Generic optimization for SMPS design with Smart Scan and Genetic Algorithm

Transcription

1 Generic optimization for SMPS design with Smart Scan and Genetic Algorithm H. Yeung *, N. K. Poon * and Stephen L. Lai * * PowerELab Limited, Hong Kong, HKSAR Abstract the paper presents a new approach for generating optimized solutions of a Switched-Mode Power Supply with the higher efficiency. At the very beginning, we initialize a preliminary power supply design with a known topology (e.g. Fly-back). Then, we choose a set of alternative parts for some critical components such as the MOSFET and transformer. It is quite a complicated and time consuming task to obtain a design with the highest efficiency and lowest cost from numerous combinations. Multi-objective Genetic Algorithm is one generic solution to solve such optimization problems. In order to encode the electrical parts as the basic units of GA, the chromosomes, and evaluate them with a numerical function, we have to model an entire power supply circuits into a Component-based System and simulate the electrical reactions by the numerical characteristics of components. This approach not only reduces the time in the design stage but provide a more convincing design before the production. The experiment results are presented to show the robustness and the effectiveness of this approach. Keywords- Genetic Algorithm; Power supply optimization; Component based system; I. INTRODUCTION In the design stage of Switched-Mode Power Supply (SMPS), the engineers use their expert knowledge and experience to draft the power supply prototype, fabricate a sample and examine its efficiency on different aspects such as power dissipation. To refine the performance and adjust the cost, they usually change the parts at some critical nodes. These steps are reiterated until the product meets certain criteria and it may consume weeks or even months. It is no doubt that these steps are unavoidable to ensure the higher quality and the lower cost of the power supply. Indeed, the procedures themselves may not be definitely completed by manipulation. We generally classify this kind of problem searching for the best one from a set of combinations as a Discrete Optimization Problem. A. Techniques for solving Discrete Optimization Problem The following is a typical Discrete Optimization a Infineon provides the Evaluation Design circuit in our experiment Problem (DOP). Some boxes are put in the fixed size container. The size of boxes is varying and there is a set of positioning and placement combinations for those boxes. There must be at least one solution that most boxes fit in the containers. There are some well-known techniques to solve the DOP. Full Search, or try-an-error, is the most reliable method to obtain the solution. All combinations are evaluated with a fitness function and the one with the highest score is the best solution. Most industrial processes will apply this technique if the optimization task is too complicated to be analyzed. However, this method is very expensive and time-consuming if the number of combinations is too large. There are some other methods to tackle DOP likes Binary Search and Nearest Neighbor Search. Despite the exponential reduction in the number of evaluation for combinations by these methods, it is still difficult to appraise the resource for optimization. With limited resource, some evolutionary computing techniques such as Genetic Algorithm (GA) [4] and Particle Swarm Optimization (PSO) [6] are proposed. They are based on the evolutional algorithm to find the solution approximating to the best one at assigned resources. Even though the solution is not always the best as Full Search does, it is not far away from that. Most important thing is that we can control the resources (e.g. the size of pool and the number of generations) to achieve different effectiveness of optimization. There are some previous works applying GA for solving optimization problems in SMPS. Reference [1] employs GA for synthesizing low power circuits. GA is applied to search the optimal commitment of thermal units in power generation in [3]. A research conducted in [5] generates the pattern of high power supply noise to estimate the maximum power supply noise of chip. Moreover, there are some works on finding the best circuit configuration in power supply controller evaluated with transfer function, as in [7]. B. Outlines In this paper, we propose using a Component-based System (CBS) accompanied with Genetic Algorithm (GA) to optimize a power supply from different combinations of the real components for higher efficiency. In the section II, the idea of GA solving Discrete Optimization Problem is overviewed. Then, the CBS of power supply in online power supply design software, PowerESim, is

2 introduced for preparing candidates in the optimization in the section III. In section IV, the fitness function to evaluate the efficiency of the modeled power supply is presented. Finally, the successful rate to obtain the efficient power supply is demonstrated in the experiment results in section V. II. GENETIC ALGORITHM A. Operations of GA Assume an optimization problem contains at least one solution and the searching space is finite. Then, Genetic Algorithm (GA) [4] is able to locate the optimal solutions within the searching space. The basic unit of GA is chromosome or candidate. They are parameterized as a list of numbers which are the features representing the chromosome. In the optimization problems, there are some parameters to be optimized and a set of parameters forms one candidate. A few candidates are generated randomly and put in a pool. They are evaluated with the fitness function, or cost function. The fittest group of candidates always survives in the pool and they are mated as the parents for next generation. These parents form some pairs and born the offspring by the crossover and mutation operation [4]. The better candidates, supposedly, are evolved from the competitions among the candidates in last generation. After several generations, the combinations remained are the elites and the final solution is the best inside the pool. B. Multi-objective GA For multi-objective optimization problems, we need multi-objective GA to solve it. For instance, we have to evaluate the efficiency, the unit price of product and the stress at extreme conditions while designing a SMPS. These evaluations are conflict to each other and no solution with the highest scores at all criteria can be achieved. In order to fit all the criteria, we can record the more than one high score candidates for each evaluations and the one with the highest average score for those criteria. User can select one of them to be the final solution. In this paper, we are going to evaluate the efficiency of SMPS ONLY such that it does not complicate the idea we proposed. III. COMPONENT BASED SYSTEM OF SMPS A. Definition of Component-based system Component-based system (CBS) [2] is a widely used approach for computerizing the industrial processes into the software. In general, any process with the descriptive participants, the procedural actions and the measurable values can be implemented as a CBS. SMPS is obvious a CBS. The components are the physical parts like resistors, capacitors and transformers. Their connections lead the electrical response from the input source and each component participates in its position. The current and voltage across the components are measurable by the meters. In our experiment, a well-developed software, called PowerESim, which is a power supply simulator built as a CBS is applied as the testing platform. Initially, user selects a converter topology and provides the specification (e.g. the range of input voltage, expected output voltage and current output current) from the interface. Then, the software provides the basic design which just fulfilled the specification and simulates the entire power dissipation at one operational cycle 1/fs where fs is the switching frequency of power supply in several milliseconds. B. Modeling component from real parts To model a real part to be a component in the software, the essential characteristics of a particular component should be defined. Use MOSFET as an example. The characteristics of the MOSFET are modeled in the software according to the specifications are shown as following. Thousands of modeled components are stored as table entries in the database. User can modify the components inside the converter, T1 controller Rrcd1 and feedback circuits. INPUT TABLE I. MODELING CHARACTERISTICS OF MOSFET Rrc_M1 Characteristics Max. Drain to Source Voltage V DSS Max. Gate to Source Voltage V GS 20V Max. Continuous Figure Drain 3. Current Circuit I diagram of the Fly-back topology D 7.3A Figure 2. Typical Capacitance Vs. Drain to Source Voltage caption is centered in the column With a known converter topology, the power dissipation of every individual part can be estimated according to their modeled characteristics. Power dissipation of the main primary MOSFET in the Fly-back converter is defined as the integration of voltage current within duration of 1/fs (1) in the software. The software provides a multiple selection interface of components whereas M1 Values 730V Max. Pulsed Drain Current I DM 21.9A Max. Pulsed Avalanche Rating E AS Max. Power Dissipation P D Max. Operating Temperature T J Typical Gate to Source Threshold Voltage V GS Max. Total Gate Charge Q g(tot) Max. Body Diode Reverse Recovery Timet rr 230mJ 83W 150 o C 3V 21nC 400ns Do1 O/P

3 users can select the alternatives as the parameters for optimization. LossM 1 1/ fs V Idt (1) 0 = C. Modeling the transformer Transformer takes a very important role in a SMPS. The main difference between transformer and other parts is that transformer constituted by the sub-parts such as magnetic core, the magnetic wires, the bobbin etc. Different arrangements (e.g. number of turns and number of parallel wires) of those sub-parts directly affect its behavior and performance. Formerly, it is not easy to model and simulate such complicated structure in component-based system. The proposed software has developed a subtle tool called Magnetic Builder providing a construction interface and simulator of the magnetic characteristics and power dissipation in a well-formed transformer. To find the best construction of transformer, we need to select multiple cores, wires and number of turns at particular winding. The number of turns in winding is quantized as a set of step values. For optimization, there are several combinations of transformer are generated by the crossover of all those alternative parameters. D. The effective index of power supply Efficiency is always the most important measurement for a power supply. In the software, the efficiency simulated is the Effective index defined as (2) where Po total is the total output power and Pd total is the total power dissipation. This becomes the fitness function for the optimization where the higher value induces higher efficiency and the maximum value is 1. Pototal Effective _ index = Pd + Po IV. total EXPERIMENT RESULTS A. Using concurrent converter topology We choose an Evaluation Design of a power supply using Fly-back topology in the software. The input voltage range is V. The expected one output voltage is 16 V and current output current is 3.75 A. The circuit diagram is shown as Figure 3. The initial Effective Index of the design is There are some critical nodes in the converter have been selected as the parameters for optimization in Table II. total (2) B. Prepare the first pool by Smart Scan Algorithm Any parts containing only one alternative will not be considered as the parameters for optimization so to reduce the complexity. The chromosome is designed as Figure 4. The chromosomes in the first pool are generally selecting from the combination of alternatives randomly. If the maximum number of executed evaluation function, Iteration allowed, is small, some alternatives might be eliminated and never participate in the optimizing space. Hence, the best combination is not guaranteed in the pool. In the power supply design, some dominating alternatives lead to high efficiency no matter what other parameters are. With this feature, an election method is proposed called Smart Scan to form the first pool intellectually as the procedures below. Index (i) TABLE II. THE COMPONENTS FOR OPTIMIZATION Part no. Description 0 Rrcd1 RCD Clamper resistor 1 M1 Primary Main MOSFET 2 Rrc_M1 Slobber resistor 3 Do2 Output Diode Number of alternatives (ksel i ) 4 T1 Main 12 (4 cores and 3 Rrcd1 0 M1 0 Rrc_M1 Transformer 0 Do2 number 0 of T1 turns 0 at Figure 4. The first chromosome selecting the primary first alternative windings) of each parameter i. One of the parameters is randomly selected for the dominating scan, e.g. Rrcd1. Other parameters are restricted to be the one randomly selected from their list of alternatives. One chromosome is formed certainly by the first alterative of Rrcd1 and the fixed alternatives of other parameters. ii. The chromosome is evaluated by the fitness function and both the score and the chromosome are pushed into the empty and fixed size pool. iii. Another alternative for Rrcd1 is chosen to form the second chromosome. It is evaluated again and pushed into the pool. When all alternatives of Rrcd1 are examined, one round of scan is finished

4 iv. The alternative of Rrcd1 in the chromosome with highest score is the dominated alternative. The second round of scan starts for other parameter, e.g. M1. The alternative of Rrcd1 in the chromosome is always set to the dominating one and others remain unchanged. v. If the pool is getting full, the chromosome with lowest score is popped up to reserve space for the better one. Finally, a pool is filled by the strong chromosomes. vi. Repeat the scan until the dominating alternatives of all the parameters are found. This election method ensures the chromosomes are strong enough to generate better offspring. However, it requires some of evaluating iterations during the election. The number of fitness function executed is calculated by (3) where N is number of parameters. If the Iteration scan is more or equal to the upper limit of iterations Iteration allowed set by user, some of alternatives may be eliminated until it is within the limitation. N 1 Iterationscan = ksel N N i= 0 C. Genetic Algorithm i ( 1) (3) After electing the pool, the chromosomes are automatically copied to the pool for next generation. The pairs of chromosomes are randomly selected from the first pool for Crossover and Mutation to generate the children. Crossover operation of the chromosomes exchanges the combination of alternatives from one to another and Mutation modifies one alternative of one parameter in the chromosome randomly. The probability of the mutation occurs for each crossover operation is 0.2. If the child is better than one in the second pool, the worst one is popped up and the new one is pushed to the pool. Otherwise, it is eliminated. This method guarantees the best throughout the generation must survive in the pool. Then the third pool is duplicated from the second pool. The optimization is terminated when the maximum number of generation is finished. N generation ( Iteration Iteration ) allowed scan = trunc 2 N pair (4) Iteration = Iteration + 2 N N (5) total Scan generation pair The number of generations in GA allowed is estimated by (4) given that Iteration allowed is set by user. The pool size (N pool ) is 50 and the number of parent pairs (no duplication) selected from the pool (N pair ) is 50. Then, the total number of iterations actually is Iteration total found by (5). In the case N generation is 0, this means the limited iterations does not allow the GA operations and the best in the first pool becomes the final solution. Figure 5 depicts the flowchart of the proposed optimization process. Get all alternatives Rrcd1 M1 Rrc_M1 Do2 T1 Smart Scan Form the Pool A Rrcd10 M1 2 Rrc_M10 Do23 T10 Rrcd10 M1 3 Rrc_M10 Do24 T15 Npoo l Rrcd13 M1 9 Rrc_M11 Do28 T110 Copy Pool A to Pool B Choose Npair pairs from Pool B and undergo Crossover and Mutation Evaluate the fitness of generated children Yes Start End Rank the Pool A and get the one with the highest score Rrcd10 M13 Rrc_M10 Do24 T15 No No. of generation < Ngeneration insert them into Pool A if their scores are higher than anyone in Pool A. Pop-up the worst to remain the Pool size Figure 5. The flowchart of GA optimization D. Summaries The experimental result of Full search is the baseline of the optimization performance. It finds the highest and the lowest Effective Index from all combinations shown as Table III. Indeed, the total number of evaluations required in Full search is the total combination of all parameters calculated by (6) where ksel i is number of alternatives at i th parameter defined in Table II. Ncomp 1 Total combination = ksel (6) i = 0 We have repeated the Smart Scan and GA optimization with different Iteration allowed from 100 to 400 and each test is repeated for 20 times. The results are summarized at the Table IV. The tests with 300 and 400 Iteration allowed complete at least one GA round. Both of them find the best combination perfectly in all tests. When Iteration allowed is 200, it is resulted from Smart Scan only. The successful rate to get the best solution is 95% and the average highest 6 effective index is 6 10 less that the highest Effective index. It induces that one of test cannot achieve the highest score but it is very close to the best one. TABLE III. THE EXPERIMENT RESULT FROM FULL SEARCH The no. of iterations run Highest Effective Index Lowest Effective Index i

5 TABLE IV. THE EXPERIMENT RESULT FROM GA OPTIMIZATION AND SMART SCAN Iteration allowed The no. of iterations run Average Highest Effective index N generation Number of alternatives are eliminated Successful rate to find the best combination % % % % % After reducing Iteration allowed to 150 and 100, some of alternatives are eliminated in the pool. 4 of alternatives are removed randomly for 150 iterations and 14 of that are removed for 100 iterations. Only 85% and 70% of tests can found the best combination in these two cases respectively. Nonetheless, the average best score results are still approximate to the highest score of all combination. To conclude, the number of the iterations of Full search is about 26 times more than that of the guarantee optimization with GA and Smart Scan proposed. V. CONCLUSIONS Achieving the high efficient converter is considered in every SMPS design. Engineers conventionally choose the alternatives and put it in a real power supply. Its efficiency is estimated by the thermal analysis in an enclosed environment. These steps are repeated until the expected efficiency is obtained. However, these procedures are expensive and time-consuming. With using the proposed method, the simulated power supply optimization is optimized by the Smart Scan of the real components modeled in the software, which parameterizes the entire power supply into a CBS and estimates the efficiency in seconds, and Genetic Algorithm. There are several extensions to this work. First, the power losses, thermal effects and stress are evaluated at the same time by a multi-objective Smart Scan and GA optimizer. Second, this approach is also applicable in design the controller and feedback compensator like [7]. The differences are the real components are selected to form the circuit and it is estimated by the expected cut-off frequency and expected phase margin behaved in the power supply. ACKNOWLEDGMENT This project has been implemented as the Smart optimizer in PowerESim developed by PowerELab Limited. REFERENCES [1] T. Arslan, E. Ozdemir, M. S. Bridge, and D. H. Horrocks, Generic Synthesis Techniques for Low-Power Digital Signal Processing Circuits, Proc. Of the IEE Colloquium On Digital Synthesis, pp 7/1 7/5, February [2] I. Crnkovic, J. A. Stafford, and H. W. Schmidt, Component-based Software Engineering, Springer-Verlag Berlin Heidelberg, [3] D. Dasgupta, and D. R. McGregor, Short Term Unit Commitment Using Genetic Algorithms, Technical Report, IKBS-16-93, August [4] D. E. Goldberg, Genetic Algorithms, Addison Wesley, [5] Y. M. Jiang, and K. T. Cheng, Vector Generation for Power Supply Noise Estimation and Verification of Deep Submicron Designs, IEEE Trans. VLSI Syst., 9(2), pp , April [6] J. Kennedy, and R. C. Eberhart, Particle swarm optimization, Proceedings of the 1995 IEEE International Conference on Neural Networks (Perth, Australia), pp , [7] A. Maiden, A. Purvis, and M. Kinghorn, The Development of a Digital Switched-Mode Power Supply Controller and Controller Design Tool, Proc. International Signal Processing Conference, Dallas, Texas, March [8] D. Whitley, A genetic algorithm tutorial, Statistics and Computing, vol. 4, pp , 1994.