With the increase of world population and industrial growth of developing countries, demand for energy, in particular electric power, has gone up at an unprecedented rate over the last four decades. To meet the demand, electric power generation by use of fossil fuel has increased enormously thereby producing increased quantity of greenhouse gases contributing more and more to atmospheric pollution which, climate Scientists believe, can adversely affect the global climate, and health and welfare of world population. In view of these, there is global awareness of looking for alternate sources of energy such as natural gas, hydropower, wind, solar, geothermal and finally biomass etc. It is recognized that this requires replacement of existing infrastructure with new systems, which cannot be achieved overnight. Optimal control theory has been widely used for the last five decades in diverse areas of physical sciences, medicine, engineering, economics and social sciences. The main motivation of this article is to use this theory to find the optimum strategy (decision or policy) for integration of all currently available renewable energy sources with the existing electric power generating systems with the ultimate goal of elimination of fossil fuel. Eight main energy sources such as Coal, Petroleum, Natural Gas, Conventional Hydro, Wind, Solar, Geothermal and Biomass are considered in a dynamic model. The state of the dynamic model represents the level of power generation from each of the sources at any time t. The proposed objective function is based on the desired target level of power generation from each of the available sources at the end of the plan period while reducing the production of greenhouse gasses. Pontryagin Minimum principle is used to determine the optimal control or decision policy. Official released data from the U.S. Energy Information Administration is used as a case study. Based on this data and a mathematical model proposed in a paper (Miah, Ahmed and Chowdhury, 2012) published by Energy Economics combined with the minimum principle, an optimal policy is presented for integration of renewable energy sources to the national power grid.

Developing optimum decision policy for gradual replacement of conventional energy sources by clean ones is an important field of current research and the main concern of this article. Eight main energy sources are considered and the decision policies are formulated with the objective of minimizing the implementation and environmental costs while meeting the electricity demand during the entire plan period. The selected energy sources are A nonlinear dynamic Lotka‐Volterra model, first introduced in Miah, Ahmed and Chowdhury [1] and later extended in Parsa, Ahmed and Yagoub [2], is used for modeling the dynamic changes in the level of electricity generation from each of the eight available energy sources. Optimal control theory is used to find the optimum decision policies for integration of renewable energy sources into the national power gird of any country. As a case study for our numerical results, official released data of United States Energy Information Administration website is used for the level of electricity generation from each of the energy sources mentioned above. Different scenarios are considered for the electricity demand. These range from U.S prediction for twenty years plan period to two percent annual growth rate for different plan periods of twenty and thirty years. The proposed methodology is general enough and hence applies to other energy problems with slight modifications based on the plannerʹs objectives.

Automatica, 2011

We characterize the dynamics of energy markets in which energy is derived from polluting (fossil) and clean (solar) resources. The analysis is based on geometric optimal control considerations. An important feature of solar energy technologies is that their cost of supply is predominantly due to upfront investment in capital infrastructure (rather than to actual supply rate) and this feature has important implications for the market allocation outcome. In particular, it gives rise to a threshold behavior in that solar energy is adopted only when the price of fossil energy exceeds a certain threshold. Under this condition solar technologies will (eventually) dominate energy supply by driving fossil energy altogether out of the energy sector. A tax on fossil energy can have a substantial impact since it changes the threshold price. A quantity restriction (e.g., a cap on fossil energy) allows for the coexistence of clean and polluting energy technologies also in the long run, and its effect on the use of fossil energy is more moderate.

Challenges in Sustainability, 2017

The existing economics literature neglects the important role of capacity in the production of renewable energy. To fill this gap, we construct a model in which renewable energy production is tied to renewable energy capacity, which then becomes a form of capital. This capacity capital can be increased through investment, which we interpret as arising from the allocation of energy, and which therefore comes at the cost of reduced general production. Requiring societal well-being to never decline-the notion of sustainability favored by economists-we describe how society could optimally elect to split energy in this fashion, the use of non-renewable energy resources, the use of renewable energy resources, and the implied time path of societal well-being. Our model delivers an empirically satisfactory explanation for simultaneous use of non-renewable and renewable energy. We also discuss the optimality of ceasing use of non-renewable energy before the non-renewable resource stock is fully exhausted.

2009

"We study the optimal harvesting of a renewable resource that cannot be continuously exploited, i.e. after the harvest the released space cannot be immediately reallocated to the resource. In the meantime, this space can be given an alternative use of positive utility. We consider a discrete time model over an infinite horizon with discounting, and characterize the optimality of two myopic policies, the greedy and the sustainable ones. We then show that the optimal strategy consists in applying one of these policies after a finite number of time steps. Value function and optimal feedback are explicitly determined."

Environmental and Resource Economics, 2014

Using the ceiling model, we characterize the optimal consumption paths of three energy resources: dirty oil, which is non-renewable and carbon emitting; clean oil, which is also non-renewable but carbon-free thanks to an abatement technology, and solar energy, which is renewable and carbon-free. The resulting energy-mix can supply the energy needs of two sectors. These sectors differ in the additional abatement cost they have to pay for consuming clean rather than dirty oil (sector 1 can abate its emissions at a lower cost than sector 2). We show that it is optimal to begin by fully capturing sector 1's emissions before the ceiling is reached. Also, there may exist optimal paths along which both capture devices have to be activated. In this case first sector's 1 emissions are fully abated before sector 2 abates partially. Finally, we discuss the effect of heterogeneity regarding the abatement cost on the uniqueness of the sectoral energy price paths.

European Transactions on Electrical Power, 2011

In view of the fact that different mechanisms for mitigating the CO 2 emission have been employed or proposed in different countries or regions, and those already implemented are still in an evolutionary procedure, the future CO 2 emission prices would be highly uncertain. Given this background, an effort is made for investigating the problem of generation investment decision-making in electricity market environment with uncertainties from the climate change policy for limiting the CO 2 emission. According to the changing characteristics of the uncertain factors, the models of the fuel prices, electricity prices, and CO 2 emission prices are respectively presented first. Next, under the existing real option approach (ROA) based methodological framework for the generation investment decision-making problem, a mathematical model accommodating multiple kinds of uncertainties and an efficient solving method are developed. Finally, the proposed model and method are illustrated by a numerical example with different scenarios.

2013 Africon, 2013

The importance of electric power in today's world cannot be overemphasized for it is the key energy source for industrial, commercial and domestic activities. Its availability in the right quantity is essential to advancement of civilization. In fact, a direct relationship can be shown to exist between (electric) power availability and per capital of a nation. The economy of a nation is easily identified with the amount of electricity it supplies. The advanced economy of the world generates a lot electric power and hence they witness rapid economical and industrial development. Third-world countries often witness epileptic or unstable supply of electric power. It is common knowledge that to have constant and stable electricity supply, a country needs to invest in its power generation. In the light of this, an optimal control model is proposed herein for the electric power generating system. In the model, the power generated and the capital investment describe the state of the sy...

2009

In the world of economics the words "Energy Management" carry different conno- tations for different groups of people. From the point of view of producers, they mean the scheme of optimization of all the different factors costing productions of different types of energy such that the total amount of revenue is maximized and the total cost of operation is minimized. They attempt to achieve both. But they must achieve at least one of these primary objectives. From the point of view of consumers, "Energy Management" means use of all different types of energy to sustain life and health most economically. Often both producers and consumers fail to understand what environmentalists mean by "Energy Management." To this group energy management must be done in such a way, so that all factors needed for production and usage of all forms of energy must meet all the strin- gent criteria to control pollutants released into the atmosphere by all agents of production ...

Policy Research Working Papers, 2014

The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.