An Augmented Jacobian Framework for Multiphase Power Flow with Special Transformer Configurations

Linear power flow formulations and optimal operation of three-phase autonomous droop-controlled Microgrids

This paper presents the inclusion of a pulse width modulated (PWM) AC link unified power flow controller into a power flow program; such device controls the magnitude and angular position of the injected series voltage to control the active and reactive power flow on the transmission line. Similarly, a PWM series compensator is embedded into a power system in order to regulate the active power flow on the corresponding transmission line; the main advantage of these FACTS controllers is that it does not require a DC link. The inclusion of these devices into a Newton-Raphson power flow algorithm is presented. Simulation results are exhibited on a 9-buses power system

For power estimation in power systems, the power flow formulation is the most commonly used method. Data-driven approach is a newly proposed technology, unlike traditional model-driven power flow calculations, it can bypass circuit parameters and environmental variables to obtain results from global bus data. However, with the development of renewable energy, more complex power grids make it difficult to obtain complete data and reduce performance. Therefore, this paper proposes a method of estimating power from incomplete bus data. The method is based on a modified data-driven power flow model, and its core is to derive and induce a regressive model through the physical model. The simulation results on IEEE standard bus 30 show that this method has higher accuracy than other models in incomplete bus data power estimation.

This study presents two approaches to handling under‐frequency regulation in isolated microgrids. The first one is a governor power flow (PF) model in which the generators steady‐state governor equations are modeled into a full Newton PF formulation resulting in an augmented sparse linearised system of equations to be solved at each iteration. As a result, it is possible to evaluate the under frequency problem in the case of microgrid islanding as well as to set the reference bus angle to evaluate the possibility of reconnection to the main grid. The second approach presents an optimal PF (OPF) formulation in which the generators governor equations are considered as additional equality constraints to determine the minimum amount of load shedding to keep the system frequency between specified limits. In both methods, it is also used an equation that provides voltage regulation in a droop‐based control. The reactive power generation limits in the OPF approach are bounded by a proposed complementarity constraint‐based method adapted for the generators' droop‐controlled terminal voltage. The proposed approaches are evaluated and validated through the study of the EHV1 Network, a 61‐bus 33/11‐kV radial distribution system, and the New England test system.

Guest Editorial: Situational awareness of integrated energy systems

To ensure stable operation of a power system, it is necessary to analyse the power system performance under various operating conditions. Analysis includes studies such as power flow and both steady-state and transient stability. To perform such studies requires knowledge about the models used to represent the various components that constitute an integrated power system. In situations where there is a risk of loss of stability, it is necessary to apply controls that can ensure stable and uninterrupted supply of electricity following a disturbance. The subject of stability thus encompasses modelling, computation of load flow in the transmission grid, stability analysis under both steady-state and disturbed conditions, and appropriate controls to enhance stability. All these topics are covered in this book, providing a comprehensive treatment of the overall subject of stability of power systems. Topics covered include modelling of the synchronous machine; the synchronous machine connected to power systems; modelling of transformers, transmission lines and loads; power flow analysis; optimal power flow; small signal stability; transient stability; transient energy function methods; artificial intelligent techniques; power system stabilizers; series compensation; shunt compensation; compensation devices; and recent technologies. The subject matter is covered at a level that is suitable for students, scientists and engineers involved in the study, design, analysis and control of power systems.

The incorporation of renewable energy sources (RES) such as wind and solar power plants into traditional power systems offers numerous technical and environmental benefits. However, improper operation of power grids with RES may lead to high operating costs and higher system losses, as well as voltage fluctuations. To solve these problems, in this paper a formulation of the dynamic optimal power flow (DOPF) problem has been proposed with the integration of RES in the grid. The maximum allowable number of switching operations in a day for on-load tap-changer (OLTC) of transformers is taken into consideration as practical constraint. For 24 hours, the objective functions were to minimize the total operating cost (including fuel cost and cost of power loss), minimize power loss and the daily number of tap operations for transformer's OLTC. The minimization of the daily number of operations for transformers was taken as the goal to preserve the service life of transformers, reduce maintenance and depreciation. The objectives were minimized by coordination between control variables such as the output power of generators, the voltage of generators, transformer tap changer, and shunt capacitor. The improved practical swarm optimization (PSO) algorithm has been employed successfully to solve DOPF with discrete and continuous decision variables in the electric power system.

Long term supporting schemes for photovoltaic (PV) system installation have led to accommodating large numbers of PV systems within load pockets in distribution grids. High penetrations of PV systems can cause new technical challenges, such as voltage rise due to reverse power flow during light load and high PV generation conditions. Therefore, new strategies are required to address the associated challenges. Moreover, due to these changes in distribution grids, a different response behavior of the distribution grid on the transmission side can be expected. Hence, a new equivalent model of distribution grids with high penetration of PV systems is needed to be addressed for future power system studies. The thesis contributions lie in three parts. The first part of the thesis copes with the PV modelling. A non-proprietary PV model of a three-phase, single stage PV system is developed in PSCAD/EMTDC and PowerFactory. Three different reactive power regulation strategies are incorporated into the models and their behavior are investigated in both simulation platforms using a distribution system with PV systems. In the second part of the thesis, the voltage rise problem is remedied by use of reactive power. On the other hand, considering large numbers of PV systems in grids, unnecessary reactive power consumption by PV systems first increases total line losses, and second it may also jeopardize the stability of the network in the case of contingencies in conventional power plants, which supply reactive power. Thus, this thesis investigates and develops the novel schemes to reduce reactive power flows while still keeping voltage within designated limits via three different approaches: 1. decentralized voltage control to the pre-defined set-points 2. developing a coordinated active power dependent (APD) voltage regulation Q(P) using local signals 3. developing a multi-objective coordinated droop-based voltage (DBV) regulation Q(V) using local signals In the third part of the thesis, furthermore, a gray-box load modeling is used to develop a new static equivalent model of a complex distribution grid with large numbers of PV systems embedded with voltage support schemes. In the proposed model, variations of voltage at the connection point simulate variations of the model’s active and reactive power. This model can simply be integrated into load-flow programs and replace the complex distribution grid, while still keeping the overall accuracy high. The thesis results, in conclusion, demonstrate: i) using rms-based simulations in PowerFactory can provide us with quite similar results using the time domain instantaneous values in PSCAD platform; ii) decentralized voltage control to specific setpoints through the PV systems in the distribution grid is fundamentally impossible due to the high level voltage control interaction and directionality among the PV systems; iii) the proposed APD method can regulate the voltage under the steady-state voltage limit and consume less total reactive power in contrast to the standard characteristic Cosf (P) proposed by German Grid Codes; iv) the proposed optimized DBV method can directly address voltage and successfully regulate it to the upper steady-state voltage limit by causing minimum reactive power consumption as well as line losses; v) it is beneficial to address PV systems as a separate entity in the equivalencing of distribution grids with high density of PV systems.

The paper presents the improvements of a commercially available train simulator, the Energy Management Model (EMM), to evaluate the power flows in DC electrified transit railways. The sequential Gauss-Seidel power flow program used in EMM has been replaced by a unified Newton-Raphson AC/DC power flow to speed up the calculations. A precise model of the uncontrolled bridge rectifier with commutation impedance has been applied to the power flow formulation. Effects of regenerative braking on rectifier operations are also taken into account. Both the improved and the original train simulators have been tested on the Blue Line of Taipei Rapid Transit System which is under construction. Simulation results show that the proposed power flow program, with excellent convergence characteristics and accuracy, is of great value for train simulation.

Base on the power flow formulations, a new power flow model that allows for power exchanges among subareas of network and automation generation control in each subarea, is established. The proposed power flow model is rendering by unified newton iteration formulation. Parameters representing the level or allocation of the unbalancing power are introduced to indicate the performance of the generators that participate in the automation generation control. The power exchange formulations for subareas are derived from the power flow equations of the interconnected branches. The Newton iteration method is used to solve the equations that consist of node power injection equations and interconnected power equations. Because of the consideration of the power balance in each subarea and the order of power exchange, the presented method is applicable for power flow problems of interconnected power networks, and is in particular applicable for the system analysis and calculation that based on the uniform iteration formulation. Case studies of IEEE 5 bus test system and IEEE RTS96 system illustrate the efficiency and the convergence of the proposed method.

Flexible AC Transmission System (FACTS) controllers are advanced power electronic devices employed in electrical power systems to enhance system stability, reliability, and power transfer capabilities. These controllers enable dynamic and flexible control of various transmission parameters such as voltage, current, impedance, and phase angle, thereby improving the overall power system performance. FACTS devices are broadly classified into series, shunt, series- series, and series-shunt configurations, each designed to manage reactive power and regulate voltage either by injecting voltage in series or current in shunt with the transmission line. Well-known FACTS devices include Static Var Compensators (SVC), Static Synchronous Compensators (STATCOM), Thyristor Controlled Series Capacitors (TCSC), Static Synchronous Series Compensators (SSSC), and Unified Power Flow Controllers (UPFC), each serving specific roles in power flow control, voltage regulation, and transient stability enhancement. The integration of these controllers provides significant benefits such as increased transmission line capacity, improved voltage stability, minimized transmission losses, and damping of power system oscillations. They are capable of rapid response during transient disturbances, effectively mitigating voltage collapses and enhancing system resilience against faults and contingencies. FACTS controllers not only improve steady-state operational parameters but also address dynamic stability and transient conditions, enabling power systems to operate closer to their stability limits while maintaining security. Their deployment helps avoid costly infrastructural expansions by optimizing existing transmission assets, which is critical given environmental and economic constraints. Recent advances in semiconductor technologies and control algorithms have made FACTS devices more reliable, efficient, and adaptable to modern grids, including renewable integration and deregulated power markets. In summary, FACTS controllers play a vital role in modern power systems by providing flexible, efficient, and reliable solutions for power flow management, voltage control, and system stability enhancement, thereby supporting the evolving demands of today's complex electrical networks.

This paper deals with the problem of reserve scheduling for power systems with wind power generation, and proposes a new set-up that incorporates an AC Optimal Power Flow (AC OPF) formulation. The AC OPF problem is nonconvex and in general hard to solve. Here we propose an approach building on convex relaxations of the AC OPF problems and discuss a modification that we believe has certain advantages when combined with the reserve scheduling formulation. Numerical simulations suggest that the proposed relaxation technique results in a feasible solution for the exact problem. Using the proposed modification of the AC OPF problem, we focus on systems with uncertain generation and formulate a chance constrained optimization problem to determine the minimum cost of production and reserves. Due to the complex structure of the resulting problem, we use a heuristic procedure to solve it numerically. This is achieved following a sampling based methodology. The proposed algorithm is applied to the IEEE-30 bus network and is compared against its DC power flow counterpart by means of Monte Carlo simulations.

TCSC with auxiliary controls based voltage and reactive power controls on grid power system

The integration of renewable energy sources alter the radial nature of the conventional distribution network and causes the power flow to reverse in some periods. As the voltage regulator is normally designed for unidirectional power flow, this may cause voltage violations on the distribution feeder resulting in faults and cuts. To solve this problem, monitoring of the distribution network is essential before taking any control or protection measures. From this fact emerges the importance of reverse power flow detection. In this paper, the optimal phasor measurement placement for reverse power flow detection is discussed. An extensive literature review and a comparison among a wide range of existing optimization algorithms is done. Then genetic algorithm is selected to solve this problem. Global Optimization Tool of Matlab are used to test the proposed algorithm on IEEE-14 and IEEE-39 node test feeders.

Compared with traditional vibration suppression methods, wave-based techniques are more effective for overcoming low-frequency, broadband vibrations in the autonomous underwater vehicles (AUVs). The paper develops a wave-based power flow framework, implemented via the wave finite element method (WFEM), to quantify the power carried by individual wave modes inside the complex assembled structures. By introducing the symplectic adjoint orthogonality (SAO), wase basis attains numerically stable bi-orthogonality, ensuring an accurate projection of the physical displacement field onto the amplitudes of wave modes. The power orthogonality among wave modes is rigorously established via the power flow formulation. The application to an electric motor housing produces a waveguides power flow transmission network from which the dominant wave propagation path and wave modes are identified, thereby enabling targeted wave-based vibration mitigation.