Optimal Linearizations of Power Systems With Uncertain Supply and Demand

Hohmann, M.; Warrington, Joseph; Lygeros, John

doi:10.1109/tpwrs.2018.2878009

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…The infinite-dimensional GMP (4) can be approximated by an SDP relaxation involving a finite number of moments of µ [17]. GMPs with constraints on certain marginal distributions have been approximated using SDP relaxations in the literature for other purposes [19,23], and the derivation in this section leading to (9) and (11) is closely related to these. There is a trade-off between the accuracy of the approximation and the computational cost involved, and this is controlled by the choice of relaxation degree k ∈ N. The lowest admissible degree is determined by the degrees of the polynomial functions defining the problem.…”

Section: Tractable Relaxation Of Gmpmentioning

confidence: 99%

A two-stage polynomial approach to stochastic optimization of district heating networks

Hohmann

Warrington

Lygeros

2019

Sustainable Energy, Grids and Networks

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In this paper, we use stochastic polynomial optimization to derive high-performance operating strategies for heating networks with uncertain or variable demand. The heat flow in district heating networks can be regulated by varying the supply temperature, the mass flow rate, or both simultaneously, leading to different operating strategies. The task of choosing the set-points within each strategy that minimize the network losses for a range of demand conditions can be cast as a two-stage stochastic optimization problem with polynomial objective and polynomial constraints. We derive a generalized moment problem (GMP) equivalent to such a two-stage stochastic optimization problem, and describe a hierarchy of moment relaxations approximating the optimal solution of the GMP. Under various network design parameters, we use the method to compute (approximately) optimal strategies when one or both of the mass flow rate and supply temperature for a benchmark heat network. We report that the performance of an optimally-parameterized fixed-temperature variable-mass-flow strategy can approach that of a fully variable strategy. systems tend to have variable mass flow control [2]. Each strategy is subject to a trade-off in terms of losses; higher supply and return temperatures lead to increased heat losses, whereas higher mass flow rates increase the hydraulic losses in the pipes. This trade-off has been studied in different contexts. A comparison of strategies for primary networks 1 can be found in [3]. Hydraulic control strategies for the primary and secondary network were optimized in [4]. New mass flow regulation schemes using pumps were compared to the traditional strategy of controlling the consumer side heat flow using valves in [5]. The performance of district heating networks with multiple sources was studied in [6].Significant effort has also been invested in simplified models of these systems. The steady-state thermal losses of a network can be modelled as an exponential temperature drop along a pipe segment [6,7,8,9].By replacing the exponential by its first order Taylor approximation, the authors of [7] and [9] obtain a polynomial representation of the pipe output temperature. The hydraulic losses, namely the pressure drop along pipes and substations, are mass flow rate dependent and can be characterised implicitly by the nonlinear Colebrook-White equation [6]. To simplify this representation, it is often assumed that a pipe segment has a constant coefficient of resistance [7,9,10], making the absolute pressure losses quadratic in the mass flow rate. Thus, both types of network loss can be modelled using polynomial functions. Two-stage stochastic programsIf the operating strategy keeps a control variable fixed (either temperature or mass flow rate), it is desirable that the fixed choice leads to acceptable performance over a range of demand conditions. Here we define this performance as the expected operational cost incurred by hydraulic and thermal losses with respect to a probability distribution of the heat de...

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Section: Tractable Relaxation Of Gmpmentioning

confidence: 99%

A two-stage polynomial approach to stochastic optimization of district heating networks

Hohmann

Warrington

Lygeros

2019

Sustainable Energy, Grids and Networks

Self Cite

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“…In [21], the authors apply Taylor approximations to linearize the AC OPF. Another linearization approach is proposed in [22], using prior knowledge on the statistics of the demand. Finally, there exist heuristic approaches that apply to both meshed and radial topologies and provide locally optimal solutions such as genetic algorithm-based schemes [23] and Lagrangian-based nonlinear optimization methods [24].…”

Section: Introductionmentioning

confidence: 99%

“…The challenge with current model-based methods is that solving the OPF for dispatching and other applications for large systems is computationally intensive and therefore often cannot exploit the full prior knowledge on the uncertainty [5,19,22]. Especially when updates to the dispatch plan are to be carried out intra-day, the available computational time is limited [18].…”

Section: Introductionmentioning

confidence: 99%

Computing Day-Ahead Dispatch Plans for Active Distribution Grids Using a Reinforcement Learning Based Algorithm

2022

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The worldwide aspiration for a sustainable energy future has led to an increasing deployment of variable and intermittent renewable energy sources (RESs). As a result, predicting and planning the operation of power grids has become more complex. Batteries can play a critical role to this problem as they can absorb the uncertainties introduced by RESs. In this paper, we solve the problem of computing a dispatch plan for a distribution grid with RESs and batteries with a novel approach based on Reinforcement Learning (RL). Although RL is not inherently suited for planning problems that require open loop policies, we have developed an iterative algorithm that calls a trained RL agent at each iteration to compute the dispatch plan. Since the feedback given to the RL agent cannot be directly observed because the dispatch plan is computed ahead of operation, it is estimated. Compared to the conventional approach of scenario-based optimization, our RL-based approach can exploit significantly more prior information on the uncertainty and computes dispatch plans faster. Our evaluation and comparative results demonstrate the accuracy of the computed dispatch plans as well as the adaptability of our agent to input data that diverge from the training data.

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Physics-Data-Driven Power Flow Linearization Considering Topological Remedial Actions

Scherrer,

Pierrou,

Jia

et al. 2024

2024 IEEE Power &Amp; Energy Society General Meeting (PESGM)

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This paper proposes a novel physics-data-driven method for the linearization of AC power flow equations in the context of topological remedial actions. As opposed to physics-based works, the proposed method does not require the re-establishment of the linear model to follow the system changes induced by remedial actions, such as line switching and phase shifting angle variations. By ingeniously leveraging physics-driven aspects, such as hierarchical topology clustering, as well as data-driven regression, the proposed approach can establish a linear mapping between power flows and remedial actions and estimate the new operating point in the event of a remedial action with high accuracy and computational efficiency. Numerical results on a real-world European power network demonstrate the effectiveness of the proposed physics-data-driven linear power flow method in a practical setting. Particularly, the proposed method outperforms purely physics-driven and datadriven methods when a topological remedial action occurs.

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Optimal Linearizations of Power Systems With Uncertain Supply and Demand

Cited by 6 publications

References 21 publications

A two-stage polynomial approach to stochastic optimization of district heating networks

A two-stage polynomial approach to stochastic optimization of district heating networks

Computing Day-Ahead Dispatch Plans for Active Distribution Grids Using a Reinforcement Learning Based Algorithm

Physics-Data-Driven Power Flow Linearization Considering Topological Remedial Actions

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