(404g) Critique of Maximum Power Point Tracking in Open-Cathode Direct Methanol Fuel Cells

Direct methanol fuel cells (DMFCs) are potential candidates for
powering portable electronic devices because they are characterized by high
energy densities, low operational temperatures, and because they can be
physically realized in a compact design that is easy to transport by an
individual user [3]. The produced electrical current can be used to power
portable electronics such as batteries and it is critical to manage and
optimize the delivered power to those devices. A control technique gaining
emerging interest in the literature seeks to dynamically adjust the power
set-point to make it match the maximum-possible power output of the device at the
current operating temperature. These maximum-power-point tracking (MPPT)
algorithms have enjoyed significant success in photovoltaic (PV)
power-generation applications, and looks appealing for fuel cells at first
glance. The purpose of this study is to analyze the advantages and
disadvantages of MPPT and advance the argument to compare it with a proposed
alternative of maximum efficiency point tracking (MEPT) strategy.

Figure 1 shows a schematic diagram of the
DMFC system considered in this work. The system follows an open-cathode
architectural design, where a fraction of the product water is vented to the
atmosphere. The core components are a mixing tank containing a diluted methanol
solution that serves as the fuel. The fuel-cell stack is represented in the
figure by the area located between the anode flow channel (AFC) that transports
the liquid fuel, and the cathode flow channel (CFC) transporting the air. A
prominent feature of the stack is the polymer exchange membrane (PEM) serving
as a porous medium for water and ions. A fuel cartridge provides a
pure-methanol stream available on demand, and a fan is used to draw air through
the cathode flow channel for the dual purpose of supplying oxygen to the stack
and adjusting the operating temperature of the device.

Power control in a DMFC is a critical element needed for a
successful operation. The control strategy of MPPT is well established in PV
cells, where it has proven to increase the solar-to-electric conversion efficiency
under real-time implementation [2]. Following this success in PV systems, several studies have
been done to implement MPPT algorithms in polymer electrolyte membrane fuel
cells and DMFCs [4, 5, 6]. While operating at the
maximum-power point in a DMFC is clearly advantageous in terms of reducing the
extent of methanol crossover and improving fuel efficiency, further
investigation is required to determine if there still a net benefit when other
fuel-cell performance metrics are taken into consideration. Examples of such
criteria include the analysis of likelihood of cathode flooding under MPPT and
the effect of the algorithm on the overall device efficiency. This study
suggests that the alternative control strategy, namely MEPT is a superior one.

Figure 2 shows characteristic
power-polarization curves for a DMFC. The vertical axis represents the power P in watts [W] while the horizontal axis represents the
current I drawn from the cells in units of ampere
[A]. Each one of the curves is a power isotherm, i.e.,
the power produced at a constant temperature. At each polarization curve, there
is only one maximum-power point (MPP) at the peak indicated by a filled circle
markers. It should be emphasized that those curves are produced by varying the
temperature of operation, while keeping constant the mixing tank’s methanol
concentration and the fuel flow rate to AFC.

As a demonstration of the maximum-power-point tracking
principle, suppose that the power required by the external load is 43W. There are many feasible options for operation at this
power level, among which are points A and B, which respectively denote the power points for the
polarization curves at 50 and 55^∘C. However, only point A is a
maximum-power point, for the load requirement in question. The task of the MPPT
control algorithm is to search for this MPP and adjust appropriate variables,
namely the current drawn and the fuel-stack temperature, to keep the cell
operating at that point in a persistent fashion.

Several advantages are realized by operating the fuel cells at
the maximum-power point for a given load demand. For demonstration purposes,
consider points A and B.
First, while both points A and B deliver the same output power, MPP A operates at a lower temperature of 50^∘C, which leads to less methanol crossover [1]. Second, the current drawn
from the cell at A is higher than that drawn at B by approximately 20%. At
point A, the cell produces higher fuel efficiency defined as

where I_x is the methanol crossover
current. Furthermore, the implementation of a real-time tracking of MPP is
feasible using standard instrumentation hardware since both current and cell
voltage E are measurable.

Despite those remarkable benefits of MPPT, several concerns are
of significance. A first concern is that, as is evident from inspection of the
power curves in Figure 1, the current corresponding to
the MPP A is very close to the limiting current of 3.8A,
defined as the zero-power point on the curve where the device stops
functioning. Therefore, operation at the MPP risks producing power failures
when the system is subjected to perturbations that temporarily move the
operation to currents located to the right of the MPP current. A second concern
is that the close proximity of the current at the MPP to the limiting current
implies that the operating regime is inside the mass-transport-limited region
of the current-voltage polarization curve, where significant voltage losses are
observed for small increases in the current. Hence, when operating at the MPP A produces a lower the voltage
efficiency

where E is the actual voltage of the
cell and E_thermo is the thermodynamic voltage
of the cell that defines the maximum theoretically-possible voltage. A third
problem of concern is that water is produced at a higher rate by the chemical
reaction ?? when the electrical current
(represented by the rate of electron generation supplied as reagents on the
left-hand side of the equation) is high. Hence it is likely that flooding
occurs in the pores of the membranes in the cathode region of the fuel cells in
the stack, completely blocking the transport of oxygen supplied as a reagent to
chemical reaction ??. The 100%
liquid saturation limit is a dangerous operating regime because it
causes oxygen starvation in the cathode, leading to a failure in the form of an
abrupt halt of device operation.

Figure 3 shows the curves for the overall
efficiency ε of the DMFC, where

where ε_thermo =  is
the ratio of the change of Gibbs energy to the change in enthalpy of the
overall electrochemical reaction. The vertical axis represents the efficiency ε in % while the
horizontal axis shows the current I in Amperes.
Each one of the curves is an efficiency isotherm. The maximum-efficiency point
(MEP) for each isotherm is indicated by a circle marker. Operating at MEP
mitigates or altogether eradicates the concerns applicable to the MPPT
algorithm. First, the issue of proximity to the limiting current is no longer a
relevant issue in this case since the MEP points are at located at least 1.2A away.
Second simulation results (not shown here for brevity) demonstrate that under
MEP operation the saturation of the pores with liquid water ranges between 40 and 60%, indicating that
cathode-side flooding is unlikely.

References