Dynamic participation in local energy communities with peer-to-peer trading

Background: Energy communities and local electricity markets (e.g., as peer-to-peer trading) are on the rise due to increasingly decentralized electricity generation and favorable adjustment of the legal framework in many European countries. Methods: This work applies a bi-level optimization model for dynamic participation in peer-to-peer electricity trading to determine the optimal parameters of new participants who want to join an energy community, based on the preferences of the members of the original community (e.g., environmental, economic, or mixed preference). The upper-level problem chooses optimal parameters by minimizing an objective function that includes the prosumers' cost-saving and emission-saving preferences, while the lower level problem maximizes community welfare by optimally allocating locally generated photovoltaic (PV) electricity between members according to their willingness-to-pay. The bi-level problem is solved by transforming the lower level problem by its corresponding Karush-Kuhn-Tucker (KKT) conditions. Results: The results demonstrate that environment-oriented prosumers opt for a new prosumer with high PV capacities installed and low electricity demand, whereas profit-oriented prosumers prefer a new member with high demand but no PV system capacity, presenting a new source of income. Sensitivity analyses indicate that new prosumers' willingness-to-pay has an important influence when the community must decide between two new members. Conclusions: The added value of this work is that the proposed method can be seen as a basis for a selection process between a large number of potential new community members. Most important future work will include optimization of energy communities over the horizon several years.

Inexact Derivative-Free Optimization for Bilevel Learning

Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by-now common strategy to resolve this issue is to learn these parameters from data. While mathematically appealing, this strategy leads to a nested optimization problem (known as bilevel optimization) which is computationally very difficult to handle. It is common when solving the upper-level problem to assume access to exact solutions of the lower-level problem, which is practically infeasible. In this work we propose to solve these problems using inexact derivative-free optimization algorithms which never require exact lower-level problem solutions, but instead assume access to approximate solutions with controllable accuracy, which is achievable in practice. We prove global convergence and a worst-case complexity bound for our approach. We test our proposed framework on ROF denoising and learning MRI sampling patterns. Dynamically adjusting the lower-level accuracy yields learned parameters with similar reconstruction quality as high-accuracy evaluations but with dramatic reductions in computational work (up to 100 times faster in some cases).

On Bilevel Optimization with Inexact Follower

Traditionally, in the bilevel optimization framework, a leader chooses her actions by solving an upper-level problem, assuming that a follower chooses an optimal reaction by solving a lower-level problem. However, in many settings, the lower-level problems might be nontrivial, thus requiring the use of tailored algorithms for their solution. More importantly, in practice, such problems might be inexactly solved by heuristics and approximation algorithms. Motivated by this consideration, we study a broad class of bilevel optimization problems where the follower might not optimally react to the leader’s actions. In particular, we present a modeling framework in which the leader considers that the follower might use one of a number of known algorithms to solve the lower-level problem, either approximately or heuristically. Thus, the leader can hedge against the follower’s use of suboptimal solutions. We provide algorithmic implementations of the framework for a class of nonlinear bilevel knapsack problem (BKP), and we illustrate the potential impact of incorporating this realistic feature through numerical experiments in the context of defender-attacker problems.

A Computationally Efficient Optimization Method for Battery Storage in Grid-connected Microgrids Based on a Power Exchanging Process

Battery storage (BS) sizing problems for grid-connected microgrids (GCμGs) commonly use stochastic scenarios to represent uncertain natures of renewable energy and load demand in the GCμG. Though taking a large number of stochastic scenarios into consideration can deliver a relatively accurate optimal result, it can also highly deteriorate the computational efficiency of the sizing problem. To make an accuracy-efficiency trade-off, a computationally efficient optimization method to optimize the BS capacities based on the power exchanging process of the GCμG is proposed in this paper. According to the imbalanced power of the GCμG, this paper investigates the power exchanging process between the GCμG, BS and external grid. Motivated by the BS dynamics, a forward/backward sweep-based energy management scheme is proposed based on the power exchanging process. A heuristic two-level optimization model is developed with sizing BS as the upper-level problem and optimizing the operational cost of the GCμG as the lower-level problem. The lower-level problem is solved by the proposed energy management scheme and the objective function of the upper-level is minimized by the pattern search (PS) algorithm. To validate the accuracy and computational efficiency of the proposed method, the numerical results are compared with the mixed integer linear programming (MILP) method. The comparison shows that the proposed method shares similar accuracy but is much more time-efficient than the MILP method.

Particle Swarm Optimization Based on Smoothing Approach for Solving a Class of Bi-Level Multiobjective Programming Problem

As a metaheuristic, Particle Swarm Optimization (PSO) has been used to solve the Bi-level Multiobjective Programming Problem (BMPP). However, in the existing solving approach based on PSO for the BMPP, the upper level and the lower level problem are solved interactively by PSO. In this paper, we present a different solving approach based on PSO for the BMPP. Firstly, we replace the lower level problem of the BMPP with Kuhn-Tucker optimality conditions and adopt the perturbed Fischer-Burmeister function to smooth the complementary conditions. After that, we adopt PSO approach to solve the smoothed multiobjective programming problem. Numerical results show that our solving approach can obtain the Pareto optimal front of the BMPP efficiently.

Minimization of cost and congestion management using interline power flow controller

Purpose The purpose of this paper is to optimally locate and size the FACTS device, namely, interline power flow controller in order to minimize the total cost and relieve congestion in a power system. This security analysis helps independent system operator (ISO) to have a better planning and market clearing criteria during any operating state of the system. Design/methodology/approach A multi-objective optimization problem has been developed including real power performance index (RPPI) and expected security cost (ESC). A security constrained optimal power flow has been developed as expected security cost optimal power flow problem which gives the probabilities of operating the system in all possible pre-contingency and post-contingency states subjected to various equality and inequality constraints. Maximizing social welfare is the objective function considered for normal state, while minimizing compensations for generations rescheduling and maximizing social welfare are the objectives in case of contingency states. The proposed work is viewed as a two level problem wherein the upper-level problem is to optimally locate IPFC using RPPI and the lower-level problem is to minimize the ESC subjected to various system constraints. Both upper-level and lower-level problem are solved using particle swarm optimization and The performance of the proposed algorithm is tested under severe line outages and has been validated using IEEE 30 bus system. Findings The proposed methodology shows that IPFC controls the power flows in the network without generation rescheduling or topological changes and thus improves the performance of the system. It is found that the benefit achieved in the ESC due to the installation of IPFC is greater than the annual investment cost of the device. ISO cannot achieve minimum total system cost by merely rescheduling generators. Instead of rescheduling, FACTS devices can be used for compensation by achieving minimum cost. IPFC can be used to compensate the congested lines and transfer cheaper power from generators to consumers. Originality/value Operational reliability, financial profitability and efficient utilization of the existing transmission system infrastructure has been achieved using single FACTS device. Instead of using multiple FATCS devices, if a single FACTS device like IPFC which itself can compensate several transmission lines is used, then in addition to the facility for independently controlled reactive (series) compensation of each individual line, it provides a capability to directly transfer real power between the compensated lines. Hence an attempt has been made in this paper to incorporate IPFC for relieving congestion in a deregulated environment. However, no previous researches have considered incorporating compensation of multi-transmission line using single IPFC in minimizing ESC. Thus, in this paper, the authors indicate how much the ESC is reduced by installing IPFC.

A New Method To Solve Bi-Level Quadratic Linear Fractional Programming Problems

In this paper, we have developed a new method to solve bi-level quadratic linear fractional programming (BLQLFP) problems in which the upper-level objective function is quadratic and the lower-level objective function is linear fractional. In this method a BLQLFP problem is transformed into an equivalent single-level quadratic programming (QP) problem with linear constraints by forcing the duality gap of the lower-level problem to zero. Then by obtaining all vertices of the constraint region of the dual of the lower-level problem, which is a convex polyhedron, the single-level QP problem is converted into a series of finite number of QP problems with linear constraints which can be solved by any standard method for solving a QP. The best among the optimal solutions gives the desired optimal solution for the original bi-level programming (BLP) problem. Theoretical results have been illustrated with the help of a numerical example.