systems. 1.3 Paper organisation Section 1 introduces the background, objectives, and contributions of this paper while reviewing the relevant technical literature. Section 2 introduces the voltage imbalance factor. Section 3 develops the mathematical models (coupling-free equivalent circuits) of various methods for the grounding of the delta-connected structure. Section 4 carries out the analysis of voltage, current, voltage imbalance factor, and compares the characteristics of various grounding methods of the delta-connected service system. Section 5 is a conclusion. 2 Concept of voltage imbalance These are many causes for power system imbalances and reduced power quality. This includes single-phase loads, single-phase distributed resources, asymmetrical three-phase equipment and devices (such as three-phase transformers with U–V connections), unbalanced faults, and poor electrical connections. The voltage unbalance is one of the most serious power quality problems. The factors affecting a voltage imbalance can be divided into two categories: normal and abnormal. (a) Normal factors may include single-phase loads and asymmetrical three-phase transformers with U–V connections. Usually, a distribution/power engineer of modern building systems reduces the voltage imbalance by properly designing the system and installing the appropriate equipment. (b) Abnormal factors may include series and shunt faults of circuits, bad electrical contacts of connectors or switches, the asymmetrical breakdown of equipment or components, asynchronous burnout of three-phase power fuses, and single-phase motor operation. These abnormal factors can cause serious damage to the system and equipment. To clarify this discussion, the definition of voltage imbalance is introduced as follows. 2.1 Definition of voltage imbalance If three-phase voltages have the same magnitude and experience a 120° phase displacement, then the three-phase voltage is called balanced. Otherwise, it is unbalanced. There are no zero-sequence voltages in balanced systems. The balanced and unbalanced voltages can be represented as follows: Balanced three-phase voltage (1) Fig. 3Open in figure viewerPowerPoint Schematic diagram of component model of distribution transformer bank (a) corner grounded; (b) center tapped-off grounded; (c) with an asymmetrical NGS or with zig-zag grounding transformer; (d) with a symmetrical NGS Unbalanced three-phase voltage (2) where (3) The zero-sequence voltage unbalance factor (VUF) for d0 is defined as follows [15]. Here, V1 and V0 are positive-sequence and zero-sequence voltages, respectively (4) 2.2 Effects of voltage imbalance The effect of a voltage imbalance on low-voltage distribution networks and equipment is extensive and serious. For low-voltage distribution networks and building technology, this imbalance may significantly reduce equipment life, speed up the replacement cycle of the equipment, and increase system operation and maintenance costs. In addition, for three-phase, four-wire, and low-voltage building systems, a voltage imbalance may lead to higher neutral wire currents and cause the relay to malfunction [16–21]. The major effects of voltage imbalance are described as follows: Extra power loss : It is known that a voltage imbalance always causes an extra power loss in the system. The higher the voltage unbalance ratio (VUR), the greater the power consumption. That means higher electricity bills. Safety deficiency : The voltage difference between the highest and lowest voltages in the unbalanced three-phase voltage is a major factor in initiating safety defects. The degree of safety defects depends primarily on the affected equipment itself. Motor failure : A voltage imbalance caused by an additional loss will heat the motor winding. This will result in winding insulation damage and eventually lead to motor failure. The negative sequence voltage caused by the voltage imbalance produces a torque in the opposite direction of motion, which causes motor vibration and noise. A serious voltage imbalance can even causes the motor to completely fail. Life-cycle attenuation : Exceeding the rated temperature of the device will greatly reduce the service life of the equipment, speed up the equipment replacement cycle, and significantly increase operating and maintenance costs. Relay failure : A high zero-sequence current caused by a voltage imbalance can cause a malfunction of the relay or make the ground relay insensitive. This can lead to serious security problems. Transformer failure : The three-phase voltage of a high VUR can cause the magnetic flux in the transformer core to be asymmetrical. This asymmetrical flux can cause additional core losses, increase the winding temperature, and, in severe cases, cause transformer failure. 3 Development of coupling-free equivalent circuits with various grounding methods Westinghouse Electric Corporation proposed the relationship between the primary and secondary windings of the transformers (see [22]). The construction of a rigorous transformer model is mainly developed to consider copper and core losses. Figs. 3a–d show the schematic diagram of the transformer bank with various grounding methods. Figs. 3a and b show the traditional grounding methods at points other than the system neutral, which includes corner-grounded and mid-tap grounded. Figs. 3c and d show the system neutral-point-grounded method, in which Fig. 3c can be a zig–zag grounding transformer or an asymmetrical NGS (i.e. with one-grounding winding). Building systems or distribution networks always operate under unbalanced loads resulting in some issues of power quality, especially the voltage imbalance rate because it can increase the system power losses. Therefore, Fig. 3d shows the schematic diagram of the proposed model of the transformer bank (delta-connected with symmetrical NGS) improving the system balance and reducing power losses. 3.1 Basic concept and components From Fig. 3, the transformers can be represented as a series and shunt block, respectively: Shunt block : The shunt block is used to represent the real and reactive power core losses of the transformer and can be approximated as functions of the primary terminal voltage. The core losses of the real and reactive powers are obtained by field tests. Typical values [23] can also be adapted to approximate the distribution transformer. Series block : The series block represents the equivalent circuit of the transformer bank. It mainly consists of resistances (R) and inductances (L) or injected currents. The equivalent circuit takes into account the characteristics of the vast majority of transformers such as copper losses, the connection of transformer windings, the voltage displacement between the primary and the secondary side, off-nominal tap, and tap settings. The voltages in a three-phase power distribution system can be stepped up or down by connecting two or three single-phase transformers to a three-phase distribution transformer bank. In this paper, we use a three-phase transformer bank composed of three single-phase transformers to perform voltage imbalance investigations for building networks. The proposed three-phase transformer bank corresponding to the coupling-free equivalent circuit is based on the existing equivalent circuit model of a single-phase transformer such as the single-phase two-winding transformer (see Section 3.1.1), single-phase three-winding transformer (see Section 3.1.2), and single-phase two-winding transformer with two tapped-off points on the secondary side (see Section 3.1.3). 3.1.1 Single-phase two-winding transformer The circuit layout of a single-phase two-winding supply transformer is shown in Fig. 4a. The coupling-free equivalent circuit of a single-phase two-winding supply transformer is shown in Fig. 4b. The nodal admittance matrix of a single-phase two-winding supply transformer was developed [24]. The mathematical model of the single-phase two-winding transformer with a nominal tap is given in (5) (5) The equivalent admittance of the transformer indicates yt, and it can be obtained by short-circuit field tests. This corresponds to the coupling-free equivalent circuit, as shown in Fig. 4b. The turns ratio (N1/N2) is equal to 1 in a pu system. Fig. 4Open in figure viewerPowerPoint Circuit diagram of a single-phase two-winding transformer with a nominal tap (a) Circuit layout, (b) Coupling-free equivalent circuit 3.1.2 Single-phase three-winding transformer The circuit layout of a single-phase three-winding supply transformer is shown in Fig. 5a. For simplicity, the equivalent circuit of Fig. 5a can be obtained by superimposing two single-phase two-winding transformers (i.e. network overlapping technique), as shown in Fig. 5b. The coupling-free equivalent circuit of a single-phase three-winding supply transformer is shown in Fig. 5c. Fig. 5Open in figure viewerPowerPoint Circuit diagram of a single-phase three-winding transformer with a nominal tap (a) Circuit layout, (b) Equivalent circuit, (c) Coupling-free equivalent circuit For β1 N2 and β2 N2 turns of the secondary windings, the nodal admittance matrixes of two subnetworks (#1, #2) can be obtained in (6) and (7), respectively (6) (7) The network overlapping technique can be applied to determine the equivalent mathematical model of single-phase three-wire transformers, as shown in (8) (8) 3.1.3 Single-phase two-winding transformer of two tapped-off points on the secondary side The circuit layout of a single-phase three-winding supply transformer with two tapped-off points is shown in Fig. 6a. For simplicity, the equivalent circuit of Fig. 6a can be obtained by superimposing three single-phase two-winding transformers (i.e. network overlapping technique), as shown in Fig. 6b. The coupling-free equivalent circuit of a single-phase three-winding supply transformer is shown in Fig. 6c. Fig. 6Open in figure viewerPowerPoint Circuit diagram of a single-phase three-winding transformer with two tapped-off points (a) Circuit layout, (b) Equivalent circuit, (c) Coupling-free equivalent circuit Following the same procedure as above, the network overlapping technique can be applied to determine the equivalent mathematical model of single-phase three-wire transformers with two tapped-off points on the secondary side, as shown in (9). However, the nodes ‘X2’ and ‘X3’ of (9) can be removed using Kron's reduction law; subsequently, the results of (9) are verified and compared with (5) (9) where . 3.2 Traditional methods of grounding at points other than NGS In this section, three traditional methods of grounding points other than NGS are examined, i.e. corner-grounding, mid-tap grounding, and zig–zag transformer grounding. We assume that three single-phase transformers are identical to simplify the modelling process. Therefore, Fig. 7 illustrates the electrical circuits of three traditional grounding methods, in which three windings of the primary side can be connected to either a wye, grounded-wye, or delta. They are described as follows: Fig. 7a illustrates the coupling-free circuit corner-grounding method and only can supply three-phase power to loads, i.e. 3ϕ 3W service. Phase C is connected to ground, which results in the other two phase-to-ground voltages being equal to the phase-to-phase (line) voltage. Fig. 7b illustrates the coupling-free circuit of a centre tapped-off grounding method, which can supply three-phase and single-phase power to loads, i.e. 3ϕ 4W service. The centre tapped-off point of phase A can be connected to the ground, in which (i) two phase-to-ground voltages (phases A and B) are 0.5 times the line voltage and (ii) another phase-to-ground voltage is 0.866 times the line voltage. Fig. 7c illustrates the coupling-free circuit grounding method of a zig–zag transformer, which can supply three-phase and single-phase power to loads, i.e. 3ϕ 4W service. The three phase-to-ground voltages are 0.577 times the line voltage. Fig. 7Open in figure viewerPowerPoint Voltage phasor diagram and coupling-free equivalent circuit of three traditional grounding methods (a) Corner method of grounding, (b) Centre tapped-off method of grounding, (c) Grounding method of a zig–zag transformer 3.3 Methods of grounding a symmetrical and asymmetrical NGS We all know that the phase-to-ground voltages of the conventional grounding methods are inconsistent. The delta-connected neutral-grounding method can adopt a one-grounded winding to obtain stable three phase-to-ground voltages. This grounding method has been proposed in [12, 13], in which one end of the grounded winding is connected to ground and the other end is connected to a ⅓ tapped-off point of an adjacent phase winding. Unfortunately, it is an asymmetrical NGS, resulting in the grounded winding possibly overheating to failure levels when operating under unbalanced loads. Fig. 8a illustrates the coupling-free circuits of an asymmetrical NGS with one-grounded winding. Therefore, a symmetrical NGS with three-grounded windings is presented to improve the problem of system imbalance and power loss for a building or distribution network. Fig. 8b illustrates the coupling-free circuits of a symmetrical NGS with three-grounded windings. Fig. 8Open in figure viewerPowerPoint Voltage phasor diagram and coupling-free equivalent circuit of an asymmetrical and symmetrical NGS (a) One-grounded winding installed at phase C, (b) One-grounded winding installed for each phase 4 Results and discussion We implemented the proposed distribution transformer of a symmetrical NGS using the MATLAB R2012a software package and tested it on a Windows XP-based personal computer with an AMD Athlon 64 3200 + processor. To verify the effectiveness and accuracy of the proposed distribution transformer with a symmetrical NGS, the IEEE 4-node test feeder is used as a benchmark system because the IEEE 4-node test feeder tests the capability of a programme to represent transformers in various configurations, full three-phase lines, and unbalanced loads. We then compared the operational characteristics of unbalanced loads with various grounding methods. That is, we carried out a potential assessment for the voltage imbalance of various grounding methods under the conditions of unbalanced operation. 4.1 Benchmark system Fig. 9 illustrates a one-line diagram of the IEEE 4-node test feeder system [25]. We observed that the major components of the system include (A) a substation (an ideal balanced three-phase power source), (B) transformers in various configurations (GY–gy, D–gy, Y–d, GY–d, D–d, and U–V), (C) full three-phase feeders, and (D) unbalanced loads. The parameters of the target system are described as below: Distribution transformer : The three-phase transformer bank of the target system has a rated capacity of 6000 kVA, rated voltage 12.47/4.16 kV, and leakage impedance of 1 + j6%. Loads : The unbalanced load is modelled as a constant PQ device as per past developments in our references [26]. The electricity demand on each phase load is between 1500 and 2500 kVA, and the power factor is between 0.85 and 0.95 lagging. Three-phase feeders : Detailed information of the conductors can be seen in our references [25]. The benchmark system of the IEEE 4-node test feeder was implemented into a commercial package software, MATLAB/Simulink. All distribution transformer configurations are based on single-phase two-winding transformers (see: Sections 3.1.1–3.1.3). These can be used to demonstrate the validity and accuracy of the distribution transformers of various configurations. The results of the benchmark system of the IEEE 4-node test feeder system are shown in Tables 2 and 3. Table 2 summarises the voltages between the simulation results and the IEEE results. Next, Table 3 compares the voltage differences and errors between the simulation results and IEEE results. The results observe that the maximum differences and errors of the bus voltages were <−1 V and −0.055%. The obtained results by the proposed approach (i.e. using single-phase transformers to build transformers of various configurations) are almost the same as the IEEE benchmark results. On the basis of this approach, we then build models for various grounding methods according to their coupling-free equivalent circuits such as a zig–zag grounding transformer and asymmetrical and symmetrical NGSs. Fig. 9Open in figure viewerPowerPoint One-line diagram of the IEEE 4-node test feeder system Table 2. Final simulation results of the voltages compared with IEEE results Vab Vbc Vca Simulation IEEE results Simulation IEEE results Simulation IEEE results Type Node Magnitude Angle Magnitude Angle Magnitude Angle Magnitude Angle Magnitude Angle Magnitude Angle GY–gy A2 7164 −0.1 7164 −0.1 7110 −120.2 7110 −120.2 7082 119.3 7082 119.3 A3 2305 −2.3 2305 −2.3 2255 −123.6 2255 −123.6 2203 114.8 2203 114.8 A4 2175 −4.1 2175 −4.1 1930 −126.8 1930 −126.8 1832 102.8 1833 102.8 D–gy A2 12,350 29.6 12,350 29.6 12,314 −90.4 12,314 −90.4 12,333 149.8 12,333 149.8 A3 2290 −32.4 2290 −32.4 2262 −153.8 2261 −153.8 2214 85.2 2214 85.2 A4 2157 −34.2 2157 −34.2 1936 −157.0 1936 −157.0 1849 73.4 1849 73.4 Y–d A2 7113 −0.2 7113 −0.2 7143 −120.4 7144 −120.4 7110 119.5 7111 119.5 A3 3896 −2.8 3896 −2.8 3972 −123.8 3972 −123.8 3875 115.7 3875 115.7 A4 3425 −5.8 3425 −5.8 3646 −130.3 3646 −130.3 3297 108.6 3298 108.6 GY–d A2 7111 −0.2 7112 −0.2 7144 −120.4 7144 −120.4 7111 119.5 7112 119.5 A3 3896 −2.8 3896 −2.8 3972 −123.8 3972 −123.8 3875 115.7 3874 115.7 A4 3425 −5.8 3425 −5.8 3646 −130.3 3646 −130.3 3297 108.6 3298 108.6 D–d A2 12,341 29.8 12,341 29.8 12,370 −90.5 12,370 −90.5 12,302 149.5 12,302 149.5 A3 3902 27.2 3902 27.2 3972 −93.9 3972 −93.9 3871 145.7 3871 145.7 A4 3431 24.3 3431 24.3 3647 −100.4 3647 −100.4 3293 138.6 3294 138.6 U–V A2 6952 0.7 6952 0.7 7171 −122.0 7172 −122.0 7313 120.5 7313 120.5 A3 3632 0.1 3632 0.1 4121 −127.6 4121 −127.6 3450 108.9 3450 108.9 A4 3307 −1.5 3307 −1.5 3907 −131.9 3907 −131.9 3073 103.1 3073 103.1 Table 3. Detailed comparison of the results between the simulations and the experiments Vab Vbc Vca Differences Errors Differences Errors Differences Errors Type Node V Deg Magnitude, % Angle, % V Deg Magnitude, % Angle, % V Deg Magnitude, % Angle, % GY–gy A2 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 A3 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 A4 0 0.0 0.000 0.000 0 0.0 0.000 0.000 −1 0.0 −0.055 0.000 D–gy A2 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 A3 0 0.0 0.000 0.000 1 0.0 0.044 0.000 0 0.0 0.000 0.000 A4 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 Y–d A2 0 0.0 0.000 0.000 −1 0.0 −0.014 0.000 −1 0.0 −0.014 0.000 A3 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 A4 0 0.0 0.000 0.000 0 0.0 0.000 0.000 −1 0.0 −0.030 0.000 GY–d A2 −1 0.0 −0.014 0.000 0 0.0 0.000 0.000 −1 0.0 −0.014 0.000 A3 0 0.0 0.000 0.000 0 0.0 0.000 0.000 1 0.0 0.026 0.000 A4 0 0.0 0.000 0.000 0 0.0 0.000 0.000 −1 0.0 −0.030 0.000 D–d A2 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 A3 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 A4 0 0.0 0.000 0.000 0 0.0 0.000 0.000 −1 0.0 −0.030 0.000 U–V A2 0 0.0 0.000 0.000 −1 0.0 −0.014 0.000 0 0.0 0.000 0.000 A3 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 A4 0 0.0 0.000 0.000 0 0.0 0.000 0.000 0 0.0 0.000 0.000 4.2 Comparison results of various grounding methods To compare the operational characteristics of a three-phase transformer delta service with a variety of grounding methods, we proposed a Monte Carlo simulation-based three-phase power-flow method for this benchmark system developed based on a deterministic three-phase power-flow analysis. The actual operating conditions of the benchmark system depend on the changes in load demands. Fig. 10 shows the results of bus voltages, line currents, and zero-sequence VUF d0. The simulation results are described as follows: The transformer of the NGS and the zig–zag grounding transformer provide a solid ground for controlling the overvoltage (phase-to-ground) to safe levels to overcome problems associated with ungrounded and other conventional grounding systems such as offsets in the neutral-point voltage [27, 28]. From the results of Figs. 10a and b, the proposed transformer of a symmetrical NGS with three-grounded windings shows that the phase-to-ground voltages and line currents vary less than other grounding methods. In other words, the power loss of the proposed transformer of a symmetrical NGS is less than the other grounding methods, to reduce the power consumption of the overall system. The results of phase-to-ground voltages show that the traditional grounding methods (corner-grounding and mid-tap grounding) are inconsistent (see Fig. 10a) which results in zero-sequence VUFs d0. These factors are higher than other grounding methods such as zig–zag grounding and NGS with one- and three-grounded windings (see Fig. 10c). Further analysis of the improvement rate (see Fig. 10d) shows that the proposed transformer of a symmetrical NGS with three-grounded windings can provide an improvement. For example, its improvement rate is about 100% for the transformer of an asymmetrical NGS and is about 262% for a zig–zag grounded transformer. The simulation results above verify that the line currents, the power loss of the system, and d0 in conventional grounding methods can be reduced by the proposed transformer with a symmetrical NGS. That is, the dielectric strength (cost) of the distribution transformer windings can be reduced because the dielectric strength in conventional grounding methods is applied to higher phase-to-ground voltage systems. Fig. 10Open in figure viewerPowerPoint Comparison results with various grounding methods (a) Bus voltages, (b) Line currents, (c) Zero-sequence VUF d0, (d) Improvement rate of d0 5 Conclusion This paper developed mathematical models of coupling-free equivalent circuits for various methods of grounding a delta-connected structure such as corner-grounding, mid-tapped grounding, a zig–zag grounding transformer, and the asymmetrical and proposed symmetrical NGS. The coupling-free equivalent circuits were realised in the benchmark system using the MATLAB/Simulink platform. The simulation results of the voltages compared with the IEEE results are shown in Table 2. The maximum bus voltage differences and errors were <−1 V and −0.055%, as shown in Table 3. A Monte Carlo simulation-based three-phase power-flow method was proposed to compare the operational performance of various methods for delta-connected grounding. From the results of Fig. 10a, the voltage of the proposed NGS is consistent and superior to other methods. From the results of Fig. 10b, the line currents of the proposed NGS are the lowest; that is, the power consumption of the overall system was improved. The improvement rate of zero-sequence VUFs is ∼100% compared with the transformer of an asymmetrical NGS and ∼262% compared with a zig–zag grounding transformer. Therefore, the feasibility of the proposed symmetrical NGS has been verified for operational performance. 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