Steady-state Operating Points Research Articles

Effect of Coupling Impedance on Stability Assessment of Grid-Forming Converters Under Various Grid Conditions

The phenomenon of frequency coupling is widely observed in grid-forming (GFM) converters due to the presence of asymmetrical controls and nonlinear blocks. However, the factors influencing frequency coupling have not been thoroughly explored. This paper introduces a systematic small-signal impedance model of GFM converters that intuitively reflects the factors affecting frequency coupling and provides a detailed analysis of how coupling impedance affects stability. It is demonstrated that the influencing factors of coupling impedance are an active power loop and reactive power loop. Specifically, the active power loop influences coupling impedance characteristics near the fundamental frequency, while the reactive power loop impacts the entire frequency range. This paper first reveals that the reactive power loop has a more pronounced effect on frequency coupling than the active power loop. Additionally, the variation in the steady-state operating points also affects the degree of frequency coupling of the GFM converters, primarily affecting the coupling impedance characteristics beyond the fundamental frequency, and the low operating points tend to affect system stability adversely. Finally, simulation results validate the accuracy of the mathematical model and theoretical analysis.

Optimization of NOX emissions of a CRDI DIESEL engine using CMA-ES method

Engine calibration is the tuning of embedded parameters in the engine control unit (ECU) software to improve vehicle characteristics and meet legal requirements. Due to the stricter emission limits and rising customer expectations, current ECU software may include variables up to 30,000, which require very much time for engine calibration development. For this reason, automotive manufacturers continuously develop mathematical-based optimization methods to find optimum operating conditions for the engines. This study aimed to develop an online optimization algorithm to conduct automated dynamometer tests in the calibration development process. A modified covariance matrix adaptation (CMA) algorithm, which is an evolutionary strategy (ES) method belonging to meta-heuristic optimization, was integrated with an automation system for online calibration optimization. Some CMA method parameters such as step size and damping factor were initially revised to achieve the method to function efficiently in online engine calibration. Optimization was conducted at three different operating points of a 2-liter common rail direct injection (CRDI) diesel engine, where NOx emission mainly impacts the New European Driving Cycle (NEDC) results. The main injection timing, rail pressure, pilot injection quantity and timing, manifold pressure, and mass air flow were controlled in the optimization process. Optimization targets were determined according to the NOx-PM Pareto curve for each operating point. Covariance matrix adaptation was used to generate Pareto curves. Sixty-five measurements were taken for each operating point in the optimization process. Once optimization targets were determined, optimization occurred at each operating point. A total NOx emission reduction of 3.8% was obtained in the NEDC test, while fuel consumption and PM remained almost the same at steady-state operating points. The modified CMA-ES algorithm is expected to be an efficient method for online calibration optimization.

Recent progress in the operational flexibility of 1 MW circulating fluidized bed combustion

In this study, various experimental tests were carried out with a 1 MWth circulating fluidized bed pilot plant at the Technical University of Darmstadt to investigate the combustion and co-combustion behaviour of different fuels under load change conditions in air and oxyfuel mode. The combustion tests were carried out with low-calorific lignite and hard coal as reference cases for co-combustion. In the co-combustion experimental tests, straw pellets, and refuse-derived fuels (high and low calorific) were used as co-fuels for coal. In addition, a comprehensive dynamic 1.5-D process simulation model was established for a 1 MWth circulating fluidized bed pilot plant. The model created with the “APROS” software precisely reproduces both the gas/solids and the water/steam side of the 1 MWth pilot plant. The dynamic process simulation model was first validated at various steady-state operation points and, in a second step, at various dynamic load changes. The numerical results, such as the pressure drop and temperature profiles along the fluidized bed riser as well as the flue gas concentrations at the cyclone outlet, were compared with the measurements and showed agreement during the long-term tests of the combustion and co-combustion processes.

Convex Relaxations of Maximal Load Delivery for Multi-Contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks

Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities in gas and power grids, where disruptions can require the curtailment of load in one or both systems. Although typically operated independently, coordination of these systems during severe disruptions can allow for targeted delivery to lifeline services, including gas delivery for residential heating and power delivery for critical facilities. To address the challenge of estimating maximum joint network capacities under such disruptions, we consider the task of determining feasible steady-state operating points for severely damaged systems while ensuring the maximal delivery of gas and power loads simultaneously, represented mathematically as the nonconvex joint Maximal Load Delivery (MLD) problem. To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem. Then, to demonstrate the relaxation’s effectiveness in determining bounds on network capacities, exact and relaxed MLD formulations are compared across various multi-contingency scenarios on nine joint networks ranging in size from 25 to 1191 nodes. The relaxation-based methodology is observed to accurately and efficiently estimate the impacts of severe joint network disruptions, often converging to the relaxed MLD problem’s globally optimal solution within ten seconds.

Steady‐state operating points of islanded virtual synchronous machine microgrid

AbstractBefore starting stability analysis of the multivirtual synchronous machine (n‐VISMA) power system, it is necessary to obtain the steady‐state operating points (SSOPs) of all dynamic nodes in the network. Modified traditional iterative schemes using the concept of droop bus technique in an islanded microgrid are not feasible for load flow analysis of VISMA microgrid incorporating non‐control dynamics. This paper proposes closed‐form steady‐state, fundamental‐frequency models for islanded VISMA microgrids using the concept of virtual swing buses. In this technique, the virtual internal buses of all VISMAs in the network are governed by the swing equation. The voltage at all buses is variable except the virtual buses in which the pole wheel voltages are prespecified. The algorithm was extended by a droop control localized to each VISMA. The suitability of the proposed algorithm to obtaining SSOPs of VISMA was tested on IEEE‐9 bus system with VISMA replacing electromechanical synchronous machines and also on a low‐voltage distribution system. To validate the applicability of the proposed algorithm and prove its accuracy, the case study systems were also modeled in the SIMULINK environment for detailed time domain analysis. The algorithm was found to be computationally effective for a load flow analysis of the VISMA microgrid. The results also reveal that the addition of external droop control improves the frequency stability of the system.

Characterization of Hydrotreated Vegetable Oil (HVO) in a Euro 6 Diesel Engine as a Drop-In Fuel and With a Dedicated Calibration

Renewable fuels can play an important role in achieving future goals of energy sustainability and CO2 reduction. In particular, hydrotreated vegetable oil (HVO) represents one of the most promising alternatives to petroleum-derived diesel fuels. Several studies have shown that conventional diesel engines can run on 100% HVO without significant modifications to the hardware and control strategies. The current activity has experimentally evaluated the potential of HVO as a “drop-in” fuel, i.e., without changes to the original baseline calibration, comparing it to conventional diesel fuel on a 2.3-litre Euro 6 compression ignition engine.Tests revealed that HVO can significantly reduce engine-out soot (by more than 60%), HC and CO emissions (by about 40%), compared to diesel, while NOx levels and fuel conversion efficiency remain relatively unchanged under steady-state warmed-up conditions. The advantages of HVO proved to be further enhanced when the engine has not yet warmed up.Using statistical techniques of design of experiments (DoE) at three warmed-up steady-state operating points, the main engine control parameters were recalibrated to demonstrate that engine-out emissions can be further optimized with a dedicated calibration.

A Linear Programming Method Based Optimal Power Flow Problem for Iraqi Extra High Voltage Grid (EHV)

The objective of an Optimal Power Flow (OPF) algorithm is to find steady state operation point which minimizes generation cost, loss etc. while maintaining an acceptable system performance in terms of limits on generators real and reactive powers, line flow limits etc. The OPF solution includes an objective function. A common objective function concerns the active power generation cost. A Linear programming method is proposed to solve the OPF problem. The Linear Programming (LP) approach transforms the nonlinear optimization problem into an iterative algorithm that in each iteration solves a linear optimization problem resulting from linearization both the objective function and constrains. A computer program, written in MATLAB environment, is developed to represent the proposed method. The adopted program is applied for the first time on Iraqi 24 bus Extra High Voltage (EHV) network (400 kV). The required are data taken from the operation and control office, which belongs to the ministry of electricity.

Overmodulation Harmonic Modeling and Suppression for Induction Motor Field-Weakening Control With Extended Voltage Tracking Method

The overmodulation strategy can improve the maximum output torque capability of induction motor field-weakening control. However, the harmonic voltages accompanied with the extended voltage would cause the harmonics of current and torque, deteriorating system performance. To reveal the generation mechanism of harmonics, an overmodulation harmonic modeling is proposed based on vector analysis. It is quantitatively proved that the constant extended voltage should be reduced as much as possible to suppress the harmonic when providing the expected torque. On this basis, an extended voltage tracking method is proposed to suppress the harmonic and achieve the high output torque capability according to different operation requirements. The flux current preselection block is designed to preset the steady-state operation point. The expected extended voltage tracking block is designed to set appropriate voltage constraint, thereby redistributing the stator current properly. Finally, the experimental results confirm that the investigated method can improve the steady-state performance with harmonic suppression, and achieve the maximum output torque during the dynamic process and the high-load driving process.

Comparison of optimal power production and operation of unmoored floating offshore wind turbines and energy ships

Abstract. As the need to transition from global reliance on fossil fuels grows, solutions for producing green alternative fuels are necessary. These fuels will be especially important for hard-to-decarbonize sectors such as shipping. Mobile offshore wind energy systems (MOWESs) have been proposed as one such solution. These systems aim to harness the far-offshore wind resource, which is abundant and yet untapped because of installation and grid-connection limitations. Two classes of MOWES have been proposed in the literature: unmoored floating offshore wind turbines (UFOWTs) and energy ships (ESs). Both systems operate as autonomous power-to-X (PtX) plants, powered entirely by wind energy, and so can be used to produce synthetic green fuels such as hydrogen or ammonia, or for other energy-intensive applications such as direct air carbon capture. The two technologies differ in form; UFOWTs are based on a conventional FOWT but include propellers in place of mooring lines for course keeping, while ESs operate like a sailing ship and generate power via hydro-turbines mounted on the underside of the hull. Though much research and development is necessary for these systems to be feasible, the promise of harnessing strong winds far offshore, as well as the potential to avoid siting regulatory challenges, is enticing. This paper develops models of each MOWES concept to compare their power production on a consistent basis. The performance of the technologies is examined at steady-state operating points across relative wind speeds and angles. An optimization scheme is used to determine the values of the control variables which define the operating point for each set of environmental conditions. Results for each model show good agreement with published results for both UFOWTs and ESs. Model results suggest that UFOWTs can generate more power than ESs under ideal environmental conditions but are very sensitive to off-design operating conditions. In above-rated wind speeds, the UFOWT is able to produce as much power as a conventional, moored FOWT, whereas the ES cannot, since some power is always consumed to spin the Flettner rotors. The models developed here and their results may both be useful in future works that focus on the routing of UFOWTs or holistically designing a mobile UFOWT. Although differences in the performance of the systems have been identified, more work is necessary to discern which is a more viable producer of green electrofuels (e-fuels).

Grid-Forming Control of Wind Turbines for Diode Rectifier Unit Based Offshore Wind Farm Integration

Offshore wind farms are the main trend of future wind power exploitation. The diode rectifier unit (DRU) shows great potential in offshore wind power integration due to its economy and reliability benefits, and stable AC voltage control of the offshore gird is the key technology of the DRU based scheme. In this paper, the sensitivities of the DRU based system are defined and the sensitivity calculation method is proposed. According to the sensitivity characteristics analysis, the relationship between the wind turbine (WT) active power (or reactive power) and the WT output voltage (or system frequency) is clarified. On this basis, a grid-forming control strategy for WT converters is proposed. The stable operation mechanism of the grid-forming WTs in the DRU based system is demonstrated according to the analysis of steady state operation point existence and small disturbance stability. The time domain simulations of two DRU based offshore wind farm integration systems are carried out in PSCAD/EMTDC, and the feasibility of the proposed grid-forming control is verified.

Comprehensive investigation of membrane sorption and CFD modeling of a tube membrane humidifier with experimental validation

The humidification of PEM fuel cells is critical for their performance and efficiency and for ensuring a long durability. In most PEM fuel cell systems for mobile applications membrane humidifiers are used to humidify the fresh air. In this process, the water contained in the cathode exhaust gas is used to increase the humidity of the supply air. Despite the simple design of membrane humidifiers, the simulation of the water transfer is difficult and so far there exist hardly any precise models to calculate the absorption and desorption processes. Common approaches that use the Sherwood number to determine the sorption rates cannot account for the influence of the local water content of the membrane. This ultimately leads to an inaccurate simulation of humidifier behavior, as these models cannot consider the fact that desorption is nearly ten times faster than absorption.In this study, an empirical formula for an accurate determination of the sorption rate is derived based on experimental data. This function accounts for the different absorption and desorption rates by finding a sorption rate coefficient as a function of the local membrane water content, temperature, pressure and flow velocity.Furthermore, a CFD model is derived from the geometry of a commercially available membrane humidifier, which is also investigated on a test bench. Using the experimental data, the CFD model is validated and it is shown that the developed sorption rate formula leads to good agreements between simulations and experiments at steady-state operating points of the humidifier.

Control-oriented dynamic process optimization of solid oxide electrolysis cell system with the gas characteristic regarding oxygen electrode delamination

Fast response, strong reliability, and high efficiency as the critical objectives of a solid oxide electrolysis cell (SOEC) system, which requires the system to operate under optimal operating conditions and switching manners. Therefore, various research has been carried out on its characteristic security. Most of them focus on the thermal characteristics security without further considering the security of gas characteristics regarding oxygen electrode delamination. However, this is one of the most critical degradations of SOEC. Herein, a novel SOEC system dynamic model with the gas characteristic regarding oxygen electrode delamination is proposed for the first time to optimize operation. Specially, the advantages are discussed through the optimization analysis of both the secure operation range regarding certain operating conditions and the steady-state operating points of the system. Subsequently, the dynamic process constraints of oxygen electrode delamination, fuel starvation, and power fast tracking during dynamic switching are investigated. The feasibilities of multi-step, parabola, and ramp schemes in solving the problems above are also evaluated. The outcomes show that the ramp scheme is preferred. Furthermore, the priority issue between oxygen electrode delamination and fuel starvation is studied, and corresponding dynamic process optimization strategies are developed for high and low initial power with a two-step switching method. After that, the dynamic process optimizations of two representative cases are investigated in detail. The optimization results show that the system efficiency is increased, and the safe ramp duration under the low initial power is significantly shortened. The findings of this study could provide a basis for developing control strategies for SOEC systems with fluctuating energy input.

Design Optimization of the Magnet-Free Synchronous Homopolar Motor of a Subway Train

Synchronous homopolar motors have no permanent magnets and their excitation winding is fixed at their stator. However, they can be a good alternative to induction and permanent magnet motors in traction applications requiring a wide constant power speed range. They provide an excitation flux control and a highly reliable brushless rotor design. This article presents the procedure and results of optimizing a 370 kW synchronous homopolar motor for driving subway train. The optimization procedure was developed to take into account the subway train moving trajectory. The analysis considers only a limited number of steady-state operating points of the motor to reduce computation time. The optimization results show a significant improvement of the target parameters of the traction drive. The optimization makes it possible to significantly reduce the losses in the operating cycle, as well as the torque ripple of the motor and the current rating of the traction inverter.

Numerical and experimental study of co-combustion of refuse-derived fuels in a circulating fluidized bed during load change

This study presents a comprehensive dynamic process simulation model of a 1 MWth circulating fluidized bed test facility applied for lignite and refuse-derived fuel co-combustion. The developed dynamic process simulation model describes the circulating fluidized bed riser and the supplying system with a high level of detail considering heat transfer, gas-solid interaction, combustion, and fluid dynamics. The model was first tuned at two steady-state operation points and was then validated by the measured data from a long-term test campaign of the 1 MWth circulating fluidized bed test facility at various loads (60%–80% to 100%). During the load changes, the simulated pressure and temperature profiles along the combustor as well as the flue gas concentrations agree very well with the measurement data. Finally, increasing the proportion of waste-derived fuel in the co-combustion process was investigated to evaluate the flexibility of its use in power generation to further reduce CO2 emissions.

Comparative small-signal evaluation of advanced grid-forming control techniques

This paper presents the small-signal modelling and analysis of the most recent grid-forming control techniques, namely the matching control (MC) and the dispatchable virtual oscillator (dVOC). These are compared to more classical SME techniques such as synchronverters (SV) and voltage-controlled virtual synchronous machines (VCVSM) under different grid conditions. In addition to studying the time-domain response (inertial behaviour, steady-state operation point, etc.), a thorough evaluation of the dominant eigenvalues of each control is carried out by obtaining the participation factors and the sensitivity to physical and control parameter variations. Simulation results are obtained for a grid-forming converter connected to a dynamic grid model that emulates different properties of low-inertia power systems—e.g. primary reserve, inertial strength, coupling strength, etc. Besides, hardware-in-the-loop experimental results are presented to validate the analysis.

Stability analysis and parameter configuration of parallel virtual synchronous generators in microgrid

The current small-signal stability analysis and parameter selection of converters that mimic synchronous generators usually ignore some dynamic characteristics and the changes of steady-state operating points for simplicity. It could only judge the trend of small-signal stability and the analysis result was not accurate enough. Firstly, this paper established a small-signal model that mimics synchronous generators by connecting two isolated converters in parallel, the eigenvalues of the system were calculated and some of their physical meanings were obtained. Following that, in order to demonstrate the relationship of eigenvalues and state variables, the participation factor was calculated. Considering that, there will be some variability of the operating points with the parameters variation. As a function of the system settings, numerous root locus plots were created. For individual eigenvalue close to the real axis, in order to reveal the contribution of different parameters to the oscillation patterns, a separate eigenvalue sensitivity analysis was performed. The rules of the influence are essential to guide the design of parameters and their optimization of isolated converters connected in parallel that mimic synchronous generators.

Data-Driven Dynamic Modeling in Power Systems: A Fresh Look on Inverter-Based Resource Modeling

This article introduces ways to identify dynamic system models using measurement data. In power system analysis, a static model represents the time-invariant input–output relationship of a system, while a dynamic model describes the behavior of the system over time. For example, how will a system transit from one steady-state operation point to another?

Power loss minimization with simultaneous location and sizing of distribution generation units using artificial algae algorithm

Power loss is one <span lang="EN-US">of the important pointers used to measure the performance of distributions networks. Many optimization algorithms have been proposed to solve various optimal power flow problems in Electrical Engineering. In this paper, a novel technique, artificial algae algorithm is developed to robustly detect the optimal location and size of distributed generation (DG) units for minimization of total power losses without violating the equality and inequality constraints. The main objective of optimal power flow (OPF) is to maximize or minimize the objective function using various constraint so that steady-state operation point is achieved. The concept of optimal power flow in power system helps to minimize real power loss. In the proposed approach, various control variables like generator bus, voltage magnitudes, and transformer tap settings are considered. The proposed algorithm is simulated in MATLAB and effectiveness is carried on IEEE 33 bus radial distribution system and satisfactory results are achieved when compared with other optimization techniques. A notable improvement in reduction of active power losses with 3 DG operating at different power factors are 65.5%, 42.4%, and 77.8% respectively, were achieved in comparison to the system without DGs and as compared with other research papers.</span>

Investigation of in-cylinder soot formation in a DISI engine during transient operation by simultaneous endoscopic PIV and flame imaging

A single-cylinder full-metal engine with a real combustion chamber geometry was used to investigate particulate number emissions resulting from transient engine operation. The formation of particulate number emissions depends on mixture formation influenced by the in-cylinder flow and injection, and the formation of fuel films on the in-cylinder walls. For the investigation of this multi-parameter process, simultaneous endoscopic PIV and combustion visualization were applied. Hence, the measurement techniques allowed the investigation of in-cylinder flow, flame propagation, and soot formation. The test rig was modified to apply a generic load step and a realistic tip-in with Miller cycle. The reproducibility of the engine parameters during the transient allowed statistical analysis and the comparison between steady-state operating points. Cause-and-effect chains concerning the formation of soot are concluded by correlation analysis of parameters extracted from the flow field, the flame propagation and the soot luminosity.

An Experimental and Computational Investigation of Tailor-Developed Combustion and Air-Handling System Concepts in a Heavy-Duty Gasoline Compression Ignition Engine

This study investigates using tailor-developed combustion and air-handling system concepts to achieve high-efficiency, clean gasoline compression ignition (GCI) combustion, aimed at addressing a future heavy-duty ultralow NOx standard of 0.027 g/kWh at the vehicle tailpipe and the tightening CO2 limits around the world by combining GCI with a cost-effective engine aftertreatment system. The development activities were conducted based on a 15 L heavy-duty diesel engine. By taking an analysis-led design approach, a first-generation (Gen1) GCI engine concept was developed and tested, encompassing tailor-designed piston bowl geometry, fuel spray pattern, and swirl motion paired with a customized, fixed-geometry, two-stage turbocharging system and a high-pressure EGR loop with two-stage cooling. Across four key steady-state operating points, the Gen1 GCI concept demonstrated 85–95% lower smoke and 2–3% better diesel-equivalent gross indicated fuel consumption compared to the diesel baseline at 1 g/kWh engine-out NOx. By upgrading to a Gen2 air-handling concept that was composed of a prototype, single-stage, variable-geometry turbocharger and a less restrictive EGR loop, 1D system-level analysis predicted that the pumping mean effective pressure was reduced by 43–54% and the diesel-equivalent brake-specific fuel consumption was improved by 2–4%, thereby demonstrating the performance enhancement potential of refining the air-handling system.