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# A Generalized Nash Equilibrium Analysis of Electric Power Transmission-Distribution Coordination

Mezghani, Ilyès; Papavasiliou, Anthony; Le Cadre, Hélène

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"description": "<p>The integration of renewable energy resources leads to an impor- tant change in the way electricity markets are operated and orga- nized. The common approach to the optimization of electric power system operations has focused on the high-voltage Transmission Network (TN), while the Distribution Network (DN) is typically not accounted for in detail. Nevertheless, the proliferation of distributed renewable resources (for example, solar panels and electric vehicles) in the DN, coupled with the presence of a substantial amount of load flexibility in the residential and commercial sector, implies that a considerable amount of intelligence will have to be integrated at the distribution level of electric power systems. Consequently, Distribution System Operators (DSOs) will have a more active role in the operation of electric power systems and electricity markets in the future.</p>\n\n<p>The current paradigm of power system operations places all the intelligence in resources that are connected to the TN. Given the vast amount of unexploited flexible resources that are connected to the DN, the existing power system paradigm puts an important part of the system aside by only approximating the distribution system. The TN is the only part of the electricity supply chain that is currently optimized. The flexibility in the DN is mainly originating from active residential and commercial demand-side management, which we will need to exploit effectively in the coming decades if we wish to maintain the quality of service that we currently enjoy [<a href=\"#_bookmark36\">3</a>]. However, the DN is, in itself, a system of massive scale which presents a host of operational challenges. On the one hand, the&nbsp;</p>\n\n<p>amount of renewable resources that are located in the DN, mainly in the form of solar panels, has been growing and becoming an increasingly important component of the electric power supply chain. On the other hand, due to distribution constraints and the unpredictability of renewable resources, a certain amount of this renewable power needs to be consumed locally [<a href=\"#_bookmark41\">8</a>]. Coordination of operations in electricity markets has also been discussed in [<a href=\"#_bookmark52\">19</a>], <a href=\"#_bookmark47\">[14], </a><a href=\"#_bookmark53\">[20].</a></p>\n\n<p>This work draws inspiration from [<a href=\"#_bookmark52\">19</a>], where the authors focus on the counter-trading of re-dispatching resources between two Transmission System Operators (TSOs), in the context of conges- tion management. The authors investigate whether there should exist a separate market for transmission capacity by resorting to Generalized Nash Equilibrium (GNE), due to the influence of each TSO&rsquo;s action on the other TSO&rsquo;s decisions. We transpose this frame-</p>\n\n<p>work to the context of TSO-DSO coordination, where the activation of distribution system reserves1 by the TSO has an impact on the feasible actions of DSOs. We specifically focus on two coordination</p>\n\n<p>schemes inspired by the EU SmartNet project on TSO-DSO coordi- nation [<a href=\"#_bookmark45\">12</a>], [<a href=\"#_bookmark34\">1</a>]. Even if we will only provide preliminary results a on a small example in this paper, the SmartNet initiative is willing to implement these schemes on pilot test cases in Denmark, Italy and Spain. Possible inefficiencies due to decentralization then need to be quantified. Although we envision the trading of real power at the transmission-distribution system interface as a viable ap- proach towards TSO-DSO coordination, the SmartNet coordination schemes are not all aligned with such a setup. We therefore aim at comparing the efficiency of the schemes set forth by SmartNet, by relying on a GNE approach.</p>\n\n<p>The focus of our paper is (i) to model various TSO-DSO coordina- tion schemes which have been proposed in the SmartNet project as non-cooperative games, (ii) to propose a method for solving these problems, (iii) to interpret the solutions, and (iv) to compare the relative strengths and weaknesses of the different schemes.</p>\n\n<p>For our modeling, we resort to Generalized Nash Equilibrium, which is a computationally difficult problem [<a href=\"#_bookmark49\">16</a>]. We propose a solution strategy which is based on the theory of Nabetani, Tseng and Fukushima [<a href=\"#_bookmark48\">15</a>]. Our simple example unveils multiple equilibria, a phenomenon which has been well-studied in the literature (see for example [<a href=\"#_bookmark44\">11</a>], [<a href=\"#_bookmark35\">2</a>]), and we comment on the quality of these equilibria in our numerical example.</p>\n\n<p>The rest of the paper is organized as follows: we present the context of TSO-DSO coordination and our notation in section <a href=\"#_bookmark1\">2.</a> We present the Generalized Nash Equilibrium models of two TSO- DSO coordination schemes in section <a href=\"#_bookmark2\">3. </a>The implementation of the different schemes is illustrated through numerical results presented on a toy example in section <a href=\"#_bookmark27\">4. </a>Section <a href=\"#_bookmark33\">5 </a>concludes the paper.</p>",
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