Electronic Power Transformer for Applications in Power Systems

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1 Electronic Power Transformer for Applications in Power Systems Pedro Miguel Costa Fernandes Department of Electrical and Computer Engineering Instituto Superior Técnico - Technical University of Lisbon, Portugal Pedro.c.fernandes@tecnico.ulisboa.pt Abstract The evolution of technology in the field of power electronics has been very evident in recent years, including the development of new semiconductors that are prepared to operate in systems with high working voltage, as in the case of ultra high voltage device. On the other hand, there has also been a large development in high-frequency transformers, in particular ferromagnetic alloys that promote a high saturation flux density, that means a high power density as well as lower losses ensuring good efficiency of the transformer. This paper proposes a high frequency power transformer for applications in power systems, that is, beyond the reduction / increase of voltage levels and galvanic isolation garnished by the classic transformer, the proposed transformer allows many other features such as: large capacity control, lower volume of the transformer core, good performance against voltage fluctuations. This transformer is designated Solid State Transformer, and it is composed of a Modular Matrix Converter, a Three Phase Matrix Converter and High Frequency Transformer. The SST allows to obtain a system of adjustable output voltage under load, not only in amplitude but also in frequency. The Modular Matrix Converter was designed during the course of the dissertation. In addition to being able to operate in MV systems, it also enables the unsaturation of the transformer. Index Terms Solid State Transformer; High Frequency Transformer; Matrix Converter; Space Vector Modulation; Voltage Regulator; Current Regulator N I. INTRODUCTION owadays power transformers are essential devices in the power distribution system. The widespread use of this device has resulted in a cheap, efficient, reliable and mature technology and any increase in performance are marginal and come at great cost []. Despite their great utility, they present some disadvantages such as [2]:. Bulky size and heavy weight 2. Transformer oil can be harmful when exposed to the environment 3. Core saturation produces harmonics, which results in large inrush currents 4. Unwanted characteristics on the input side, such as voltage dips, are represented in output waveform 5. Sensitivity to the harmonics of the output current 6. Voltage regulation inefficient In 98, researcher James Brooks implemented the first prototype of the SST. Due to major technological limitations at the time he had little success. However, after a few years, the concept of SST developed, with different architectures and topologies, and in the last years, the architecture and topology of SST has been adapted to enable new applications, especially in energy systems. In recent years, interest in Solid State Transformers has grown so much that in 2 the SST technology was named by MIT "Massachusetts" Institute of Technology ", as one of the technologies greater relevance in future power distribution systems. In recent years, many researchers have been studying new applications of SST, resulting in different architectures and topologies, which are associated with different applications [3]. VAC 5/6Hz Modular Matrix Converter High Frequency Transformer High Frequency > khz Figure SST Concept Three-phase Matrix Converter 5/6Hz The Solid State Transformer (SST) provides an alternative to the Low Frequency Transformer (LFT). The proposed SST is presented in Figure is based on one three phase High Frequency Transformer supported by power electronic converters. The input is connected with a Modular Matrix Converter with an innovative feature that guarantees the nonsaturation of the HFT. Given the voltages applied to the SST, and the limitations of the used semiconductor, has been designed a modular matrix converter, which ensures that each semiconductor support a small fraction of the maximum system voltage. Thus, it is possible to ensure that the maximum voltage applied to the semiconductor never exceeds the maximum allowable values. VAC

2 Load The output is connected with a three phase Matrix Converter controlled by Space Vector Modulation (SVM). II. SOLID STATE TRANSFORMER (SST) A. Modular Matrix Converter The modular matrix converter consists of single-phase matrix converters in series, ensuring that the maximum voltage applied to the semiconductors is compatible with existing semiconductors in the market. Thus, it is possible to preserve the proper operation thereof (Figure 3) B. Single-Phase Matrix Converter The single-phase matrix converter consists of four bidirectional switches fully controlled, allowing the interconnection of two single-phase systems, one with characteristics of voltage source and another with characteristics of current source (Figure 4). Assuming that the bidirectional semiconductor switches have an ideal behaviour (zero voltage when they are ON, zero leakage current when they are OFF and nearly zero switching time), and each of the switches can be represented mathematically by a variable S kj which can take the value of "" if the switch is closed (ON) and the value of "" if the switch is open (OFF). One can represent the state of the converter in a 2x2 matrix (). Va Ia S S2 Vb Ib S2 IA S22 IB Figure 3 - Simplified scheme of the association in series of singlephase matrix converters VA Figure 4 Single-Phase Matrix Converter VB Input Filter Three-phase Matrix Converter Output Filter Modular Matrix Converter High Frequency Transfomer Figure 2 - Simplified schematic of the SST model

3 We must take into account compliance with the topological constraints, implying that in each time step, each phase output is only connected to one and only one input phase. S = [ S S 2 S 2 S 22 ] () In Table I are described four possible states, with the respective correlations between the electrical variable combinations. Table I Possible switch combination for a Single-Phase Converter The S matrix represents the states of the switches and enables a mathematical correlation between the line-to-neutral output voltages V A, V B, V C and the line-to-neutral input voltages V a, V b, V c. Still, the transpose of matrix S correlates the input currents i a, i b, i c with the output currents (3). V A [ V B ] = S [ VC V a V b ] [ ] = S T [ ] (3) V C Ic IC Finally, the three-phase Matrix Converter has now 27 possible combinations to represent the input currents and output voltages. I a I b I A I B State Si Si 2 Si 2 Si 22 V A V B i A i B V a V b I A I B 2 V b V a I B I A 3 V a V a 4 V b V b C. Three Phase Matrix Converter The three-phase Matrix Converter, which is represented in Figure 5. It consists of nine controlled bidirectional switches making a 3x3 matrix (2) that allows a connection between two three-phase systems; the input with voltage source characteristics and the output system with characteristics of current source. These converters allow direct AC-AC conversion, without an intermediate but with a high efficiency guaranty. By assuming ideal semiconductors, each switch can be mathematical represented by S kj =, k {,2,3}, a binary variable with two possible states: S kj = if the switch is ON, and S kj = if it OFF. Due to electrical limitations of the MC topology, each line of the matrix can only have one switch ON. (2) S S 2 S 3 3 S = [ S 2 S 22 S 23 ] S kj =, k {,2,3} (2) S 3 S 32 S 33 j= D. SVM Space Vector Modulation SVM approach, including Indirect SVM and Direct SVM proposed in [4] and [5] were often used in MC for it s appropriate in operation. Conventional SVM approach is used to synchronize the input voltage by zero cross detecting of the input phase voltage, which can be seen in Figure 6 a), and assuming a balanced input voltage in rated value. Figure 6 b) c) shows MC s output voltage space vectors and output voltage synthesis, where, I, II, III, IV, V and VI stand for six vector sectors, and V -V 6 stand for active voltage vector, V and V 7 stand for zero. +Vmax -Vmax V3(C, D, C) Zona Zona 2 Zona 3 Zona 4 Zona 5 Zona 6 Zona III V2(D, D, C) II rad a) θv V(D, C, C) dβ Vβ Vβ Va Ia S S2 S3 IV V7(C, C, C), V8(D, D, D) θv V I V7 V8 dv π/3 θv dα Vα Vrefαβ Vb Ib V4(C, D, D) V VI V6(D, C, D) Vα S2 S22 S32 Vc Ic V5(C, C, D) b) c) IA IB IC VA VB VC Figure 5 Three-Phase Matrix Converter Figure 6 - Line-to-line output voltage sectors; b) Space location of vectors V to V7, defining 6 sectors in the αβ plane; c) Representation of the synthesis process of V orefαβ using the space vectors adjacent to the sector where the reference vector is located.

4 With access to the adjacent space vectors V α, V β and V shown in Figure 6 c) obtains the voltage vector V orefαβ, wherein the duty cycle associated with each of these vectors are d α, d β and d o. Theoretically, assuming that the switching frequency is much higher than the input frequency f >> f s, it is possible for each commutation period to define the reference vector V orefαβ as (4). V orefαβ V α d α + V β d β + V d o (4) The reference vector V orefαβ (5) of the line-to-line output voltage describes a circular trajectory in the plane αβ and is synthesized using the space vectors represented in Figure 6 c). V orefαβ (t) = 3 V oc e jω ot = 3 2 V oc max e jω ot (5) After setting the duty cycles (7), it is necessary to determine the order in which the vectors should be applied to the matrix converter ensuring control of output voltage and input current. The selection of vectors to be applied shall be governed by some priorities, such as minimizing harmonic distortion of the input current or minimize the number of commutations of the switches [7]. The choice of vectors to use depends on the location of the sector composed of the reference voltage output and the sector location of the input current. Based on these conditions, it becomes possible to identify the vectors to be used in the modulation process (Table II). Table II - Matrix Converter s vectors used in the modulation of line-to-line output voltages and input currents V Ii dϒdα V Ii The maximum of the output voltage reference (5) can achieve the same voltage is imposed V DC will output rectifier. Therefore, we can conclude that the output voltage of the rectifier/inverter model is limited by the rectifier. Additionally, similar procedure is implemented for the MC rectifier stage, which leads to nine active vectors. It is assumed that the adjacent vectors I -I 6 are Iδ, Iϒ and zero vectors I 7, I 8 and I 9 with the respective duty cycles dδ (for Iδ), dϒ (for Iϒ) and d (for one of the zero vector). Considering that the switching frequency is much higher than the input frequency fs>>fi, it is possible for each commutation period to define the reference vector I irefαβ as (6) I irefαβ I γ d γ + I δ d δ + I d (6) From [4] and [5] the duty cycles dδ, dϒ and d can be calculated by using a trigonometric analysis. The rectifier stage requires two non-zero vectors to the modulation of the input current of the inverter stage which takes two non-zero vectors to the modulation of the output voltage, thus resulting modulation will require four non-zero vectors and null vector. For the modulation of the input current and the output voltage, the switching time (7) for each vector is obtained by multiplying the cycle factors obtained for the rectifier and the inverter [6]. d γ d α = m c m v sin ( π 3 θ i) sin ( π 3 θ v) The duty cycle used in the modulation process of the matrix converter are calculated based on the output voltages and input current reference (7). In order to know the action time of the vectors, was used a technique that compares a triangular carrier according to signals from the duty cycle. (Figure 7). d γ d β = m c m v sin ( π 3 θ i) sin ( θ v ) d δ d α = m c m v sin(θ i ) sin ( π 3 θ v) (7) d δ d β = m c m v sin( θ i ) sin( θ v ) { d = d γ d α d γ d β d δ d α d δ d β

5 Duty Cycle Signals Duty Cycle Signals d d Tempo Va Vb Vc Ia Ib Ic S S2 S2 S22 S3 S32 IA IB IC VA VB VC III. CONTROL OF THE OUTPUT CURRENT The current regulator block diagram is show in Figure 8, where I odqref is the reference current and I odq the load current. Both are multiplied by α i, the current sensor gain, and the difference between the two currents, i.e., the current error is applied to the controller Ci(s). This controller generates the modulating voltage used by the SVM. d d Time Figure 7 - Modulation process used to select the space vectors and the time interval when they are applied Idq ref α i + - Hdq Vdq Idq Load The selection of vectors to be applied in the control of matrix converter is not only based on the analysis of Figure 7 but also in Table II. Figure 7 show the driving time of each vector. This information together with the location of the input current and the output voltage follows for Table II, from which the result vectors to be applied to three-phase matrix converter switches. The Figure 8 is a simplified way of obtaining the final vector to apply to the matrix converter. Input current Location T Vector -4 Output Voltage Location Figure 8 - Selection scheme for the SVM vectors SST proposed in this paper, the modulation method must be modified to ensure non-saturation of the high frequency transformer. E. Modified SVM Modified SVM is a switching a strategy based on SVM that to ensure non-saturation of transformer. Figure 9 represents the modulation process already used with appropriate modifications to prevent saturation of the transformer. Figure 8 Output current regulator block diagram C(s) is a Proportional-Integral (PI) Controller, which ensures a dynamic second order closed chain. This compensator ensures a null static error and an acceptable rise time. For the sizing of the current regulator, the three-phase matrix converter can be represented as transfer function of the first order (8) with a given delay time T d. G(s) = α i + s T d (8) To calculate the T z and T p parameters, it is considered that the zero of C (s) cancels the lowest frequency pole, introduced by the output filter. From (9), one obtains T z where R out is the sum of the internal resistance of the coil with the load resistance. T z = L out R out (9) The value of Tp is calculated by (), where αi is the current gain and Td is the average delay of the system. T p = 2 α i T d R out () Modular Matrix Converter High Frequency Transformer Three-Phase Matrix Converter Gate Gate Signal + - SVM Modified SVM Figure 9 Modified SVM

6 IV. CONTROL OF THE OUTPUT VOLTAGE In sizing the voltage controller, care has based on this singleline diagram in Figure 9. ISystem ILoad In this dissertation was used High frequency transformer with a power of 63KVA with a working frequency of 2Hz In Figure and Figure 2 are shown the waveforms of the voltage in the load as well as the respective current. The waves have a sinusoidal forms with a fundamental frequency of 5Hz. ic 4 System Cf VLoad 3 2 Figure 9- Load voltage regulator The voltage regulator has to ensure that the load voltage, which is the same as the capacitor voltage (). V Load = i c sc f () In the design of the controller, it is considered that the load current (Iload) is a disturbance of the system [8], [9]. As the current output of the matrix converters is controlled, it is also possible to consider that the matrix converters, filters and transformer leakage inductances can be represented by the current source Isystem. In Figure is presented the voltage regulator block diagram, G i αi wherein the block represents the matrix converter st d + controlled by current, []. Corrente [A] Figure Line to-neutral load voltage Figure 2 Load current VLoad ref αv + - ILoad Iref matrix Iline - Ic VLoad + αv Figure Block diagram of the voltage regulator In Figure 3 was compared the reference voltage with the control voltage, and conclude that the reference tracking is achieved with a greatly reduce error Finally, the proportional gain K p and the integral gain K i are obtain by (2): - K p = 2.5C fα i α v T d (.75) 2 C f α i K i = { α v T 2 d (.75) 3 (2) Figure 3- Line-to neutral load reference voltage (Red), and lineto-neutral load voltage (Blue)) 3 V. RESULTS The SST developed in this dissertation was implemented in MATLAB / Simulink software in order to evaluate and test the performance and robustness in several operating scenarios. A. Scenario Ideal conditions In the first scenario is take analysis of the system before normal operation without any disruption in the network Figure 4 Error between in reference voltage and control voltage.

7 Figure 5 represents the output voltage of the modular matrix converter, applied to a primary winding. Figure 6 represents the input voltage of the three-phase converter T [s] Figure 5 Voltage applied to a primary winding of transformer 6 x Figure 8 Medium voltage. Figure 9 represents the load voltage, and it can be concluded that the voltage suffered no change Figure 9 Load voltage T [s] Figure 6 - Voltage applied to a secondary winding of transformer Figure 7 represents the input currents of SST. The currents contais the high frequency harmonics arising from the highfrequency semiconductor switching converters In Figure 2 was compared the reference voltage with the control voltage, and conclude that the reference tracking is achieved with a greatly reduce error Corrente [A] Figure 2 - Line-to neutral load reference voltage (Red), and lineto-neutral load voltage (Blue)) Figure 7 Input currents of SST (MV) B. Scenario 2 Voltage sag In this section it was the behavior of the SST when confronted with a voltage sag on the medium voltage. In Figure 8 can check the wave disturbance in the input voltage. The perturbance caused a lowering in input voltage during two periods of the network. C. Scenario 2 Voltage swell In this section, the behavior of the SST was evaluated for a voltage swell on the medium voltage. In Figure 2 it can be seen the wave disturbance in the input voltage. The disturbance caused a substantial increase in the input voltage during two periods of the grid.

8 x 4 x Figure 2 Medium voltage Figure 22 the sinusoidal load voltage. Faced with an voltage swell at the entrance of the SST, the waveforms of voltages underwent no significant changes, which shows the good response of the SST Figure 24 Medium voltage The voltage at the load (Figure 25) shows a nearly sinusoidal wave with a small ripple Figure 22 Load voltage In Figure 23 was compared the reference voltage with the control voltage, and conclude that the reference tracking is achieved with a greatly reduce error Figure 23 - Line-to neutral load reference voltage (Red), and lineto-neutral load voltage (Blue)) D. Scenario 3 Harmonic Distortion on the medium voltage In this operating scenario, consider the existence of harmonics of the medium voltage. In the test scenario is considered the 5th harmonic, ensuring that its amplitude does not exceed the threshold of 6% set by the standard (EN 56). In Figure 24 is represented the wave of the input voltage in SST. There is the effect of the 5th harmonic, responsible for wave distortion of the input voltage Figure 25 Load voltage VI. CONCLUSIONS AND FUTURE WORK This work aimed to develop a electronic power transformer for distribution systems, capable of producing voltages of variable magnitude and frequency at the output. During the development of this project, emerged several concerns, such as non-saturation of the transformer, that with the change in the characteristics of the modulation SVM was achieved. Another major concern is the limited voltage imposed by semiconductor constituting the matrix converters, not facilitating the integration of the matrix converter in the medium-voltage side. Known the problem, we developed a modular matrix converter, which regulates the voltage to levels that do not cast doubt on the operability of used converters. The current controller, based in PI controller, was tested with a good performance, with a static error close to zero, and allowing a quick response while ensuring system stability for various load scenarios. The power factor might not be unitary since it depends on the input filter and the load conditions. Finally, it is important to note that this system has many other utilities that may be developed in the near future, such as integration into a smart grid or in substations fitted to renewable energy systems. REFERENCES [] van der Merwe, J., W.; du T. Mouton, H.; The solid-state transformer concept: A new era in power distribution, in AFRICON 29, 29; [2] Hassan, R.; Radman, G.; "Survey on Smart Grid" IEEE 2 SoutheastCon, Proceedings of the power electronic application

9 conference, vol., no., pp.2 23, March 2; [3] She, X.; Review of Solid-State Transformer Technologies and Their Application in Power Distribution Systems, Future Renewable Electr. Energy Delivery & Manage. Syst. Center, North Carolina State Univ., 23; [4] Huber, L., Borojevic, D., Burany, N., Analysis, Design and Implementation of the Space-Vector Modulator for Forced- Commutated Cycloconverters; IEE Proceedings-B Electric Power Applications, vol 39, No 2, March 992; [5] Nielsen, P.; Blaabjerg, F.; Pedersen, J.; Space-Vector Modulated Matrix Converter with Minimized number of Switchings and a Feedforward Compensation of Input Voltage Unbalance ; Proc. PEDES 96 Conference, Vol. 2, pp , New Delhi, India. [6] Huber, L.; Borojevic, D.; Space Vector Modulated Three-Phase to Three-Phase Matrix Converter with Input Power Factor Correction ; IEEE Transactions on Industry Applications, Vol. 3, No 6, pp , November/December 995. [7] Nielsen, P.; Blaabjerg, F.; Pedersen, J.; Space-Vector Modulated Matrix Converter with Minimized number of Switchings and a Feedforward Compensation of Input Voltage Unbalance ; Proc. PEDES 96 Conference, Vol. 2, pp , New Delhi, India. [8] Pinto, S., Silva, J. F., Silva, F., Frade, P., Design of a Virtual Lab to Evaluate and Mitigate Power Quality Problems Introduced by Microgeneration, in Electrical Generation and Distribution Systems and Power Quality Disturbances, Intech, 2. [9] Alcaria, P, Pinto, S. F., Silva, J. F., Active Voltage Regulators for Low Voltage Distribution Grids: the Matrix Converter Solution, Proc. 4th International Conference on Power Engineering, Energy and Electrical Drives, PowerEng 23, pp , Istanbul, Turkey, May 23. [] Pinto, S.; Silva, J.; Gambôa, P.; Current Control of a Venturini Based Matrix Converter, IEEE International Symposium on Industrial Electronics ISIE 26, Vol. 4, pp , Montréal, Canada, July 26.