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Comparative analysis of three-phase to five-phase transformer connections.

1. Introduction

Multiphase systems (more than three phases) attracted major attention of the researchers since their introduction in the late 1960s due to their essential advantages over their three-phase counterparts (Abdel-Khalik, Masoud, and Williams 2012; Abdel-Khalik et al. 2014; Glukhov and Muravleva 2003; Levi 2008; Levi et al. 2007; Parsa 2005; Wheeler 2012). Multiphase motor drives have been extensively investigated in the last decade for possible employment in niche application areas due to the numerous advantages that they offer when compared to three-phase motor drives. The advantages include lower torque pulsation and pulsation at a higher frequency that can be easily filtered out, lower per phase current without increasing voltage that translates into lower supplying converter switch rating, higher fault redundancy and a greater degree of freedom in control. Multiphase power generation is a new research area and higher torque density and higher fault tolerance are attracting the attention. Multiphase generation is especially investigated in conjunction with wind energy generation (Kumar and Munda 2014; Singh 2008). Multiphase transmission systems have recently been explored and several researchers have reported six-phase and 12-phase systems with the aim of maximising the power transfer capability without paying for higher right of way (de Barros Jul 1995; Dorazio 1990; Kumar and Singh 2011; Nounou et al. 2014; Pandya and Kelkar 2006; Stewart, Dale, and Klein 1993; Tiwari and Bin Saroor 1995). Another area where the multiphase system is extensively used is the multi-pulse rectifier system where a reduction in current ripple is a major concern (Choi, Lee, and Enjeti 1997; Garg, Singh, and Bhuvaneswari 2006, 2008; Singh and Gairola 2008). It is seen that multiphase systems have proved to be advantageous in the field of electric power generation, transmission and utilisation.

Multiphase supply is used to drive multiphase motors employed in applications that demand high reliability such as electric/hybrid vehicles, electric propulsion systems in ships and aerospace applications. Traditionally, AC-DC-AC converters were used to supply multiphase motors to obtain variable voltage and variable frequency output. However, the voltage/current obtained by this method is not purely sinusoidal and contains ripples due to switching actions of the power converter switches. High-performance motor drives such as field-oriented control, direct torque control and other non-linear control (back stepping, multiscale model control and feedback linearisation control) need precise motor parameters (Abu-Rub, Iqbal, and Guzinski 2012; Hamdi et al. 2014; Jalal Rastegar Fatemi et al. 2014; Mehazzem et al. 2009). A block diagram of a five-phase induction motor supplied by a transformer for testing is shown in Figure 1. To obtain motor parameters, several tests are conducted on the motor such as no-load test and blocked rotor test. Such tests require pure sinusoidal supply in order to obtain correct values of motor parameters. Static transformers are thus needed in order to generate a pure sinusoidal, balanced five-phase supply while the input supply is a balanced three-phase. Several solutions are presented in the literature to obtain five-phase output from three-phase input using a transformer (Abdel-Khalik 2014; Iqbal et al. 2010).

The fixed frequency, fixed voltage three-phase supply available from the grid can be transformed into fixed frequency, fixed voltage five-phase output. An autotransformer may be used to obtain a variable output if needed. Depending upon the application, the transformer may be connected in several configurations such as:

(1) Input star, output star

(2) Input delta, output delta

(3) Input star, output delta

(4) Input delta, output star

Either one of the windings may be connected in zigzag, also known as interconnected star connection which combines the advantages of both, delta and star connections. In such a winding, each output is the vector sum of two phases offset by 120 degrees, thereby allowing a neutral connection to be created in an ungrounded three-phase system, providing a return path through which fault current may flow. Another major advantage of the zigzag connection is its ability to suppress triple harmonic currents and hence decrease the total harmonic distortion within a power distribution system.

The primary windings are to be connected in the typical fashion (star or delta) since the input is three-phase. However, the secondary windings need to be connected in specific ways to ensure that a balanced, five-phase output is produced. Some examples of such connection schemes have been analysed in this paper. Comparison of different transformer connections is also presented on the basis of their connection schemes and other design parameters such as the requirement of iron and copper materials and overall cost of the system.

2. Three-phase to five-phase connections

The notion of multiphase passive transformation system dates back to the early 1950s of twentieth century. At that time, the general theory of phase transformation to convert n to m phases on a k-limbed transformer was introduced (Parton 1952). The general theory of instantaneous and average power under unbalanced and distorted current condition is further elaborated in (Malengret and Gaunt 2011, 2012). This idea has been used to develop transformers that will produce five-phase (Abdel-Khalik 2014; Iqbal et al. 2010) or seven-phase (Moinoddin, Iqbal, and Abu-Rub 2012) outputs when fed from a three-phase supply.

To obtain a multiphase output from transformer connections, the general idea of the solutions mentioned below is to have three separate cores, each consisting of one primary coil and more than one secondary coil. The secondary coils have the different number of turns and are connected in specific ways so as to produce the desired phase shift of 72 degrees between two adjacent phases.

2.1. Solution 1

The connection scheme presented in (Parton 1952) and reviewed in (Abdel-Khalik 2014) uses 15 secondary coils to achieve the desired five-phase output. It consists of three magnetic cores, each carrying one primary coil and five secondary coils as shown in Figure 2. Due to the higher number of coils on the secondary side, the size, volume and weight of the transformer will be significantly higher than that of the other two solutions discussed below. Moreover, a greater number of total turns will lead to an increase in the resistance of windings, thereby causing greater copper losses. This solution also exhibits a high magnetising reactance, which would lead to greater iron losses. The increase in copper and iron losses will have an adverse effect on the efficiency of the transformer.

2.2. Solution 2

A similar connection scheme proposed in (Iqbal et al. 2010) is based on the assumption that the three-phase input supply is perfectly balanced. This assumption makes it possible to obtain a five-phase output using only eight secondary coils, thus reducing the total number of turns and consequently the size of the transformer as compared to the other solutions discussed in this paper. However, a major drawback of this scheme is that delta connection cannot be made at the secondary side. In fact, the secondary windings can only be connected in star, thus limiting the use of the transformer. Moreover, the three-phase currents in this connection scheme show a significant zero sequence components. This requires the primary side to be delta connected or the connection of a star point in the primary winding to allow for neutral current flow. Furthermore, an unbalance of the input three-phase supply will cause an unbalance in the desired five-phase output voltages. Figure 3 shows the circuit connection diagram of this solution.

2.3. Solution 3

Similar to the alternative solutions discussed above, this paper proposes a new connection scheme to transform a three-phase input supply into a balanced five-phase output. The proposed transformer consists of three separate cores, each of which uses one primary and three secondary coils. This will lead to a total of nine secondary coils, as opposed to 15 and eight coils in the connections analysed above. This will allow the secondary side to be connected in both, star and delta configurations. Moreover, all secondary coils will have the same cross-sectional area unlike the second solution, in which one secondary coil would have a larger cross-sectional area to handle the currents of two phases. In high rating transformers, this can cause an uneven distribution of losses, leading to different thermal loading and hence complex cooling systems. The number of turns needed in the secondary coils will be less than what would be required if the first solution was to be implemented. This will considerably reduce the cost and increase the efficiency of the designed transformer. Figure 4 shows the winding connections and the phasor diagram of the proposed solution. The obtained turn ratios and Standard Wire Gauge (SWG) to be used for this solution is shown in Table 1.

(1) Phasor Diagram:

Vector calculations and trigonometric properties were used to obtain the ratios of the secondary windings that would allow obtaining five outputs of the same magnitude but phase shifted by 72 degrees. An example of this analysis for output phase 'b' is shown in Figure 4(b), and the complete phasor diagram is shown in Figure 4(c). The governing calculations are given below:

[V.sub.b] = OC = OB + BC

[DELTA]OBA:

[mathematical expression not reproducible]

[DELTA]BAC:

[mathematical expression not reproducible]

[V.sub.b] = OC = ([c.sub.3][c.sub.4]) cos(12) + ([b.sub.5][b.sub.6]) cos(48)

[mathematical expression not reproducible]

AB is common

[mathematical expression not reproducible]

[therefore]A[B.sub.1] = A[B.sub.2] [right arrow] ([c.sub.3][c.sub.4]) sin(12) = ([b.sub.5][b.sub.6]) sin(48)

[mathematical expression not reproducible]

[therefore][V.sub.b] = ([c.sub.3][c.sub.4]) cos 12 + ([b.sub.5][b.sub.6]) cos 48 = 1

[right arrow] (4.165)[b.sub.5][b.sub.6] = 1 [right arrow] [b.sub.5][b.sub.6] = 0.24

[c.sub.3][c.sub.4] = (3.574)[b.sub.5][b.sub.6] = (3.574)(0.24) = 0.858

Since the input consists of three phases, [V.sub.x], [V.sub.y] and [V.sub.z] are phase shifted by 120[degrees] and the consecutive phases of the five-phase output will have a phase shift of 72[degrees]. The equations deduced can be represented in terms of sine, as shown in the matrix below:

[mathematical expression not reproducible]

3. Simulation results

The viability of the proposed solution was tested using Simulink software. The specifications of the transformer such as the number of windings turn ratios, etc. were set and the winding connections were done as per the phasor diagram. The input voltage is fixed at 110 V and the obtained output voltage was seen to be the same since the transformer has a 1:1 turn ratio. The output of the transformer is connected to an R-L load with R = 50 O and inductor L = 1 H. Only the results of solution 3 are shown below since the results are identical for all the three solutions. The Simulink block diagram and the obtained waveforms are shown in Figures 5-7. The output voltages show balanced five-phase voltages that prove the feasibility of the derived analytical expressions. A slight unbalance is noticed in the primary side current since all windings do not carry equal currents.

4. Comparison of transformer connections

A comparison of the three transformer connections in terms of various design parameters is given in Table 2. This table shows that solution 1 uses a considerably higher number of turns than the other two solutions. This increases the cost of the transformer and also leads to greater iron and copper losses. Also, it requires more space than the other two solutions. Considering cost and efficiency as the main deciding factors for optimisation, solution 1 is not feasible.

As for solution 2, it uses the lowest number of turns, which would translate into lower cost and better efficiency. However, as mentioned earlier, the secondary of solution 2 can only be connected in delta; thus, making the transformer unsuitable for pentagon loads. Moreover, since the secondary windings are not symmetrical, they will not carry the same current. Thus, the thickness of the wires to be used will be different which will lead to unequal losses, and therefore, unequal heating.

Solution 3 proves to be the optimum solution; it allows the use of lower number of turns, thus, fulfilling the cost and efficiency constraints of this design. It can also be used to connect pentagon loads. Moreover, symmetrical secondaries will ensure the same cross-sectional area of all secondary coils, thus leading to even distribution of losses and heating.

5. Experimental results

A prototype 0.5 kVA 110/110 V transformer was built in the laboratory. Three separate cores were wound with one primary on each leg and three secondaries. The transformer was built to transform three-phase input to five-phase output voltages with 1:1 ratio in order to prove the feasibility of the proposed phase conversion scheme. The resulting waveforms are presented in Figure 8 where five-phase balanced output voltage is shown under no-load and loaded conditions. A slight unbalance is due to the difference in theoretical and experimental turn ratios. Some of the turn ratios are in the fraction which is rounded to next integer and hence this introduces error leading to slight unbalancing among the phases. This confirms the feasibility of the proposed scheme to convert available three-phase to five-phase. As expected, the output voltage obtained under no-load condition is equal to the supply voltage since this is a unit ratio transformer. However, once the transformer is loaded, the resistance and reactance of the load cause voltage drop, thereby causing a slight decrease in the output voltage as shown.

6. Discussion

As shown in the previous section, the proposed connection scheme is validated using simulation and experimental approaches. The prototype was tested under both, resistive and inductive loads to ensure that a balanced five-phase output is obtained. Moreover, the performance of the transformer was assessed via standard tests on each unit of transformers such as open circuit (OC) and short circuit (SC) tests.

The OC test gives an indication of the saturation characteristics of the transformer core by plotting a B-H curve where B is the flux density and H is the magnetisation force. Since magnetisation force is directly proportional to magnetisation current and flux density is directly proportional to applied voltage, the B-H curve can be replaced by a V-I curve to estimate the saturation characteristics. Increasing the magnetisation force (i.e. increasing the current) causes the flux generated in the core to increase up to a certain point. Once the core enters saturation region, any further increase in the magnetisation force does not lead to an increase in flux, i.e. an increase in magnetisation current does not lead to an increase in voltage. This test was performed by applying the rated voltage at the primary side in steps.

At each step, the voltage applied and the corresponding current was recorded and then plotted against each other as shown in Figure 9. As expected, the V-I curves shown in Figure 9 is linear up to a certain point, after which it becomes non-linear and then start entering into the saturation region. The saturation characteristics of transformers 1 and 2 are identical, while that of transformer 3 is slightly different. This could be due to the fact that the E-I laminations used in the third transformer were different than those used in the other two.

The open and short circuit tests are used to estimate the core and copper losses of the transformer, respectively. To perform the open circuit test, the rated voltage was applied at the primary side with the secondary side kept open. This ensures that the transformer draws only the current needed to set up the flux. Therefore, copper losses can be neglected and the power loss in the transformer during this test is entirely due to the core loss. On the other hand, the short circuit test was performed by applying rated current at the primary side, with the secondary windings shorted. Since the applied voltage is very small, the core losses can now be neglected and the power loss is entirely due to the copper losses in the windings.

Readings from the OC and SC tests were used to determine the parameters of the shunt and the series branches of the equivalent circuit of the transformers. Data obtained, formulae and calculations are shown in the Appendix 1. As mentioned earlier, the E-I laminations used in the third transformer were not identical to those used in the other two transformers. This is why the open circuit test results of the third transformer and hence its core parameters are considerably different than those of the first two transformers.

7. Conclusion

This paper investigates several connection schemes to obtain a five-phase output from a three-phase supply using a static transformer. A literature review was initially done and two existing solutions from the literature were analysed. A new connection scheme to achieve this transformation was then proposed. A comparison of some basic parameters of the three solutions was then tabulated.

The general idea of all three connections studied in this paper is to use a three-limb magnetic core or three single magnetic cores, each having one primary coil and several secondary coils. These secondary coils have different number of turns and are connected in specific ways to produce the desired phase shift of 72 degrees between adjacent phases. The first connection scheme employs a total of 15 secondary coils divided equally among the three single magnetic cores. However, this scheme exhibits a considerable increase in the size of the transformer. This is primarily caused by the large number of secondary coils, which also causes an adverse effect on the efficiency. Assuming that the input three-phase supply is perfectly balanced, this connection can be simplified to lead to the second connection scheme investigated in this paper. This assumption allows the number of secondary coils to be reduced to only eight, thus causing a significant decrease in the size, cost and losses of the transformer. On the other hand, this scheme cannot be used for Pentagon or zigzag loads as the secondary side can only be connected in star. Another drawback of this solution is the absence of symmetry in the secondary side since one magnetic core has only two secondary coils, while the other two cores consist of three secondary coils each. In this case, the two secondary coils will need to have a larger cross-sectional area to handle the currents of two phases. In high rating transformers, this can cause an uneven distribution of losses, leading to different thermal loading and hence complex cooling systems.

Considering these demerits of the two existing solutions, a new solution was proposed. The proposed connection scheme consists of three separate magnetic cores, each consisting of three secondary coils. This leads to a total of nine secondary coils. Even though the proposed solution exhibits a slight increase in the size and losses of the transformer as compared to the second solution, it helps to overcome the problem of unequal thermal loading and allows the connection of pentagon loads on the secondary side. The governing phasor equations and phasor diagram of the proposed solution are shown. Simulation and experimental results confirm the feasibility of the proposed connection scheme. The performance of the fabricated transformer was assessed using several tests as explained above.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by the Qatar University [grant number QUST-CENG-SPR-14/15-8].

References

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Appendix 1

Design of the transformer (0.5 kVA, 110/110 V)

(1) Core design: Volts per turn ([E.sub.t]). Assuming k = 0.7,

[mathematical expression not reproducible]

Using the general emf equation with maximum flux density [B.sub.m] assumed to be 1.25 Wb/[m.sup.2] and frequency 50 Hz,

[mathematical expression not reproducible]

(2) Primary winding: Number of turns in each primary winding ([T.sub.p])

[mathematical expression not reproducible]

Since the transformer consists of three primary windings, 3*129 =387 total primary turns.

(3) Secondary windings: Number of turns of each secondary winding can be computed according to the turn ratios shown in Table 1 and summed up to obtain the total number of secondary turns.

(4) Conductor sizes: Assuming 90% efficiency of the transformer and current density J = 4A/m[m.sub.2]

[mathematical expression not reproducible]

[mathematical expression not reproducible]

[mathematical expression not reproducible]

[mathematical expression not reproducible]

Considering these parameters, SWG 14 was chosen for the primary and SWG 17 for the secondary.

(5) Primary resistance:[R.sub.p] = 387 * [[rho]*l]/A where length of mean turn, l = [pi] * d and area of conductor, A = [pi]/4 [d.sup.2]. According to the IEEE C57.134-2000 standards, performance of a transformer is typically calculated at 75 [degrees]C. At this temperature, the resistivity of Copper is 0.021 [mu][ohm]m. From SWG table, the chosen primary conductor (SWG 14) has a diameter of 2.032 mm. Therefore,

[mathematical expression not reproducible]

(6) Secondary resistance: Secondary resistance can be calculated in the same way. From SWG table, the chosen secondary conductor (SWG 17) has a diameter of 1.422 mm. Therefore,

[mathematical expression not reproducible]

Open circuit and short circuit test results

(1) The following data were obtained during the open circuit test of the transformers:

The power factor was obtained using:

P = VI cos [phi]

Magnetising reactance ([X.sub.M]) and core resistance ([R.sub.C]) were then calculated using:

[mathematical expression not reproducible]

[mathematical expression not reproducible]

(2) The following data were obtained during the short circuit test of the transformers:

The following formulae were then used to calculate the equivalent resistance ([R.sub.eq]) and equivalent reactance ([X.sub.eq]) of each transformer:

[mathematical expression not reproducible]

[mathematical expression not reproducible]

[mathematical expression not reproducible]

Enas Mohammad (a), Fatima Khan (a), Hadeel Bassel (a), Atif Iqbal (a) and Ahmed Riyaz (b)

(a) Department of Electrical Engineering, Qatar University, Doha, Qatar; (b) Department of Electrical Engineering, IIT (ISM), Dhanbad, India

CONTACT Atif Iqbal [??] atif.iqbal@qu.edu.qa

ARTICLE HISTORY

Received 18 January 2016

Accepted 28 January 2018

https://doi.org/10.1080/1448837X.2018.1437678
Table 1. Design of the proposed transformer.

Primary  SWG  Secondary           Turn Ratio (Np/Ns)  SWG

Phase X  14   [a.sub.1][a.sub.2]  1                   17
              [a.sub.3][a.sub.4]  0.47                17
              [a.sub.5][a.sub.6]  0.47                17
Phase Y  14   [b.sub.1][b.sub.2]  0.68                17
              [b.sub.3][b.sub.4]  0.858               17
              [b.sub.5][b.sub.6]  0.24                17
Phase Z  14   [c.sub.1][c.sub.2]  0.68                17
              [c.sub.3][c.sub.4]  0.858               17
              [c.sub.5][c.sub.6]  0.24                17

Table 2. Comparison of the three solutions.

Parameter                       Solution #1  Solution #2  Solution #3

Primary Turns                    387          387          387
Secondary Turns                  825          648          709
Total Turns                     1212         1035         1096
Primary Resistance ([ohm])         0.053        0.053        0.053
Secondary Resistance ([ohm])       0.049        0.038        0.042
Space needed by primary          418          418          418
(m[m.sub.2])
Space needed by                 1310         1030         1126
secondary (m[m.sub.2])
Total space needed              1728         1448         1544
(m[m.sub.2])

Transformer  [V.sub.OC]  [I.sub.OC]  [P.sub.OC]

1            110         0.325       11.6
2            110.2       0.328       12.1
3            110.1 V     0.699 A     19.2 W

Transformer  [V.sub.SC]  [I.sub.SC]  [P.sub.SC]

1            2.8 V       4.75 A      12.6 W
2            3.2 V       4.58 A      13.7 W
3            3.1 V       4.29 A      12.8 W

Parameter             Transformer 1  Transformer 2  Transformer 3

[X.sub.M] ([ohm])      357.96        355.9          162.6
[R.sub.C] ([ohm])     1039.6         999.7          628.5
[X.sub.eq] ([ohm])       0.158         0.248          0.199
[R.sub.eq] ([ohm])       0.558         0.653          0.695
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Author:Mohammad, Enas; Khan, Fatima; Bassel, Hadeel; Iqbal, Atif; Riyaz, Ahmed
Publication:Australian Journal of Electrical & Electronics Engineering
Date:Mar 1, 2017
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