Linear Price Sensitivity

Transactive energy systems should also be able to represent non-binary opportunities like price-sensitive quantities. See Figure 3. The use of price sensitivity in bids and offers can improve the accuracy and effectiveness of energy balance achieved via auctions, especially as the system diverges from its normal, expected trajectory. Complete bid and supply curves can also reduce
the numbers of iterations needed to discover prices using iterative consensus and game price-discovery mechanisms.
Price sensitivity appears quite naturally in conventional generator supply curves that are typically derived from their quadratic cost curves. If a cost curve is truly quadratic (not linear), offer prices are a linear function of generated quantity.
Price sensitivity also appears in transactive energy systems that discover price via centralized or distributed locational marginal pricing algorithms. Most notable is the effect of transport losses that make price become a function of system losses, which are in turn a function of transported quantity.
Price sensitivity comes into play for most controllable DER when time intervals become longer than what can be accommodated using binary on/off binary flexibility. Simple heuristic methods (e.g., thermostat bids based on zone temperatures) begin to fail when applied to relatively long future prediction horizons and long market intervals. Under these cases, bids and offers must
more accurately predict the actual energy quantity and the impacts of any flexibility. One strategy is to optimize the likely outcome while monetizing the state of the utility (e.g., comfort or discomfort level) that is provided. The result of such an optimization is an indifference curve that expresses the willingness of a prosumer to exchange energy and money.
As suggested by Figure 3, CTS might be extended to support simple price sensitivity from an individual object if it were to support a second price/quantity pair. However, the next section will argue that CTS should preferably support communication of many price/quantity pairs if it is to
represent effects of aggregation. Even individual objects might require multiple price/quantity pairs when their price sensitivity cannot be adequately represented by only two price/quantity pairs.

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