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- 1. 1 Departement of electrical engineering Option: Electrical Engineering and Control of Industrial systems Control by output state feedback of an electric vehicle with hybrid energy storage Réalisés par : - ABBAZE Abdelouahed - EL JAZOULI Mouad - OKAIL Fakhreddine - CHAKIR Ismail Encadré par : M. LJOUAD Rachid College year 2021/2022
- 2. 2 Introduction : With increasing concerns on global warming and climate change the auto mobile industry is moving towards electrification of automobiles using partial hybridization to fully electric vehicles. Apart from the advantage of more efficiency and less emissions for EVs compared to conventional combustion engine vehicles, there are numerous other advantages such as higher starting torque and easy control of power flow for electric motors. In combustion engines the starting torque is less so they require a transmission system to increase the torque The on board energy storage system (ESS) plays a very important role in knowing the performance and electric vehicles electric range. Most of the electric vehicles nowadays use Lithium ion rechargeable batteries because of their high energy density and design flexibility and some exceptional electrochemical properties exhibited by lithium. For effective operation of the electric vehicle, the ESS should possess high energy and high power densities which is not available in any single energy source. Batteries generally have higher energy density but low specific power and life cycle. Also battery efficiency reduces if the load draws very high current in case of peak demands when the battery state of charge (SOC) is low and it might lead to thermal stress in the battery. Here comes the importance of supercapacitor which has higher power density, life cycles and efficiency and a fast response on charge/discharge cycles when drawing high current, but has lower energy density. In this report we will deal with an output feedback control of an electric vehicle with hybrid energy storage with the use of an asynchronous machine, with theoretical study and simulation on matlab simulink.
- 3. 3 Function scheme of electric vehicle with hybrid energy storage: 1. Asynchronous machine: 1.1 Definition of the asynchronous motor: An induction motor or asynchronous motor is an AC electric motor in which the electric current in the rotor needed to produce torque is obtained by electromagnetic induction from the magnetic field of the stator winding. An induction motor can therefore be made without electrical connections to the rotor. An induction motor's rotor can be either wound type or squirrel-cage type. in our project we worked on the asynchronous motor squirrel-cage type. squirrel-cage type
- 4. 4 1.2 Principle of operation of the asynchronous cage machine: The pulsating stator currents create a rotating field at the so-called Synchronism speed S N and which has the same frequency as the stator current. This field passes through the rotor winding and induces "f.e.m" electromotive forces there. These f.e.m produce currents because the winding of the rotor is short-circuited. The action of the currents on the rotating field which induced them (according to Lentz's law the induced currents oppose the cause which gives rise to them) creates the couple. This motor is often called an induction machine. If the rotor is rotating at the synchronous speed NS, as fast as the rotating field, the field across each rotor coil is constant. The induced f.e.m no longer exist at the rotor therefore no more current or torque. It is therefore necessary that Nr speed of rotation of the rotor differs from NS speed of synchronism so that there is a torque hence the name of asynchronous machine. Motor operation is characterized by the relative difference between these two speeds; this is the slip g defined by: 1.3 Modeling of SIG-AC/DC converter: The model of SIG in the (α, β) coordinates system linked to the stator is given by the following equations: 𝑑Ω 𝑑𝑡 = 𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 (∅𝑟𝑎𝑖𝑠𝛽 − ∅𝑟𝛽𝑖𝑠𝛼) − 𝑇𝐿 𝐽 − 𝑇𝑠𝑒𝑐 𝐽 − 𝐹 𝐽 Ω 𝑑𝑖𝑠𝛼 𝑑𝑡 = −𝛾𝑖𝑠𝛼 + 𝑀𝑠𝑟 𝑅𝑟 𝜎𝐿𝑠 𝐿𝑟2 ∅𝑟𝑎 + 𝜌Ω 𝑀𝑠𝑟 𝜎𝐿𝑠 𝐿𝑟 ∅𝑟𝛽 + 1 𝜎 𝐿𝑠 𝑣𝑠𝛼 𝑑𝑖𝑠𝛽 𝑑𝑡 = −𝛾𝑖𝑠𝛽 + 𝑀𝑠𝑟 𝑅𝑟 𝜎𝐿𝑠 𝐿𝑟2 ∅𝑟𝛽 − 𝜌Ω 𝑀𝑠𝑟 𝜎𝐿𝑠 𝐿𝑟 ∅𝑟𝑎 + 1 𝜎 𝐿𝑠 𝑣𝑠𝛽 𝑑∅𝑟𝑎 𝑑𝑡 = − 𝑅𝑟 𝐿𝑟 ∅𝑟𝑎 − 𝜌Ω ∅𝑟𝛽 + 𝑅𝑟 𝑀𝑠𝑟 𝐿𝑟 𝑖𝑠𝛼 𝑑∅𝑟𝛽 𝑑𝑡 = − 𝑅𝑟 𝐿𝑟 ∅𝑟𝛽 + 𝜌Ω ∅𝑟𝑎 + 𝑅𝑟 𝑀𝑠𝑟 𝐿𝑟 𝑖𝑠𝛽 with isα, isβ, φrα, φrβ, Ω and TG are respectively, the stator currents, rotor fluxes, angular speed, and generator torque.
- 5. 5 The parameters γ and σ are defined by: where Rs and Rr are the stator and rotor resistances; Ls and Lr are the stator and rotor self- inductances, and Msr is the mutual inductance between the stator and the rotor windings; p is the number of pole-pair; J is the inertia of system (generator and wind turbine) and f is the viscous friction coefficient. The vsα, vsβ denote the stator voltages in (α, β) coordinates. The rectifier is featured by the fact that the stator voltages vsα, vsβ can be controlled independently. To this end, these voltages are expressed in function of the corresponding control action: with u1 and u2 are (averaged versions) of the (α,β) components of the three-phase duty ratio system (s1, s2, s3). 1.4 Extended Kalman : The extended Kalman filter is a fairly widespread method for estimating the state of a nonlinear system. Its design is based on the generalization of the nonlinear Kalman filter, using classical techniques for the linearization of nonlinear dynamics. Thus the matrices A and C are replaced by the Jacobian matrices A_J and H, and evaluated in X ̂(t) . a- theoretical study : In this part, the standard Kalman filter is applied for the estimation of the stator current along the axes (α , β) of a three-phase cage asynchronous machine. State variables: 𝑥1 = Ω , 𝑥2 = is𝛼, 𝑥3 = is𝛽 , 𝑥4= ∅𝑟𝛼 , 𝑥5= ∅𝑟𝛽 So: 𝑥1 ̇ = 𝑑Ω 𝑑𝑡 , 𝑥2 ̇ = 𝑑is𝛼 𝑑𝑡 , 𝑥3 ̇ = 𝑑is𝛽 𝑑𝑡 , 𝑥4 ̇ = 𝑑∅𝑟𝛼 𝑑𝑡 , 𝑥5 ̇ = 𝑑∅𝑟𝛽 𝑑𝑡 𝑥1 ̇ = 𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 (𝑥3𝑥4 − 𝑥4 𝑥5) − 𝑇𝐿 𝐽 − 𝑇𝑠𝑒𝑐 𝐽 − 𝐹 𝐽 𝑥1 𝑥2 ̇ = −𝛾𝑥2 + 𝑀𝑠𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟2 𝑥4 + 𝜌𝑥1 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥5 + 1 𝜎𝐿𝑠 𝑣s𝛼
- 6. 6 𝑥3 ̇ = −𝛾𝑥3 + 𝑀𝑠𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟2 𝑥5 − 𝜌𝑥1 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥4 + 1 𝜎𝐿𝑠 𝑣s𝛽 𝑥4 ̇ = − 𝑅𝑟 𝐿𝑟 𝑥4 − 𝜌𝑥1𝑥5 + 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝑥2 𝑥5 ̇ = − 𝑅𝑟 𝐿𝑟 𝑥5 + 𝜌𝑥1𝑥4 + 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝑥3 ∇fX = [ − 𝐹 𝐽 −𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 𝑥5 𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 𝑥4 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥5 −𝛾 0 − 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥4 −𝜌𝑥5 𝜌𝑥4 0 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 0 −𝛾 0 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 𝑥3 𝑀𝑠𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟2 − 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 − 𝑅𝑟 𝐿𝑟 𝜌𝑥1 −𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 𝑥5 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 𝑀𝑠𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟2 −𝜌𝑥1 − 𝑅𝑟 𝐿𝑟 ] A(𝑥) ̂ = [ − 𝐹 𝐽 −𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 𝑋5 ̂ 𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 𝑋4 ̂ 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 X5 ̂ −𝛾 0 − 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑋4 ̂ −𝜌X5 ̂ 𝜌X4 ̂ 0 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 0 −𝛾 0 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 𝑋3 ̂ 𝑀𝑠𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟2 − 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑋1 ̂ − 𝑅𝑟 𝐿𝑟 𝜌𝑋1 ̂ −𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 𝑋5 ̂ 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 X1 ̂ 𝑀𝑠𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟2 −𝜌𝑋1 ̂ − 𝑅𝑟 𝐿𝑟 ] P = AP + 𝑃𝐴𝑇 - 𝑃𝐶𝑇 𝑉−1 CP + Q The extended kalman observer applied to an asynchronous motor. 𝑃11 ̇ =- 2𝑓 𝑗 𝑃11 − 2𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥5 ̂ 𝑃12 + 2𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥4 ̂ 𝑃13 + 2𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥3 ̂ 𝑃14 − 2𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥5 ̂ 𝑃15 − 𝑃12 2 + 𝑃13 2 + 𝑄11 𝑃12 ̇ =-- 2𝑓 𝑗 𝑃12 − 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥5 ̂ 𝑃22 + 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥4 ̂ 𝑃23 + 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥3 ̂ 𝑃24 − 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥5 ̂ 𝑃25 + 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥5 ̂ 𝑃11 − 𝛾𝑃12 + 𝑀𝑆𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟 2 𝑃14 + 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 ̂ 𝑃15+𝑃12𝑃22 + 𝑃13𝑃23 𝑃13 ̇ =-- 2𝑓 𝑗 𝑃13 − 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥5 ̂ 𝑃23 + 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥4 ̂ 𝑃33 + 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥3 ̂ 𝑃34 − 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥5 ̂ 𝑃35 − 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥4 ̂ 𝑃11 − 𝛾𝑃13 + 𝑀𝑆𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟 2 𝑃15 − 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 ̂ 𝑃14+𝑃12𝑃24 + 𝑃13𝑃34 𝑃14 ̇ =-- 2𝑓 𝑗 𝑃14 − 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥5 ̂ 𝑃24 + 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥4 ̂ 𝑃34 + 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥3 ̂ 𝑃44 − 𝜌 𝑀𝑆𝑟 𝐽𝐿𝑟 𝑥5 ̂ 𝑃45 − 𝜌𝑥5 ̂ 𝑃11 + 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝑃12 − 𝑅𝑟 𝐿𝑟 𝑃14 − 𝜌𝑥1 ̂ 𝑃15+𝑃12𝑃25 + 𝑃13𝑃35 𝑃22 ̇ = +2 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥5 ̂ 𝑃12 − 2 𝛾𝑃22 + 𝑀𝑆𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟 2 𝑃24 + 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 ̂ 𝑃25 + 𝑃12 2 + 𝑃23 2 + 𝑄22 𝑃23 ̇ = 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥5 ̂ 𝑃13 − 𝛾𝑃23 + 𝑀𝑆𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟 2 𝑃34 + 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 ̂ 𝑃35 − 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥4 ̂ 𝑃12 − 𝛾𝑃23 + 𝑀𝑆𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟 2 𝑃25 − 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 ̂ 𝑃24+𝑃22𝑃23 + +𝑃23𝑃33 𝑃24 ̇ = 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥5 ̂ 𝑃14 − 𝛾𝑃24 + 𝑀𝑆𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟 2 𝑃44 + 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 ̂ 𝑃45 − 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥5 ̂ 𝑃12 + 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝑃22 − 𝑅𝑟 𝐿𝑟 𝑃24 − 𝜌𝑥1 ̂ 𝑃25+𝑃22𝑃24 + +𝑃23𝑃34
- 7. 7 𝑃25 ̇ = 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥5 ̂ 𝑃15 − 𝛾𝑃25 + 𝑀𝑆𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟 2 𝑃55 + 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 ̂ 𝑃55 + 𝜌 𝑀𝑆𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥4 ̂ 𝑃12 + 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝑃23 − 𝑅𝑟 𝐿𝑟 𝑃25 − 𝜌𝑥1 ̂ 𝑃24+𝑃22𝑃25 + +𝑃23𝑃35 𝑥1 ̂ ̇ = 𝜌 𝑀𝑠𝑟 𝐽𝐿𝑟 (𝑥4 ̂𝑥3 ̂ − 𝑥5 ̂ 𝑥2 ̂) − 𝑇𝐿 𝐽 − 𝑇𝑠𝑒𝑐 𝐽 − 𝐹 𝐽 𝑥1 ̂ +𝑃12(𝑥2 − 𝑥2 ̂) + 𝑃13(𝑥3 − 𝑥3 ̂) 𝑥2 ̂ ̇ = −𝛾𝑥2 ̂ + 𝑀𝑠𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟2 𝑥4 ̂ + 𝜌 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥1 ̂ 𝑥5 ̂ + 1 𝜎𝐿𝑠 𝑣s𝛼+𝑃22(𝑥2 − 𝑥2 ̂) + 𝑃23(𝑥3 − 𝑥3 ̂) 𝑥3 ̂ ̇ = −𝛾𝑥3 ̂ − 𝑀𝑠𝑟𝑅𝑟 𝜎𝐿𝑠𝐿𝑟2 𝑥5 ̂ − 𝜌𝑥1 ̂ 𝑀𝑠𝑟 𝜎𝐿𝑠𝐿𝑟 𝑥4 ̂ + 1 𝜎𝐿𝑠 𝑣s𝛽 + 𝑃23(𝑥2 − 𝑥2 ̂) + 𝑃33(𝑥3 − 𝑥3 ̂) 𝑥4 ̂ ̇ = − 𝑅𝑟 𝐿𝑟 𝑥4 ̂ − 𝜌𝑥4 ̂ 𝑥5 ̂ + 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝑥2 ̂ + 𝑃24(𝑥2 − 𝑥2 ̂) + 𝑃34(𝑥3 − 𝑥3 ̂) 𝑥5 ̂ ̇ = − 𝑅𝑟 𝐿𝑟 𝑥5 ̂ + 𝜌𝑥1 ̂𝑥4 ̂ + 𝑅𝑟𝑀𝑠𝑟 𝐿𝑟 𝑥3 ̂+𝑃25(𝑥2 − 𝑥2 ̂) + 𝑃35(𝑥3 − 𝑥3 ̂) b- Simulation in Matlab: Parameter of asynchronous motor
- 8. 8 Modeling and observation of asynchronous machine Park transformation:
- 9. 9 Model of asynchronous machine: Model of asynchronous machine Extended Kalman observation:
- 11. 11 2. Supercapacitor: 2.1 Definition: A supercapacitor is a high-capacity capacitor with a capacitance value much higher than other capacitors, but with lower voltage limits, that bridges the gap between electrolytic capacitors and rechargeable batteries. It typically stores 10 to 100 times more energy per unit volume or mass than electrolytic capacitors, can accept and deliver charge much faster than batteries, and tolerates many more charge and discharge cycles than rechargeable batteries. Supercapacitor 2.2 Model: The model of supercapacitor is a simple series RC model, as illustrated in figure, the supercapacitor is nothing but a simple capacitor having large electric charge storing capacity. This equation shows the voltage and current relationship of supercapacitor. Supercapacitor Model.
- 12. 12 3. Modeling of DC/AC inverter: A power inverter is a power electronic device or circuitry that changes direct current (DC) to alternating current (AC). The resulting AC frequency obtained depends on the particular device employed. Inverters do the opposite of converters which were originally large electromechanical devices converting AC to DC. The input voltage, output voltage and frequency, and overall power handling depend on the design of the specific device or circuitry. The inverter does not produce any power, the power is provided by the DC source. The three-phase electrical grid is connected to a converter which consists of 6 semiconductors (IGBTs with anti-parallel diodes for bidirectional current flow mode) displayed in three legs 1, 2 and 3. The 6 semiconductors are considered as ideal switches. Only one switch on the same leg can be conducting at the same time. Applying Kirchhoff’s laws, this subsystem is described by the following set of differential equations: where [in123] = [in1 in2 in3] T is the grid input currents vector, [en123] = [en1 en2 en3] T is the sinusoidal three-phase grid voltages (with known constant frequency ωn), io designates the input current inverter, and ki is the switch position function taking values in the discrete set {1,0}. Specifically: To simplify the three-phase representation for the synthesis of control laws, the Park transformation is invoked again:
- 13. 13 Where (End, Enq), (ind, inq) and (u3, u4) denote the averaged network voltage, current and inverter signal control, respectively in the coordinate (d,q) fixed to the rotor (Park’s transformation). The power absorbed by the DC/AC converter is given by the well-known expression Pload = iovdc. On the other hand, the power released by the network is given by Pout = [en123] T [in123] = Endind + Enqinq. Using the power conservation principle, equations (9a - 9c) become: The above inverter model rewrites as follows: - Simulation of inverter in Matlab/Simulink:
- 14. 14 Conclusion: In this work Hybrid Energy Storage System with a combination of battery and supercapacitor powering the BLDC motor in electric vehicle is proposed. The supercapacitor powering the motor initially speeds up the motor in few seconds when compared to battery with the same voltage. We have explained how an electrical vehicle work , by detailing the principal parts of the transmission wich are the moter and the control system of it , we ve mobilized by using matlab simulink the electrical asynchronousmachine the ac/dc converter , the dc dc converter and the energie storing components wich are in our case the batteryand the super capacitor. We ve lunched the simulation and we extracted some data that show how much we was close to a valid model. Also we have proposed a solution for non control with feedback . For powering the motor for longer duration, the capacity of supercapacitor has to be still higher. Therefore, a support with battery will provide high power density and supercapacitor with high energy density is the hybrid.