Adaptive Price Estimation in Cognitive Radio Enabled Smart Grid Networks

Abstract

This paper focuses on the allocation of resources to cognitive users in a two-way cognitive radio facilitated smart grid (SG) network. The resources are essential in controlling the performance of demand response management in the SG, ensuring profit to the power supplier and simultaneously cost-saving to the consumers. However, cognitive users need more power for their data transmission, which compels the utility company to increase its electricity price. Hence, we propose an adaptive resource allocation algorithm based on normalized least mean squares (NLMS) to estimate the electricity price that benefits both the supplier and consumers with optimal allocation of power demands under the constraints of transmission power, system throughput, and the probability of detection. The simulation results validate the performance of our proposed scheme by comparing it with the application of metaheuristic algorithms for maximizing aggregate profit. The impact of the channel parameters on system performance is also studied.

Appendix I

Proof of $B_{nt}$ is a concave function of $d_{nt}$ at a constant $P_{tnt}$.

Proof

Taking the first derivative of Eq. (11) for a constant value of $P_{tnt}$.

$$ \frac{{dB_{nt} }}{{ \left. {d_{nt} } \right|_{{P_{tnt} = {\mathrm{constant}}}} }} = \omega_{n} \left( {1 - O_{ot} } \right) - \alpha \left( {1 - O_{ot} } \right)^{2} d_{nt} - \rho_{t} O_{ot} $$

(27)

It is known that if the Hessian matrix $H\left( {B_{nt} } \right)$ is negative, $B_{nt}$ is concave in $d_{nt}$. Taking the second derivative of Eq. (11) w.r.t $d_{nt}$

$$ \frac{{d^{2} B_{nt} }}{{\left. { d^{2}_{nt} } \right|_{{P_{tm,tl} = {\mathrm{constant}}}} }} = \left\{ {\begin{array}{ll} { - \alpha \left( {1 - O_{ot} } \right)^{2} , \;{\mathrm{at}} \;t{\mathrm{th}}\;{\mathrm{slot}}} \\ {0, \;{\mathrm{at}}\;{\mathrm{other}}\;{\mathrm{slot}}} \\ \end{array} } \right. $$

(28)

Hence, diagonal elements of $H\left( {B_{nt} } \right)$ are negative and other elements are zero. It shows that $B_{nt}$ is strictly concave in $d_{nt}$.