Mario Paolone

Konstantina Christakou, Jean-Yves Le Boudec, Mario Paolone et al.

The problem of optimal control of power distribution systems is becoming increasingly compelling due to the progressive penetration of distributed energy resources in this specific layer of the electrical infrastructure. Distribution systems are, indeed, experiencing significant changes in terms of operation philosophies that are often based on optimal control strategies relying on the computation of linearized dependencies between controlled (e.g. voltages, frequency in case of islanding operation) and control variables (e.g. power injections, transformers tap positions). As the implementation of these strategies in real-time controllers imposes stringent time constraints, the derivation of analytical dependency between controlled and control variables becomes a non-trivial task to be solved. With reference to optimal voltage and power flow controls, this paper aims at providing an analytical derivation of node voltage and line current flows as a function of the nodal power injections and transformers tap-changers positions. Compared to other approaches presented in the literature, the one proposed here is based on the use of the [Y] compound matrix of a generic multi-phase radial unbalanced network. In order to estimate the computational benefits of the proposed approach, the relevant improvements are also quantified versus traditional methods. The validation of the proposed method is carried out by using both IEEE 13 and 34 node test feeders. The paper finally shows the use of the proposed method for the problem of optimal voltage control applied to the IEEE 34 node test feeder.

Vladimir Sovljanski, Mario Paolone

This paper investigates the identification of observable low-frequency (LF) parameters of battery cell's equivalent circuit models (ECMs) using time-domain voltage and current measurements sampled at low frequency by built-in battery management systems (BMS) during operation. Accurate estimation of such parameters is challenging due to measurement resolution available in practical settings. To address this, a modeling and identification framework is proposed in which fractional constant phase element (CPE), commonly used to model LF diffusion phenomena of battery cells, is approximated in the time domain using a high-order RC network with a recursive definition. The parameter estimation problem is formulated as a constrained, non-convex least-squares problem in a discretized state-space representation. To improve robustness, parameter initialization strategies, bounds, and a procedure for selecting the number of RC branches are rigorously derived. The method is evaluated in a numerical study based on a power system application where the battery under the study provides primary frequency control to the grid. Under noise levels representative of typical BMS measurements, the proposed approach achieves, from time-domain measurements, accurate LF parameter estimation (including the CPE), with average errors below 1 %.

Fabrizio Sossan, Lorenzo Nespoli, Vasco Medici et al.

We consider the problem of estimating the unobserved amount of photovoltaic (PV) generation and demand in a power distribution network starting from measurements of the aggregated power flow at the point of common coupling (PCC) and local global horizontal irradiance (GHI). The estimation principle relies on modeling the PV generation as a function of the measured GHI, enabling the identification of PV production patterns in the aggregated power flow measurements. Four estimation algorithms are proposed: the first assumes that variability in the aggregated PV generation is given by variations of PV generation, the next two use a model of the demand to improve estimation performance, and the fourth assumes that, in a certain frequency range, the aggregated power flow is dominated by PV generation dynamics. These algorithms leverage irradiance transposition models to explore several azimuth/tilt configurations and explain PV generation patterns from multiple plants with non-uniform installation characteristics. Their estimation performance is compared and validated with measurements from a real-life setup including 4 houses with rooftop PV installations and battery systems for PV self-consumption.

Enrica Scolari, Fabrizio Sossan, Mario Paolone

Due to the increasing proportion of distributed photovoltaic (PV) production in the generation mix, the knowledge of the PV generation capacity has become a key factor. In this work, we propose to compute the PV plant maximum power starting from the indirectly-estimated irradiance. Three estimators are compared in terms of i) ability to compute the PV plant maximum power, ii) bandwidth and iii) robustness against measurements noise. The approaches rely on measurements of the DC voltage, current, and cell temperature and on a model of the PV array. We show that the considered methods can accurately reconstruct the PV maximum generation even during curtailment periods, i.e. when the measured PV power is not representative of the maximum potential of the PV array. Performance evaluation is carried out by using a dedicated experimental setup on a 14.3 kWp rooftop PV installation. Results also proved that the analyzed methods can outperform pyranometer-based estimations, with a less complex sensing system. We show how the obtained PV maximum power values can be applied to train time series-based solar maximum power forecasting techniques. This is beneficial when the measured power values, commonly used as training, are not representative of the maximum PV potential.

Andreas Martin Kettner, Mario Paolone

This letter provides conditions determining the rank of the nodal admittance matrix, and arbitrary block partitions of it, for connected AC power networks with complex admittances. Furthermore, some implications of these properties concerning Kron Reduction and Hybrid Network Parameters are outlined.

Andreas Martin Kettner, Mario Paolone

This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced polyphase power systems. To this end, the grid is represented by a polyphase multiport network model (i.e., compound hybrid parameters), and the aggregate behavior of the devices in each node by Thévenin Equivalents (TEs) and Polynomial Models (PMs), respectively. The proposed VSI is a generalization of the known L-index, which is achieved through the use of compound electrical parameters, and the incorporation of TEs and PMs into its formal definition. Notably, the proposed VSI can handle unbalanced polyphase power systems, explicitly accounts for voltage-dependent behavior (represented by PMs), and is computationally inexpensive. These features are valuable for the operation of both transmission and distribution systems. Specifically, the ability to handle the unbalanced polyphase case is of particular value for distribution systems. In this context, it is proven that the compound hybrid parameters required for the calculation of the VSI do exist under practical conditions (i.e., for lossy grids). The proposed VSI is validated against state-of-the-art methods for voltage stability assessment using a benchmark system which is based on the IEEE 34-node feeder.

Rahul Gupta, Fabrizio Sossan, Enrica Scolari et al.

This paper describes a two-layer control and coordination framework for distributed energy resources. The lower layer is a real-time model predictive control (MPC) executed at 10 s resolution to achieve fine tuning of a given energy set-point. The upper layer is a slower MPC coordination mechanism based on distributed optimization, and solved with the alternating direction method of multipliers (ADMM) at 5 minutes resolution. It is needed to coordinate the power flow among the controllable resources such that enough power is available in real-time to achieve a pre-established energy trajectory in the long term. Although the formulation is generic, it is developed for the case of a battery system and a curtailable PV facility to dispatch stochastic prosumption according to a trajectory at 5 minutes resolution established the day before the operation. The proposed method is experimentally validated in a real-life setup to dispatch the operation of a building with rooftop PV generation (i.e., 101 kW average load, 350 kW peak demand, 82 kW peak PV generation) by controlling a 560 kWh/720 kVA battery and a 13 kW peak curtailable PV facility.

Konstantina Christakou, Dan-Cristian Tomozei, Jean-Yves Le Boudec et al.

The optimal power-flow problem (OPF) has played a key role in the planning and operation of power systems. Due to the non-linear nature of the AC power-flow equations, the OPF problem is known to be non-convex, therefore hard to solve. Most proposed methods for solving the OPF rely on approximations that render the problem convex, but that may yield inexact solutions. Recently, Farivar and Low proposed a method that is claimed to be exact for radial distribution systems, despite no apparent approximations. In our work, we show that it is, in fact, not exact. On one hand, there is a misinterpretation of the physical network model related to the ampacity constraint of the lines' current flows. On the other hand, the proof of the exactness of the proposed relaxation requires unrealistic assumptions related to the unboundedness of specific control variables. We also show that the extension of this approach to account for exact line models might provide physically infeasible solutions. Recently, several contributions have proposed OPF algorithms that rely on the use of the alternating-direction method of multipliers (ADMM). However, as we show in this work, there are cases for which the ADMM-based solution of the non-relaxed OPF problem fails to converge. To overcome the aforementioned limitations, we propose an algorithm for the solution of a non-approximated, non-convex OPF problem in radial distribution systems that is based on the method of multipliers, and on a primal decomposition of the OPF. This work is divided in two parts. In Part I, we specifically discuss the limitations of BFM and ADMM to solve the OPF problem. In Part II, we provide a centralized version and a distributed asynchronous version of the proposed OPF algorithm and we evaluate its performances using both small-scale electrical networks, as well as a modified IEEE 13-node test feeder.

Riccardo Ramaschi, Mario Paolone, Sonia Leva

In the first part of this two-part paper a game-theoretic decentralized real-time control is proposed in the context of Electric Vehicle (EV) Charging Station (CS). This method, relying on a Stackelberg Game-based Alternating Direction of Multipliers (SG-ADMM), intends to steer the EVs' individual objectives towards the CS optimum by means of an incentive design mechanism, while controlling the EV power dispatch in a distributed manner. We integrate SG-ADMM in a hierachical multi-layered Energy Management System (EMS) as the real-time control algorithm, formulating the two-layer approach so that the SG leader (i.e., the CS), holding commitment power, trades off the available power with the incentives to the EVs, and the SG followers (i.e., the EVs) optimizes their charging curve in response to the leader decision. In this second part, we demonstrate the applicability of SG-ADMM as a incentive design mechanism inside an EVCS EMS, testing it in a large-scale EVCS. We benchmark this method with a decentralized (ADMM-based), a centralized and a uncontrolled approach, showing that our method exploits EV-level flexibility in a cost-effective, fair and computationally efficient manner.

Riccardo Ramaschi, Mario Paolone, Sonia Leva

Large-scale Electric Vehicle (EV) Charging Station (CS) may be too large to be dispatched in real-time via a centralized approach. While a decentralized approach may be a viable solution, the lack of incentives could impair the alignment of EVs' individual objectives with the controller's optimum. In this work, we integrate a decentralized algorithm into a hierarchical three-layer Energy Management System (EMS), where it operates as the real-time control layer and incorporates an incentive design mechanism. A centralized approach is proposed for the dispatch plan definition and for the intra-day refinement, while a decentralized game-theoretic approach is proposed for the real time control. We employ a Stackelberg Game-based Alternating Direction Method of Multipliers (SG-ADMM) to simultaneously design an incentive mechanism while managing the EV control in a distributed manner, while framing the leadership-followership relation between the EVCS and the EVs as a non-cooperative game where the leader has commitment power. Part I of this two-part paper deals with the SG-ADMM approach description, literature review and integration in the abovementioned hierarchical EMS, focusing on the modifications needed for the proposed application.

Riccardo Ramaschi, Mario Paolone, Sonia Leva

Electric Vehicle (EV) fast charging stations require forecasting techniques both at the single charger level and aggregated level. While for the latter several models exist, forecasting individual EV charging profiles is still underexplored in literature. However, such methods may be potentially used by battery-aware scheduling, leading to a more granular update of the charging station aggregated forecast and provide a more accurate estimation of EVs departure times. Nonetheless, the variable extent of available information in time and in different settings could jeopardize these benefits. For this reason, we propose a hybrid and lightweight method to estimate the EV charging profile before and during the charging process. Besides evaluating this method on multiple EVs from a public dataset, we also assess the impact of different level of information in the time transposition of the charging profile.

César García-Veloso, Mario Paolone, Federico Milano

This letter seeks to clarify the different existing definitions of both instantaneous complex phase and frequency as well as their equivalence under standard modeling assumptions considered for transmission systems, i.e. balanced positive sequence operation, sole presence of electro-mechanical transient dynamics and absence of harmonics and interharmonics. To achieve this, the two fundamental definitions, i.e., those based on either the use of (i) analytic signals or (ii) space vectors, together with the premises used for their formulation, are presented and their relationship shown. Lastly, a unified notation and terminology to avoid confusion is proposed.

Enea Figini, Mario Paolone

The global race to artificial intelligence competitive advantage is challenging electricity grids by demanding growing data center capacity. Addressing this challenge requires synergistic operational strategies that integrate data centers into electricity markets while supporting grid operation. This work proposes a bilateral power purchase agreement between small-scale data centers and distribution system operators, enabling data center participation in the day-ahead electricity market. To facilitate market participation, we develop a scenario-based, risk-averse bidding strategy that leverages flexibility from local energy resources, waste heat recovery, and data center workload. The strategy jointly minimizes operational costs and carbon emissions, creating a carbon-aware cost-effective framework for data center integration in the electricity day-ahead market. The method is evaluated on a study case comparing a conventional time-of-use supply scheme with the proposed custom power purchase agreement, showing a potential 22\% cost reduction, thus highlighting financial opportunities for small-scale data centers day-ahead electricity market participation. Two additional case studies illustrate the marginal effects of: (i) data center flexible workload on energy costs and (ii) virtual de-rating of grid transfer capacity.

Yanan Niu, Roy Sarkis, Demetri Psaltis et al.

Accurate intraday solar irradiance forecasting is crucial for optimizing dispatch planning and electricity trading. For this purpose, we introduce a novel and effective approach that includes three distinguishing components from the literature: 1) the uncommon use of single-frame public camera imagery; 2) solar irradiance time series scaled with a proposed normalization step, which boosts performance; and 3) a lightweight multimodal model, called Solar Multimodal Transformer (SMT), that delivers accurate short-term solar irradiance forecasting by combining images and scaled time series. Benchmarking against Solcast, a leading solar forecasting service provider, our model improved prediction accuracy by 25.95%. Our approach allows for easy adaptation to various camera specifications, offering broad applicability for real-world solar forecasting challenges.

Andreas Martin Kettner, Mario Paolone

Most techniques for power system analysis model the grid by exact electrical circuits. For instance, in power flow study, state estimation, and voltage stability assessment, the use of admittance parameters (i.e., the nodal admittance matrix) and hybrid parameters is common. Moreover, network reduction techniques (e.g., Kron reduction) are often applied to decrease the size of large grid models (i.e., with hundreds or thousands of state variables), thereby alleviating the computational burden. However, researchers normally disregard the fact that the applicability of these methods is not generally guaranteed. In reality, the nodal admittance must satisfy certain properties in order for hybrid parameters to exist and Kron reduction to be feasible. Recently, this problem was solved for the particular cases of monophase and balanced triphase grids. This paper investigates the general case of unbalanced polyphase grids. Firstly, conditions determining the rank of the so-called compound nodal admittance matrix and its diagonal subblocks are deduced from the characteristics of the electrical components and the network graph. Secondly, the implications of these findings concerning the feasibility of Kron reduction and the existence of hybrid parameters are discussed. In this regard, this paper provides a rigorous theoretical foundation for various applications in power system analysis

Fabrizio Sossan, Emil Namor, Rachid Cherkaoui et al.

We propose and experimentally validate a control strategy to dispatch the operation of a distribution feeder interfacing heterogeneous prosumers by using a grid-connected battery energy storage system (BESS) as a controllable element coupled with a minimally invasive monitoring infrastructure. It consists in a two-stage procedure: day-ahead dispatch planning, where the feeder 5-minute average power consumption trajectory for the next day of operation (called \emph{dispatch plan}) is determined, and intra-day/real-time operation, where the mismatch with respect to the \emph{dispatch plan} is corrected by applying receding horizon model predictive control (MPC) to decide the BESS charging/discharging profile while accounting for operational constraints. The consumption forecast necessary to compute the \emph{dispatch plan} and the battery model for the MPC algorithm are built by applying adaptive data driven methodologies. The discussed control framework currently operates on a daily basis to dispatch the operation of a 20~kV feeder of the EPFL university campus using a 750~kW/500~kWh lithium titanate BESS.