The marginal cost of electricity used as backup for solar hot water systems: A case study

In this study, a method is developed for estimating the long run marginal cost to electric utilities of providing backup service for solar residential heating and hot water (HHW) systems. This method accounts for all investment, fuel, and operating costs required to provide the added electric service for HHW. From the information produced using this method, the impacts of various rate design philosophies and of government tax and regulatory policies on annual homeowner costs, fuel consumption patterns, environmental pollutants, and the net social cost of providing HHW service can be computed. Also, the differences in these parameters among solar, electric, and conventional HHW systems can be compared.In an initial study, it was found that for one Northeastern utility the estimated marginal cost of electricity for backup to solar hot water (HW) systems was less than that for comparable electric HW systems for the period of the mid to late 1990s. Load management (shifting all electricity use to off-peak periods) substantially reduced marginal costs for both electric and solar systems and essentially eliminated any difference between them. In all cases, the marginal cost was lower than the average cost of all electricity generated for market penetration rates that can realistically be expected to be experienced. The impact on total annual costs to homeowners of various electricity rate schemes and the impacts of Federal tax credits and property tax exemptions were computed. Net changes in resource consumption patterns due to the use of solar systems were estimated.     

Optimisation of minimum backup solar water heating system

Current flat plate solar water heaters overproduce slightly in summer and have poor performance in winter at the time of maximum load. They use an expensive absorber plate over the entire absorbing aperture of the collector and fail to use the backside of the absorber. They often have under insulated tanks and are not optimised as integrated systems. This paper describes a design approach taken to use existing commercial flat plate absorber and tank components in a new way to maximise solar contribution and minimise material usage in the construction of the system. The design criterion used is not maximum peak efficiency, but minimum annual backup energy supplied to the system to meet an annual load. This corresponds to meeting a minimum greenhouse emissions requirement in both invested pollution during manufacture and pollution from backup energy supplied. Two new designs are shown which allow the solar fraction of systems to be increased to approximately 80–90% in Sydney Australia using a standard model of domestic hot water usage specified in Australian Standard AS4234. Pollution from fuel use drops to as little as 40% of that of conventional flat plate solar water heaters. These new designs use one absorber plate instead of two and a smaller and better insulated tank. Comparisons of solar fraction are evaluated for a range of climatic conditions. An important insight is that with such a performance optimised system the ultimate solar fraction is limited by occasional long duration cloud cover at the site of installation and making the system larger only increases dumped energy, not utilisable energy. Technical efficiency improvements only reduce the required collector area. However, some additional backup fuel reductions can be made through manual control of backup energy use, because this allows finer control of backup relative to real demand. Pollution from backup fuel usage may be able to be reduced to 1/4 that of current flat plate solar water heaters.     

The marginal cost of CO2 emissions

Haraden's model for estimating the economic cost of global warming is analysed. We change his method of discounting and some of his input parameters in a manner consistent with physical and economic theory as well as empirical data. We then find much higher costs than Haraden found. These costs are compared to the cost of reducing CO₂ emissions and we find that deep cuts of the emissions of CO₂ are preferable. A check of the sensitivity of our results with respect to some crucial parameter values does not alter that conclusion.     

Pricing district heating by marginal cost

A vital measure for industries when redirecting the energy systems towards sustainability is conversion from electricity to district heating (DH). This conversion can be achieved for example, by replacing electrical heating with DH and compression cooling with heat-driven absorption cooling. Conversion to DH must, however, always be an economically attractive choice for an industry. In this paper the effects for industries and the local DH supplier are analysed when pricing DH by marginal cost in combination with industrial energy efficiency measures. Energy audits have shown that the analysed industries can reduce their annual electricity use by 30% and increase the use of DH by 56%. When marginal costs are applied as DH tariffs and the industrial energy efficiency measures are implemented, the industrial energy costs can be reduced by 17%. When implementing the industrial energy efficiency measures and also considering a utility investment in the local energy system, the local DH supplier has a potential to reduce the total energy system cost by 1.6 million EUR. Global carbon dioxide emissions can be reduced by 25,000 tonnes if the industrial energy efficiency measures are implemented and when coal-condensing power is assumed to be the marginal electricity source.     

Technical note Estimation of electrical backup for solar box cooker

Incorporation of an electrical backup in a Solar Box Cooker (SBC) makes it operative throughout the year. The backup should be such that the essential characteristics of the solar cooker are retained and the energy consumption should be as low as possible. An estimate of electrical power requirement of a heater for an Indian SBC is presented considering its no-load figure of merit and energy balance at stagnation. It is found that a 160 W heater is sufficient for cooking.     

Technical change and the marginal cost of abatement

We address one aspect of the treatment of technical change in the environmental economics literature: how technical change impacts the marginal cost of abatement. We review a selection of papers that employ a variety of representations of technical change, and show that these representations have quite different, and sometimes surprising, effects on the marginal costs of pollution reductions. We argue that these varied representations in fact correspond to a variety of different technology options. We then present results indicating that this representation matters — the impacts of technical change on the marginal cost of abatement can crucially impact policy analysis.     

The performance of a low cost clay solar cooker

This paper reports the development of a low cost clay solar cooker. The main features of this cooker are that it is made from cheap, locally available materials, and needs no skilled labour. One of the new design features of the solar cooker is the replacement of the absorber plate with locally available black sontes. The effects of using the black stones instead of the abrosber plate resulted in solar cooker capable of storing solar energy, hence making late cooking possible.     

The cost estimate for a novel cheap solar cell

The estimate for the lowest cost of SODL (silicon on defect layer) solar cell is made according to the price standard of present market. The estimate shows that the PV (photovoltaics) energy costs can be reduced from today's 25–30 cents/(kW h) to 7–8 cents/(kW h) which is comparable with the present cost of electricity generated by traditional energy sources such as fossil and petroleum fuels. The PV energy costs could be reduced to a value lower than 7–8 cents/(kW h) by developing SODL technology. The SODL solar cell manufacture featuring simple processes is suitable to large scale automated assembly lines with high yield of large area cells. Some new ideas are suggested, favoring the further reduction in the cost of commercial solar cells.     

Realistic generation cost of solar photovoltaic electricity

Solar photovoltaic (SPV) power plants have long working life with zero fuel cost and negligible maintenance cost but requires huge initial investment. The generation cost of the solar electricity is mainly the cost of financing the initial investment. Therefore, the generation cost of solar electricity in different years depends on the method of returning the loan. Currently levelized cost based on equated payment loan is being used. The static levelized generation cost of solar electricity is compared with the current value of variable generation cost of grid electricity. This improper cost comparison is inhibiting the growth of SPV electricity by creating wrong perception that solar electricity is very expensive. In this paper a new method of loan repayment has been developed resulting in generation cost of SPV electricity that increases with time like that of grid electricity. A generalized capital recovery factor has been developed for graduated payment loan in which capital and interest payment in each installment are calculated by treating each loan installment as an independent loan for the relevant years. Generalized results have been calculated which can be used to determine the cost of SPV electricity for a given system at different places. Results show that for SPV system with specific initial investment of 5.00 $/kWh/year, loan period of 30 years and loan interest rate of 4% the levelized generation cost of SPV electricity with equated payment loan turns out to be 28.92 ¢/kWh, while the corresponding generation cost with graduated payment loan with escalation in annual installment of 8% varies from 9.51 ¢/kWh in base year to 88.63 ¢/kWh in 30th year. So, in this case, the realistic current generation cost of SPV electricity is 9.51 ¢/kWh and not 28.92 ¢/kWh. Further, with graduated payment loan, extension in loan period results in sharp decline in cost of SPV electricity in base year. Hence, a policy change is required regarding the loan repayment method. It is proposed that to arrive at realistic cost of SPV electricity long-term graduated payment loans may be given for installing SPV power plants such that the escalation in annual loan installments be equal to the estimated inflation in the price of grid electricity with loan period close to working life of SPV system.     

The importance of marginal cost electricity pricing to the success of greenhouse gas reduction programs

The efficient reduction of GHG emissions requires appropriate retail pricing of off-peak electricity. However, off-peak electricity for residential consumers is priced at 331% above its marginal cost in the United States as a whole (June 2009). Even for the 1% of residences that are on some form of time-of-use (TOU) rate schedule, the off-peak rate is almost three times higher than the marginal cost. A barrier to marginal-cost based TOU rates is that less than 9% of U.S. households have the “smart” meters in place that can measure and record the time of consumption. Policies should be put in place to achieve full deployment. Another important barrier is consumer concern about TOU rate design. Two TOU rate designs (baseline and two-part tariff) are described that utilize marginal-cost based rates, ensure appropriate cost recovery, and minimize bill changes from current rate structures. A final barrier is to get residences on to these rates. Should a marginal-cost based TOU rate design remain an alternative for which residences could “opt-in,” or become the default choice, or become mandatory? Time-invariant rates are a historical anachronism that subsidize very costly peak-period consumption and penalize off-peak usage to our environmental detriment. They should be phased out.     

A low cost design solar desalination unit

A novel low cost design solar still is described and performance data are presented. The proposed design eliminates the need for support or side-walls, as required in most conventional solar still designs. A comparison of the measured still productivity values between the proposed design and a large solar distillation plant constructed in India has shown that our design simplification has not affected still performances. An economic analysis, based upon the fraction of still construction cost dedicated to the still wall construction, has indicated that the proposed design should reduce the overall cost/m² of the solar still construction by at least 20%.     

Low cost double-sided buried-contact silicon solar cells

The cost of a solar cell, using the buried-contact technology, can be cut down if the many high temperature processing sequences are reduced to only one. The use of liquid or solid sources at elevated temperatures has been the practice for both emitter and groove diffusions. The use of spin-on dopants would enhance the realization of one high temperature processing. The characterization of groove diffusion with spin-on dopants as carried out in this work has shown some promising results. Also, the use of a laser beam for grooving, as well as driving the dopants into the grooves has resulted in large area cells with energy conversion efficiency in excess of 13% on CZ, p-type, 0.7 Ω cm.     

A low cost high flux solar simulator

A low cost, high flux, large area solar simulator has been designed, built and characterized for the purpose of studying optical melting and light absorption behavior of molten salts. Seven 1500 W metal halide outdoor stadium lights are used as the light source to simulate concentrating solar power (CSP) heliostat output. Metal halide bulbs and ballasts are far less costly per-watt than typical xenon arc lamp solar simulator light sources. They provide a satisfactory match to natural sunlight; although ‘unfiltered’ metal halide lights have irradiance peaks between 800 and 1000 nm representing an additional 5% of measured energy output as compared to terrestrial solar irradiance over the same range. With the use of a secondary conical concentrator, output fluxes of approximately 60 kW/m² (60 suns) peak and 45 kW/m² (45 suns) average are achieved across a 38 cm diameter output aperture. Unique to the design of this simulator, the tilt angle and distance between the output aperture and the ground are adjustable to accommodate test receivers of varying geometry. Use of off-the-shelf structural, lighting and electrical components keeps the fabrication cost below $10,000.     

Simulation and cost optimization of solar heating of buildings in adverse solar regions

In the present study a model has been developed which simulates the effects of hourly weather conditions on the performance and cost of a combined solar/conventional heating system for buildings in cold, cloudy climates. The model exhibits the effects of several system and cost parameters on combined system cost so that optimal designs can be determined.Performance and cost results are presented for 1971 Ottawa, Ontario, weather data. The economic analysis, which treats both collector and conventional system fuel costs parametrically, shows that solar heating of a typical house in cold, cloudy climates is economically competitive with fuel oil heating only if the price of oil rises to approximately 80¢/gal.     

Short- and long-run marginal cost pricing: On their alleged equivalence

The equivalence between short-run marginal cost (SRMC) and long-run marginal cost (LRMC) in a fully adjusted equilibrium has been proved over and over again. In the literature dealing with public utility pricing, this basic result has been taken to imply that it is optimal to set prices at LRMC. Important contributions to this literature are reviewed in this paper. The equivalence, however, is valid only under the very restrictive assumption that the capacity can be varied continuously. This means that indivisibilities, irreversibilities and durability of investments are ignored. Where such phenomena exist, as in electricity production and distribution, pricing according to LRMC is neither theoretically valid nor applicable. It is not surprising that it has been difficult for public utilities to define the LRMC concept operationally; average cost concepts are used as ‘approximations’. Under these circumstances we find it advisable to dispense with the LRMC concept altogether and rely on pricing based on SRMC.     

Optimization of the investment cost of solar based grid

A new optimization method of the investment cost of a distribution grid supplied by photovoltaic (PV) sources. This method consists of determining the optimal grid cables cross sections and the optimal grid supply point (GSP) position, such that the sum of the joule losses and the cables investment costs are optimized. The determination of these parameters are performed by the programming of analytical equations using Matlab software, taking into account the influence of technical and economical requirements on the choice of the cables cross sections and the possibility of using several photovoltaic generators (PVG) with separated grids for spaced loads from a long distance, by optimizing the grouping loads combination. The obtained results show that: for a lowest global investment cost, the optimal GSP is referred to the minimum cost center (MCC), for the grid joule losses minimization, it can be in the minimum joule losses cost center (MJLCC); or in the center of the minimum investment cost of cables (CMICC) in the case of the cables investment cost minimization. The adoption of the optimal cross sections, the optimal PVGs (GSPs) number and their optimal positions achieve significant economic gains in terms of the investment cost.     

Parametric performance and cost models for solar concentrators

The development of parametric performance and cost models for various solar concentrators is discussed. The equations are derived in the context of an optimization scheme which can be applied to many different problems which arise when heat is generated by means of solar concentrators. Thus, while the results presented were developed for finding a minimum cost solar electric energy power plant, the method employed has been found to have general applicability. Sensitivity analysis of the subsytems is also discussed. Finally, numerous illustrative examples are presented.     

A low cost collector-cum-storage type solar water heater

A low cost collector-cum-storage type solar water heater has been developed. The cost of the heater is reduced by replacing window glass cover with 0.2 mm thick PVC film to avoid glass breakage in transportation and maintenance. In this paper the performances of solar water heaters having double glazing of PVC and glass have been compared. It was found that their performances are similar. Moreover, by providing an insulating cover in the night, the water remains warm till next morning for taking a bath etc. in the early hours when there is no sunshine.     

Market modeling for assessment of demand side programs using the marginal cost

Demand side management is nowadays considered as a fundamental step in the energy planning process. The criteria proposed for the assessment of the demand side programs (DSPs) are usually based on the balance between the marginal supply cost and the mean DSP cost. These criteria could not support the allotting of the invested capital to incentives for the consumers and advertising. This paper presents a methodology to support the utility planning at this point with more reliability. It proposes the expansion of the assessment criteria with the use of the marginal cost of the DSP. For the calculation of the DSP marginal cost, a dynamic model is developed and it is used for the simulation of the penetration of a DS Program. Using the ‘least‐cost’ criterion as the decision rule for the simulation, the planner has a distribution of the available investment capital throughout the whole planning period. The use of the ‘most‐value’ criterion supports the separation of the invested capital between incentives for the consumers and supportive expenses, e.g. advertising, marketing costs, etc. Copyright © 2000 John Wiley & Sons, Ltd.