Energy Storage - Module 02 PDF

Master of Engineering Program in Sustainable and Renewable Energy www.kfupm.edu.sa/MEG-SEN Electrical Engineering Department Energy Storage Systems: Comparative Ratings and Properties By: Dr. Muhammad Khalid  Obj...

Master of Engineering Program in Sustainable and Renewable Energy www.kfupm.edu.sa/MEG-SEN Electrical Engineering Department Energy Storage Systems: Comparative Ratings and Properties By: Dr. Muhammad Khalid  Objectives § To introduce the students to the definitions of basic System Ratings § To get acquainted with Ragone Charts and to understand the theory and application of Ragone Charts for various Energy Storage systems § To understand how to determine major system ratings and parameters using practical examples KFUPM - SEN Program 2 www.kfupm.edu.sa/MEG-SEN  Lecture Outline § System Ratings, Energy Density, Power Density and Specific Power § Ragone Chart § Theory of Ragone Plots § Ragone Plot of a Battery § Ragone Plot of a Capacitor § Case of Superconductive Magnetic Energy Storage § Typical Efficiencies, Lifetime and Costs § Exercise 1 with Solution: Normal and Fast Charge of Batteries in EVs § Exercise 2 with Solution: Kinetic Energy Recovery System 3 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  SYSTEM RATINGS § To choose the right storage design solution in relation to a given application. § A comparative evaluation of the possible capacity and performance of the storage device is important. § In this regard, the two most important ratings are: § Power Range § Energy Capacity w.r.t. System Autonomy 4 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  SYSTEM RATINGS § The horizontal axis represents the Power Range, represented in six decades, starting from the 1kW level up to the GW level. § The vertical axis of the figure illustrates the System Autonomy, in powers of 10 h. KFUPM - SEN Program 5 www.kfupm.edu.sa/MEG-SEN  SYSTEM RATINGS § The product of the power multiplied by the time gives the Energy Capacity. § This parameter corresponds to the surface delimited by the horizontal and vertical lines of the represented values in the diagram. 6 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  SYSTEM RATINGS § The product of the power multiplied by the time gives the energy capacity. § This parameter corresponds to the surface delimited by the horizontal and vertical lines of the represented values in the diagram. 7 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  SYSTEM RATINGS § The conventional technologies considering real systems are represented in the lower half with a possible autonomy of up to tens of hours. § These include Flywheels, Li-Ion and Lead-acid batteries etc. 8 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  SYSTEM RATINGS § For long-term storage, the so-called seasonal storage with up to 103 h autonomy. § Example: Transformation from solar power to hydrogen, defined over 3 months (100 days). 9 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  ENERGY DENSITY § On the vertical axis, the Weight energy density is indicated. § The symbol used for the weight energy density is 𝒆𝐦 [𝐖𝐡/𝐤𝐠] , generally indicated in 𝐖𝐡/𝐤𝐠, or in 𝐤𝐖𝐡/𝐭𝐨𝐧. 10 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  ENERGY DENSITY § The horizontal axis shows the Volume energy density. § The symbol used for the volume energy density is 𝒆𝐯 [𝐖𝐡/𝐝𝐦𝟑 ]. § This parameter is indicated in 𝐤𝐖𝐡/𝐦𝟑 , or in 𝐖𝐡/𝐝𝐦𝟑. 11 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  ENERGY DENSITY § The parameters on energy density are important with regard to the choice of technology for a given application. § Mobile applications are the most concerned by the Weight energy density. § In this context, an extreme case of application is the “Solarimpulse” project. § It uses modern high- performance batteries in order to be able to fly overnight with energy accumulated during the day by photovoltaic (PV) cells placed on the airplane wings. 12 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  POWER DENSITY AND SPECIFIC POWER § To compare storage devices, their power capability can be quantified via power density or specific power. Power Density § The power density is the amount of power (time rate of energy transfer) per unit volume. It is also called the volume power density. § The symbol used for the power density is 𝒑𝐯 [𝐖/𝐝𝐦𝟑 ]. It is expressed in 𝐖 /𝐝𝐦𝟑 , 𝐤𝐖/𝐦𝟑 , or rarely, 𝐖/𝐦𝟑. Specific Power § The power-to-weight ratio or specific power is the power generated by a source divided by the mass. § The symbol used for the power-to-weight ratio is 𝒑𝐦 [𝐖/𝐤𝐠]. This parameter is given in 𝐖/𝐤𝐠 or in 𝐤𝐖/𝐭𝐨𝐧, or sometimes in 𝐤𝐖/𝐤𝐠 (for powerful devices such as supercapacitors or thermal generators). 13 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  RAGONE CHART § The Ragone chart is used for performance comparison of various energy storage devices (ESDs). § The represented values on a Ragone chart are: Specific energy or weight energy density (in 𝐖𝐡/𝐤𝐠) 𝒆𝐦 versus Specific power or power-to- weight ratio (in 𝐖/𝐤𝐠) 𝒑𝐦 § The axes of a Ragone chart are logarithmic, which allow comparing the performance of very different devices (e.g., extremely high and extremely low power). 14 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  THEORY OF RAGONE PLOTS You may recall… § The energy efficiency of a storage device is related to the different losses. § Charging and discharging losses as well as the self-discharge losses influence directly the round-trip efficiency. § As a consequence, the amount of energy that can really be recovered from a fully charged storage device has to be defined depending on the instantaneous power of the energy transfer. § This principle of interdependency between the energy density and the power density is described by “The Theory of Ragone plots”. 15 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  THEORY OF RAGONE PLOTS § In this regard, a general circuit is associated with Ragone plots. § The Energy Storage Device (ESD) feeds a load with constant power P. § The ESD contains elements for energy storage. § Due to constant power, energy supply occurs only for a finite time 𝑡$%& (𝑃). § The energy available for the load 𝐸, depending on the power 𝑃, defines a Ragone plot. 16 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  THEORY OF RAGONE PLOTS § Consider the general circuit shown in Figure, the ESD may consist of a voltage source, 𝑉(𝑄), depending on the stored charge 𝑄, an internal resistor 𝑅, and an internal inductance 𝐿. § Note that this ESD can describe many kinds of electric power sources. § The ESD is connected to a load that draws a constant power 𝑃 ≥ 0. § Such a load can be realized with an electronically controlled power converter feeding an external user. § The current I and voltage U at the load are then related nonlinearly by 𝑼 = 𝑷/𝑰. 17 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  THEORY OF RAGONE PLOTS Provided reasonable initial conditions are given, the electrical dynamics is governed by the following ordinary differential equation: (3.1) where the dot indicates differentiation with respect to time. This equation applies not only to electrical ESD but covers many kinds of physical systems (mechanical, hydraulic, etc.). 18 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  THEORY OF RAGONE PLOTS Without making reference to a specific physical interpretation of Relation (3.1), the Ragone curve can be defined as follows: § At time 𝑡 = 0, the device contains the stored energy (3.2) § For 𝑡 > 0, the load draws a constant power 𝑃, such that 𝑄(𝑡) satisfies Relation (3.1). § It is clear that for finite 𝐸' and 𝑃, the ESD is able to supply this power only for a finite time, say 𝑡$%& (𝑃). 19 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  THEORY OF RAGONE PLOTS § A criterion is given either by when the storage device is cleared or when the ESD is no longer able to deliver the required amount of power. § Since the power is time independent, the available energy is (3.3) The curve 𝐸(𝑃) versus 𝑃 corresponds to the Ragone plot. 20 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Ragone Plot of a Battery § First, and regarding the model leading to the Relation (3.1), we assume the condition 𝐿 = 0. § Then, the ideal battery with a capacity of 𝑄' is characterized by a constant cell voltage: § 𝑉 = 𝑈' , if 𝑄' ≥ 𝑄 > 0 § and 𝑉 = 0, if 𝑄 = 0. § In a first step, the leakage resistor 𝑅( is neglected. Then Relation (3.1) reads: where § 𝑈 is the terminal voltage § 𝐼 = 𝑄̇ is the current 21 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Ragone Plot of a Battery § The solutions of the quadratic equation are as follows: (3.4) § At the limit 𝑃 → 0, the two branches correspond to a discharge current: § For the ideal battery, the constant power sink can also be parametrized by a constant load resistance 𝑅)*+,. § The two limits belong then to 𝑅)*+, → 0 (short circuit) and 𝑅)*+, → ∞ (open circuit), respectively. § Clearly, in the context of the Ragone plot, we are interested in the latter limit, such that we have to take the branch with the minus sign, 𝐼 = 𝐼- in Equation (3.2). 22 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Ragone Plot of a Battery § Now the battery is empty at time 𝑡$%& = 𝑄' /𝐼, § where the initial charge 𝑄' is related to the initial energy 𝐸' = 𝑄' 𝑈'. § It is now easy to include the presence of an ohmic leakage current into the discussion. § The leakage resistance 𝑅( increases the discharge current I by 𝑈' /𝑅(. § The energy being available for the load becomes (3.5) § Equation (3.5) corresponds to the Ragone curve of the ideal battery. In the presence of leakage, 𝐸. 0 = 0. § For the extracted energy, there exists a maximum at 23 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Ragone Plot of a Battery § Without leakage 𝑅/𝑅( → 0, the maximum energy is available for vanishing low power 𝐸. 𝑃 → 0 = 𝐸'. § From Equation (3.5), one concludes that there is a maximum power, 𝑃/+0 1 = 𝑈' /4𝑅, associated with an energy 𝐸' /2 (a small correction due to leakage is neglected). § This point is the endpoint of the Ragone curve of the ideal battery, where only half of the energy is available, while the other half is lost at the internal resistance. § Finally, the expression of the Ragone plot is given in the dimensionless units using: (3.6) 24 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Ragone Plot of a Battery Ragone curves according to Equation 3.5, with and without leakage, are shown in the plot on the right for the ideal battery. The branch belonging to 𝐼$ is plotted by the dashed curve. 25 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Ragone Plot of a Capacitor § In the case of an ideal electric capacitor (see Figure below), an ordinary differential equation (ODE) rather than an algebraic equation has to be solved. § The electric potential depends linearly on the charge via a capacitance 𝐶: § According to the contemporary relative complex calculations, the Ragone curve of a capacitor can be expressed by (3.7) (3.8) 26 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Ragone Plot of a Capacitor § Where in Equation (3.8) the initial capacitor voltage 𝑈2,' is related to the total energy by 𝐸' : § In the dimensionless units (3.9) § and § The Ragone curve reads (3.10) 27 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Ragone Plot of a Capacitor The Ragone curve of the capacitor is given below and represented in the following Figure: 28 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN Ragone Plot of Superconductive Magnetic Energy Storage § The normalized Ragone curves for inductive ESDs with Coulomb (C), Stokes (S), and Newton (N) friction are given in the Figure below. § The dashed double-dotted curve corresponds to an SMES with an ohmic bypass (4𝑅/𝑅. = 0.001). § This resistance 𝑅. is used for the modeling of the losses of all freewheeling paths, with a dominant contribution of the freewheeling elements of the power electronic converter 29 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  TYPICAL EFFICIENCIES, LIFETIME, AND COSTS § The efficiencies and lifetimes of different storage technologies are shown below. § These parameters are of high importance, in the context of Energy Economy. 30 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  TYPICAL EFFICIENCIES, LIFETIME, AND COSTS § Classical as well as modern batteries show very good energy efficiencies. § But they suffer from limited life cycles or lifetimes in the range of only several hundreds to several thousands of cycles. § This is a limiting factor in the domain of renewable energy sources. 31 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  TYPICAL EFFICIENCIES, LIFETIME, AND COSTS § On the right side, technologies with higher numbers of cycles are represented. § They generally belong to the category of solutions based on reversible physics. 32 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  TYPICAL EFFICIENCIES, LIFETIME, AND COSTS § The capital costs related to different storage solutions are shown in the chart. § This representation is related to the time and evolution of the costs of the technologies. § Especially the costs of new techniques must be periodically reevaluated. 33 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  TYPICAL EFFICIENCIES, LIFETIME, AND COSTS The criteria for selection of a given technology must be evaluated together with the technical performance criteria: § Lifetime of ESD § Efficiency § Context of utilization Hence a more realistic model for costs of the storage infrastructure is given as: 2+4$5+)/7%89:; 34 Real costs = (3.17) www.kfupm.edu.sa/MEG-SEN KFUPM - SEN Program ($&85$/8.7&=$>$8%>; EXERCISE 1: NORMAL AND FAST CHARGE OF BATTERIES IN EVs - THE QUESTION OF ENERGY EFFICIENCY § Modern batteries claim high C-rates up to factors 8 (short-term 15), which could make possible fast charge in the electric vehicle (EV) applications. § A system is studied where the energy can be collected from PV panels and pre- stored during the day. § The energy transfer from the local battery to the vehicle battery at the end of the day can then be realized in a longer or shorter time. 35 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: NORMAL AND FAST CHARGE OF BATTERIES IN EVs - THE QUESTION OF ENERGY EFFICIENCY § Even if no PV panels are used, the pre-charge of the local battery is done from grid electricity. § Then the role of that local battery will be to serve as a buffer, avoiding the high power solicitation from the grid during the fast charge (high power) of the EV battery. § The batteries present, however, not negligible internal resistance, and the energy transfer is affected by losses. 36 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: GIVEN TECHNICAL PARAMETERS Local Battery § The local battery is realized with 135 elements of 3.7 V and 0.7 mΩ internal resistance. § No-load voltage of the local battery: 500 V. § The local battery energy capacity is equal to 25 kWh. § From the nominal capacity of the elements (50 Ah) the rated current is defined as 50 A, corresponding to a C-factor equal to 1 (under C = 1 conditions, the charging time is equal to 1 h). 37 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: GIVEN TECHNICAL PARAMETERS Car Battery § The car battery is realized with 108 elements of 3.7 V and 0.7 mΩ internal resistance (identical elements as for the local battery). § No-load voltage of the car battery: 400 V. Converter Losses The converter losses are calculated through the conduction loss of the silicon devices with a forward voltage of the devices (transistors and diodes) equal to 1.5 V. 38 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: GIVEN TECHNICAL PARAMETERS PV Panels § The PV panel surface is designed according a charging time of the local battery within 7 h, from SOC 20% to full charge (SOC = 100%). § The required panel surface must be calculated for the following conditions: § ε = 800 W/m2 (mean value) § ηcells = 10% 39 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: GIVEN TECHNICAL PARAMETERS Structure of the System, Converters, and Cascaded Conversions The electric scheme of the system with the different converters should be drawn. a. Slow charge (7 h) § The current in both the PV panels and the local battery should be “non- discontinuous.” § It is smoothed with inductors: 𝐿 = 9.15 mH, 𝑅( = 0.2 Ω b. Fast energy transfer from the local battery to the car battery (C-rate = 8). § In order to reduce costs, there is only one converter for both batteries (step- down converter). § The current in the car battery is smoothed with an inductor: 𝐿 = 9.15 mH, 𝑅( = 0.32 Ω 40 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: REQUIRED TECHNICAL PARAMETERS Energy Efficiency a. Calculate the energy efficiency of a charge from the PV panels (slow charge, 7h). § For this case (a), there is a step-up converter cascaded with a step-down converter. § Between the two converters, a constant DC voltage link is formed via a buffer capacitor. § The energy efficiency is calculated on the base of the different power losses (converters, smoothing inductors, internal losses of the battery). b. Calculate the energy efficiency of a charge of the car battery (from the local battery, case b), for different charging times (using the C-rates of 2, 4, 6, 8, 10, 12). The goal of this exercise is: § To set in evidence the importance of the different losses. § To show what components have the most influence on the efficiency. § To show how the losses are depending on the charging speed. 41 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Model of the Local Battery The local battery can be modeled through the equivalent scheme shown. § The battery no-load voltage is § The internal resistance is § The battery energy capacity is 42 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Model of the Car Battery The Car battery can be modeled through the equivalent scheme shown. § The battery no-load voltage is § The internal resistance is § The battery energy capacity is 43 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION PV Panels § The slow charge (7 h) of 80% of the (local) battery capacity defines the charging power: § The solar (irradiance) power is consequently § For a simplified design of the PV generator, the supposition is made that the solar irradiance is of a constant average value of 800 W/m2 during 7 h. § The PV panel surface becomes 44 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Charging in 7h § The charging current is calculated as (80% of battery capacity in 7 h): § In the system represented in Figure below, the power produced by the PV panels is transferred to the intermediate DC circuit with the help of the boost converter. § This converter assumes the function of the adaptation of the voltage of the panels to a constant DC voltage. In addition, this converter allows the optimal operation of the PV panels at their point of maximum power (MPPT). Scheme of the charging system 45 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Charging in 7h § The characteristic curves of the PV panels are represented on the right. § The voltage of the intermediate DC circuit is also represented (𝑈DC = 550 V). § This value allows the boost converter to be operated with any value of the voltage of the PV panels. § The represented MPP point corresponds to maximum of power under a solar irradiance of 𝜀 = 1 and a temperature 𝜃 = 0°. Scheme of the charging system 46 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Charging in 7h § From the intermediate circuit, the power is transferred to the local battery using the buck converter. § This converter assumes the transfer of power under constant current control. § The use of the cascade of a boost and of a buck converter implies a slightly reduced energy efficiency due to the double conversion. § But the main advantage is that the current at both the input and the output sides is non-discontinuous. Scheme of the charging system 47 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Charging in 7h § The charging system with buck and boost converters is affected by power losses in the following elements (simplified estimation): § Ohmic losses in the inductors § Conduction losses in the power semiconductors of the boost and buck converters § Ohmic losses in the battery Scheme of the charging system 48 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Charging in 7h § For the estimation of the losses, it is considered that the PV panels are operated at a voltage level corresponding approximately to the voltage level of the local battery. § As a consequence, one can suppose the input current of the boost converter being identical to the output current of the buck converter. Scheme of the charging system 49 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Charging in 7h The losses in the inductor of the boost converter are calculated as follows: The losses in the buck inductor are calculated as follows: For the conduction losses in the converters, Scheme of the charging system 50 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Charging in 7h The ohmic losses in the battery are given by The total transfer losses are then The efficiency of the charging process is further Scheme of the charging system 51 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Fast Charge from the Buffer It is assumed that the car battery as well as the buffer (local) battery can be overloaded with a factor of 8C. The car battery is then For the fast transfer from the local battery to car battery, the following scheme is chosen. The scheme uses a single buck converter on the basis of economic considerations. Scheme for the fast charge from the buffer battery 52 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Fast Charge from the Buffer To estimate the energy efficiency of the fast charge, the following elements are considered: § Ohmic losses in the local battery § Ohmic losses in the car battery § Conduction losses in the power semiconductors The ohmic losses in the inductor are neglected. Scheme for the fast charge from the buffer battery 53 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Fast Charge from the Buffer For the calculation of the losses in the local battery, its current must be calculated. This can be done using the equivalent circuit scheme of the fast charging as shown below. This current depends on the duty cycle of the buck converter corresponding to the ratio of the input to the output voltages: Equivalent scheme of the fast charge 54 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Fast Charge from the Buffer The scheme of Figure below can be used as follows: Equivalent scheme of the fast charge 55 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Fast Charge from the Buffer with the numerical values The second solution of the quadratic equation corresponds to a value of D = 15, which is incompatible with the normal operation of a buck converter. It must be ignored. Equivalent scheme of the fast charge 56 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Fast Charge from the Buffer The current in the local battery is And the losses in the local battery: The losses in the car battery: Equivalent scheme of the fast charge 57 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Fast Charge from the Buffer The conduction losses in the semiconductors: The total losses related to the fast charge are consequently Equivalent scheme of the fast charge 58 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Transferred Power The power related to the fast charge is calculated. This value corresponds to the power that is really accumulated in the car battery: Finally, the efficiency of the fast charge is given by Equivalent scheme of the fast charge 59 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 1: SOLUTION Transferred Power The value of efficiency corresponds to a charging current of 400 A. With this value of current, the car battery is charged within a time equal to Efficiency as a function of the battery charging time Equivalent scheme of the fast charge 60 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM § The kinetic energy recovery system (KERS) is a power assistance system based on the recovery of a moving vehicle’s kinetic energy under braking. § The recovered energy is stored in a reservoir for later reuse under acceleration. § Such systems are developed for race cars based on different storage technologies. 61 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM § In this study, a supercapacitor-based storage system was chosen (e.g. of such system is Formula S2000). § It makes possible the recovery of successive small amounts of braking energy before allowing the driver to benefit from an additional acceleration power through a function called “push-to-pass.” 62 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM § The profile of the power recovered into the storage device is represented in the top-right Figure, together with the typical power impulse reused for acceleration. § The voltage of the supercapacitors USC is also represented. § The power profile shows braking recovery impulses of 10 kW followed by an acceleration power of −30 kW. § The duration of the additional 63 acceleration is specified to 6 s. KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM The objective of the exercise is § To evaluate the energy efficiency of the described design using supercapacitive storage for its discharge. § To compare the result with another design using a Li-ion battery. 64 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 Calculate the maximum and minimum energy efficiency of the described solution using supercapacitors. § The maximum efficiency corresponds to the case where the supercapacitors are fully charged. § The minimum to the case where the supercapacitor voltage is the lowest and where simultaneously the discharge current is the highest when the discharge occurs under constant power. Technical data: § Supercapacitors: Maxwell, 𝐶 = 310 F, 𝑅$ = 0.4 mΩ, 𝑈 = 2.7 V § Acceleration power (boost power): 30 kW § Energy capacity of the storage device: 𝐸 = 180,000 J for a minimum voltage of 50% (selected for an additional power of 30 kW during 6 s). 65 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 With the goal to illustrate the influence of the power level on the efficiency of the discharge, § Repeat the calculation of the minimum and maximum efficiency for discharge powers of 15, 6, and 3 kW. § The values of the efficiency can now be represented graphically in an MRR (logarithmic scale for the power level). § For the different power levels, the different values of the efficiency can be represented by vertical segments illustrating the domain between the minimum and maximum values. § For the logarithmic scale: log10 (2) ~ = 0.3, log10 (5) ~ = 0.7 66 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 SOLUTION: Design with Supercapacitors The energy stored in a supercapacitor charged at its maximum voltage is calculated as follows: The remaining amount of energy after discharge down to 50% of the voltage is The extracted amount of energy becomes The number of supercapacitors to be used for a total capacity of 180 kJ is then The maximum voltage of the storage device (all elements connected in series) becomes 67 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 SOLUTION: Design with Supercapacitors For a power delivery of 30 kW, the current in the supercapacitors is At the end of the discharge with constant power, the current takes the value of For the calculation of the efficiency, the following relation is used: The voltage drop on the internal resistance of the supercapacitors must be calculated. 68 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 SOLUTION: Design with Supercapacitors For the whole storage device (213 elements in series) and The corresponding efficiencies are then 69 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 SOLUTION: Design with Supercapacitors For a discharge at reduced power, only the minimal value of the efficiency is calculated. It has to be evaluated at the lower limit of the supercapacitor’s voltage after discharge. The extracted energy after a 15 kW impulse during 6 s is leading to the state of energy of one element of the corresponding voltage of the elements being 70 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 SOLUTION: Design with Supercapacitors At this point, the discharge current is leading to an efficiency of The efficiency is recalculated for the lowest values of the power (6 and 3 kW) and is represented on the right. 71 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 SOLUTION: Design with Supercapacitors The efficiency is recalculated for the lowest values of the power (6 and 3 kW) and is represented in the plot on the right. The plot shows that the design of the storage device on the base of supercapacitors presents an MRR where the efficiency is of high value (above 96%) within a full decade of the power level of the discharge, between 10% and 100% of the nominal power. 72 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 2 Calculate the energy efficiency of a storage device realized with a Li-ion battery. Technical data: The design of the storage device must especially take into account that the Li-ion battery elements have a limited discharge current. This will lead to an oversize of the energy capacity. Represent the properties of this storage device (Li-ion) in an MRR (P = 30, 15, 6, 3 kW). 73 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 2 SOLUTION: Design with a Li-ion Battery Parameters of the battery element The energy content of such an element is For the 30 kW/6 s discharge capacity, the number of required elements would be with a voltage of the whole battery of the corresponding current of the 30 kW discharge being This value of current is around 10 times the admissible battery current! 74 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 2 SOLUTION: Design with a Li-ion Battery The design of the battery pack must be oversized. In order to reduce the current to an acceptable value, the number of elements is multiplied by 10, leading to The efficiency of the discharge at 30 kW becomes The calculations for the current and efficiency at reduced power give 75 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 2 SOLUTION: Design with a Li-ion Battery § The values of the efficiency are represented in the diagram. § In opposition to the properties of the supercapacitor-based design, where the efficiency is over 96% in the whole range of operation (power). § The design with the Li-ion battery presents problematic energy efficiency values for the upper range of the operation power (0.6 at rated power). 76 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN EXERCISE 2: KINETIC ENERGY RECOVERY SYSTEM – PART 1 & PART 2 DESIGN COMPARISON Supercapacitor based design Li-ion Battery based design 77 KFUPM - SEN Program www.kfupm.edu.sa/MEG-SEN  Thank you! King Fahd University of Petroleum & Minerals Master of Engineering Program in Sustainable and Renewable Energy www.kfupm.edu.sa/MEG-SEN  Q&A King Fahd University of Petroleum & Minerals Master of Engineering Program in Sustainable and Renewable Energy www.kfupm.edu.sa/MEG-SEN