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We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the network feedback. Then, a reduced network is built, where each node represents the aggregate dynamics of each coherent group, and the reduced network captures the dynamic coupling between the groups. We provide an upper bound on the approximation error when the network graph is randomly generated from a weight stochastic block model. Finally, numerical experiments align with and validate our theoretical findings. 

Electricity markets are cleared by a two-stage, sequential process consisting of a forward (day-ahead) market and a spot (real-time) market. While their design goal is to achieve efficiency, the lack of sufficient competition introduces many opportunities for price manipulation. To discourage this phenomenon, some Independent System Operators (ISOs) mandate generators to submit (approximately) truthful bids in the day-ahead market. However, without fully accounting for all participants' incentives (generators and loads), the application of such a mandate may lead to unintended consequences. In this paper, we model and study the interactions of generators and inelastic loads in a two-stage settlement where generators are required to bid truthfully in the day-ahead market. We show that such mandate, when accounting for generator and load incentives, leads to a {generalized} Stackelberg-Nash game where load decisions (leaders) are performed in day-ahead market and generator decisions (followers) are relegated to the real-time market. Furthermore, the use of conventional supply function bidding for generators in real-time, does not guarantee the existence of a Nash equilibrium. This motivates the use of intercept bidding, as an alternative bidding mechanism for generators in the real-time market. An equilibrium analysis in this setting, leads to a closed-form solution that unveils several insights. Particularly, it shows that, unlike standard two-stage markets, loads are the winners of the competition in the sense that their aggregate payments are less than that of the competitive equilibrium. Moreover, heterogeneity in generators cost has the unintended effect of mitigating loads market power. Numerical studies validate and further illustrate these insights. 

This paper proposes a market mechanism for multi-interval electricity markets with generator and storage participants. Drawing ideas from supply function bidding, we introduce a novel bid structure for storage participation that allows storage units to communicate their cost to the market using energy cycling functions that map prices to cycle depths. The resulting market-clearing process--implemented via convex programming--yields corresponding schedules and payments based on traditional energy prices for power supply and per-cycle prices for storage utilization. We illustrate the benefits of our solution by comparing the competitive equilibrium of the resulting mechanism to that of an alternative solution that uses prosumer-based bids. Our solution shows several advantages over the prosumer-based approach. It does not require a priori price estimation. It also incentivizes participants to reveal their truthful costs, thus leading to an efficient, competitive equilibrium. Numerical experiments using New York Independent System Operator (NYISO) data validate our findings.