Abstract:
Equipment and methods for estimating and regulating the state of charge (SOC) of a battery in a hybrid fuel cell-battery system for use in a moving vehicle. The SOC is continuously estimated and the fuel cell power is regulated to maintain the SOC at a level such that the battery has enough stored energy to operate motors used in the vehicle, and enough spare capacity to accept regenerative energy from these motors during further operations.

Description:
This application claims priority to U.S. Provisional Application No. 61/253,013, filed Oct. 19, 2009, and U.S. Provisional Application No. 61/259,813, filed Nov. 10, 2009, both of which are incorporated by reference in their entirety. 
    
    
     Electric vehicles powered by batteries, such as forklift trucks and golf carts, are frequently used in manufacturing, wholesale and retail operations for transporting and/or lifting of people and products. However, these electric vehicles can have shortcomings. For example, a forklift truck must be recharged every six to eight hours, requiring warehouse space for spare batteries and charging equipment. Moreover, the performance of the vehicle progressively decreases as the batteries get depleted. 
     In contrast, fuel cell powered electric vehicles can be quickly refilled, maintain their performance over a shift, and allow cost savings by eliminating the need to reserve valuable warehouse space for battery storage and charging equipment. The hybrid fuel cell system described herein can address at least one of these benefits. 
     A hybrid fuel cell system used herein refers to a system comprising a fuel cell and a battery. The term “battery” used herein broadly refers to a device that can repeatedly store and dispense electric power, including but not limited to chemical batteries (e.g., a lead-acid battery, a lithium ion battery, a nickel-metal hydride battery, a nickel-cadmium battery) and ultra capacitors. 
     In the hybrid power system, the fuel cell supplies power to the motors and to the battery during normal operation. The battery buffers electric demand, supplementing the fuel cell power at peak load and absorbing regenerative energy. For fork lifts, for example, the management of the state-of-charge (“SOC”) of this battery is important, as the battery should contain enough energy to meet the peak electrical demand of the traction and lift motors, but must also not be fully charged so that it can accept regenerative energy when the vehicle undergoes regenerative events, such as braking or lowering a load. If the battery SOC is too high during regenerative events, the battery voltage can rise to an unsafe level that may damage the battery, the motors, or the motors&#39; controllers, thereby causing system failures and shutdowns. 
     The management of the battery SOC typically requires a SOC estimate, as direct measurement of the SOC is often impractical. It is known in the art to use a current integration method (also called Coulomb counting) to obtain a SOC estimate of a battery. However, this method suffers from long term drift that renders the SOC estimate inaccurate over time. 
     The present disclosure provides a method that uses the battery voltage and the battery current to obtain a SOC estimate. The estimator in this disclosure is a Luenberger observer based on a model derived from an electrical equivalent circuit of the battery. In certain embodiments, the SOC estimate is then used by a regulator that throttles the fuel cell power to maintain the SOC at a level that is such that the battery has enough stored energy to supply the traction and lift motors, and enough spare capacity to accept regenerative energy from these motors. 
     Accordingly, one embodiment of the present invention is directed to a method for managing the state of charge of a battery in a hybrid electric power system comprising a battery and a fuel cell, the method comprising: defining a setpoint; estimating the present state of charge of the battery using the battery current and the battery voltage; and regulating the state of charge of the battery by manipulating a fuel cell current supplied from the fuel cell to the battery based on the difference between the setpoint and the estimated present state of charge of the battery. This embodiment can maintain the battery state-of-charge at the setpoint. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic of an embodiment of a hybrid fuel cell system for use in a forklift truck. 
         FIG. 2  is an equivalent circuit used to model the battery. 
         FIG. 3  is a flowchart showing the estimation and control of the battery SOC. 
         FIG. 4  is a table with values of parameters according to one embodiment of this disclosure. 
         FIG. 5  and  FIG. 6  show experimental data from a simulated run of the hybrid power system having battery SOC control. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a hybrid fuel cell system for use in a forklift truck. Connected in parallel on the same electrical conductor (also called “bus”) are the battery pack, the fuel cell stack in series with a DC/DC converter, the balance-of-plant components (BoP), the traction motor, and the lift motor. The BoP typically comprises an air compressor, a water pump, a fan, an electronic control unit, and valves used for hydrogen delivery, water purge and nitrogen purge. The BoP consumes a current of I BoP  at a voltage V Bus . The fuel cell stack generates a current I FC  at a voltage corresponding to the polarization curve of the specific fuel cell. The DC/DC converter regulates the fuel cell voltage to the bus voltage V Bus , generating a current I DC/DC . The traction motor current I Traction  is positive if the truck is accelerating, and negative if the truck is braking. The lift motor current I Lift  is positive if the truck is lifting a charge, and negative if it is lowering a charge. The load current I Load  is the combination of the traction and the lift motors current:
 
 I   Load   =I   Traction   +I   Lift .
 
     The battery current I Battery  is equal to the load current plus the BoP current minus the DC/DC output current:
 
 I   battery   =I   Load   +I   BOP   −I   DC/DC .  (1)
 
     The battery voltage V Bus  is made available to the hybrid fuel cell control unit either by direct voltage measurement or sensed by the DC/DC converter and then communicated to the control unit. The battery current I battery  can either be measured directly or can be calculated according to Equation (1) based on measured or estimated values for I Load , I BOP , and I DC/DC . 
       FIG. 2  shows an equivalent circuit used to model the battery. 
     C c  is a large capacitor that models the battery capacity and is chosen such that SOC=1 for a fully charged battery:
 
 C   c =Battery amp hour rating*3600
 
The battery capacity is then adjusted to take into account the battery discharging and charging inefficiency:
 
 C   c ( I   b )=3600*Battery amphour rating* e   −Discharging coeff*I     battery     (k)  if  I   battery ≧0,
 
 C   c ( I   b )=3600*(Battery amphour rating−Charging coeff* I   battery ( k )) if  I   battery &lt;0.
 
The capacitor C c  is connected in parallel with a current source with current I battery (k), to model the discharging and charging of the battery.
 
     The battery voltage V Bus  is modeled as the output of a circuit having a voltage source corresponding to the battery open circuit voltage V oc  in series with a resistor R Series  that models the impedance of the battery. 
     The battery open circuit voltage is assumed to have a linear relationship with SOC:
 
 V   oc   =V   oc Slope*           ( k− 1)+ V   oc Offset.
 
Accordingly, the battery model is

                   {             SOC   .     =     -       I   battery         C   c     ⁡     (     I   b     )                           V   bus     =       V   oc     -       R   Series     ⁢     I   battery           ,                   (   2   )               
where the dot symbol denotes the time derivative.
 
     The battery model could also include a resistor placed in parallel with C c  to model the battery self-discharge, or have a nonlinear relationship between SOC and V oc , or have a network of resistors and capacitors added to the series impedance to more accurately model transients in battery voltage. 
       FIG. 3  is a flowchart of the SOC estimation and regulation. Building upon the battery model shown in Equations (2), a Luenberger observer gives an estimate of the SOC based on the measured or calculated battery voltage and current V bus  and I battery : 
                     SOC     ^   .       =       -       I   battery       C   c         +     L   ⁡     (       V   bus     -       V   bus     ^       )                 (   3   )               
where            =V oc −R Series I battery , with V oc =V oc Slope*         +V oc Offset, and where the hat symbol denotes an estimate of the corresponding variable.

     The Luenberger observer is known in the art, and the observer gain L can be calculated using various methods including pole placement and Kalman filtering. A Kalman filtering design would assume a process and measurement noise structure to the system dynamics, and give the gain L that would minimize the steady-state error covariance of the system state. 
     The observer shown in Equation (3) needs to be discretized in order to be implemented on the digital control unit of the hybrid fuel cell system. Assuming a sampling time T s  for the estimation algorithm, and a Euler approximation of the time derivative of            
               (       i   .   e   .           ⁢     SOC     ^   .         ≈           SOC   ^     ⁡     (   k   )       -       SOC   ^     ⁡     (     k   -   1     )           T   s         )     ,         
the following discrete implementation of the observer is obtained:
 
                 SOC   ^     ⁡     (   k   )       =         SOC   ^     ⁡     (     k   -   1     )       +       T   s     ⁡     [       -         I   battery     ⁡     (   k   )           C   c     ⁡     (     I   b     )           +     L   ⁡     (         V   bus     ⁡     (   k   )       -     V   oc     +       R   Series     ⁢       I   battery     ⁡     (   k   )           )         ]               
which can also be expressed as follows:
 
                 SOC   ^     ⁡     (   k   )       =         SOC   ^     ⁡     (     k   -   1     )       +         T   s     ⁡     [       -         I   battery     ⁡     (   k   )           C   c     ⁡     (     I   b     )           +     L   ⁡     (         V   bus     ⁡     (   k   )       -       V   oc     ⁢   Slope   *       SOC   ^     ⁡     (     k   -   1     )         -       V   oc     ⁢   Offset     +       R   series     ⁢       I   battery     ⁡     (   k   )           )         ]       .             
The SOC estimate is then coerced between 0 and 1:
 
           ( k )=max{0;min{1;         ( k )}}.

     The SOC estimate has its initial value equal to a recorded value of the estimate taken during the previous system shutdown. If the forklift truck is used in a light power consuming mode, or not actively operated, a system shutdown mechanism will be triggered by a threshold high SOC value and cuts off the electric current from the fuel cell, thus preventing the batteries from overcharging. On the other hand, a load detecting mechanism that detects an electric load that draws power from the battery to a threshold value (e.g., I load =20 amp and higher) will allow recharge of the battery by restarting the fuel cell system. 
     The SOC estimate is regulated to a desired setpoint value (SOC SP ) by manipulating the fuel cell current I FC . In the present embodiment, a proportional controller is used for SOC regulation, but other control techniques can be used including but not limited to Proportional-Integral, Proportional-Integral-Derivative, Linear Quadratic Regulator, other classical control methods, modern, nonlinear, robust, optimal, stochastic, adaptive, intelligent. The proportional controller can be expressed as follows:
 
 I   FC ( k )=(SOC SP −           ( k )* K   SOC reg  
 
where the control gain K SOC reg  can be chosen as

               K     SOC   ⁢           ⁢   reg       =       C   c       SOC   ⁢           ⁢   Ctrl   ⁢           ⁢   Time   ⁢           ⁢   Constant             
to achieve a closed loop dynamic of the SOC that has approximately a time constant of SOC Ctrl Time Constant seconds.
 
     The fuel cell current setpoint I FC (k) is then coerced between a minimum value I FC     min    and a maximum value I FC     max    in order to maximize the fuel cell stack durability:
 
 I   FC ( k )=max{ I   FC     min   ;min{ I   FC     max     ;I   FC ( k )}}.
 
     The SOC can also be regulated by manipulating the DC/DC output current I DC/DC  instead of manipulating the fuel cell current I FC . 
       FIG. 5  and  FIG. 6  show data collected from a hybrid fuel cell-battery power system under various load conditions simulated by a Dynaload electronic load.  FIG. 5  shows the load current I Load  and bus voltage V bus  while  FIG. 6  shows the state of charge estimate             and fuel cell current I FC . For example, it can be seen from  FIG. 6  that the state of charge is successfully maintained within 5% of its setpoint of 90%.
     The methods disclosed herein can be applied, for example, in a hybridized forklift truck. However, the methods are applicable to a variety of applications that involve a hybrid fuel cell-battery power system, including auxiliary power units, backup power systems, portable generators, and fuel cell power plants in passenger vehicles.