Outline. Vehicle Propulsion Systems Lecture 6. Hybrid Electrical Vehicles Serial. Hybrid Electrical Vehicles Parallel

Transcription

1 Vehicle Propulsion Systems Lecture 6 Non Electric Hybri Propulsion Systems Lars Eriksson Associate Professor (Docent) Vehicular Systems Linköping University November 8, Pneumatic Hybri Engine Systems Case stuies / 48 3 / 48 Hybri Electrical Vehicles Parallel Two parallel energy paths One state in QSS framework, state of charge Hybri Electrical Vehicles Serial Two paths working in parallel Decouple through the battery Two states in QSS framework, state of charge & Engine spee 4 / 48 5 / 48 Optimization, Optimal Control, Dynamic Programming What gear ratios give the lowest fuel consumption for a given rivingcycle? Problem presente in appenix 8. Optimal Control Problem Motivation Car with gas peal u(t) as control input: How to rive from A to B on a given time with minimum fuel consumption? Infinite imensional ecision variable u(t). Cost function t f ṁf (t)t Constraints: Moel of the car (the vehicle motion equation) Problem characteristics Countable number of free variables, i g,j, j [, 5] A computable cost, m f ( ) A computable set of constraints, moel an cycle The formulate problem min i g,j, j [,5] s.t. m f (i g,, i g,, i g,3, i g,4, i g,5 ) moel an cycle is fulfille 6 / 48 m v t t v(t) = F t(v(t), u(t)) (F a (v(t)) + F r (v(t)) + F g (x(t))) x(t) = v(t) ṁ f = f (v(t), u(t)) Starting point x() = A En point x(tf ) = B Spee limits v(t) g(x(t) Limite control action u(t) 7 / 48 General problem formulation Performance inex J(u) = φ(x(t b ), t b ) + System moel (constraints) State an control constraints tb t a L(x(t), u(t), t)t t x = f (x(t), u(t), t), x(t a) = x a u(t) U(t) x(t) X(t) 8 / 48 Dynamic programming Problem Formulation Optimal control problem min J(u) = φ(x(t b ), t b ) + s.t. x = f (x(t), u(t), t) t x(t a ) = x a u(t) U(t) x(t) X(t) tb t a L(x(t), u(t), t)t x(t), u(t) functions on t [t a, t b ] Search an approximation to the solution by iscretizing the state space x(t) an maybe the control signal u(t) in both amplitue an time. The result is a combinatorial (network) problem 9 / 48

2 Deterministic Dynamic Programming Basic algorithm N J(x ) = g N (x N ) + g k (x k, u k ) k= x k+ = f k (x k, u k ) Algorithm iea: Start at the en an procee backwars in time to evaluate the optimal cost-to-go an the corresponing control signal. x Deterministic Dynamic Programming Basic Algorithm Graphical illustration of the solution proceure x 3 3 k = N N t 4 JN(xN) ta tb k = N N t ta tb / 48 / 48 Arc Cost Calculations Parallel Hybri Example There are two ways for calculating the arc costs Calculate the exact control signal an cost for each arc. Quasi-static approach Make a gri over the control signal an interpolate the cost for each arc. Forwar calculation approach Matlab implementation it is important to utilize matrix calculations Calculate the whole bunle of arcs in one step A bounary an constraint checks Fuel-optimal torque split factor u(soc, t) = Te motor T gearbox ECE cycle Constraints SOC(t = t f ).6, SOC [.5,.7] D an 3D gri examples on whiteboar / 48 3 / 48 Pneumatic Hybri Engine Systems Case stuies Examples of Systems 4 / 48 5 / 48 F FIA allowe the usage of 6 kw, KERS (Kinetic Energy Recovery System) in F in 9. Technologies: Flywheel Batteries Super-Caps Basic Principles for Hybri Systems Kinetic energy recovery Use best points Duty cycle. Run engine (fuel converter) at its optimal point. Shut-off the engine. Engine Torque [Nm] Engine efficiency map Engine Spee [rpm] 6 / 48 7 / 48

3 Power an Energy Densities Asymptotic power an energy ensity The Principle Pneumatic Hybri Engine Systems Case stuies 8 / 48 9 / 48 Causality for a hybri-inertial propulsion system Flywheel accumulator Energy store (Θ f = J f ): E f = Θ f ωf Wheel inertia Θ f = ρ b r π r r =... = π Area ρ 4 6 ( q4 ) / 48 / 48 Flywheel accumulator Design principle Quasistatic of FW Accumulators Energy store (SOC): E f = Θ f ωf Wheel inertia Θ f = ρ b r π r r =... = π Area ρ 4 6 ( q4 ) Wheel Mass m f = π ρ b ( q ) Energy to mass ratio Flywheel spee (SOC) P (t) power out, P l (t) power loss E f = m f 6 ( + q )ωf = u 4 ( + q ) Θ f ω (t) t ω (t) = P (t) P l (t) / 48 3 / 48 Power losses as a function of spee Air resistance an bearing losses (CVT) 4 / 48 5 / 48

4 CVT Principle CVT Transmission (gear) ratio ν, spees an transmitte torques ω (t) =ν(t) ω (t) T t (t) =ν (T t (t) T l (t)) Newtons secon law for the two pulleys Θ t ω (t) =T (t) T t (t) Θ t ω (t) =T (t) T t (t) System of equations give T (t) = T l (t) + T (t) ν(t) + Θ CVT (t) ν(t) t ω (t) + Θ t ν(t) ω (t) 6 / 48 7 / 48 CVT Transmission (gear) ratio ν, spees an transmitte torques ω (t) =ν(t) ω (t) T t (t) =ν (T t (t) T l (t)) Efficiencies for a Push-Belt CVT An alternative to moel the losses, is to use an efficiency efinition. 8 / 48 9 / 48 Examples of Systems Pneumatic Hybri Engine Systems Case stuies 3 / 48 3 / 48 Causality for a hybri-hyraulic propulsion system of a Hyraulic Accumulator principle Energy balance m g c v t θ g(t) = p t V g(t) h A w (θ g (t) θ w ) Mass balance (=volume for incompressible flui) Ieal gas law t V g(t) = Q (t) p g (t) = m g R g θ g (t) V g (t) Power generation P (t) = p (t) Q (t) 3 / / 48

5 Moel Simplification Simplifications mae in thermoynamic equations to get a simple state equation. Assuming steay state conitions. Eliminating θ g an the volume change gives p (t) = h A w θ w m g R g V g (t) h A w + m g R g Q (t) Combining this with the power output gives Q (t) = V g(t) m g h A w P (t) R g θ w h A w R g P (t) Integrating Q (t) gives V g as the state in the moel. of the hyraulic systems efficiency, see the book. A etail for the assignment This simplification can give problems in the simulation if parameter values are off. (Division by zero.) 34 / 48 Pneumatic Hybri Engine Systems Case stuies 35 / 48 Hyraulic Pumps of Hyraulic Motors Efficiency moeling P (t) P (t) = η hm (ω (t), T (t)), P (t) > P (t) =P (t) η hm (ω (t), T (t)), P (t) < Willans line moeling, escribing the loss P (t) = P (t) + P e Physical moeling Wilson s approach provie in the book. 36 / / 48 Pneumatic Hybri Engine Systems Case stuies Pneumatic Hybri Engine System 38 / / 48 Conventional SI Engine Compression an expansion moel p(t) = c v(t) γ log(p(t)) = log(c) γ log(v(t)) gives lines in the log-log iagram version of the pv-iagram Super Charge Moe 4 / 48 4 / 48

6 Uner Charge Moe Pneumatic Brake System 4 / / 48 Case Stuy 3: ICE an Flywheel Powertrain Pneumatic Hybri Engine Systems Case stuies Control of a ICE an Flywheel Powertrain Switching on an off engine 44 / / 48 Problem escription Case Stuy 8: Hybri Pneumatic Engine For each constant vehicle spee fin the optimal limits for starting an stopping the engine Minimize fuel consumption Local optimization of the engine thermoynamic cycle Different moes to select between Dynamic programming of the moe selection Solve through parameter optimization Map use for control 46 / / 48