This paper compares and assesses several numerical methods that solve the steady-state power flow problem on integrated transmission-distribution networks. The integrated network model consists of a balanced transmission and an unbalanced distribution network. It is important to analyze these integrated electrical power systems due to the changes related to the energy transition. We classified the existing integration methods as unified and splitting methods. These methods can be applied to homogeneous (complete three-phase) and hybrid (single-phase/three-phase) network models, which results in four approaches in total. These approaches were compared on their accuracy and numerical performance—CPU time and number of iterations—to demonstrate their applicability on large-scale electricity networks. Furthermore, their sensitivity towards the amount of distributed generation and the addition of multiple distribution feeders was investigated. The methods were assessed by running power flow simulations using the Newton–Raphson method on several integrated power systems up to 25,000 unknowns. The assessment showed that unified methods applied to hybrid networks performed the best on these test cases. The splitting methods are advantageous when complete network data sharing between system operators is not allowed. The use of high-performance techniques for larger test cases containing multiple distribution networks will make the difference in speed less significant.@en

Steady-state power flow models are essential for daily operation of the electricity grid. The changing electrical environment requires a shift from separated power flow models to integrated transmission-distribution power flow models. Integrated models incorporate the coupling of the networks and the interaction that they have on each other, representing the power flow within this changing environment accurately. In this paper we conduct a comparison study on the numerical performance of methods that solve the integrated power flow problem. The methods of study can be divided into unified or splitting methods. In addition, the integrated networks can be modeled as homogeneous or as hybrid networks. Our study shows that the methods have several advantages and disadvantages, but that unified methods in combination with hybrid network models have the best numerical performance. Splitting methods running on hybrid network models have an advantage when full network data sharing between system operators is not allowed.@en

Electrical power systems are complex systems and traditionally modeled in two separate systems. Power is generated at the transmission system and at several substations converted to the distribution systems. The increasing amount of generation produced at distribution level can eventually effect the transmission network. An integrated model of both systems can help studying these effects and prevent harmful events on the power system. Transmission and Distribution systems differ significantly from each other. Where transmission systems are assumed to be balanced and therefore modeled as a single-phase system, the distribution systems are in general unbalanced and should be modeled in three-phase. Furthermore, high R/X ratios of distribution lines, the lower voltage level, the radial structure and the presence of unbalanced loading lead to different solution techniques. Connecting these two systems pose complications for both the solution method and the connection method. In this report, we present several methods to solve the integrated Transmission-Distribution system. One of them is to omit the simplifications we can make in a transmission system and solve both systems as a three-phase system. Another method is to use a master-slave splitting approach and solve both systems iteratively, using a boundary state. A last method is building an interconnected network which solves the system at once, respecting both the transmission and distribution conditions. Some artificial currents and voltages have to be injected on the boundary. We compare the different methods on CPU-time, convergence, accuracy and complexity and present the preferable method for the specific network criteria. @en

Power flow computations are important for operation and planning of the electricity grid, but are computationally expensive because of nonlinearities and the size of the system of equations. Linearized methods reduce computational time but often have the disadvantage that they are not applicable to general grids. In this paper we propose a novel linearized power flow (LPF) technique that is able to handle PQ- and PV-buses, and works on both transmission and distribution networks. This technique is based on previous work on handling PQ-buses by connecting them to artificial-additional ground buses. We extend this idea to PV-buses. Test-cases show that the novel LPF method leads to similar accuracy as nonlinear power flow (NPF) methods while significantly reducing computation time. Therefore, the general LPF methods is a good alternative to NPF methods.@en

Fluctuating electricity prices offer potential economic savings for the consumption of electricity by flexible assets such as Electric Vehicles (EVs). This study proposes an operational bidding framework that minimizes the charging costs of an EV fleet by submitting an optimized bid to the day-ahead electricity market. The framework consists of a bidding module that determines the most cost-effective bid by considering an electricity price and an EV charging demand forecast module. In this study we develop and evaluate several regression and machine learning models that forecast the electricity price and EV charging demand. Furthermore, we examine the composition of a most optimal operational bidding framework by comparing the outcome of the bidding module when fed with each of the forecast models. This is determined by considering the day-ahead electricity price and imbalance costs due to forecast errors. The study demonstrates that the best performing self-contained forecast models with the objective of electricity price and EV charging demand forecasting, do not deliver the best overall results when included in the bidding framework. Additionally, the results show that the best performing framework obtains a 26% cost savings compared to a reference case where EVs are charged inflexibly. This corresponds to an achieved savings potential of 92%. Consequently, along with the developed bidding framework, these results provide a fundamental basis for effective electricity trading on the day-ahead market.@en

Integrated electrical power flow simulations are concerned with solving the steady-state load flow problem on integrated transmission and distribution electricity networks. We have developed a framework to run these simulations efficiently, whilst keeping in mind the differences between these network types and accommodating the practical considerations of system operators. We need such a framework to analyse the interaction that these systems might have as a result of the energy transition. To develop a framework to run integrated power flow simulations, we have worked in two stages. Firstly, we have studied how we can model an integrated network. We have found two ways of modelling an integrated network: using a homogeneous configuration in which both networks are modelled using three phases and using a hybrid network configuration in which both networks keep their original configuration but in which the coupling substation takes care of the phase dimension mismatch between the two sides. Next to that, we have found two ways of solving an integrated system: either by coupling them into one system and solving that as a whole (we call this the unified approach) or by keeping two separate systems and iterating between these networks (we call this the Manager‐Fellow Splitting (MFS) method). We have concluded that the unified methods are generally faster than MFS methods and that a hybrid network configuration leads to faster results, making the interconnected method the most efficient. In the second stage, we have focused on the efficiency of these simulations. During every Newton‐Raphson iteration in power flow simulations, a linear system is solved. We have therefore studied several Krylov subspace and preconditioning techniques that can solve this linear system efficiently. We have applied Krylov and preconditioning combinations to integrated network simulations to check again the performances of the simulations on large test cases . During this stage, we applied them to networks up to a size of 800,000 buses as we were interested in efficient scaling of the methods that were originally the object of study. In the second stage, we saw that the MFS methods were performing better than unified methods. Furthermore, preconditioned Krylov subspace methods had a similar performance to direct methods. t is difficult to judge why this happened. A reason could be that the library in which we performed these simulations, PETSc, is optimised for parallel computations in which multiple smaller blocks are solved at the same time whilst we were doing only sequential computations. Finally, we have striven to incorporate operational convenience for Transmission and Distribution System Operators (TSOs and DSOs) during the development of this integration framework, by considering their computational and privacy concerns. The way that this framework is built, can take away some of their concerns. To summarise, we have created an open‐source framework to run efficient steady-state power flow simulations on integrated transmission and distribution networks. This framework is tested on simplified test cases but shows potential for large system simulations. Moreover, it takes into account the considerations of system operators and can be utilised in other applications besides integrated analysis. @en

An integrated network consists of a transmission network and at least one distribution network which are connected to each other via a substation. One way to do power flow simulations on these integrated networks is the Master-Slave splitting method. This method splits the integrated network and iterates between the separate transmission (the master) and distribution (the slave) network. In this paper, we extend the method to hybrid networks: a network consisting of a balanced transmission and an unbalanced distribution network. An extra handling is necessary to get the Master-slave splitting to work on hybrid networks. We explain two approaches to use the Master-Slave splitting on a hybrid network and compare these approaches on accuracy, computational time, and convergence, by doing test-simulations. The Master-Slave splitting is interesting when distribution and transmission systems have different characteristics, are in geographically distinct locations, or when system operators are not able or allowed to share data of their network with each other. The extension to hybrid networks makes this method generally applicable and an interesting choice to do power flow simulations on integrated networks.@en

Power system simulations should be adapted to be applicable to the trends that are currently evoked by the energy transition. This transition is pushing our power system from a traditional hierarchical system to a modern interactive system. In order to keep the supply and transport of energy safe and reliant, we need to change the way we perform power system simulations. This requires a comprehensive framework in which both transmission and distribution systems are simultaneously analyzed. This chapter describes how transmission and distribution networks are modeled together as an integrated network and used to do steady-state operation analysis in order to assess the interaction of these two networks. Furthermore, we investigate the influence of the increasing amount of imbalance at distribution level on the transmission network that is evoked by the increase of highly variable resources and loads at distribution level. This influence is not taken into account in traditional power system simulations as power networks are analyzed on its own. We show that the hybrid network representation is a powerful tool to analyze modern power systems and that the effects of increased PV penetration under normal operating conditions are limited@en

Power ow simulations form an essential tool for electricity network analysis but conventional models are designed to work on a separated transmission or distribution network only. The continuing growth of electricity consumption, demand side participation, and renewable resources makes the electricity net- works co-dependent. Integrated models incorporate the coupling of the net- works and interaction that they have on each other, representing the power ow within this changing environment accurately. Several numerical methods are available to solve the power ow problem on integrated networks. They can be categorized as a untied or as a splitting method and networks can be modelled as a homogeneous or hybrid network. In this paper, we review and assess these methods on the network models by running simulations on small test networks and comparing the outcome on their numerical performance, ie on convergence rate and CPU-time. The re- view shows that the convergence rate is comparable for most of the methods, but that hybrid networks have a slight advantage in computational time. Realistic network models, running on millions of buses and with large distribution networks, should give a better insight into the speed of the computations. @en