DIY 3D Solar Panels

Energy demand

Annual end-use electric demand 5.066 trillion kWh

Annual transportation fuel demand 4.589 trillion kWh

Light duty vehicles 1.254 trillion kWh

Freight transport 1.697 trillion kWh

Aircraft 1.638 trillion kWh

Primary energy supply

Transportation delivered natural gas price $6.93-8.31/GJ

Utility natural gas price $5.54/GJ

Reference case annual gas consumption 43 EJ/yr

Annual solar capacity factor 29.5%

Annual wind capacity factor 43.3%

Maximum wind capacity 1.0 TW

Nuclear/hydro capacity 0.1 TW

Economic and environmental

Discount rate 5%

Natural gas emission factor (combustion) 54g C/kWht

Fuel cycle emissions (production, compression, leakage) neglected

Electric generation technology assumptions

Nuclear Fission $2200/kW

Life 40 years

Operating cost 1 cent/kWh

Combined cycle plant $600/kW

Life 30 years

Non-fuel operating cost 0.5 cents/kWh

Efficiency 57%

Wind $655/kW

Life 15 years

Solar photovoltaic $1500/kWp

Life 30 years

Fuel cells (peak) $200/kW

Life 20 years

Efficiency (LHV hydrogen) 50%

Electric transmission and distribution $200/kW

Life 30 years

Hydrogen production and storage technology assumptions

Steam electrolysis (baseload) $500/kW

Life 20 years

Efficiency (LHV) 91%

Steam electrolysis (peak) $250/kW

Life 20 years

Efficiency (LHV) 83%

Hydrogen compression $100/kW

Life 15 years

Efficiency (LHV) 91%

Maintenance 0.1 cent/kWh

Compressed hydrogen storage (5000 psi) $4.50/kWh

Life 20 years

Hydrogen liquefier $500/kW

Life 20 years

Efficiency 71%

Maintenance 0.1 cents/kWh

Liquid hydrogen storage (large scale) $0.30/kWh

Life 20 years

To conduct these studies we modeled an energy system potentially drawing on a range of resources, both conventional and renewable, and supplying electricity and transportation fuels. The model can be set up to represent an entirely conventional system, a system that relies entirely on renewable energy, or any mixture. When modeling a renewable system, the model includes a fuel cell to cover peak electric demands. In these analyses the system was always configured to reliably serve the electric load.

The technological parameters (efficiencies and costs) represent a system that might be developed some decades in the future (see Table 6.2 for cost and performance assumptions). We have used optimistic estimates of the costs and efficiencies of various technologies including natural gas technologies, since this should give a more useful picture of the tradeoff between these technologies in a future context.

Figure 6.1 shows a system schematic. The primary resources are wind, solar, nuclear, and a gas fired turbine. A fuel cell is provided with enough capacity to cover the electric demand if the wind and solar are not sufficient. This is sized to just cover the maximum shortfall, not the maximum electric demand. A flywheel storage option is also included in some of the runs. This can take electricity from the grid and return it later.

The hydrogen transportation fuel sector is modeled directly within the model. These analyses evaluate various scenarios on the fraction of transportation fuel that is met by hydrogen. It is assumed that the balance of the transportation fuel is provided by natural gas. The costs and emissions from the natural gas fueled transportation are included in final cost and emissions results.

Both compressed hydrogen and liquid hydrogen storage have been included, along with the compression and liquefaction capacity needed to provide their outputs. For given capacities of long and short-term storage, the model determines the rates of filling and discharge for each of the storage devices each hour to minimize the overall cost. The model determines the required level of long-term storage capacity. Short-term storage capacity is varied based on the assumptions about wind and solar capacities and the transportation fuel demand.

Each scenario analyzed in this chapter required the optimization of both the system structure and annual operations under a set of constraints. The system structure is defined by the capacities of each of the components (e.g. generators, electrolyzers, storage, compressors, etc.). The system operations specify exactly how each component will be dispatched hour-by-hour over the year. This includes the allocation of electric demands to the generators each hour and the allocation of hydrogen production between the two electrolyzers. The storage devices must also allocate their purchases of hydrogen over time so as to meet their demands at the lowest cost.

Several constraints must be observed in the solution: the total demands for electricity and hydrogen must be met, and in most cases the maximum capacities of specific generating technologies were constrained. Once the capacity of a given generating unit is set, its production each hour is constrained. For the dispatchable technologies (the natural gas turbine and the nuclear generator) the constraint is constant each hour. For the renewable technologies the constraint each hour is a function of the capacity of the generator and the resource availability in each hour.

This requires a bi-level optimization approach: the structure of the system must be optimized and the operation of the system, given the structure, must be optimized. We have extended the META^Net economic modeling system (Lamont, 1994) to make these analyses. META^Net is a software system that allows the user to structure and solve models of economic systems. The system is modeled as a network of nodes representing end-use demands, conversion processes (such as generation or storage), markets, and resources. The markets represent the points in the system where a total demand (e.g. for electricity) will be allocated among a set of suppliers. META^Net finds a set of allocations each hour that is an economic equilibrium - all the demands are met and each market is in equilibrium.

META^Net finds the equilibrium solution through a series of iterations. Each iteration consists of a down pass and an up pass. On the down pass, the end-use demand nodes (here they are electric demand and demands for hydrogen transportation fuels) pass their demands down to the next nodes. When a node receives a demand it determines how to supply that demand. Market nodes sum up the total demand each period and then allocate that demand to all of its suppliers based on the prices that the suppliers require in that period. Conversion nodes determine the amount of each input they require in order to produce the demand. A conversion node may have several inputs. For example, a hydrogen compressor produces compressed hydrogen from uncompressed hydrogen using both hydrogen and electricity. They then pass the demands for the required inputs down the network to the nodes that provide those inputs.

Eventually the demands are passed down to the resource nodes. At this point the up-pass starts. The resource nodes determine the price (marginal cost) that must be charged in order to meet the demand. They then pass this price back up the network. When a conversion node receives the prices for its inputs, it computes the price required for its output including any capital or other operating costs. All nodes set prices to meet a target rate of return. These prices eventually are passed up to the end-use demand nodes. In general META^Net allows for price sensitive demands, however in this case the demands are fixed each hour. Through a series of iterations the allocations at the market nodes are adjusted until the total quantity demanded each hour is in equilibrium with the prices charged each hour. Further, the allocations within the market node are made until the prices (i.e. marginal costs) from the suppliers are equalized.

The economic equilibrium solution is equivalent to a cost minimization solution. Hogan and Weyant (1982) provide the formal proof of the equivalence between the equilibrium and cost optimization solutions for these sorts of network models. Intuitively the equivalence can be seen as follows: each of the production nodes determine their marginal cost of production each hour given the demands for output that they see. The market nodes allocate demand to each of the suppliers such that the marginal costs of production between the competing suppliers are equalized. The storage nodes are somewhat like market nodes, in that they have a total demand for releases - or "production" - over time. They attempt to minimize costs by purchasing this total amount at the hours when costs are minimum. The algorithm for the storage node also equalizes the marginal costs of purchases over time periods. In fact, correctly modeling the optimal operation of storage devices is very computation intensive. The algorithm used in this version of META^Net is an approximation to the true optimum. Through side calculations we find that the resulting system cost is within a percent or two of the true minimum cost.

The renewable technologies have constraints in each hour, reflecting the hourly availability of the resource and the capacity that has been set. Each of the dis-patchable technologies also has constraints reflecting the actual capacity available. These constraints are enforced by computing shadow prices whenever the demand to a node exceeds its constraint. The market allocations are actually based on these shadow prices. The shadow prices are adjusted until the constraints are just met.

The discussion above describes the optimization of operation and dispatch for each hour of the year. The model also optimizes the capacities of the components. The capacities are adjusted each iteration, but once they are set, they are constant for the entire year. Essentially, the capacities are adjusted until the marginal value of capacity is equal to the marginal cost of additional capacity. Note that we can also place maximum constraints on the capacity for any node.

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