Manual Systems Optimization Methodology, Part I

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The reverse model and dynamic optimization technique are extended to virtually optimize variable displacement engine operation taking gear and clutch control interaction effects into account. The reverse model is used for establishing design criteria, such as minimum engine part throttle torque requirements, by determining the required speeds and loads to traverse drive cycles. The advantages of the reverse dynamic optimization approach are demonstrated by performing powertrain matching analyses i.

Size: 7MB. Format: PDF. The amount of current flow through the fuel cell is given by Eq. Like CPV and electrolyzer design, the fuel cell design is also based upon the maximum possible number of cells needed to meet the total load demand. As per the considered fuel cell characteristics [ 25 ], the maximum power per cell is Therefore, for maximum load requirement of the customer, the total number of cells required in the design of a fuel cell is given by Eq. As mentioned earlier, the produced hydrogen is compressor by a mechanical compressor to be stored in the storage tank as the mechanical compression system provides a most compact and reliable storage solution.

The performance model for mechanical compressor, for its power requirements, is based upon the thermodynamic equation depending upon the pressure ratio, that is, pressure at inlet and outlet of compressor, which is given by Eq. It must be noted that the hydrogen produced by the electrolyzer goes to the compressor as they are connected in series. Therefore, the flow of hydrogen through compressor is the same as the rate of hydrogen production in electrolyzer.

In addition, the compressor operating pressure is also assumed to be the same as the electrolyzer operating pressure as hydrogen directly goes to the compressor after production. A cylindrical tank of 3. It has been mentioned that the main motivation of this study is to optimize the individual component of the CPV-Hydrogen system for uninterrupted power supply to consumer load, while meeting the system operational power requirements.

However, for such system design problem, there can be many system size configurations that can fulfill the condition of steady power supply to the consumer. The main purpose of this optimization is to define a set of objective functions to look for system configuration which will not only provide uninterrupted power supply but at minimum cost and optimum system performance.

Therefore, to achieve such a target, three objective functions are defined to be met as per proposed optimization strategy to find optimum system size configuration. First, the main objective function defined is the power supply failure time PSFT which defines the number of seconds for which the system was unable to meet the total load requirements, that is, consumer load plus system operational power requirements.

This objective function is of prime importance and has main priorities, before proceeding to the second objective function.


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In order to start the optimization simulation cycle, it is assumed that the gas storage tanks are filled with a certain amount of gases so that the optimization cycle can be started. Otherwise, in case of empty tanks, the simulation cycle will be stuck in achieving the first objective function if the input weather data value is poor at the start. However, at the end of the simulation cycle, such initial amounts of stored gases must be stored so that it can be assured that the system is self-sustaining and it was not operating because of the initial stored energy.

Therefore, the second objective function for such a study is defined by Eq. On the other hand, L1 and L2 define the upper and lower limit of the difference between state of hydrogen tank before and after simulation cycle. The current simulation cycle is operated in a yearly manner. Therefore, the second objective function is computed at the end of each year. The lower value L1 is kept minimum because it is desired that the system recovers to initial state at the end of the simulation cycle. However, the upper limit is kept a bit high so that system is well prepared for the simulation cycle and it can handle the load requirements with enough available storage, in case of poor weather conditions.

The last and the most important objective function is the overall system cost, including investment cost, operational cost and replacement cost. The overall system cost function is given by Eq.


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The cost functions associated with individual components of the system are given by Eqs. Therefore, the cost parameters associated with each component of the system are given in Table 2 [ 35 ]. Costing parameters considered for techno-economic evaluation of CPV-hydrogen system [ 17 ]. It must be noted that the cost associated with the voltage converters is assumed to be included in the cost of the primary component of the system.

The solar trackers cost is included in the cost of the CPV system. However, cost for water storage is not considered due to its negligible effect on the overall system cost. As mentioned earlier, the micro-genetic-algorithm micro-GA is considered as the main optimization algorithm to search for the optimum system configuration, as per defined objective functions. The program consists of two parts. The first part is associated with the performance simulation of CPV-Hydrogen system, based upon the developed model. The second part is associated with the system optimization, based upon the defined objective function, to find the optimum system size configuration using micro-GA.

There are only two sizing parameters which are given as input to the program to be optimized, that is, the total number of CPV modules needed and the amount of initial hydrogen needed at the start of simulation and optimization cycle. However, the remaining parameters are calculated from these input parameters. The micro-GA is run with a population size of 5 and maximum generations. The results of the study are presented in the next section.

In order to simulate the system performance, the direct normal irradiance DNI data, obtained under tropical conditions of Singapore, at the rooftop of EA building of National University of Singapore, are shown in Figure 6. To capture the DNI data, the pyrheliometer from Eppley Laboratory was mounted onto a two-axis solar tracker with tracking accuracy of 0.

This acts as the input to the simulation cycle for consumer load demand. The actual load data were in megawatt units, which are scaled down to watts. The shown ambient temperature data were obtained from NEA national environment agency Singapore. The weather data shown in Figure 6 act as the primary input for which the system performance is calculated and the optimum configuration of CPV-Hydrogen system is proposed. As per the proposed system performance model, presented weather and load input data, energy management and optimization strategies and objective functions, the system optimization was performed by the developed program in FORTRAN using micro-GA.

The optimization results are shown in Figure 7.

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From these results, it can be seen that the optimization calculations converge after 52 generations, with minimum overall system cost. It can also be seen that for all generations, the PSFT factor is zero and the difference between states of stored hydrogen, before and after the simulation cycle, is within the defined limits of L1 and L2. However, the stored hydrogen difference is closer to L1 limit, which shows that the system has successfully restored its state to initial conditions and it is ready for the next-year performance cycle. If the overall system cost is broken down, then the details are shown in Figure 7.

In order to see the variations in the stored hydrogen energy against the operational period, the state of hydrogen and oxygen storage tanks is shown in Figure 8. It can be seen that the state of stored gases is decreasing during initial months of operation.

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This is because of the fact that for these months, the received DNI is also decreasing, which can be seen in Figure 6. These months represent the rainy season of Singapore and that is why the received DNI is lower for these months. The share of fuel cell, to meet the load demand during diurnal period, is also shown in Figure 8. However, after this rainy season period, the state of energy storage tanks starts to recover and the received DNI as well as the fuel cell share also stabilize.

This is because of the tropical weather conditions as one cannot get clear sky for the whole day. However, the good thing is the stabilized weather conditions with less variations, which is good for the reliable operation of the designed system. The presented data are normalized for per m 2 area. The trend of system output for both parameters is similar to the received monthly DNI, except for rainy season. The electrical output of the system dropped about three times in December than the usual operating month.

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That is why, a sharp decrease in the state of stored hydrogen was observed during this period. As the presented data are in per m 2 format, therefore, if the main objective of the system is to produce electricity or hydrogen, instead of standalone operation, then the system can be designed based upon the presented performance data. Table 3 shows the overall summary of optimized CPV-Hydrogen system for standalone operation for defined objective functions and with minimum system cost. The interesting thing to be observed is that the power rating of electrolyzer is same as CPV. This is because of the fact that the design of electrolyzer is depending upon the maximum excess power available, which is proportional to the size of CPV.

That is why a higher portion of cost was associated with the electrolyzer, even higher than the CPV. That was due to the replacement cost. It can also be seen that the power rating of CPV system is very large as compared to the consumer load. First, this is because of the fact that the system is designed to be operated in standalone mode while also meeting the system operational power needs, and at night, there is only stored hydrogen which can supply power to the load.

Therefore, enough excess power is generated during the daytime to have enough storage for night operation. Second, as the weather input data were based upon tropical climate conditions, therefore, the system is oversized to have enough hydrogen generated to sustain during rainy period.

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This design summary is only for the mentioned location and the consumer load data. However, the main objective of proposing design methodology for standalone operation of CPV-Hydrogen system is achieved which can be easily implemented for any load requirement and weather conditions. Aganovic, Z.

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Beeler 1 H. Tran 2 H. Banks 3 1. Personalised recommendations. Cite article How to cite? ENW EndNote. Buy options.