Modeling and control of tubular solid-oxide fuel cell systems: II. Nonlinear model reduction and model predictive control

This paper describes a systematic method for developing model-based controllers for solid-oxide fuel cell (SOFC) systems. To enhance the system efficiency and to avoid possible damages, the system must be controlled within specific operating conditions, while satisfying a load requirement. Model predictive control (MPC) is a natural choice for control implementation. However, to implement MPC, a low-order model is needed that captures the dominant dynamic behavior over the operating range. A linear parameter varying (LPV) model structure is developed and applied to obtain a control-oriented dynamic model of the SOFC stack. This approach effectively reduces a detailed physical model to a form that is compatible with MPC. The LPV structure includes nonlinear scheduling functions that blend the dynamics of locally linear models to represent nonlinear dynamic behavior over large operating ranges. Alternative scheduling variables are evaluated, with cell current being shown to be an appropriate choice. Using the reduced-order model, an MPC controller is designed that can respond to the load requirement over a wide range of operation changes while maintaining input-output variables within specified constraints. To validate the approach, the LPV-based MPC controller is applied to the high-order physical model.     

Model predictive control for wind turbines with distributed active flaps: incorporating inflow signals and actuator constraints

This paper describes the implementation of system identification and controller design techniques using model predictive control (MPC) for wind turbines with distributed active flaps for load control. An aeroservoelastic model of the 5 MW NREL/Upwind reference wind turbine, implemented in the code DU_SWAMP, is used in an industry‐based MPC controller design cycle, involving the use of dedicated system identification techniques. The novel multiple‐input multiple‐output MPC controllers, which incorporate flap actuator constraints and the use of local inflow measurement signals, are designed and implemented for various operating points. The controllers are evaluated in standard power production load cases and fatigue load reductions up to 27.3% are achieved. The distributed flaps controller scheme is also compared with simpler single‐flap single‐input single‐output and individual pitch controller schemes. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear model predictive control of SOFC based on a Hammerstein model

To protect solid oxide fuel cell (SOFC) stack and meet the voltage demand of DC type loads, two control loops are designed for controlling fuel utilization and output voltage, respectively. A Hammerstein model of the SOFC is first presented for developing effective control strategies, in which the nonlinear static part is approximated by a radial basis function neural network (RBFNN) and the linear dynamic part is modeled by an autoregressive with exogenous input (ARX) model. As we know, the output voltage of the SOFC changes with load variations. After a primary control loop is designed to keep the fuel utilization as a steady-state constant, a nonlinear model predictive control (MPC) based on the Hammerstein model is developed to control the output voltage of the SOFC. The performance of the MPC controller is compared with that of the PI controller developed in [Y.H. Li, S.S. Choi, S. Rajakaruna, An analysis of the control and operation of a solid oxide fuel-cell power plant in an isolated system, IEEE Trans. Energy Convers. 20 (2) (2005) 381–387]. Simulation results demonstrate the potential of the proposed Hammerstein model for application to the control of the SOFC, while the excellence of the nonlinear MPC controller for voltage control of the SOFC is proved.     

Model predictive control of sea wave energy converters – Part II: The case of an array of devices

This paper addresses model predictive control (MPC) of highly-coupled clusters of sea wave energy converters (WECs). Since each WEC is not only a wave absorber but also a wave generator, the motion of each WEC can be affected by the waves generated by its adjacent WECs when they are close to each other. A distributed MPC strategy is developed to maximize the energy output of the whole array and guarantee the safe operation of all the WECs with a reasonable computational load. The system for an array is partitioned into subsystems and each subsystem is controlled by a local MPC controller. The local MPC controllers run cooperatively by transmitting information to each other. Within one sampling period, each MPC controller performs optimizations iteratively so that a global optimization for the whole array can be approximated. The computational burden for the whole array is also distributed to the local controllers. A numerical simulation demonstrates the efficacy of the proposed control strategy. For the WECs operating under constraints explored, it is found that the optimized power output is an increasing function of degree of WEC–WEC coupling. Increases in power of up to 20% were achieved using realistic ranges of parameters with respect to the uncoupled case.     

Dynamic modelling and controlling strategy of polymer electrolyte fuel cells

A comprehensive dynamic control oriented model of a polymer electrolyte fuel cell (PEFC) is developed, considering the mixed effects of temperature, gas flow and capacitance. The fractional relationship between the dynamic output voltage and the capacitance, which escaped the attention in most previous studies is also addressed. Moreover, based on the developed PEFC model, a proportional integral and derivative (PID) controller is designed to stabilize the output voltage at a determined value by regulating the input hydrogen mass flow rate under a series of disturbance in the input. The dynamic PEFC model and controller are simulated in Matlab/Simulink. The simulation results illustrate that the PEFC system model is capable of characterizing dynamic properties of PEFCs. Additionally, the developed PID controller is effective in stabilizing the output voltage with a rather small overshoot and rather faster response, which also proves that the developed model is suitable for PEFC control algorithms development.     

Control‐oriented nonlinear modelling of molten carbonate fuel cells

Performance and availability of molten carbonate fuel cells (MCFC) stack are greatly dependent on its operating temperature. Control of the operating temperature within a specified range and reduction of its temperature fluctuation are highly desirable. The models of MCFC stack existing are too complicated to be suitable for design of a controller because of its lack of clear input–output relations. In this paper, according to the demands of control design, a quantitative relations model of control‐oriented MCFC between the temperatures of the stack and flowrates of the input gases is developed, based on conservation laws. It is an affine nonlinear model with multi‐input and multi‐output, the flowrates of fuel and oxidant gases as the manipulated vector and the temperatures of MCFC electrode–electrolyte plates, separator plates as the controlled vector. The modelling and simulation procedures are given in detail. The simulation tests reveal that the model developed is accurate and it is suitable to be used as a model in designing a controller of MCFC stack. Copyright © 2004 John Wiley & Sons, Ltd.     

An improved thermal control of open cathode proton exchange membrane fuel cell

Proton exchange membrane fuel cell is a well-known technology that has shown high efficiency and performance as a power system compared to conventional sources such as internal combustion engines. Especially, open cathode proton exchange membrane is growing more popular thanks to its simple structure, low cost and low parasitic losses. However, the open cathode fuel cell performance is highly related to the operating temperature variation and the airflow rate which is adjusted through the fan voltage. In this regard, the present study investigates the thermal management of an open cathode proton exchange membrane fuel cell. The objectives are the stack performance improvement and the stack degradation prevention. Indeed, a safety and optimal operating zone governed by the load current, the stack temperature and the air stoichiometry, is designed. This optimal operating zone is defined based on the system thermal balance and the operating constraints. Hence, the proposed control strategy deals concurrently with the stack temperature regulation and the air stoichiometry adjustment to guarantee the goals achievement. The performance of the proposed control strategy is verified through experimental studies with different operating conditions and results prove its efficiency. To properly design an appropriate control strategy, a multiphysic fuel cell model is developed based on acausal approach by mean of Matlab/Simscape and experimentally validated.     

Optimal operations for hydrogen-based energy storage systems in wind farms via model predictive control

Efficient energy production and consumption are fundamental points for reducing carbon emissions that influence climate change. Alternative resources, such as renewable energy sources (RESs), used in electricity grids, could reduce the environmental impact. Since RESs are inherently unreliable, during the last decades the scientific community addressed research efforts to their integration with the main grid by means of properly designed energy storage systems (ESSs). In order to highlight the best performance from these hybrid systems, proper design and operations are essential. The purpose of this paper is to present a so-called model predictive controller (MPC) for the optimal operations of grid-connected wind farms with hydrogen-based ESSs and local loads. Such MPC has been designed to take into account the operating and economical costs of the ESS, the local load demand and the participation to the electricity market, and further it enforces the fulfillment of the physical and the system's dynamics constraints. The dynamics of the hydrogen-based ESS have been modeled by means of the mixed-logic dynamic (MLD) framework in order to capture different behaviors according to the possible operating modes. The purpose is to provide a controller able to cope both with all the main physical and operating constraints of a hydrogen-based storage system, including the switching among different modes such as ON, OFF, STAND-BY and, at the same time, reduce the management costs and increase the equipment lifesaving. The case study for this paper is a plant under development in the north Norway. Numerical analysis on the related plant data shows the effectiveness of the proposed strategy, which manages the plant and commits the equipment so as to preserve the given constraints and save them from unnecessary commutation cycles.     

One-dimensional thermal model of cold-start in a polymer electrolyte fuel cell stack

A transient, one-dimensional thermal model for a generic polymer electrolyte fuel cell (PEFC) stack is developed to investigate the cold-start ability and the corresponding energy requirement over different operating and ambient conditions. The model is constructed by applying the conservation of energy on each stack component and connecting the component's relevant boundaries to form a continuous thermal model. The phase change of ice and re-circulation of coolant flow are included in the analytical framework and their contribution to the stack thermal mass and temperature distribution of the components is also explored. A parametric study was conducted to determine the governing parameters, relative impact of the thermal mass of each stack component and ice, and anticipated temperature distribution in the stack at start-up for various operating conditions. Results indicate that 20 cells were sufficient to accurately experimentally and computationally simulate the full size stack behavior. It was observed that an optimum range of operating current density exists for a chosen stack design, in which rapid start-up of the stack from sub-zero condition can be achieved. Thermal isolation of the stack at the end plates is recommended to reduce the start-up time. Additionally, an end plate thickness exceeding a threshold value has no added effect on the stack cold-start ability. Effect of various internal and external heating mechanisms on the stack start-up were also investigated, and flow of heated coolant above 0 °C was found to be the most effective way to achieve the rapid start-up.     

大型风电机组模型预测独立变桨控制器设计

针对恒转速运行时,大型风电机组承受的不平衡载荷问题,提出一种多输入多输出的风电机组模型预测(MPC)独立变桨控制策略.首先,建立风电机组旋转坐标系下的状态空间模型,经过坐标变换得到固定坐标系下的平均周期模型,分析表明模型在非对角存在无法忽视的耦合;然后,计算所需观测器和控制器的参数,进一步设计基于Kalman状态观测器...     

Model-based decoupling control for the thermal management system of proton exchange membrane fuel cells

As one of the most promising sustainable energy technologies available today, proton exchange membrane fuel cell (PEMFC) engines are becoming more and more popular in various applications, especially in transportation vehicles. However, the complexity and the severity of the vehicle operating conditions present challenges to control the temperature distribution in single cells and stack, which is an important factor influencing the performance and durability of PEMFC engines. It has been found that regulating the input and output coolant water temperature can improve the temperature distribution. Therefore, the control objective in this paper is regulating the input and output temperature of coolant water at the same time. Firstly, a coupled model of the thermal management system is established based on the physical structure of PEMFC engines. Then, in order to realize the simultaneous control of the inlet and outlet cooling water temperature of the PEMFC stack, a decoupling controller is proposed and its closed-loop stability is proved. Finally, based on the actual PEMFC engine platform, the effectiveness, accuracy and reliability of the proposed decoupling controller are tested. The experimental results show that with the proposed decoupling controller, the inlet and outlet temperatures of the PEMFC stack cooling water can be accurately controlled on-line. The temperature error range is less than 0.2 °C even under the dynamic current load conditions.     

基于自适应非奇异智能终端滑模观测器的风力机载荷增广预测控制

为有效降低风力机在高风速运行时的不平衡载荷,提出一种基于自适应非奇异智能终端滑模观测器的载荷增广预测控制策略。首先,针对模型不匹配导致的模型预测控制性能下降的问题,将指令跟踪误差与系统状态的变化量增广为状态向量,设计增广预测模型以消除稳态跟踪误差;其次,设计自适应非奇异终端滑模观测器对系统状态进行估计,以提高控制系统的可靠性;然后,设计多目标变速灰狼优化算法同时对控制器和观测器参数寻优;最后,基于Simulink仿真平台验证了所提控制策略的有效性。结果表明,所提控制策略可有效消除稳态误差,缩短调节时间并提高控制性能。     

A lumped parameter model of the polymer electrolyte fuel cell

A model of a polymer electrolyte fuel cell (PEFC) is developed that captures dynamic behaviour for control purposes. The model is mathematically simple, but accounts for the essential phenomena that define PEFC performance. In particular, performance depends principally on humidity, temperature and gas pressure in the fuel cell system. To simulate accurately PEFC operation, the effects of water transport, hydration in the membrane, temperature, and mass transport in the fuel cells system are simultaneously coupled in the model. The PEFC model address three physically distinctive fuel cell components, namely, the anode channel, the cathode channel, and the membrane electrode assembly (MEA). The laws of mass and energy conservation are applied to describe each physical component as a control volume. In addition, the MEA model includes a steady-state electrochemical model, which consists of membrane hydration and the stack voltage models.     

Equivalent circuit elements for PSpice simulation of PEM stacks at pulse load

The PEFC stack in a commercial power system was operated with room air and pure hydrogen. After the system reached a steady temperature, an ac impedance test was conducted on the fuel cell power system. The impedance data were real-time response generated by the ac sinusoidal excitation. Data for a single PEM stack and PEM stacks operating in parallel and series were collected with or without an embedded system controller board and electronic devices. The equivalent circuit model with three time constants and the non-linear least square fitting program (NLLS) were applied for fitting the stack impedance spectrum. The Levenberg–Marquardt algorithm utilized in the NLLS fitting process automatically adjusted the parameter values of the physical elements in the model to find the best fit result. From the preliminary results, data interpretation and the equivalent circuit model identified the physical elements, the related electrochemical processes, and the phenomenon inside the fuel cells or stacks. Losses from ohmic conduction, anode activation, cathode activation, and mass transfer were separated and analyzed. Further PSpice simulation curves using these equivalent circuit elements demonstrate good agreement with the pulse testing data measured from the PEFC power system.     

A spatially resolved physical model for transient system analysis of high temperature fuel cells

This work builds upon previous high temperature fuel cell (HT-FC) modeling studies, capturing both steady state performance and transient behavior of HT-FC stacks by merging simplified dimensional aspects of a planar fuel cell stack with first principles physical modeling. Dynamic simulations are developed that spatially resolve fluctuations in temperature, pressure and concentration distributions during transient operation. A significant portion of the heat transfer occurs prior to and after the air passes over the electrochemically active portions of the cell, justifying additional heat transfer pathways from the stack to the air in order to accurately characterize the thermal transients and temperature distributions in the HT-FC stack. The highly configurable MatLab-Simulink® model developed can simulate both solid oxide and molten carbonate fuel cells utilizing either direct or indirect internal reforming. The perturbation response characteristics of the dynamic model to load, fuel flow, air flow and composition perturbations are discussed, and control strategies are introduced that minimize temperature fluctuations. Analysis indicates air flow and inlet temperature controls are sufficient to control average temperature and average internal temperature gradients. Internal heat transfer dynamics substantially change the spatial temperature distribution and local temperature gradients during typical operating conditions and perturbations.     

Effect of temperature uncertainty on polymer electrolyte fuel cell performance

The temperature of operation is a key parameter in determining the performance and durability of a polymer electrolyte fuel cell (PEFC). Controlling temperature and understanding its distribution and dynamic response is vital for effective operation and design of better systems. The sensitivity to temperature means that uncertainty in this parameter leads to variable response and can mask other factors affecting performance. It is important to be able to determine the impact of temperature uncertainly and quantify how much PEFC operation is influenced under different operating conditions. Here, a simple lumped mathematical model is used to describe PEFC performance under temperature uncertainty. An analytical approach gives a measure of the sensitivity of performance to temperature at different nominal operating temperatures and electrical loadings. Whereas a statistical approach, using Monte Carlo stochastic sampling, provides a ‘probability map’ of PEFC polarisation behaviour. As such, a polarisation ‘area’ or ‘band’ is considered as opposed to a polarisation ‘curve’. Results show that temperature variation has the greatest effect at higher currents and lower nominal operating temperatures. Thermal imaging of a commercial air-cooled stack is included to illustrate the temporal and spatial temperature variation experienced in real systems.     

Modeling of the heat transfer in a portable PEFC system within MATLAB-Simulink

A dynamic model of a (portable) polymer electrolyte fuel cell system including the heat transfer between stack and periphery – here stack and metal hydride storage – has been developed within MATLAB-Simulink. The implemented equations describe the steady-state as well as the dynamic operation of the PEFC system with sufficient accuracy, although considerable simplifications have been made to keep model complexity and computing time low. As simulations are performed in 100-fold real time, different operating conditions and control strategies for PEFCs can be analyzed and evaluated in short-time. Here, emphasis is given to the operation limits of the PEFC system, i.e. the conditions for trouble-free operation at different loads and high or low ambient temperature are established. The model has been validated by experiments on a home-made portable system.     

过热汽温多内模控制

针对火电厂过热汽温被控对象具有大迟延、大惯性的特点,且对象特性随负荷变化较大等因素,很难实现稳定和高性能的控制。针对这一特点,提出了基于多模型的内模控制策略,通过在不同工况辩识得到局部模型,根据加权因子计算出全局多模型,设计出相应的内模控制器,根据运行工况选择相应的控制器,从而实现全工况运行的自适应控制。仿真结果表明,该控制策略比常规的单内模控制在更大范围具有较好的控制品质。     

一种基于T-S模型的模糊PID控制器的设计及应用研究

基于Tзkзgi和Sugeno的模糊控制模型，设计了一种基于T-S模型的模糊PID控制器，这种设计方法可以充分借鉴常规PID控制器参数调整的各种成熟经验，使模糊控制规则的制定和参数的调整更简单易行，且物理意义明确。通过对电加热炉的仿真和实时控制表明，该控制器有着很强的适应性和鲁棒性，改善了系统的动静态性能。     

Water balance in a polymer electrolyte fuel cell system

Polymer electrolyte fuel cell (PEFC) systems operating on carbonaceous fuels require water for fuel processing. Such systems can find wider applications if they do not require a supply of water in addition to the supply of fuel, that is, if they can be self-sustaining based on the water produced at the fuel cell stack. This paper considers a generic PEFC system and identifies the parameters that affect, and the extent of their contribution to, the net water balance in the system. These parameters include the steam-to-carbon and the oxygen-to-carbon ratios in the fuel processor, the electrochemical fuel and oxygen utilizations in the fuel cell stack, the ambient pressure and temperature, and the composition of the fuel used. The analysis shows that the amount of water lost from the system as water vapor in the exhaust is very sensitive to the system pressure and ambient temperature, while the amount of water produced in the system is a function of the composition of the fuel. Fuels with a high H/C (hydrogen to carbon atomic ratio) allow the system to be operated as a net water producer under a wider range of operating conditions.