Hybrid reformulation based on a new hybrid Ohm s law for an electrical energy hybrid systems

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1 Hybrid reformulation based on a new hybrid Ohm s law for an electrical energy hybrid systems SANG C. LEE* Division of IoT-Robot convergence research DGIST 333, Techno jungang, Dalseong-Gun, Daegu Republic of KOREA sclee@dgist.ac.kr, (*corresponding author) DOO SEOK LEE College of Transdisciplinary DGIST 333, Techno jungang, Dalseong-Gun, Daegu Republic of KOREA dslee@dgist.ac.kr Abstract: In modern society, social and political problems are deeply connected with energy inequality, which is overcome through renewable energy sources such as solar cell, fuel cell, and wind generator, etc. However, individual devices have their own limitations due to their intrinsic properties, i.e. specific power (W/kg) and specific energy (Wh/kg). The hybridization of two or more energy sources is tremendous popularity concerned by academia and industry. In this paper, new definition of hybridization and approaching method are proposed. Firstly, hybrid system is explained with the view points of electrical, mechanical, and thermal energy systems having some examples. Secondly, a new hybrid Ohm s law is derived on the basis of graphical and mathematical explanation at the same time. Furthermore, hybrid Ohm s laws are derived respectively for the passive, semi-active, and active topologies consisting of fuel cell and battery hybridization. The modelling methodology might be applied to tackle the future application goal, such as a hybrid engine design. Key Words: Hybridization, Passive hybrid, Active hybrid, Hybrid factor, Next generation hybrid engine 1 Introduction Hybrid or hybridization means that two or more elements are combined to achieve a specific goal. So, although generally this term has been known as hybrid body or mixed two kinds of combination among diverse cases, however originally the fauna and flora is referred to as hybrid. In this paper, it can be covered beyond the original hybrid, manmade product and energy, etc. Hybrid ones around us are getting a lot of discovery. Here, the technical terms related to the hybrid phenomenon may present the following examples. Firstly, Hybridization is originally found at the bio-technology area. Hybridization between different plants and animals: If each species in different organisms genetically bonds bear a seed of hybrids. It is separated by the case mating with and without possible. Secondly, it is examined the hybrid from an IT perspective. Hybrid signal: Continuous signal and discrete signal are present at the same time. Two types of equation, i.e. differential equation and difference equation, are utilized to represent a dynamic system. Hybrid computer: Analogue computer performs mathematical calculations accurately and digital computer is to perform a logical operation. Hybrid computer combines the advantages of numerical each other. Hybrid platform: Separate platforms (i.e. telephones, radio, TV, recorder) are integrated to perform a plurality of functions on one platform. Thirdly, energy hybridization is explained as follows. Hybrid power plants: Different kinds of renewable energy sources (solar cell, fuel cell, wind generator, etc.) to produce electrical energy combined together overcome the inherent limitations by providing a reliable power system from each type. Hybrid vehicle: Hybrid vehicle with the electric motor for generating driving force is being produced in order to achieve improved fuel efficiency and performance improvement of the existing internal combustion engine cars at the same time. Those are divided into two types, i.e. parallel hybrid type and the serial hybrid type. In particular, this paper explores the hybridization of energy systems. In section 2, Energy hybridization is classified with some examples. A new hybrid ISBN:

2 Ohm s law is derived in each different topologies in section 3. The electrical hybrid engine is given as a potential application in section 5. 2 Energy hybridization Energy hybridization can be classified based on the electrical energy, mechanical energy, and thermal energy, which are shown in Figure 1, Figure 2, and Figure 3, respectively. Elements having unique characteristic can be defined by device, thus the energy from the device is different from each other devices after energy conversion. Two different energy devices can be hybridized if two conditions are matched. For the good performance after hybridization, each devices should have unique characteristics. And also the output energy type should be equal to be combined. 2.1 Electrical energy hybrid 2.2 Mechanical energy hybrid Hybrid electric vehicles will combine the mechanical torque from the internal combustion engine (ICE) and electrical torque from the electric motor to increase fuel efficiency and thrust. For this, a mechanical hybrid engine couples the torque as follows. Series hybrid : Designed to extend the range of EVs on a single charge. The ICE is solely used to generate electricity. Parallel hybrid : Designed to increase fuel efficiency of ICE and to decrease exhaust emissions. The engine provides main propulsion, and the generator works in parallel to assist the engine. Series-Parallel hybrid : Combination of series and parallel hybrid systems. The vehicle is powered by both ICE and a motor either independently or jointly. For the fuel cell, energy density is high but the power density is low. The secondary battery (or Ultracapacitor) is used as the power source adding the power density. For example, unmanned aerial robot (or Unmanned Areal Robot) require a long flight time after self take-off. However the secondary battery ensures the flight time of 30 minutes because of the weight. Also, it must be overcome the slow rate of reaction of the fuel cell to the self take-off. To this end, a combination of the secondary battery and the fuel cell can meet the 2 hours of flight time and self take-off characteristics at the same time. Figure 2: Example of a mechanical energy hybrid: hybrid electric vehicle. Figure 1: Example of an electrical energy hybrid: hybrid power supply. 2.3 Thermal energy hybrid As shown in Figure 3, the ISCC (Integrated Solar Combined Cycle) is driving the power generator by controlling the amount of fossil fuel in accordance with the sunshine condition at full capacity in optimal conditions. It may continue to produce a certain amount of electricity without sunshine in night time. That is, the thermal energy from the auxiliary heat source, such as a burner, for a stable operation of the steam turbine is designed to supplement. All the solar energy supplied can be utilized for power generation. ISBN:

3 Figure 4: Hybrid Ohm s law derived graphically and mathematically at fuel cell and battery hybridization. of the mathematical expressions that are expressed in the characteristic equation of energy element. It approaches the problem through the linearization process and non-linearity will be able to handle for improving accuracy. 3.1 Passive hybridization For a fuel cell and a secondary battery parallel interconnection, it is possible to make the relationship from the inherent properties of the two devices if hybridized as shown in Figure 4. K V = K R K I (1) Figure 3: Example of a thermal energy hybrid: hybrid power plant. 3 Hybrid modelling : Hybrid Ohm s law So far the hybrid energy devices have been made widely and utilized in a variety of applications. However, there has not been a systematic design procedure and a common methodology does not exist. Here we propose a systematic methodology to model the hybrid system for the first time. We propose a method to determine the relationship between devices and calculate the hybrid equation. In other words, at the same time we use a graph drawn by the characteristic curve where, K R = R B /R F, K V = (V B0 V L )/(V F0 V L ), and K I = I B /I F are a resistance ratio, a voltage ratio, and a current ratio between a fuel cell and a battery, respectively. It can be seen here that the hybrid device can be understood by the ratio of the specific characteristic values of the each devices. If individual devices satisfy the Ohm s law, the hybrid device also satisfies Ohm s law. By extension, the relationship of a typical hybrid combination including a secondary battery and a solar cell can be verified the same as above. 3.2 Semi-active hybridization In previous studies it conducted hybridization of the fuel cell and the secondary battery without changing internal operating status. For changing the state of charge (SoC) in the secondary battery, it induces the open circuit voltage variation as shown in equation (2). And also, controlling the operating status of the ISBN:

4 fuel cell such as relative humidity, we can have the effect on the internal resistance variation as shown in equation (3). K I (SoC) = K V(SoC) K R (2) K I (RH) = K V K R (RH) (3) D B and D F denote a duty ratio of the battery output augmented and fuel cell output augmented cases, respectively as shown in Figure 6 (a) and (b). Figure 6: Active topologies of (a) output augmented battery and a fuel cell hybrid, (b) output augmented fuel cell and a battery hybrid. Figure 5: Semi-active topologies of (a) state of charge (SoC) controlled battery and a fuel cell hybrid, (b) relative humidity (RH) controlled fuel cell and a battery hybrid. 3.3 Active hybridization The topology is called as active hybridization if we can adjust the voltage or current utilizing a power converter, where the power converters are added to each device. The role of the DC-DC converter is to transform the I-V characteristic curves of a device to proper I-V curves for an application through duty ratio control. Therefore, the voltage and internal resistance for the load are varied by the converter. In other words, the main function of the converter is to change the open circuit voltage (OCV) and internal resistance of the device at the same time. K I (D B ) = K V(D B ) (4) K R (D B ) K I (D F ) = K V(D F ) (5) K R (D F ) 4 Hybrid reformulation The derived hybrid model equations, i.e. hybrid Ohm s laws, are summarized in Table 1 and Table 2. The model equation of the battery augmented hybrid can be rewritten as follows. K V (D B ) = αd B β (6) K R (D B ) = γdb 2 (7) where, α = V B0 /(V F0 V L ), β = V L /(V F0 V L ), and γ = R B /R F, which are constant values at the given condition. The current of hybrid device can be written as a function of D B. K I (D B ) = αd B β γd 2 B = ˆα 1 D B ˆβ 1 D 2 B (8) where, ˆα = α/γ = V B0 /( ) R F /R B and ˆβ = β/γ = V L /(V F0 V L ) R F /R B. The next step will be calculating the trajectory of the function depending on the load condition. ISBN:

5 Battery controlled Fuel cell controlled Table 1: Hybrid Ohm s law equations of semi-active hybridization Resistance ratio Voltage ratio Current ratio = I B IF K R = R B R F K R (RH) = R B R F (RH) K V (SoC) = V B 0 (SoC) V L K V = V B 0 V L K I (SoC) = K V (SoC) K R K I (RH) = K V K R (RH) Battery augmented Fuel cell augmented Table 2: Hybrid Ohm s law equations of active hybridization Resistance ratio Voltage ratio Current ratio = I B IF K R (D B ) = D2 B R B R F K R (D F ) = R B DF 2 R F K V (D B ) = D BV B0 V L K I (D B ) = K V (D B ) K R (D B ) K V (D F ) = V B 0 V L D F K I (D F ) = K V (D F ) K R (D F ) On the other hand, the model equation of the fuel cell output augmented hybrid can be rewritten as follows. K V (D F ) = K R (D B ) = 1 αd F β 1 γd 2 F (9) (10) where, α = V F0 /(V B0 V L ), β = V L /(V B0 V L ), and γ = R F /R B, which are constant values at the given condition. The current of hybrid device can be written as a function of D F. K I (D F ) = γd2 F αd F β = D 2 F ˆαD F ˆβ (11) where, ˆα = α/γ = V F0 /(V B0 V L ) R B /R F and ˆβ = β/γ = V L /(V B0 V L ) R B /R F. The above equation is inverse of the battery output augmented hybrid. 5 Application goal: Fuel cell hybrid engine design On the basis of the hybrid modelling methodology studied so far, the fuel cell module and the electric motor integration modelling might be tried. This integration can perform the same function as the device for generating the mechanical power from the fuel, which is same as a conventional internal combustion engine. In other words, optimal configuration among fuel cells, power converters, and electric motors makes a new generation of environmentally friendly electric propulsion engine. Combining the mechanical force to the mechanical force is clearly different from the fuel cell-motor hybrid engine. This is called a hybrid engine combining electric power. Figure 7: Schematic of a fuel cell powered electric engine combined with converter and electric motor. Acknowledgements: This work was supported by the DGIST R&D Program of the Ministry of Education, Science and Technology of Korea(16-IT-05). References: [1] Sang C. Lee, et al., Graphical and mathematical analysis of fuel cell/battery passive hybridization with K factors, Applied Energy 114, 2014, pp [2] D. Cericola and R. Kotz, Hybridization of rechargeable batteries and electrochemical capacitors: Principles and limits, Electrochimica Acta 72, 2012, pp [3] A. Kuperman and I. Aharon, Batteryultracapacitor hybrids for pulsed current loads: A review, Renewable and Sustainable Energy Reviews 15, 2011, pp [4] S.N. Motapon et al., A comparative study of energy management schemes for a fuel cell hybrid emergency power system of more-electric aircraft, IEEE Transactions on Industrial Electronics 61, 2014, pp ISBN:

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