Transformer and LCL Filter Design for DPFCs

Transcription

1 Transformer and LCL Filter Design for DPFCs Ivo M. Martins 1, J. Fernando A. Silva, Sónia Ferreira Pinto, and Isménio E. Martins 1 1 INESC-id, Deartment of Electrical Engineering, ISE, University of Algarve, Faro, Portugal INESC-id, Deartment of Electrical and Comuter Engineering, IST, TU Lisbon, Portugal Abstract. Flexible AC Transmission Systems (FACTS) can be used for ower flow control in AC transmission grids, allowing simultaneous control of the bus voltage and line active and reactive ower. However, due to high costs and reliability concerns, the alication of this technology has been limited in such alications. Recently, the concet of Distributed FACTS (DFACTS) and Distributed Power Flow Controller (DPFC) has been introduced as a low cost high reliability alternative for ower flow control. This aer resents the design of a couling transformer and a LCL filter for DPFC devices. To extract the electromagnetic energy from the transmission line a transformer with a single turn rimary is designed and otimized. A third-order LCL filter is used to guarantee high order harmonics filtering. Simulations results are resented and discussed. Keywords: FACTS, DFACTS, UPFC, DPFC. 1 Introduction Nowadays the electrical network is facing increasing congestion and loss of reliability. Under this contingency, it is essential to imrove the erformance of existing ower lines and otimize ower flow. Flexible AC Transmission systems (FACTS) can be used for ower flow control, both in static and dynamic conditions, making transmission systems more flexible [1]. Although FACTS devices offer several benefits, they have not seen widesread commercial accetance due to a number of reasons []. As an alternative aroach, the concet of distributed FACTS devices (DFACTS) has been roosed as a lower cost and higher reliability solution []. However, since the Distributed Static Series Comensator (DSSC) has no ower source, it can only adjust the line imedance and is not as owerful as UPFC. Using the concet of DFACTS devices, a new concet of distributed ower flow controller (DPFC) has been roosed [3] to achieve the same functionality as the UPFC. The DPFC is derived from the UPFC but eliminates the common DC link between the shunt and series converters. As UPFC, DPFC devices give the ossibility to control system arameters, such as line imedance and ower angle. After stating the Contribution to Collective Awareness System (section ) this aer details the oeration rincile and configuration of DPFC devices (section 3). In section 4 the design of a couling transformer that extracts electromagnetic energy from the transmission line is resented and in section 5 the design of a third-order LCL filter is shown. Simulation results are resented and discussed in section 6, using switching models of converters connected to the transformer secondary. L.M. Camarinha-Matos et al. (Eds.): DoCEIS 014, IFIP AICT 43, , 014. IFIP International Federation for Information Processing 014

2 45 I.M. Martins et al. Contribution to Collective Awareness Systems This work follows revious research where sliding-mode controllers, based on switched state-sace models, to achieve cross-decouled (indeendent) control of active and reactive ower flow were resented and two different DPFC series converter toologies were roosed [4], [5]. This aer rooses a ower transformer and a third-order LCL filter to be art of a DPFC device. DPFC devices can contribute to sustainability of electrical ower. This research work on energy management and smart grids might benefit from future collective awareness systems in order to imlement cooerative control, or erform informed decision making or the effective involvement of the electrical or sustainable energy systems. 3 Distributed Power Flow Controller DPFC devices can be used for ower flow control in existing transmission lines. Multile DPFC devices are distributed along the transmission line, cooerating together allowing cross-decouled control of active and reactive ower flow. Each DPFC device (Fig. 1) consists of a ower IGBT full-bridge single-hase converter, with a DC caacitor caable to rovide the required DC voltage, a series clam-on transformer to be used in the connection to the transmission line and a low ass filter to reduce the switching frequency harmonics injected into the grid by the converter. Fig. 1. DPFC configuration From the concetual viewoint each DPFC device can be reresented by two controllable voltage sources, connected in series with the transmission line. Each voltage source generates voltage at a different frequency, one at fundamental frequency, v o,1h, and the other at the third-harmonic frequency, v o,3h, so that the converter outut voltage is,,. The voltage source v o,1h injects a voltage vector with controllable magnitude and hase angle at fundamental frequency, allowing cross-decouled control of the active and reactive ower flow (P 1h and Q 1h ). The voltage source v o,3h is resonsible to maintain the DC bus voltage (U dc ) of the DPFC converter by using the third-harmonic frequency ower. Therefore, using the third-harmonic line current, a controllable voltage vector is injected in series with the line, absorbing or generating active ower from the third-harmonic current (P 3h ).

3 Transformer and LCL Filter Design for DPFCs Transformer Design 4.1 Oeration Princile A clam-on transformer (COT) is used [6] to use the electromagnetic energy of the transmission line. The COT comrises two halves of a cylindrical torus magnetic core surrounding the ower line, as shown in Fig. 1. The ower line carrying the current i acts as the single-turn rimary winding of the transformer ( 1), being the secondary winding with n s turns coiled around the magnetic core. The low ass filter and the AC/DC converter are connected to the transformer secondary terminals. 4. Transformer Design Assuming linear oeration and neglecting resistive and leakage voltage dros, the main transformer design equation, which relates the voltage V across the rimary winding having n turns, given the maximum magnetic flux density B max, frequency f s and core section effective area A fe, is [6]: B A (3 V + V ) (1) max fe,1 h,3h 6π fn s Selecting the transformer magnetic material and establishing the allowed maximum transformer B max value, knowing V,1h, V,3h and frequency f s, since 1, the core section effective area A fe can be then calculated. The transformer rimary winding voltage V,1h, V,3h is the voltage injected in series with the transmission line by the DPFC device and must be established according to secifications. For design uroses, consider a 0 kv, 300 MVA transmission line with a total of 4500 DPFC devices (1500 devices distributed along one hase) with 0.0 u line ower flow control caability. Each DPFC device must handle 13.3 kva. This means that the DPFC maximum outut voltage at fundamental frequency is, V, where Z line and V n are the transmission line imedance and hase-to-hase voltage at fundamental frequency. Since the maximum line current is, 787 A, the DPFC outut aarent ower is,,.45 kva. Considering the hase angle δ of the outut voltage V,1h as 10%, the maximum active ower generated by the DPFC is cos 383 W. This active ower generated at fundamental frequency must be equal (neglecting losses) to the active ower P 3h absorbed at the third-harmonic frequency. Considering the transformer losses, low-ass filter and DPFC converter, it is assumed W, where,,. To guarantee a low harmonic distortion of the transmission line current, the injected third-harmonic current I line,3h should not exceed 10% of the line nominal current (, 0.1, ). Thus, from the above conditions, the DPFC maximum outut voltage at third-harmonic frequency is, 7.3 V. To start the transformer design from equation (1), the B m value must be established according to the core magnetic material characteristics. Normally this value is chosen

4 454 I.M. Martins et al. from the material magnetization curve as the highest B m value before the saturation zone. Assuming a transformer core using M4 grade Grain-Orientation (GO) 3% Silicon Steel (Si-Fe) laminations, this value is estimated as 1.8 T. Thus, given the required outut voltages V,1h and V,3h, asthe rimary number of turns is 1 and the fundamental frequency 50 Hz, the core section effective area can be calculated as m. For the calculated A fe value, the size and shae of the core is designed to minimize the total weight of the transformer (magnetic core and coer windings). To start the design, the secondary winding number of turns n s is set according to the maximum current and voltage values in the secondary side of the transformer. Making 18 and considering the maximum current density 4 A/mm, the section of the secondary winding wires is chosen as 10 mm. Therefore, the cross-sectional area of the secondary winding is 180 mm. Taking into account the section of the ower line cable 500 mm, the total area of coer in the transformer window is 680 mm. Given the window sace factor is nearly 0.33, calculated by the emirical formula 10 30, where KV hv is the voltage of the secondary winding exressed in kv, the transformer window area is calculated as.1 10 m. This means that a transformer core with 5.1 cm inner diameter is needed. The core cross-section width around the ower line cable and the transformer length can be now sized to otimize the total weight of the transformer. Reresenting the transformer core dimensions by the core average magnetic ath length M gl, the weight of the magnetic core and secondary winding as function of M gl is resented in Fig.. As shown, the otimum value for M gl is in the range 19-0 cm. Making m the core outer diameter is 7.4 cm. Given the calculated core section effective area, a 1. m long transformer is obtained. Wfe, Wfe+Wcu (Kg) Wfe+Wcu 11 8 Wfe 10 7 Wcu Otimum Zone for Mgl Mgl (cm) Fig.. Transformer weight otimization Wcu (Kg) 5 LCL Filter In grid-connected alications reduced levels of harmonic distortion are required to comly with IEEE standard. Therefore, a low ass outut filter is used to connect the DPFC device to the electric ower system (Fig. 1), to reduce the switching frequency harmonics injected to the grid by the DPFC converter.

5 Transformer and LCL Filter Design for DPFCs 455 Since between the filter and the grid a transformer is used, which inserts a leakage inductance seen by the grid, the outut filter comrises an LC filter lus the transformer leakage inductance ( ), which can be seen as an LCL filter but with constant leakage inductance L f on the outut. Neglecting arasitic resistances and considering the outut equivalent imedance seen from the transformer, for the low ass third-order order filter the transfer function is: Lo Ro (s + ) V ( ) 1( ) o s C f L f L f + Lo Lo = () VPWM ( s) 3 R L o f 1 + L f + Lo Ro s + s + s + L + L C L ( L + L ) C L ( L + L ) f o f f 1 f o f f 1 f o While the numerator of the transfer function () has one real zero set by the outut imedance ( ), the denominator has one real ole ( 1 ) and two comlex conjugate oles and can be reresented by the olynomial, where ξ is the daming factor and ω the angular assband edge frequency. Equating the denominator coefficients from () with the olynomial d(s), the filter arameters may be calculated from: L Ro( ξ ω + ξω + 1ξ) Ro Lo1 Loξω f1 = Lf = 1ω ( 1 + ξω ) 1 + ξω ( 1 + ξω ) C f = Roω ( ξ ω + ξω + 1ξ),, Usually ξ and ω are set according to the desired filter characteristics, the ole 1 is used to cancel z 1 and should be laced as near as ossible from z 1 (ideally ) to reduce the filter attenuation ( 0log ) bellow ω. However, to fulfill the condition 0 in (3), for a given ω, the values of ξ and 1 are constrained by and. Setting L f as the transformer leakage inductance ( 1.55 µh) then ξ and 1 can be established from and. Setting the assband edge frequency 750 Hz and ole 0.9, the filter arameters are obtained ( 0.15 Ω and 4.9 mh) as 0.55 mh and 91.6 µf. At the resonant frequency khz the daming factor of the filter is and the resonant eak 0log db. The magnitude bode lot of the undamed filter is resented in Fig. 4. (3) 5.1 Damed Filter Design Since assive LCL filters have low daming characteristics at resonant frequency, they can cause instability. Therefore, the filter should be damed to avoid resonances without reducing attenuation at the switching frequency or affecting the fundamental. Several assive daming toologies can be used, each one having its articular roerties [7]. Fig. 3 illustrates two ractical aroaches to dam the LCL low-ass filter.

6 456 I.M. Martins et al. a) b) Fig. 3. Practical aroaches to the daming of the LCL filter: a) Parallel R d and L d in series with the shunt caacitor. b) Series R d, L d and C d in arallel with the shunt caacitor Parallel R d and L d Daming in Series with the Shunt Caacitor A daming resistor R d can be added in series with the shunt caacitor C f as shown in Fig. 3a. Since at the resonant frequency the imedance of the filter is zero, the aim of the daming is to insert imedance at this frequency to avoid oscillation. The main drawback of this daming method is that its transfer function contains a highfrequency zero ( 1 ). The addition of R d degrades the sloe of the highfrequency asymtote, from 40 db/decade to 0 db/decade, reducing the filter attenuation above the resonant frequency. Hence, R d must be chosen so that the value of z is significantly greater than ω r. This condition can be exressed as 1. Setting the daming resistor imedance at a third of the caacitance at the resonant frequency then 0.77 Ω. The daming factor is now and the resonant eak 9.6 db. Fig. 4 illustrates how addition of the daming resistor modifies the magnitude of the transfer function, reducing oscillations in 54. db, but also reducing the filter attenuation above the resonant frequency from 40 db/decade to 0 db/decade. To avoid significant ower dissiation in R d, an inductor L d can be laced in arallel with the daming resistor roviding a low frequency byass, as shown in Fig. 3a. To allow R d to dam the filter, at the resonant frequency the inductor L d should have an imedance magnitude sufficiently greater than R d. However, increasing the inductance L d increases weight and energy stored. Thus, the inductor is selected as mh Series R d, L d and C d Daming in Parallel with the Shunt Caacitor Another aroach to dam the filter is to add resistor R d in arallel with the shunt caacitor, as illustrated in Fig. 3b. The resistor results in increased ower losses, therefore just by itself it is not a ractical solution. To obtain the same daming factor as the revious method the resistor is calculated from: Lf + Lo Rd = = 6.9 Ω (4) C ( + ξω )( L + L ) C R f 1 f o f o Fig. 4 illustrates how the arallel daming resistor reduces filter oscillations at the resonant frequency without reducing attenuation above this frequency. One ractical solution to significantly reduce the ower dissiation in R d is to add a tuned L d -C d circuit in series with R d, as illustrated in Fig. 3b. To allow R d to dam the filter, the value of the high-frequency blocking inductor L d and the DC blocking

7 Transformer and LCL Filter Design for DPFCs 457 caacitor C d are chosen such that, at the filter resonant frequency, the imedance of the daming branch is dominated by the resistor R d. Therefore, the inductor is selected as 1.5 mh and the caacitor from 1 31 µf. Fig. 4. Magnitude bode lot of the LCL filter 6 Simulation Results The resented transformer and filter with arallel R d and L d daming in series with the shunt caacitor has been modeled and simulated in Matlab/Simulink environment, considering the imlementation of the DPFC devices in a transmission network. The simulations values were obtained for a ower system consisting of the sending and receiving end voltages V s and V R, connecting the load R load, L load through a transmission line R line, L line, with 4500 DPFC devices (1500 devices er hase). Fig. 5a shows the PWM voltage v PWM injected by the converter and its reference v oref. The reference voltage is calculated according to the secified levels of active and reactive ower. Fig. 5b shows the rimary and secondary winding voltages v and v s, where v s is divided by the secondary winding number of turns n s. As can be noted the effective transformer turns ratio is not exactly n s /n, due to windings and leakage voltage dros. Vwm, Voref (V) Vwm Voref a) t (s) b) t (s) Fig. 5. a) Converter PWM outut voltage. b) Transformer winding voltages. Vs/Ns, V (V) Vs/Ns V

8 458 I.M. Martins et al. 7 Conclusions In this aer a ower transformer and a third-order LCL filter to be art of a DPFC device was resented. To coule the DPFC device to the transmission line, the transformer is clamed in series with the ower line, avoiding galvanic contacts. The LCL low-ass filter interfaces the transformer with the single-hase full-bridge IGBT based converter, to reduce the high frequency switching harmonics. For the designed filter, two assive daming methods were resented. Simulation results were resented showing the effectiveness of the designed transformer and filter. Acknowledgments. This work was suorted by Portuguese national funds through FCT - Fundação ara a Ciência e a Tecnologia, under roject PEst- OE/EEI/LA001/013. References 1. Gyugyi, L., Hingorani, N.G.: Understanding FACTS: Concets and Technology of Flexible AC Transmission Systems. IEEE Press, New York (1999). Divan, D., Johal, H.: Distributed FACTS A New Concet for Realizing Grid Power Flow Control. IEEE Trans. Power Electronics, (007) 3. Yuan, Z., de Haan, S.W.H., Ferreira, B.: A New FACTS comonent Distributed Power Flow Controller (DPFC). In: Euroean Conference on Power Electronics and Alications, Aalborg,. 1 4 (007) 4. Martins, I.M., Silva, F.A., Pinto, S.F., Martins, I.E.: Control of distributed ower flow controllers using active ower from homoolar line currents. In: IEEE 13th International Conference OPTIM 01, Brasov, (01) 5. Martins, I.M., Silva, F.A., Pinto, S.F., Martins, I.E.: Indeendent Active and Reactive Power Control in Distributed Power Flow Controllers (submitted for ublication) 6. Silva, F.A., Loes, D., Sequeira, J.: Designing Transformers for the Power Suly of a Transmission Line Insection Robot. In: Congrès 01 CIGRÉ Canada, Montréal,. 4 6 (01) 7. Ahmed, K.H., Finney, S.J., Williams, B.W.: Passive Filter Design for Three-Phase Inverter Interfacing in Distributed Generation. In: Comatibility in Power Electronics 007, Gdansk,. 1 9 (007)