The framework of Koopman operator theory is discussed along with its connections to Dynamic Mode Decomposition (DMD) and (Kernel) Extended Dynamic Mode Decomposition (EDMD). This paper provides a succinct overview with consistent notation. The authors hope to provide an exposition that more naturally emphasizes the connections between theory and algorithms which may result in a sense of clarity on the subject.

This paper proposes a generalized passivity sensitivity analysis for power system stability studies. The method uncovers the most effective instability mitigation actions for both device-level and system-level investigations. The particular structure of the admittance and nodal models is exploited in the detailed derivation of the passivity sensitivity expressions. These proposed sensitivities are validated for different parameters at device-level and at system-level. Compared to previous stability and sensitivity methods, it does not require detailed system information, such as exact system eigenvalues, while it provides valuable information for a less conservative stable system design. In addition, we demonstrate how to utilize the proposed method through case studies with different converter controls and system-wide insights showing its general applicability.

Rising electricity demand and the growing integration of renewables are intensifying congestion in transmission grids. Grid topology optimization through busbar splitting (BuS) and optimal transmission switching can alleviate grid congestion and reduce the generation costs in a power system. However, BuS optimization requires a large number of binary variables, and analyzing all the substations for potential new topological actions is computationally intractable, particularly in large grids. To tackle this issue, we propose a set of metrics to identify and rank promising candidates for BuS, focusing on finding buses where topology optimization can reduce generation costs. To assess the effect of BuS on the identified buses, we use a combined mixed-integer convex-quadratic BuS model to compute the optimal topology and test it with the non-linear non-convex AC optimal power flow (OPF) simulation to show its AC feasibility. By testing and validating the proposed metrics on test cases of different sizes, we show that they are able to identify busbars that reduce the total generation costs when their topology is optimized. Thus, the metrics enable effective selection of busbars for BuS, with no need to test every busbar in the grid, one at a time.

State estimation allows to monitor power networks, exploiting field measurements to derive the most likely grid state. In the literature, measurement errors are usually assumed to follow zero-mean Gaussian distributions; however, it has been shown that this assumption often does not hold. One such example is when considering pseudo-measurements. In distribution networks, a significant amount of pseudo-measurements might be necessary, due to the scarcity of real-time measurements. In this paper, a state estimator is presented which allows to model measurement uncertainty with any continuous distribution, without approximations. This becomes possible by writing state estimation as a general maximum-likelihood estimation-based constrained optimization problem. To realistically describe distribution networks, three-phase unbalanced power flow equations are used. Results are presented that illustrate the differences in accuracy and computational effort between different uncertainty modeling methods, for the IEEE European Low Voltage Test Feeder.

HVDC is a critically important technology for the large-scale integration of renewable resources such as offshore wind farms. Currently, only point-to-point and multi-terminal HVDC connections exist in real-life operation. However, with the advancement of VSC-based converter technologies, future HVDC systems are foreseen to develop into meshed HVDC grids. Bipolar HVDC grids can be operated in an unbalanced way during single pole outages or in form of mixed monopolar and bipolar grids. However, currently, there are no (optimal) power flow tools to study the feasibility of such systems. Therefore, we develop an optimal power flow (OPF) model for hybrid AC-DC grids to capture the DC side unbalances and allowing to efficiently plan and operate such future grids. In this paper, we present a multi-conductor OPF model with separate modeling of the positive pole, negative pole, metallic return conductors, and ground return. The capabilities of the model are demonstrated on a small test case, including monopolar tapping over a bipolar DC link. It is demonstrated that the developed OPF model can capture the loop flows between the different poles in unbalanced conditions, as opposed to the existing single-wire representations in the literature. Further, numerical results are presented for multiple test cases with various system sizes, starting from an 11-bus system to a 3120-bus system to demonstrate the computational tractability of the chosen model formulation.

Policy makers are formulating offshore energy infrastructure plans, including wind turbines, electrolyzers, and HVDC transmission lines. An effective market design is crucial to guide cost-efficient investments and dispatch decisions. This paper jointly studies the impact of offshore market design choices on the investment in offshore electrolyzers and HVDC transmission capacity. We present a bilevel model that incorporates investments in offshore energy infrastructure, day-ahead market dispatch, and potential redispatch actions near real-time to ensure transmission constraints are respected. Our findings demonstrate that full nodal pricing, i.e., nodal pricing both onshore and offshore, outperforms the onshore zonal combined with offshore nodal pricing or offshore zonal layouts. While combining onshore zonal with offshore nodal pricing can be considered as a second-best option, it generally diminishes the profitability of offshore wind farms. However, if investment costs of offshore electrolyzers are relatively low, they can serve as catalysts to increase the revenues of the offshore wind farms. This study contributes to the understanding of market designs for highly interconnected offshore power systems, offering insights into the impact of congestion pricing methodologies on investment decisions. Besides, it is useful towards understanding the interaction of offshore loads like electrolyzers with financial support mechanisms for offshore wind farms.

Power flow analysis plays a critical role in the control and operation of power systems. The high computational burden of traditional solution methods led to a shift towards data-driven approaches, exploiting the availability of digital metering data. However, data-driven approaches, such as deep learning, have not yet won the trust of operators as they are agnostic to the underlying physical model and have poor performances in regimes with limited observability. To address these challenges, this paper proposes a new, physics-informed model. More specifically, a novel physics-informed loss function is developed that can be used to train (deep) neural networks aimed at power flow simulation. The loss function is not only based on the theoretical AC power flow equations that govern the problem but also incorporates real physical line losses, resulting in higher loss accuracy and increased learning potential. The proposed model is used to train a Graph Neural Network (GNN) and is evaluated on a small 3-bus test case both against another physics-informed GNN that does not incorporate physical losses and against a model-free technique. The validation results show that the proposed model outperforms the conventional physics-informed network on all used performance metrics. Even more interesting is that the model shows strong prediction capabilities when tested on scenarios outside the training sample set, something that is a substantial deficiency of model-free techniques.

Lithium-ion batteries are widely used in transportation, energy storage, and consumer electronics, driving the need for reliable battery management systems (BMS) for state estimation and control. The Single Particle Model (SPM) balances computational efficiency and accuracy but faces challenges in parameter estimation due to numerous parameters. Current SPM models using parabolic approximation introduce intermediate variables and hard to do parameter grouping. This study presents a control-oriented SPM reformulation that employs parameter grouping and parabolic approximation to simplify model parameters while using average and surface lithium-ion concentrations as model output. By parameter grouping, the original 17 parameters were reduced to 9 grouped parameters. The reformulated model achieves a reduced-order ordinary differential equation form while maintaining mathematical accuracy equivalent to the pre-grouped discretized SPM. Through Sobol sensitivity analysis under various current profiles, the grouped parameters were reduced from 9 to 6 highly sensitive parameters. Results demonstrate that estimating these 6 parameters achieves comparable practical accuracy to estimating all 9 parameters, with faster convergence. This control-oriented SPM enhances BMS applications by facilitating state estimation and control while reducing parameter estimation requirements.

Optimal investment in battery energy storage systems, taking into account degradation, sizing and control, is crucial for the deployment of battery storage, of which providing frequency control is one of the major applications. In this paper, we present a holistic, data-driven framework to determine the optimal investment, size and controller of a battery storage system providing frequency control. We optimised the controller towards minimum degradation and electricity costs over its lifetime, while ensuring the delivery of frequency control services compliant with regulatory requirements. We adopted a detailed battery model, considering the dynamics and degradation when exposed to actual frequency data. Further, we used a stochastic optimisation objective while constraining the probability on unavailability to deliver the frequency control service. Through a thorough analysis, we were able to decrease the amount of data needed and thereby decrease the execution time while keeping the approximation error within limits. Using the proposed framework, we performed a techno-economic analysis of a battery providing 1 MW capacity in the German primary frequency control market. Results showed that a battery rated at 1.6 MW, 1.6 MWh has the highest net present value, yet this configuration is only profitable if costs are low enough or in case future frequency control prices do not decline too much. It transpires that calendar ageing drives battery degradation, whereas cycle ageing has less impact.

Uniform flow distribution across parallel channels directly impacts the performance and efficiency of many fluid and energy systems. However, designing efficient flow manifolds that ensure uniform flow distribution remains a challenge. This issue is even more pronounced in the design of multichannel three-dimensional manifolds. Hence, this study presents a scalable topology optimization framework for the systematic design of multi-channel flow manifolds. The proposed method extends the conventional density-based topology optimization formulation by introducing a flow maldistribution coefficient as an explicit constraint. This novel approach was implemented using the incompressible Navier-Stokes flow solver available in the open-source CFD suite SU2. The performance of the proposed method was benchmarked against two established topology optimization strategies using an exemplary planar z-type flow manifold, wherein both the inlet and outlet manifoldswere designed simultaneously. The results demonstrate that the proposed method achieves flow uniformity comparable to that obtained by established approaches while significantly reducing the associated computational cost. Furthermore, when applied to large-scale three-dimensional problems, the proposed method produces feasible designs that achieve uniform flow distribution and exhibit innovative geometrical features. Thus advocating for the robustness and scalability of the proposed method.

The integration of distributed generation (DG) is essential to the energy transition but poses challenges for lowvoltage (LV) distribution networks (DNs) with limited hosting capacity (HC). This study incorporates multiple fairness criteria, utilitarian, egalitarian, bounded, and bargaining, into the HC optimisation framework to assess their impact. When applied to LV feeders of different sizes and topologies, the analysis shows that bargaining and upper-bounded fairness provide the best balance between efficiency and fairness. Efficiency refers to maximising the social welfare of the LV DNs, while fairness is proportional to the minimisation of disparity in opportunity for installing DG. Feeder topology significantly influences fairness outcomes, while feeder size affects total HC and the inherent fairness of feeders. These results emphasise the importance of regulatory incentives and network designs in order to facilitate fair and efficient DG integration.

The increased deployment of intermittent renewable energy generators opens up opportunities for grid-connected energy storage. Batteries offer significant flexibility but are relatively expensive at present. Battery lifetime is a key factor in the business case, and it depends on usage, but most techno-economic analyses do not account for this. For the first time, this paper quantifies the annual benefits of grid-connected batteries including realistic physical dynamics and nonlinear electrochemical degradation. Three lithium-ion battery models of increasing realism are formulated, and the predicted degradation of each is compared with a large-scale experimental degradation data set (Mat4Bat). A respective improvement in RMS capacity prediction error from 11\% to 5\% is found by increasing the model accuracy. The three models are then used within an optimal control algorithm to perform price arbitrage over one year, including degradation. Results show that the revenue can be increased substantially while degradation can be reduced by using more realistic models. The estimated best case profit using a sophisticated model is a 175% improvement compared with the simplest model. This illustrates that using a simplistic battery model in a techno-economic assessment of grid-connected batteries might substantially underestimate the business case and lead to erroneous conclusions.

In this work, the Nusselt number is examined for periodically developed heat transfer in micro- and mini-channels with arrays of offset strip fins, subject to a constant heat flux. The Nusselt number is defined on the basis of a heat transfer coefficient which represents the spatially constant macro-scale temperature difference between the fluid and solid during conjugate heat transfer. Its values are determined numerically on a single unit cell of the array for Reynolds numbers between 1 and 600. Two combinations of the Prandtl number and the thermal conductivity ratio are selected, corresponding to air and water. It is shown that the Nusselt number correlations from the literature mainly apply to air in the transitional flow regime in larger conventional channels if the wall temperature remains uniform. As a result, they do not correctly capture the observed trends for the Nusselt number in micro- and mini-channels subject to a constant heat flux. Therefore, new Nusselt number correlations, obtained through a least-squares fitting of 2282 numerical simulations, are presented for air and water. The suitability of these correlations is assessed via the Bayesian approach for parameter estimation and model validation. The correlations respect the observed asymptotic trends and limits of the Nusselt number for all the geometrical parameters of the offset strip fins. In addition, they predict a linear dependence of the Nusselt number on the Reynolds number, in good agreement with the data from this work. Nevertheless, a detailed analysis reveals a more complex scaling of the Nusselt number with the Reynolds number, closely related to the underlying flow regimes, particularly the weak and strong inertia regimes. Finally, through 62 additional simulations, the influence of the material properties on the Nusselt number is illustrated and compared to the available literature.

This contribution presents a parameter identification methodology for the accurate and fast estimation of model parameters in a pseudo-two-dimensional (P2D) battery model. The methodology consists of three key elements. First, the data for identification is inspected and specific features herein that need to be captured are included in the model. Second, the P2D model is analyzed to assess the identifiability of the physical model parameters and propose alternative parameterizations that alleviate possible issues. Finally, diverse operating conditions are considered that excite distinct battery dynamics which allows the use of different low-order battery models accordingly. Results show that, under low current conditions, the use of low-order models achieve parameter estimates at least 500 times faster than using the P2D model at the expense of twice the error. However, if accuracy is a must, these estimated parameters can be used to initialize the P2D model and perform the identification in half of the time.

Parameter estimation in electrochemical models remains a significant challenge in their application. This study investigates the impact of different operating profiles on electrochemical model parameter estimation to identify the optimal conditions. In particular, the present study is focused on Nickel Manganese Cobalt Oxide(NMC) lithium-ion batteries. Based on five fundamental current profiles (C/5, C/2, 1C, Pulse, DST), 31 combinations of conditions were generated and used for parameter estimation and validation, resulting in 961 evaluation outcomes. The Particle Swarm Optimization is employed for parameter identification in electrochemical models, specifically using the Single Particle Model (SPM). The analysis considered three dimensions: model voltage output error, parameter estimation error, and time cost. Results show that using all five profiles (C/5, C/2, 1C, Pulse, DST) minimizes voltage output error, while {C/5, C/2, Pulse, DST} minimizes parameter estimation error. The shortest time cost is achieved with {1C}. When considering both model voltage output and parameter errors, {C/5, C/2, 1C, DST} is optimal. For minimizing model voltage output error and time cost, {C/2, 1C} is best, while {1C} is ideal for parameter error and time cost. The comprehensive optimal condition is {C/5, C/2, 1C, DST}. These findings provide guidance for selecting current conditions tailored to specific needs.

This article deals with the problem of finding the best topology, pipe diameter choices, and operation parameters for realistic district heating networks. Present design tools that employ non-linear flow and heat transport models for topological design are limited to small heating networks with up to 20 potential consumers. We introduce an alternative adjoint-based numerical optimization strategy to enable large-scale nonlinear thermal network optimization. In order to avoid a strong computational cost scaling with the network size, we aggregate consumer constraints with a constraint aggregation strategy. Moreover, to align this continuous optimization strategy with the discrete nature of topology optimization and pipe size choices, we present a numerical continuation strategy that gradually forces the design variables towards discrete design choices. As such, optimal network topology and pipe sizes are determined simultaneously. Finally, we demonstrate the scalability of the algorithm by designing a fictitious district heating network with 160 consumers. As a proof-of-concept, the network is optimized for minimal investment cost and pumping power, while keeping the heat supplied to the consumers within a thermal comfort range of 5 %. Starting from a uniform distribution of 15 cm wide piping throughout the network, the novel algorithm finds a network lay-out that reduces piping investment by 23 % and pump-related costs by a factor of 14 in less than an hour on a standard laptop. Moreover, the importance of embedding the non-linear transport model is clear from a temperature-induced variation in the consumer flow rates of 72 %.

The examination of the maximum number of electric vehicles (EVs) that can be integrated into the distribution network (DN) without causing any operational incidents has become increasingly crucial as EV penetration rises. This issue can be addressed by utilizing dynamic operating envelopes (DOEs), which are generated based on the grid status. While DOEs improve the hosting capacity of the DN for EVs (EV-HC) by restricting the operational parameters of the network, they also alter the amount of energy needed for charging each EV, resulting in a decrease in the quality of service (QoS). This study proposes a network-aware hosting capacity framework for EVs (EV-NAHC) that i) aims to assess the effects of DOEs on active distribution networks, ii) introduces a novel definition for HC and calculates the EV-NAHC based on the aggregated QoS of all customers. A small-scale Belgian feeder is utilized to examine the proposed framework. The results show a substantial increase in the EV-NAHC with low, medium, and high-daily charging energy scenarios.

Lithium-ion batteries are increasingly being deployed in liberalised electricity systems, where their use is driven by economic optimisation in a specific market context. However, battery degradation depends strongly on operational profile, and this is particularly variable in energy trading applications. Here, we present results from a year-long experiment where pairs of batteries were cycled with profiles calculated by solving an economic optimisation problem for wholesale energy trading, including a physically-motivated degradation model as a constraint. The results confirm the conclusions of previous simulations and show that this approach can increase revenue by 20% whilst simultaneously decreasing degradation by 30% compared to existing methods. Analysis of the data shows that conventional approaches cannot increase the number of cycles a battery can manage over its lifetime, but the physics-based approach increases the lifetime both in terms of years and number of cycles, as well as the revenue per year, increasing the possible lifetime revenue by 70%. Finally, the results demonstrate the economic impact of model inaccuracies, showing that the physics-based model can reduce the discrepancy in the overall business case from 170% to 13%. There is potential to unlock significant extra performance using control engineering incorporating physical models of battery ageing.

In this paper, a transmission-distribution systems flexibility market is introduced, in which system operators (SOs) jointly procure flexibility from different systems to meet their needs (balancing and congestion management) using a common market. This common market is, then, formulated as a cooperative game aiming at identifying a stable and efficient split of costs of the jointly procured flexibility among the participating SOs to incentivize their cooperation. The non-emptiness of the core of this game is then mathematically proven, implying the stability of the game and the naturally-arising incentive for cooperation among the SOs. Several cost allocation mechanisms are then introduced, while characterizing their mathematical properties. Numerical results focusing on an interconnected system (composed of the IEEE 14-bus transmission system and the Matpower 18-bus, 69-bus, and 141-bus distributions systems) showcase the cooperation-induced reduction in system-wide flexibility procurement costs, and identifies the varying costs borne by different SOs under various cost allocations methods.