Online Algorithms for Dynamic Matching Markets in Power Distribution Systems

In this paper we address the problem of designing online algorithms for dynamic matching markets in distribution systems whose objective is to maximize social welfare while being effective in integrating renewable energy by leveraging load flexibility. With the intuition that the performance of any online algorithm would worsen with increasing randomness, we propose two indicators for measuring the effectiveness of an online algorithm. First one is convergence to optimality (CO) as the randomness goes to zero. The second one focuses on the deviation from optimality measured as a function of the standard deviation, $\sigma$, of the underlying randomness: renewable generation and customer loads. We take into account the fact that a customer's value decreases with delay in load servicing. We present a pair of online matching algorithms for the following generation-consumption conditions: (i) when the mean of renewable generation ($\mu_s$) is greater than the mean of the number of customers ($\mu_n$) (assumed to be unit demand), and (ii) when the condition (i) is reversed. The online algorithm we present for the first case satisfies CO with a deviation that varies as $\sim O(\sigma)$. But the same algorithm fails to satisfy CO for the second case. We then present an extension of this algorithm and show that the modified algorithm satisfies CO for the second case with a deviation that varies as $\sim O(\sigma)$ plus an offset that is $O(\mu_n - \mu_s)$. Thus, there are two distinct regimes in the set of all possible generation-consumption conditions, with the platform requiring a distinct algorithm for each regime to be effective in terms of the indicators described above.