See Appendix D. Asset Fair Market Value. With respect to any asset, as of the date of ----------------------- determination, the cash price at which a willing seller would sell, and a willing buyer would buy, each being apprised of all relevant facts and neither acting under compulsion, such as in an arm's-length negotiated transaction with an unaffiliated third party without time constraints.
See Appendix D. Theorem 4 proves that insurance contracts are always feasible for the framework analyzed, which considers an unconstrained network. In Sec- tion 5.2, we show that the feasibility of the contract will depend on the loca- tion of these players in the grid, due to the differences in locational marginal prices across the network. The worst-case scenario for the storage unit occurs when the renewable shortage is at least as large as the reserve amount established in the contract. In this case, the storage unit will incur the operational cost of supplying the full reserve. For a given insurance contract, we can use this fact to establish a lower bound on the expected profit of the storage.
Corollary 5. Let the storage unit follow the arbitrage policy to charge when the day-ahead price is minimum and offer the reserve u+ = emaxE in the insurance contract. Then, the contract with a reserve price π = λ
See Appendix D. Thus, transmitting in the maximal-eigenvalue eigenspace Since Tr(RT ) = mS, then λT 1. This implies ˙unif (0) C˙ (0) which explains the inefficiency of uniform power allocation in the low power regime. Nonetheless, as later simulations suggest, the performance of uniform power allocation is comparable to the optimal strategy in the low- SNR regime. This can be explained by the following corollary.
Corollary 1. The second derivative achieved by a uniform power allocation is greater than the secret-key capacity second derivative, with equality in case of uncorrelated transmit correlation.
