The quadratic cost function (ax2+bx+c) is used for the cost of power generated by conventional generators like thermal and hydro. Recent literature trend is to use the same function for the renewable power generation also. When the fuel for renewable generation is free of cost, how can the quadratic cost function be used for renewable generators? Experts, please throw light on this.
My remembrance is that the quadratic cost function is for thermal generation only; not for hydel. But, I also agree that there is a constant embedded cost independent of power generated or 'c' for any kind of generation. The proportional cost, as applicable to fuel cost is difficult to identify in renewable power unless addressing variability, reliability is convolutely proportional to PG or PG2 but I wonder. I agree with you, also on hydel.
Recent literature trend is to use the same function for the renewable power generation also applicable under prevailing assumptions.
In some papers only have considered a little cost for service and maintenance of these energy sources. There is some work in this area in IEEE and elsevier site and other publishers.
Thanks everyone for the concern.
My understanding is the graph between the amount of power generated and the total cost of generation raises non-linearly in any case, either conventional or non-conventional generators and hence can be represented by a quadratic function. Rate of raise/curvature of the curve depends on the constants of the equation. Therefore the application of quadratic cost function is equally justified to renewable sources also. Please do comment.
Using a quadratic equation to represent the cost function of a renewable energy resource is just a lazy work of a researcher or their ignornace. These quadratic cost functions for thermal units are based on 'input-output' characteristics of these thermal plants. Thermal plants have very unique input-output characteristics. If you look at the input-output characteristics of renewable energy, such as wind or solar, the input cost if almost free, so why need a quadratic cost function? The small cost that a renewable energy resource can have is; operation and maintenance cost (O&M cost), which can be very small. This can be modeled. Will it be linear? or quadratic? the historical data can provide the answer. Another possibility of having a non-linear cost function for a RE is; the owner of the plant has to pay some money for taking blowing wind or shining sun. Someone is already charging those free resources?
Partially agree with the answer of Jeremy Lin but it may not be true and valid for all geographical conditions. In conventional plant the cost of fuel is very high whereas renewable energy can be tapped at the location of its consumption but the other cost for generation of energy in renewable is profound to be more prominent in the context of integrating it with grid. Since the high cost in populated areas because of a large area of land required therefore no reclaimations of such land is possible till the plant is decommissioned.
Jitendra,
I understood what you said. I think what you talked about is 'fixed cost' such as the cost of securing a piece of land or even the cost of network upgrades to connect the RE resources.
What we are talking about is; in economic terms: 'Variable Cost', which typically includes fuel cost, emission cost, O&M, and other smaller miscellaneous costs. For a conventional generator, fuel cost takes up the majority of the cost. And their cost function has a typical shape of quadratic function.
For RES, the variable cost is almost zero because the fuel cost is zero (fuel is free). If you can consider emission cost (RES pollute emissions?) , O&M cost and other small cost, their sum of cost is almost nothing. And they need a quadratic function to represent that very small cost?
Dear Prakash, you can find detailed analytical expressions for renewable generators in the following papers:
Uncertainty Cost Functions for Solar Photovoltaic Generation, Wind Energy Generation, and Plug-In Electric Vehicles: Mathematical Expected Value and Verification by Monte Carlo Simulation
https://www.researchgate.net/publication/314134905_Uncertainty_Cost_Functions_for_Solar_Photovoltaic_Generation_Wind_Energy_Generation_and_Plug-In_Electric_Vehicles_Mathematical_Expected_Value_and_Verification_by_Monte_Carlo_Simulation
Uncertainty Cost Function Formulation in Small Hydropower Plants Inside a Microgrid
https://www.researchgate.net/publication/314218327_Uncertainty_Cost_Function_Formulation_in_Small_Hydropower_Plants_Inside_a_Microgrid
Game-Theoretic Dispatch Control in Microgrids Considering Network Losses and Renewable DER Integration
https://www.researchgate.net/publication/312048170_Game-Theoretic_Dispatch_Control_in_Microgrids_Considering_Network_Losses_and_Renewable_DER_Integration
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Article Uncertainty Cost Function Formulation in Small Hydropower Pl...
Article Game-Theoretic Dispatch Control in Microgrids Considering Ne...
Prakash are you using quadratic function to model wind cost function?
Hi, does Mr. Lin have any research papers to compliment his response for and against using the cost function for PV.
paper related: Quadratic Modelling of Uncertainty Costs for Renewable Generation and its Application on Economic Dispatch
Cost Based Dynamic Load Dispatch for an
Autonomous Parallel Converter Hybrid AC-DC
Microgrid
please refer this
but ,here parameters considered not clearly ,mentioned for cost function
Interesting, in most of the literature emission function is also quadratic. If we don't take installation cost for thermals as the Minimization function comprises only fuel and start-up costs, then why taking installation cost for renewables?what will be the basis for levelized cost of energy? How the cost of BESS will be taken?
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