|Year : 2010 | Volume
| Issue : 4 | Page : 202-212
Analysis and Implementation of LCC Resonant DC-DC Converter for Automotive Application
M Prabhakar, V Kamaraj
Department of EEE, Sri Venkateswara College of Engg, PO Box No. 3, Pennalur, Sriperumbudur, Tamil Nadu, India
|Date of Web Publication||24-Sep-2010|
Department of EEE, Sri Venkateswara College of Engg, PO Box No. 3, Pennalur, Sriperumbudur, Tamil Nadu
| Abstract|| |
In this paper, a non-isolated inductor-capacitor-capacitor (LCC) topology based DC-DC converter for automotive application is practically implemented. The resonant tank with one inductor and two capacitors provides soft switching of the inverter switches and a voltage gain of 2. All possible LCC topologies are listed and categorized based on the order of their voltage gain expression. Based on the source/sink requirement for automotive application, some topologies are found to be realizable. For all these realizable topologies, voltage gain expressions are obtained and plotted against normalized frequency. From the voltage gain plots, one candidate topology is chosen and analyzed further. Expressions for current gain, stress across resonant tank elements, circulating reactive power and stored energy in the tank are obtained. The optimum value of Q which results in smallest possible resonant tank is determined and is found to be 0.545. The resonant tank is designed and implemented based on the optimum value of Q. Experimental results show that soft switching is achieved for a wide load range and is suitable for automotive application.
Keywords: DC-DC power conversion, Frequency domain analysis, Power electronics, Resonant power conversion
|How to cite this article:|
Prabhakar M, Kamaraj V. Analysis and Implementation of LCC Resonant DC-DC Converter for Automotive Application. IETE J Res 2010;56:202-12
| 1. Introduction|| |
Power electronic based converters play a significant role in automotive application. These converters are used in some automotive applications like temperature control unit, power steering unit, headlamps, etc.  . The ever increasing electrical loads in an automobiles compel the use of higher voltage rating and higher power rated converters , . With increased power rating, the challenges faced by converters designed for automotive application include high efficiency, compactness, cost effective and resilience to harsh environmental conditions ,, .
Some DC-DC converter topologies have already been employed for automotive application ,,,, . In , , a soft switched quasi resonant inverter and a resonant dc link inverter were designed for a battery powered vehicle. Both these converters were designed to drive the main motor. In  , a two stage soft switched DC-AC inverter was proposed. In this converter, the initial stage was a voltage step-up mode which was incorporated using a push pull quasi resonant converter and the second stage was a conventional DC-AC inverter. Though the converter is highly efficient, the presence of transformer with large turns ratio makes the converter bulky. A magnetic less four level DC-DC converter for dual voltage bus was proposed in  . The converter had slightly complicated control to enable multilevel operation. A bi-directional DC-DC converter for a fuel cell based vehicle was proposed in  . The converter had large transformers and inductors making it bulky. The performance of some DC-DC converters for automotive application has been compared in , . However, these converters were designed for an electric vehicle and hence fed the main drive motor only. In addition, traditional soft switched resonant converters were not considered.
Due to the sinusoidal behavior of resonant converters, their switching losses are much reduced. Therefore, it is possible to operate these converters at high frequencies and thus reduce the size of their reactive components. Consequently, several of today's resonant DC-DC converters operate in megahertz frequency range ,, . The series and parallel resonant converters are basic resonant converter topologies. Generally, the resonant tank consists of only two energy storage elements. Compared with the conventional second order resonant converters, higher order converters are shown to possess more desirable characteristics.
Resonant converter topologies in which the tank circuit consists of more than two or three energy storage elements have been reported in , . A generalized analysis for the third order resonant converter based on sinusoidal approximation was presented and the investigation was limited to six topological "schemes" in  . Investigation of three and four energy storage elements was reported and few topologies based on third and fourth order circuits were analyzed in  . However, most of the third order resonant DC-DC converters available in literature are isolated and use the transformer leakage parameter as one of their resonant elements. Though this is advantageous, the behavior of all available inductor-capacitor-capacitor (LCC) topologies, particularly non-isolated topology, has not been analyzed so far, especially for their suitability in automotive application.
The objective of this paper is to analyze all possible third order LCC resonant converters for their suitability in automotive loads like wind shield wiper motor, head lamp, etc. Based on the desired voltage gain characteristic plot, one LCC topology is analyzed in detail. Closed form expressions for kVA/kW and energy stored in the resonant tank are obtained. From these expressions, the optimum value of Q which gives smallest possible resonant tank is determined, designed and implemented for practical verification.
| 2. Selection of Topologies|| |
2.1 Preference for LCC Topologies
For a converter to be used in automotive application, the converter must be compact so that least space is occupied by the converter in an already limited volume. In converter technical terms, we know that the size of the converter is mainly dictated by the size of the reactive elements, especially inductor. Hence, for a converter to be as compact as possible, the number of inductive elements must be minimum. Therefore, all LLC and isolated topologies which use transformers are not considered. Thus, only LCC topologies are considered for analysis and implementation.
Arrangement of one inductor and two capacitors in various possible combinations results in 18 possible topologies  . The analysis of LCC topologies is well documented in literature ,,,,,,,,,,,,,, . However, only one topology has been analyzed in all the references quoted and hence the motivation behind the analysis of remaining LCC topologies is particularly for their suitability in automotive application.
2.2 Determination of Order of Resonant Tank
[Figure 1] shows a generalized representation of the resonant converter. The operation of the circuit is well known and hence is not discussed in this paper. The order of the converter is defined by the order of its commutational network. All the 18 possible network combinations of LCC topologies are shown in [Figure 2].
The voltage gain of the system is determined from the resonant tank transfer function. All the LCC resonant topologies shown in [Figure 2] can be categorized based on the order of the resonant tank transfer function. The order is determined based on the following criteria.
The order of the system is determined by the number of elements that contribute to dynamical change in energy.
Elements connected in shunt with the source and load do not contribute to the dynamical change in energy. Hence, the voltage gain (order) of such systems will always be unity. Topologies 7 and 18 exhibit this behavior and hence the order is 1 for both topologies.
A loop formed by two elements in which there is no possibility of dynamical change in energy between them, can be combined as a single element.
When a possibility of dynamical energy change between this resultant element and another element exists, then the order of the system will be 2. For instance, in topology 3, input, C1 and C2 form a loop. Hence, C1 and C2 are combined as a single element. There is a possibility of dynamical change in energy between this combination and L. Hence, the order is 2.
Based on the above criteria, 18 possible LCC topologies are classified as unit gain, first, second and third order systems as shown in [Table 1] [Figure 1] and [Figure 2].
2.3 Choice of Topology Based on Source/Sink Combination
The resonant tank can be excited from either a voltage (v) or current (i) source and can be used to feed either a voltage or current sink. Thus, two individual source and sink combinations are possible. These two individual combinations can be suitably arranged to give four possible source/sink combinations: v/v, v/i, i/i and i/v.
In automotive application, the input power is fed from the battery. The converter output should exhibit good voltage regulation. Hence, the converter which is used for automotive application should be of v/v type source/sink combination.
2.4 Realizable Topologies for Automotive Application
For a particular LCC topology to be realizable, the following conditions should be satisfied: (a) loop containing capacitor(s) and voltage source or sink should not be formed; (b) cutset containing inductor(s) and a current source or sink should not be formed.
This is because when the converter is driven or terminated by a two state square wave voltage source or sink, respectively, when the voltage changes its state instantly, an infinite current spike will occur in the capacitor. Similarly, when the converter is driven or terminated by a two state current source or sink, respectively, when the source or sink current changes state instantly, an infinite voltage spike will occur across the inductance.
Based on these conditions, only eight topologies which are shown in [Figure 3] are realizable for automotive application. Voltage gain for all the eight topologies are obtained using AC analysis as explained in the next section.
| 3. Analysis of Topologies|| |
3.1 Methods of Analysis
There are several methods to model and analyze the performance of resonant converters of all nature and types. All these methods have been successfully applied to analyze resonant converters and are well documented in the literature ,,,,,,,,,,,,,,,,,,,,,,,,,, . Some of the methods reported are (a) fundamental harmonic approximation (FHA) or fundamental frequency approximation or AC analysis ,,,,,,,,,,,,,,, , (b) state-plane analysis ,,,,, , (c) discrete time domain analysis , , (d) cyclic averaging method , and (e) extended fundamental frequency analysis (EFFA)  . Generally, the preferred attributes of a particular method are mathematical simplicity, providing insight into required details, ease of practical implementation, lesser time consumption or faster to solve and acccuracy. All the methods mentioned above possess some attributes and lack some other attributes. Based on the application requirement, a choice is made in favor of one particular method of analysis  . Recently, EFFA has been applied to obtain more accurate results compared to FHA. However, when the converter is operated below the resonant frequency, both EFFA and conventional FHA methods produce almost similar results. The difference is significant only at resonant frequency and the region beyond the resonant frequency  . Because of this reason, researchers continue to use conventional FHA methods to analyze and design resonant converters ,,,,,, . Therefore, in this paper also, conventional FHA method is used to analyze and obtain the necessary performance parameters.
3.2 Introduction to AC Analysis
In AC analysis method, the output rectifier and the filter are replaced by their equivalent AC resistance and the square wave input voltage source is replaced by its fundamental sinusoidal equivalent. The power transfer from input to output is assumed to be only via the fundamental component and the contribution of all the harmonics is neglected  .
The equivalent AC resistance for the rectifier with capacitive filter and the RMS value of the fundamental component of square wave voltage (input to resonant tank) are given by
The resonant frequency and the normalized switching frequency are defined as
The characteristic impedance and Q of the resonant network are given by
The voltage and current gain are defined as
The voltage and current base values are given by
Voltage gain for all candidate topologies is computed by using Equations (1)-(5). From the voltage gain expression, a characteristic plot of voltage gain vs. normalized frequency with x = 1 is obtained for each topology. This is compared with the desired characteristic plot to decide upon the suitability for automotive application. [Table 2] gives the voltage gain expression for all candidate topologies.
3.3 Desired Voltage Gain Plot
For automotive application, fixed frequency operation over wide load range is preferred. This will ensure open loop mode of operation of the converter and thus results in simple configuration. In addition, it is desirable if the converter has good load regulation. This means that the output voltage or in turn the voltage gain, needs to remain a constant at any one normalized frequency for various values of Q. [Figure 4] shows the nature of desired voltage gain characteristics.
3.4 Topology Selection Based on Voltage Gain Plot
Voltage gain plots for all the eight candidate topologies are plotted. Only two topologies, 1 and 2, meet the desired requirement. [Figure 5] and [Figure 6] show the voltage gain plots for 1 and 2, respectively. Other topologies do not possess the desired voltage gain characteristic. [Figure 7] and [Figure 8] show the voltage gain plots for topologies 6 and 8, respectively. For instance, in topology 6, voltage gain converges to zero at a normalized frequency of 1. This feature is not desirable as the output voltage would not be sufficient enough to meet the load requirements. In topology 8, voltage gain never remains a constant when Q is varied. In order to obtain desired voltage gain, switching frequency has to be changed in accordance with load variation. Hence, it cannot be used in automotive application without using complicated closed loop control to change the frequency to obtain the required voltage gain. Similar justification can be applied to remaining topologies also.
3.5 Stresses Across Resonant Elements
To design a resonant converter, the voltage and current stress of the resonant elements must be known. The voltage and current stresses are derived from circuit theory basics as given in Appendix. [Table 3] and [Table 4] give expressions for normalized voltage and current stresses experienced by resonant elements L, C1 and C2 for topologies 1 and 2, respectively [Figure 4],[Figure 5],[Figure 6],[Figure 7],[Figure 8].
| 4. Optimization of Resonant Tank Size|| |
The size of the resonant tank depends on the energy stored in the tank elements and the (kVA/kW) ratio. In order to obtain smallest possible resonant tank, the energy stored in resonant tank and (kVA/kW) ratio has to be minimum at a particular value of loaded quality factor Q. The energy and (kVA/kW) ratio are computed from the stress equations. These parameters are plotted with respect to Q. From the plot, the value of Q which gives smallest possible resonant tank is determined.
From [Figure 5] and [Figure 6], it is observed that the voltage gain for both topologies remain constant at wn = 0.7. Hence, the energy and (kVA/kW) ratio are computed at this operating point. The expressions for these parameters are given by Equations (6)-(9) for topologies 1 and 2.
[Figure 9] and [Figure 10] show the energy and (kVA/kW) ratio plots, respectively. It is observed that at Q = 0.545, these parameters are minimum. Thus, the size of the resonant tank is expected to be minimum when Q = 0.545. The resonant tank elements are designed based on this optimum value of Q.
| 5. Experimental Results|| |
A wind shield wiper motor was considered as load. The resonant tank elements were designed for the following specifications: input voltage = 12 V, output voltage = 24 V and output power = 100 W. Thus, a gain of 2 was required. In [Figure 5] and [Figure 6] it is observed that only topology 1 possessed a gain of 2 with good load regulation at a normalized frequency of 0.7. Therefore, the resonant tank elements of topology 1 alone were designed.
The load resistance was measured and found to be 5.76 ohms. For a resonant frequency of 75 kHz and an optimal value of Q = 0.545, the values of L and C were found out to be 6.6 micro henry and 0.67 micro farad, respectively. However, Q increases as load increases. Hence, the design was done for a worst case of Q = 2. The values of L and C were calculated by using Equations (2) and (3) and were found to be 12 micro henry and 0.36 micro farad, respectively. The resonant frequency for these values of L and C was calculated by using Equation (2) and was found to be 76.4 kHz. For a normalized frequency of 0.7, the switching frequency was calculated by using Equation (2) and was found to be 53.5 kHz. Ferrite core was used to construct the inductor and the measured value was 11.5 micro henry. Four capacitors, each with a value of 0.1 micro farad, were connected in parallel to get the required resonant capacitor value. Measured value of capacitor was 0.4 micro farad. The switching frequency for these values of inductor and capacitor was calculated by using Equation (2) and was equal to 51.9 kHz.
Four IRF540N (100 V, 33 A, 0.044 ohm) MOSFETs were used as inverter switches and four MUR8100E (800 V, 8 A, 1.8 V) ultrafast recovery diodes were used to construct the bridge rectifier. [Table 5] gives the summary of experimental set-up used.
[Figure 11]a shows the simulated waveforms of the resonant converter. [Figure 11]b shows the hardware output waveforms of the resonant converter. It is observed that the load voltage is around 20 V. The voltage drop across rectifier diodes and inductor has contributed to reduction in output voltage. However, the output obtained was sufficient to drive the wiper motor which was operating at normal load condition.
|Figure 11: (a) Simulated waveforms: (from top to bottom) output voltage, gate pulse applied to switch S1, resonant inductor current and inverter output voltage; (b) hardware output waveforms.|
Click here to view
In order to study the soft switching characteristics of the converter over a wide load range, a 100 ohm/10 W resistor was connected as load so as to obtain the lightly loaded characteristics. [Figure 12] shows the voltage across the MOSFET switch S 1 , current through S 1 and the output voltage under lightly loaded conditions. We observe that zero voltage turn-on is achieved.
[Figure 13] shows the switching loss waveform under light load condition. The waveforms clearly show that turn-on loss is completely zero and the conduction loss is negligible. However, during turn off, the voltage stress on the device increases rapidly, and consequently, this causes the switching loss also to shoot up for a very short duration. Overall, the switching loss is very much reduced and satisfactory during lightly loaded condition.
The converter performed satisfactorily under light load and normal load conditions when it fed the wind shield wiper motor. The load range was further increased to verify if soft switching could be achieved over a wider load range. [Figure 14] shows the voltage across S 1 , current through S 1 and the output voltage under full load condition. The output voltage is slightly reduced compared to light loaded conditions. This is because of the increased voltage drop across the resonant inductor. In addition, as loaded quality factor Q increases, the gain reduces. Therefore, we observe a slight reduction in output voltage. Inspite of slightly overloading the converter, we observe that zero voltage turn-on is achieved.
[Figure 15] shows the switching loss waveforms under full load condition. The waveforms clearly show that turn-on loss is completely zero while the conduction loss is slightly increased compared to light load conditions. During turn off, the voltage stress on the device is slightly reduced compared to light load condition. This is mainly due to reduced gain when compared to light load condition. As a result of reduced voltage stress, the switching loss also reduces during turn off. Overall, the total losses will be slightly increased because of increased conduction loss.
| 6. Conclusion|| |
A non-isolated soft switched LCC topology was analyzed, designed and implemented for a wind shield wiper motor application. The topology was carefully selected by considering the load requirement. The resonant elements were designed with an optimal value of Q which was obtained from the energy and kVA/kW plot. The required voltage gain of 2 was provided by the resonant tank elements themselves and no additional elements or control was required. The converter operated under open loop mode and soft switching was achieved over a wide load range. Reasonably good voltage regulation was obtained over the entire load range which was considered. As a transformer is not used and only one inductor is used, this converter would fulfill the power density requirement of automotive application.
| 7. Acknowledgments|| |
The authors wish to thank the management and staff of Sri Venkateswara College of Engineering, Sriperumbudur, and SSN College of Engineering, Kalavakkam, for providing the necessary encouragement and support while carrying out this work.
| 8. Appendix|| |
In order to find the voltage gain M, output current Io is computed from basic circuit theory as shown below.
[Figure 16] shows the circuit to find voltage gain. Output current
Input impedance as seen by the source Zin can be found as
By substituting Equations (A1) and (A2) in Equation (4), voltage gain is computed and is given as
Voltage gain M can be simplified by using Equations (1)-(3) and is given as
The normalized value of voltage stress across resonant inductor is given by
Substituting (A2) in (A5), we get
Substituting s = jw, we get
Simplifying, we get
The normalized value of inductor current stress is given by
Substituting (A2) in (A11), we get
Substituting s = jw and Equation (1) in (A12), we get
Simplifying, we get
Expression for voltage and current stress of capacitors can be derived similarly.[Additional file 1]
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| Authors|| |
M. Prabhakar received his B.E. from University of Madras in the year 1998 and M.E from Bharathidasan University in the year 2000. He is currently pursuing his Ph.D in Anna University, Chennai. His areas of interest include dc - dc0 converters and power electronics.
V. Kamaraj obtained his B.Tech. from Calicut university, M.E. and Ph.D. form Anna University. He has 20 years of teaching experience. His area of research includes networks and power electronics.
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13], [Figure 14], [Figure 15], [Figure 16]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]