Invited paper for the World Renewable Energy Congress V, Florence 19-25. Sep. 1998
preprint submitted to Renewable Energy
Roskilde University, Institute 2, Energy & Environment Group
P.O.Box 260, DK-4000 Roskilde, Denmark
fax +45 4674 3020, email:, Web:


In contrast to conventional energy modelling made on a national basis, we consider energy use and supply per unit of land area. This is particularly suited for dealing with dispersed energy resources such as renewable energy, and by making the match of demand with supply on this basis in a geographical information system (GIS), we are able to directly identify any mismatch entailing needs for energy trade and establishment of energy exchange facilities (power grids, gas distribution lines, etc.). The model is being applied to several global energy scenarios and constitutes a quite general tool for system modelling, assesment and planning.


Geographical information system; renewable energy systems; global energy modelling.


Global renewable energy data are assessed on the basis of a longitude-latitude grid and different exploitation models are formulated. An energy demand model is similarly created on an area basis, using UN population forecasts and various assumptions on economic activity and technology for efficient use of energy. Demand and supply is then compared, still on an area basis, and any mismatch is handled by import or export (via grids or carriers).


According to UN estimates, the world population will increase to around 1010 by the mid-21st century, with uncertainty coming from issues of health and economic wellbeing (World Bank, 1988). We take the present population density distribution from CIESIN (1997), recalculated to a latitude-longitude grid of 0.5× 0.5, and use the UN regional projections for year 2050.

Over recent decades, energy demands have risen much less than measures of economic activity such as gross national products. The expectation is that this trend will continue, and due to technical requirements the energy intensity of e.g. computer-related activities will continue to decrease, while the number of installations will increase. Based i.a. on such factors, the energy demand by year 2050 has been estimated for different regions in the world, using the following methodology (Sørensen, 1996; see also appendix in Kuemmel et al, 1997): Current energy supplied to the end-user (taken from statistics, such as OECD, 1996) is analysed with regard to the efficiency of the final conversion step, translating energy into a useful product or service. The net energy demand is taken as that used by the most efficient equipment available on the present market or definitely proven (e.g. available as a prototype). The assumption is thus that by 2050, the average of all equipment used will have an energy efficiency equal to the best currently marketed or nearly marketed. This neglects the certain invention of new methods and equipment working on principles different from current ones and possibly improving efficiency by much more than marginal factors. The factor multiplying demand to reflect increase of economic activity is three for Western Europe, Japan and the United States of America, and higher elsewhere.

Figures 1-3 gives for the present system, for the assumed mid-21st century system, and for a system with full satisfaction of primary and a range of secondary goals (including some that are not anticipated now and therefore has been included only as an overall growth percentage), the amounts of energy made useful by the end-user per unit of area, including human food intake as an energy input - a choice made because it is useful in analysing future energy use with a supply system using bio-energy for both food and energy purposes. The goal values vary only due to different needs for heating and cooling, due to different transportation needs depending on settlement densities, and due to the mix of industrial activities assumed for each region. Note that the definition of end-use energy introduced above differs from what some statistical sources denote "end-use" or "final" energy. The scenario shown in Figure 2 assumes a development in most parts of the world, that by 2050 is very close to the "goal society" of Figure 3. Only Africa is by 2050 still far from the goal. The scenario technique offers the possibility to investigate the implications of various alternative political views on global development.


Major potential sources of renewable energy are direct solar radiation, wind energy and biomass. The following will restrict the discussion to these three, although a number of additional, minor renewable sources may enter into future energy systems.

We use solar radiation incident on a plane tilted towards North or South by an angle equal to the latitude, estimated on the basis of horizontal area solar radiation data, which again have been estimated from satellite data for top-of-the-atmosphere radiation combined with cloud and reflectance (albedo) data (NASA, 1997), by a method devised by Pinker and Laszlo (1992). The estimations for January and July are based on the horizontal area data for October and April, having approximately the characteristics of inclíned surface measurements for the two months in question, apart from local peculiarities caused by unusual patterns of cloud cover (Sørensen, 1979). The grid used is 2.5 × 2.5.

The actual energy derived from solar panels is estimated on the basis of two assumptions: One is that the area of suitably oriented surfaces used for energy collection is at most 0.1% of the horizontal land area (the collectors being actually mounted on building roofs and facades, or in dedicated park-like collector fields) and the other a fixed average efficiency of collectors. This efficiency, which pertains to year 2050 technology, is conservatively taken as 15% for flat-plate photovoltaic panels and 20-60% for flat-plate thermal collectors. The upper limit is for immediate use of the hot water produced, while the lower figures include losses in storage, increasing with the length of storage (up to seasonal storage for high-latitude locations).

For wind, we use 1995 wind speed data from a reanalysis of meteorological station data, performed by Kalney et al., 1996. The selection of data from the 1000mb pressure level ensures that the surface roughness experienced by a wind turbine with a hub height around 50m is reflected. However, the data are monthly mean wind speeds <v> constructed on the basis of zonal and meridional winds, and in order to assess the power in the wind, a model of the relationship between <v>3 and <v3> is required. Simple models imply a rough proportionality between these two quantities, as used e.g. in the US wind atlas prepared by the Pacific NW Laboratory (Swisher, 1995) and also apparent from the Weibull distribution approach of the European wind atlas (Troen and Petersen, 1989). A further complication is the non-linear response of wind turbines, where modern designs aiming at a high annual production typically start producing only around 5 m/s and reach a fixed maxi-mum production B at around 12 m/s. Thus there would not be any production for a monthly average windspeed below 5 m/s, if this were made up of nearly constant values throughout the time range. However, actual time series of windspeeds reflect the passage of weather fronts and typically oscillates with periods of some two weeks, and actually entails some power production from the above type of wind turbine at practically all monthly average wind speeds, down to zero. The approaches mentioned thus allows us to parametrise the average power production from wind turbines as P=A×min{C×<v>3; B}, in W per m2 of horizontal area, where B is the turbine's production per m2 of vertical area swept for large wind speeds (typically 500 W/m2), C a factor around unity, and A the maximum vertical swept area of installed wind turbines considered feasible per unit of horizontal area, a typical value for which would be 10-3.

For biomass harvest, factors of importance are soil type, temperatures, solar radiation, access to water and nutrients, with substantial variations depending on the particular type of crop. On fertilized land in regions such as Denmark (modest radiation, good soil and water access), the average crop energy production is 0.3 W per m2 of cultivated land or 0.22 W/m2 for the entire Danish land area. Currently, close to 10% of this energy is contained in the food consumed in Denmark, so an estimate of the energy potentially available for energy purposes in a setup different from the current one (based on animal raising and export) would be around 0.2 W/m2 of land. In Southern Europe, the specific yields are half the Danish ones, and in Equatorial regions even less, with water being the chief limiting factor (if irrigation is not feasible). Energy production would be another factor two below the crop yields, for technologies such as methanol, biogas or hydrogen production from biomass (Jensen and Sørensen, 1984). Thus, one will get potential bioenergy yields of the order of 0.05 W/m2 in areas of land suited for agriculture, assuming that as in Denmark, most of the total area of such regions is in fact used for agricultural production. It will in many cases be possible to combine food and energy production on the same land, as the modest estimate of energy transfer into food made above suggests. On marginal land unsuited for food crops, there is a possibility of engineering suitable energy crops.


Once the energy demand and potential renewable energy production is determined on an area basis, it is possible to assess the matching ability of a future renewable energy system. It can be determined, if there is enough renewable energy to cover all demands, or if other energy sources must be invoked. For a given system layout, the need for exchange of power by electricity transmission, biogas or hydrogen pipelines, liquid biofuel transport or district heating lines can be determined. All the necessary data are kept in a geographical information system, including typical seasonal variations allowing the need for energy storage to be determined. Typically, the matching of supply and demand can be based upon local energy storage or upon trade in energy, or a combination of the two. Factors to include in the scenario construction include the energy loss in each conversion between supply and demand. For electricity producing sources (e.g. wind and photovoltaics) these are usually small (such as 4-6% transmission losses), also for conversions taking place at the end-user, in case electricity is used for purposes where it is not the final energy form demanded. For combustion of hydrogen or biogas in automotive applications, the losses can be substantial, and any process of converting heat or electricity into a storable energy form and back entails losses that can be substantial, notably for long-term storage. These considerations are made on a quantitative level, in the actual comparison of supply and demand.

Figures 4 and 5 gives the surplus and deficit of estimated wind plus photovoltaic potential energy production relative to 2050 scenario demand. We have not yet completed the biomass estimation. It is seen that already the two sources could on average cover the estimated demand (because both produce electricity, system losses are only some 5-15% power transmission losses), given some regional exchange of power. Adding biomass will ease the supply and make the system morte resilient.


The presentation above is based on an ongoing project on global energy alternatives performed for the Danish Energy Agency, looking at two renewable energy scenarios (centralized or decentralized), a carbon dioxide controlling fossil scenario and an advanced nuclear technology "safe nuclear" scenario.


BTM Consult, 1995. International wind energy development: Status by 1995 and forecast 1995-2000, Report prepared for the Danish Energy Agency, Copenhagen

CIESIN, 1997. Gridded population of the world. David Simonett Center for Space Studies at University of Santa Barbara, California, NCGIA Technical Report TR-95-6; Consortium for Int. Earth Science Information Network website

IEA, 1997. Photovoltaic power systems in selected IEA member countries. Report Int. Energy Agency PV Power Systems Programme Ex.Co./Task 1, 1997:1

IPCC, 1996. Climate Change 1995: Impacts, adaptation and mitigation of climate change: Scientific-technical analysis. Contribution of WGII (Watson et al., eds.), Cambridge University Press, 572 pp.

Jensen, J. and Sørensen, B., 1984. Fundamentals of energy storage. 345 pp. Wiley, New York

Kalney, E. et al., 1996. The NCEP/NCAR 40-year reanalysis project. Bulletin of the American Meteorological Society; data available at website in the catalogue of NOAA NCEP-NCAR CDAS-1 data sets.

Kuemmel, B., Nielsen, S. and Sørensen, B., 1997. Life-cycle analysis of energy systems. Roskilde University Press, Copenhagen. 216 pp.

NASA, 1997. Surface solar energy data set v1.0, obtained from NASA Langley Research Center EOSDIS Distributed Active Archive Center at website

OECD, 1996. Energy balances of OECD countries 1993-4. Energy statistics of OECD countries 1993-4, Energy statistics of non-OECD countries 1993-4. Paris

Pinker, R. and Laszlo, I., 1992. Modelling surface solar irradiance for satellite applications on a global scale. J. Applied Meteorology, vol. 31, pp. 194-211

Sørensen, B., 1979. Renewable Energy. 687 pp. Academic Press, London and New York

Sørensen, B., 1995. History of, and recent progress in, wind-energy utilization. Annual Review of Energy & Environment, vol. 20, pp. 387-424

Sørensen, B., 1996. Scenarios for greenhouse warming mitigation. Energy Conversion and Management, vol. 37, pp. 693-698

Sørensen, B., 1997. Impacts of energy use, pp. 243-266 in "Human ecology, human economy" (Diesendorf and Hamilton, eds.), Allen and Unwin, New South Wales

Swisher, R., 1995. Wind power a strong contender in US energy marketplace, pp. 190-196 in "The world directory of renewable energy suppliers and services", James & James, London

Troen, I and Petersen, E., 1989. European Wind Atlas. Risø National Laboratory, Roskilde

World Bank, 1988. World population projections (Zacharia and Wu, eds.). Baltimore



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