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  Down the learning curve with emerging technologies

Down the learning Curve with Emerging Technologies

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Figure 1. Experience curve for photovoltaic modules, 1976-1992 (William and Terzian 1993).


Promising new technologies that are still very expensive will become less costly if they are manufactured in large numbers. The exponential reduction in cost with increased production can be specified by an “experience curve”. However, linear programming models of energy systems do not properly account for this nonlinearity. Initial steps with a nonlinear, nonconvex model, GENIE, that explicitly contains experience curves for emerging technologies, suggest that photo-voltaics and fuel cells could come to dominate electricity generation if a long enough and broad enough view is taken, especially if future carbon dioxide emissions must be restricted.

Proponents of photovoltaic technology argue that expected reductions in its cost will make it more and more competitive as time goes on. This expectation is based on the observation that the unit costs of a manufactured product progressively decrease as more units are manufactured. The pattern of this reduction among many different types of technology has been remarkably consistent, following an exponential reduction variously named a learning curve, progress curve, or experience curve.

The rate of reduction in an experience curve can be defined by the percen- tage reduction in the unit cost with successive doubling of the quantity manufactured. For photovoltaics, for example, an 82 percent experience curve has been postulated based on early experience (Figure 1). The cost of the hundredth unit will be 82 percent of the fiftieth, the costs of the two-hundredth 82 percent of the hundredth, etc. While the reduction on an experience curve would theoretically continue indefinitely, the amount of the reduction between successive units eventually becomes minuscule, and at some point the unit cost can be considered constant.

Experience curves as an empirical fact must be ignored in linear programming formulations for the future development of the technologies comprising a national energy system, because they constitute a nonlinearity. Linearity requires that successive units each cost the same. This is an important problem when new technologies, far from the point where unit costs have levelled out, are to be considered.

In a dynamic linear programming model in which successive time periods are represented, it has been the practice to assume successively lower unit costs in future time periods for technologies initially high on the experience curve. The solution space remains bounded by a convex curve consisting of linear elements, with optimization at the intersection of two such elements assured. However, the solution may omit the early expensive applications of the technology, igno-ring the fact that the initial investment is necessary to bring down the subsequent cost. It is not a matter of time, but of continued production.

“Some have suggested that technical progress is a factor that may justify deferring carbon dioxide emission abatement”, notes Niclas Mattsson of Sweden’s Chalmers University of Technology. “Autonomous energy efficiency improvement over time is usually explicit in top-down models, and it is implicit in bottom-up models. However, new technologies do not appear automatically. Both technology push - such as publicly funded R&D - and market pull are needed for the dissemination of a new technology. The significance of market pull is that it enables learning by doing to take place. Unless the high initial costs of introducing emerging technologies are paid, they may be locked out before they can contribute to future carbon dioxide emission abatement”.

With the costs of individual technologies characterized by experience curves, determining the best mix of energy technologies to meet future requirements becomes a nonlinear, nonconvex optimizing problem. To address this problem, Mattsson and Clas-Otto Wene developed the dynamic, nonlinear model named GENIE (Global ENergy system with Internalized Experience curves). GENIE models long-term development of the global electricity system, spanning the years 1995-2075 with eight ten-year time periods. The objective of GENIE is to minimize the present value of the total cost of the global electric system, assuming perfect foresight. The main purpose of GENIE is to provide qualitative insights into the dynamics of technological development in the energy system. It is not intended as a complete tool for general energy policy analysis.

There are two conceptual ways to address the nonlinear, nonconvex optimization problem:
By keeping the continuous experience curve and solving the resulting nonconvex problem directly, using modern algorithms for global optimization.
By breaking the experience curve into successive discrete units, assuring the sequential order, and solving the problem using mixed-integer programming.

Mattsson and Wene began with the first approach, starting with an ad hoc optimization procedure. This alternative is very simple to implement and solves rapidly to a local optimum, according to Mattsson, but the global optimum cannot be proved. Many model runs from different starting points are therefore necessary to satisfy the user that the global optimum has indeed been found.

In subsequent work reported in his thesis for the degree of licentiate of engineering at Chalmers, Mattsson used GENIE in the second approach. The great advantage of this method is the guarantee of finding the global optimum. However, the implementation is more complicated, and solution times are several orders of magnitude larger.

The model consists of four world regions; North, South, East and West. The nonconventional electricity generation technologies for producing electricity are advanced coal power, e.g. pressurized fluidized bed combustion or integrated gasification combined-cycle gas turbines (CCGT), wind power, fuel cells using natural gas, photovoltaics (PV), and photovoltaic hydrogen production (PV-H2). PV generates electricity intermittently, when the sun is shining. PV-H2, on the other hand, provides power on demand as it uses PV electricity to electrolyze water, stores the resulting hydrogen and oxygen, and when required recombines them in fuel cells.

To minimize computational difficulty, only technologies with a large potential for experience-based cost reduction are treated in the model by experience curves. The modular technologies PV, PV-H2 and fuel cells were assumed to have the steepest progress ratios (0.82, 0.85 and 0.85, respectively), the small-scale technologies CCGT and wind power slightly less steep ratios (both 0.88), while the large-scale technologies display little (advanced coal, 0.95) or no experience-based learning (all others). The reduction in cost is approximated by linear segments in the cumulative investment cost curve, i.e., the integral of the experience curve. The maximum allowed growth rate for all technologies was taken as 30 percent per year.

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