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Hosting capacity (HC) and dynamic operating envelopes (DOEs), defined as dynamic, time-varying HC, are calculated using three-phase optimal power flow (OPF) formulations. Due to the computational complexity of such optimisation problems, HC and DOE are often calculated by introducing certain assumptions and approximations, including the linearised OPF formulation, which we implement in the Python-based tool ppOPF. Furthermore, we investigate how assumptions of the distributed energy resource (DER) connection phase impact the objective function value and computational time in calculating HC and DOE in distribution networks of different sizes. The results are not unambiguous and show that it is not possible to determine the optimal connection phase without introducing binary variables since, no matter the case study, the highest objective function values are calculated with mixed integer OPF formulations. The difference is especially visible in a real-world low-voltage network in which the difference between different scenarios is up to 14 MW in a single day. However, binary variables make the problem computationally complex and increase computational time to several hours in the DOE calculation, even when the optimality gap different from zero is set.

The challenges of power quality are an emerging topic for the past couple of years due to massive changes occurring in low voltage distribution networks, being even more emphasized in the years marked by the novel COVID-19 disease affecting people's behaviour and energy crisis increasing the awareness and need of end-users energy independence. Both of these phenomena additionally stress the need for changes in distribution networks as the traditional consumption patterns of the end-users are significantly different. To overcome these challenges it is necessary to develop tools and methods that will help Distribution System Operators (DSOs). In this paper, we present a geographic information system (GIS)-based tool that, by using open source technologies, identifies and removes errors both in the GIS data, representing a distribution network, and in the consumption data collected from the smart meters. After processing the initial data, a mathematical model of the network is created, and the impact of different electricity consumption scenarios on power quality (PQ) indicators voltage magnitude, voltage unbalance factor, and total voltage harmonic distortion are calculated. The results of simulations are visualised using a GIS tool, and based on the results, time periods that are most affected by the change of end-users behaviour are detected. The potential of the end-users in the PQ improvement is investigated and an algorithm that shifts consumption to more adequate time periods is implemented. The results show that the pandemic negatively affect all analysed PQ indicators since the change in the average value of PQ disturbances increased both during the hard and post-lockdown period. The time-shifting of consumption shows significant potential in how the end-users can not only reduce their own energy costs but create power quality benefits by reducing all relevant indicators.

The share of end-users with installed rooftop photovoltaic (PV) systems is continuously growing. Since most end-users are located at the low voltage (LV) level and due to technical limitations of LV networks, it is necessary to calculate PV hosting capacity. Most approaches in calculating a network's hosting capacity are based on three-phase optimal power flow (OPF) formulations. Linearized and relaxed three-phase OPF formulations respectively lose their accuracy and exactness when applied to solve the hosting capacity problem, and only non-linear programming (NLP) models guarantee the exact solution. Compared to linearized or relaxed models, NLP models require a higher computational time for finding an optimal solution. The binary variables uplift the problem to mixed-integer (MI)NLP and increase the computational burden. To resolve the scalability issues in calculating the hosting capacity of single-phase connected PVs, we propose a method that does not entail binary variables but still ensures that PVs are not connected to more than one phase at a time. Due to a risk of a sub-optimal solution, the proposed approach is compared to the results obtained by the MINLP formulation. The comparison includes values of the solution time and technical quantities such as network losses, voltage deviations, and voltage unbalance factor.

End-users more often decide to invest in distributed generation (DG) units that help them in decreasing electricity bills and allow them to become a market player by selling the excess produced electricity. However, the installation of DG is often limited by technical constraints of the network, standards, and national grid codes. As a method for removing the mentioned obstacles, the potential of dynamic operating envelopes (DOEs) is recently becoming recognized as a way for maximizing the benefits of installing DG. In this paper, we present an improvement of the already developed models that often neglect voltage unbalance constraints or are not based on an optimization approach. To test the model, two realistic case studies are defined. The results show that not all technical constraints are equally important, that the voltage unbalance constraint impacts the calculated DOEs for single-phase installed DG units, and that neglecting the temporal and spatial component in determining the limitation power is inadequate., Comment: This paper has been accepted for the presentation at the IEEE Powertech 2023 conference

Challenges in the planning and operation of distribution networks caused by the integration of distributed energy resources (DERs) create the need for the development of tools that can be easily used by system operators, industry, and the research society but are also easily upgraded with new functionalities. The full implementation of one such open source tool, named pp OPF (pandapower Optimal Power Flow), is presented in this paper. Pp OPF is the tool used for three-phase optimal power flow (OPF) calculations and it is based on already existing functionalities of pandapower, a Python library for power system calculations. The developed tool enables the possibility to use both power-voltage and current-voltage formulation in different OPF problems, such as determining the photovoltaics (PVs) hosting capacity in three-phase distribution networks, the problem on which the functionality of the developed tool is tested. Additionally, the accuracy of pp OPF is verified by comparing the results with ones obtained by pandapower power flow calculation for the same set of input values. The open-source implementation allows further upgrades, the addition of new functionalities, and the creation of new case studies relevant to the planning and operation of distribution networks.

This is a second part of the research on AC optimal power flow being used in the lower level of the bilevel strategic bidding or investment models. As an example of a suitable upper-level problem, we observe a strategic bidding of energy storage and propose a novel formulation based on the smoothing technique. After presenting the idea and scope of our work, as well as the model itself and the solution algorithm in the companion paper (Part I), this paper presents a number of existing solution techniques and the proposed one based on smoothing the complementary conditions. The superiority of the proposed algorithm and smoothing techniques is demonstrated in terms of accuracy and computational tractability over multiple transmission networks of different sizes and different OPF models. The results indicate that the proposed approach outperforms all other options in both metrics by a significant margin. This is especially noticeable in the metric of accuracy where out of total 422 optimizations over 9 meshed networks the greatest AC OPF error is 0.023% that is further reduced to 3.3e-4% in the second iteration of our algorithm.

The existing research on market price-affecting agents, i.e. price makers, neglects or simplifies the nature of AC power flows in the power system as it predominantly relies on DC power flows. This paper proposes a novel bilevel formulation based on the smoothing technique, where any price-affecting strategic player can be modelled in the upper level, while the market clearing problem in the lower level uses convex quadratic transmission AC optimal power flow (AC OPF), with the goal of achieving accuracy close to the one of the exact nonlinear formulations. Achieving convexity in the lower level is the foundation for bilevel modeling since traditional single-level reduction techniques do not hold for nonconvex models. The bilevel market participation problem with the AC OPF formulation in the lower level is transformed into a single-level problem and solved using multiple techniques such as the primal-dual counterpart, the strong duality theorem, the McCormick envelopes, the complementary slackness, the penalty factor, the interaction discretization as well as the proposed smoothing techniques. Due to an extensive amount of information and descriptions, the overall work is presented as a two-part paper. This first part provides a literature overview, positions the work and presents the model and the solution algorithm, while the solution techniques and case studies are provided in the accompanying paper.

Shift of the power system generation from the fossil to the variable renewable sources prompted the system operators to search for new sources of flexibility, that is, new reserve providers. With the introduction of electric vehicles, smart charging emerged as one of the relevant solutions. However, electric vehicle aggregators face the uncertainty of reserve activation on one side and electric vehicle availability on the other. These uncertainty can have a negative effect on both the aggregators' profitability and their users' comfort.State-of-the art literature mostly neglects the reserve activation or the related uncertainty. Also, they rarely model European markets or use real balancing data. This paper introduces a new method for modeling the reserve activation uncertainty based on actual data for the European power system. Three electric vehicle scheduling models were designed and tested: the deterministic, the stochastic and the robust one. The results demonstrate that the current deterministic approaches inaccurately represent the activation uncertainty and that the proposed models that consider uncertainty, both the stochastic and the robust one, substantially improve the results.

The modeling of multi-energy systems (MES) is the basic task of analyzing energy systems integration. The variable energy efficiencies of the energy conversion and storage components in MES introduce nonlinearity to the model and thus complicate the analysis and optimization of MES. In this paper, we propose a standardized matrix modeling approach to automatically model MES with variable energy efficiencies based on the energy hub (EH) modeling framework. We use piecewise linearization to approximate the variable energy efficiencies; as a result, a component with variable efficiency is equivalent to several parallel components with constant efficiencies. The nonlinear energy conversion and storage relationship in EH can thus be further modeled under a linear modeling framework using matrices. Such matrix modeling approach makes the modeling of an arbitrary EH with nonlinear energy components highly automated by computers. The proposed modeling approach can further facilitate the operation and planning optimization of EH with variable efficiencies. Case studies are presented to show how the nonlinear approximation accuracy and calculation efficiency can be balanced using the proposed model in the optimal operation of EH., Comment: 10 pages, 12 figures