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In microgrids, voltage imbalance control is crucial to preserving the required level of power quality. The article presents a tracker design that mitigates the unbalance in the microgrids. The proposed microgrid model includes positive and negative sequences, whereby the positive sequences are controlled, and the negative sequence is treated as an external disturbance (whose effect must be attenuated). The uncertainty in the external disturbance is modelled in the norm-bounded form. The suggested control is based on attracting (driving) the state trajectory into a small region, including the origin (attracting ellipsoid-set). The effect of the negative sequence components is attenuated by minimizing the ellipsoid volume. When the state trajectory enters that region, it will never leave it for the future time (termed invariant-set). Two theorems were formulated for tracker synthesis that follows the desired reference and reduces the negative sequence impact. These theorems are the invariant-set method and the H ∞ approach. The validity of the suggested control is demonstrated via testing the system under various operational unbalanced scenarios, such as unbalances or faults at the load side or in the transmission lines. The simulations show the superiority of the suggested method in terms of accuracy and dynamic response when compared with the H∞. Additionally, a comparison is made between the suggested tracker and Active Disturbance Rejection Control (ADRC). • Microgrid model with positive and negative sequences is presented. • Negative sequence is treated as an uncertain disturbance. • Two developed new theorems handle this disturbance in tracker design. • A positive-sequence tracker using invariant-sets is proposed for efficient disturbance rejection. • Performance is compared to H¥ and ADRC under various operational conditions. [ABSTRACT FROM AUTHOR]

Virtual synchronous generator (VSG) control has positive effects on the stability of microgrids. In practical power systems, both single-phase loads and three-phase unbalanced loads are present. The four-leg inverter is an alternative solution for the power supply of unbalanced loads and grid connections. The traditional VSG control strategy still faces challenges when using a four-leg inverter to provide a symmetrical voltage and stable frequency in the load power supply and pre-synchronization. This paper proposes a VSG-based control strategy along with a pre-synchronization method for four-leg inverters. An improved VSG control strategy is put forward for four-leg inverters. The improved virtual impedance control and power calculation methods are integrated into the control loop to suppress the voltage asymmetry and frequency ripples. Building on the improved VSG control strategy, a pre-synchronization control approach is proposed to minimize the amplitude and phase angle discrepancies between the inverter output voltage and the power grid voltage. In addition, an optimized design method for control parameters is presented to improve VSG dynamic performance. A hardware prototype of the four-leg inverter is built; the results show that the voltage unbalance ratio can be reduced by 89%, and the response time can be shortened by 50%. [ABSTRACT FROM AUTHOR]

This paper presents the design of a disturbance observer-based controller that regulates the output voltage of three-phase four-leg voltage source inverters (VSIs) deployed for grid-forming operation in Renewable Energy-based Distributed Generation (REDG) Systems. The primary objective of the controller is to provide a symmetric and sinusoidal voltage at the output of the VSI when supplying highly unbalanced and nonlinear loads. The controller employs the feedback linearization (FL) technique and incorporates a disturbance observer (DO) to address a range of disturbances that include oscillations resulting from unbalanced loads, harmonics generated by nonlinear loads, and non-oscillatory disturbances. Notably, the controller adopts a direct control scheme without the need for nested current control loops and does not use any transformation frames. Simulation studies and experimental investigations were conducted to assess the controller's performance under various load conditions, including both linear and nonlinear types, as well as load transients. The findings demonstrate the controller's capability to accurately track references while complying with the IEEE power quality standards for the tested conditions. [ABSTRACT FROM AUTHOR]

The expansion of distributed generation and erratic loads create many challenges for electricity distribution networks (DN), like grid congestion and load unbalance. Technological advances in recent years have made the use of electric vehicles (EVs) more economical and justified for network connection. The use of smart EVs in the network scale, in addition to the peak shedding, if it is used in a single phase, it can also lead to the improvement of load unbalance. This paper proposes an energy and cost management model for the appropriate and distributed deployment of single phase EVs in distribution networks to provide network support for a DN including renewable resources. By connecting or disconnecting single-phase smart EVs to the DN, unbalanced loads in this network will be balanced as much as possible. To evaluate the proposed model, a network of 13 buses has been used, and the calculations of these energy costs have been measured during 24 h by two types of household and industrial loads. These loads are unbalanced in the DN and single-phase EVs have the ability to improve the unbalanced load of the DN. Also, the energy price is variable during the day and depends on the peak load. From the sensitivity analysis and with the relative increase or decrease of load, load change effects on the cost of each DN per-unit power have been measured and compared with the presence or absence of single-phase smart EVs to obtain more practical results. According to this paper, the use of EVs, in addition to improving the load of the DN, greatly reduces the costs of DN.

DC microgrid systems based on hybrid photovoltaic-electrical energy storage systems for power generation are widely used in new energy cruise ships. For the problem of power supply voltage unbalance arising when a daily load power supply converter is connected to an unbalanced load or single-phase load, this paper proposes a dead-beat predictive voltage control strategy based on positive and negative sequence separation of output voltage. This strategy can realize control of positive and negative sequence components of the power supply converter voltage under the positive and negative sequence coordinate systems respectively, to ensure the three-phase voltage balance of the power supply converter, enhance the anti-interference ability of the system against unbalanced load and avoid additional power quality control devices. The simulation results show that, after the proposed control strategy is adopted, the voltage unbalance of the daily load power supply converter is reduced from 28% to less than 0.5%, which verifies the effectiveness of the proposed control algorithm .

The purpose of the work is study of special asymmetric modes of new three-phase autotrans-former device for flexible connection of alternative current power systems. The universal model was developed for the device, containing two autotransformers - the main phase-shifting and the additional regulating autotransformer. The model allows studying both symmetric and almost any asymmetric modes of the considered circuit. It became possible to connect asymmetrically the loads in different phases of the regulating autotransformer, as well as arbitrary connect the regulating autotransformer itself to the hexagon taps. According to the calculated values of cur-rents, voltages and magnetic fluxes of the device the visual vectorial diagrams were constructed for the main and the regulating autotransformer, explaining specific of considered operating modes. It was shown that device’ currents in such modes contain symmetrical components of both zero and negative sequences. Also, at asymmetric connection of the regulating autotrans-former, the relative magnetic flux of the legs of the main and regulating autotransformers are asymmetrical, but in main autotransformer their sum is approximately equal to zero and magnet-ic flux practically does not escape into the surrounding space. Radically different situation is observed in the regulating autotransformer. The significant zero-sequence fluxes arise with the release of significant (about 50%) magnetic flux into the surrounding space. This requires spe-cial measures to be taken to limit its harmful effects on the operation of the autotransformer.

[Objective] At present, the underground engineering diseases and accidents caused by unbalanced load in urban rail transit are increasing gradually. In order to understand the adverse effect of unbalanced load on the deformation of deep foundation pit in urban rail transit station and reduce the construction risk, it is necessary to analyze the deformation characteristics of station deep foundation pit under unbalanced load. [Method] Based on theoretical analysis and on-site monitoring data, the aforementioned deformation characteristics are studied, the changing law regarding the retaining pile deformation, the horizontal displacement of the deep soil and ground settlement is analyzed, and the interrelation between the retaining pile deformation and the deep soil horizontal displacement, the ground settlement and excavation depth is discussed. [Result & Conclusion] The horizontal displacement curve of the retaining pile is fish-belly shaped, and the formation condition has obvious influence on the deformation of the retaining pile. There is a roughly linear relationship between the deformation of the retaining pile and the horizontal displacement of deep soil, and the empirical coefficient is proposed to be 1.30. Due to partial load, the ground settlement around the deep foundation pit is larger, and the relationship between the maximum horizontal displacement δhm of the retaining pile and the maximum ground settlement δvm is δvm=(0.9~3.0) δhm, and the proportional coefficient between them is greater than the value under symmetric load. The strong deformation resistance of rock strata limits the deformation of the retaining pile. There is a relationship of δhm=(0.009%~0.060%) He between δhm and He, and the proportional coefficient between them is smaller than the value under symmetric load. The impact area of deep foundation pit construction on the surrounding environment is mainly divided into Zone 1 (main impact zone), Zone 2 (secondary impact zone) and Zone 3 (no impact zone), and the impact area of foundation pit construction is about (0~2.5) He.

Copyright of Urban Mass Transit is the property of Urban Mass Transit Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The propulsion system for underwater vehicles, driven by a counter-rotating permanent magnet synchronous motor (CRPMSM), can enhance the operational stability and efficiency of the vehicle. Due to the influence of complex underwater flows, the load imbalance of CRPMSM's dual counter-rotating rotors may lead to severe issues of dual-rotor desynchronization rotation. Combining traditional vector control (VC) with master-slave control strategies can address the desynchronization problem when CRPMSM's load changes. However, it results in significant speed fluctuations and a long transition time during the transition from load disturbance to synchronous rotation. This paper introduces a model predictive control (MPC) strategy to effectively resolve this issue. The incremental MPC model is established based on the mathematical model of CRPMSM in the dq coordinate system. The predictive control system forecasts the d- and q-axis components of stator currents for the next four control cycles. It selects the optimal control increments to minimize the cost function based on current predictions and different inverter voltage states. The obtained optimal d- and q-axis components of stator voltage are used to control CRPMSM under unbalanced load disturbances. Simulation results demonstrate that, compared to the VC strategy, CRPMSM utilizing the MPC strategy exhibits better dynamic performance with faster speed response and reduced torque fluctuations during load and speed variations. [ABSTRACT FROM AUTHOR]

A neutral point clamped (NPC) converter is considered a forefront in industrial applications. Supplying a typically balanced stand-alone load is one of those applications. However, the loading may become unbalanced which can impact the capacitors’ current and voltage ripple. In this work, an approach is proposed that analyze the capacitor current under unbalanced loading. The proposed method is based on a combination of two-dimensional Fourier series and symmetrical components. Since, two-dimensional Fourier series sectorize the spectrum into harmonics that are either defined by multiples of, fundamental, carrier or both frequencies, the method derives the Fourier coefficients for each sector, corresponding to a sequence current. Therefore, based on the presented approach, each harmonic amplitude in the spectrum sector is defined by three Fourier coefficients reflecting zero, positive and negative sequence current. The capacitor current spectrum is obtained by vector summing sequence coefficients. The method is tested on unbalanced load conditions with (out) a ground path. Results verify feasibility of the proposed method in deriving Fourier coefficients of capacitor currents that accurately reflects the loading status of the NPC. This is vital for converter design in terms of proper sizing of DC capacitor and can help in avoiding components failure. [ABSTRACT FROM AUTHOR]

Under the influence of the unbalanced load, the negative and zero sequence components in the output voltage of the three-phase four-leg voltage source inverter(TPFL-VSI) will cause asymmetry voltage. This paper designs an individual sequencing control for the three-phase four-leg inverter to address this problem. The second-order generalized integrator is adopted to extract the current’s positive and negative sequence components. The virtual oscillator control(VOC) controls the positive sequence component, and the negative sequence component is suppressed by designing the virtual impedance and the multiple proportional resonance controller. The proportional resonance control is used to control the zero-sequence voltage of the fourth bridge arm. Considering that voltage deviation is caused by the access of negative sequence virtual impedance and load step, the secondary voltage compensation strategy is further added in the individual sequencing control to improve the droop relationship in the VOC and effectively solve the problem of system voltage instability. Ultimately, a TPFL-VSI model is built in Matlab/Simulink, and simulation results verify the feasibility and effectiveness of the proposed control strategy under different conditions.

Virtual synchronous generator (VSG) control has positive effects on the stability of microgrids. In practical power systems, both single-phase loads and three-phase unbalanced loads are present. The four-leg inverter is an alternative solution for the power supply of unbalanced loads and grid connections. The traditional VSG control strategy still faces challenges when using a four-leg inverter to provide a symmetrical voltage and stable frequency in the load power supply and pre-synchronization. This paper proposes a VSG-based control strategy along with a pre-synchronization method for four-leg inverters. An improved VSG control strategy is put forward for four-leg inverters. The improved virtual impedance control and power calculation methods are integrated into the control loop to suppress the voltage asymmetry and frequency ripples. Building on the improved VSG control strategy, a pre-synchronization control approach is proposed to minimize the amplitude and phase angle discrepancies between the inverter output voltage and the power grid voltage. In addition, an optimized design method for control parameters is presented to improve VSG dynamic performance. A hardware prototype of the four-leg inverter is built; the results show that the voltage unbalance ratio can be reduced by 89%, and the response time can be shortened by 50%.

In this paper, harmonic compensated individual-phase voltage control of four-leg inverters is proposed for microgrid applications. Individual-phase control, which is one of the promising voltage control methods of four-leg inverters, ensures robustness for high load unbalance rates. However, the odd harmonics generated by nonlinear loads and dead time deteriorate the quality of load voltages under single-phase control. The proposed method compensates for the odd harmonics included in the load voltages to improve the output power quality. In the proposed method, band-pass and all-pass filters are used to generate the virtual components for the individual-phase control. Additionally, the harmonics are compensated in the synchronous reference frame using a resonant controller, while the fundamental components are controlled by proportional-integral controllers. With the proposed method, the total harmonic distortion of the load voltages is maintained at a low level under unbalanced and nonlinear load conditions. The effectiveness of the proposed method is demonstrated through simulation and experimental results. [ABSTRACT FROM AUTHOR]

In order to further improve the loss reduction effect of low-voltage distribution network, an auxiliary decision-making method of low-voltage distribution network loss reduction based on plant information real-time database was proposed. Through PI real-time database, the line losses of three-phase line and neutral line in low-voltage distribution network were calculated, and it was judged that unbalanced load of neutral line can easily lead to large loss. Taking temperature as the main factor affecting the loss of low-voltage distribution network, by increasing the proportion of low-energy-consuming transformers, increasing the cross-sectional area of conductors and optimizing the operation mode of distribution network, the loss reduction decision of distribution network was completed. The test results in a trunk-type low-voltage distribution network in a city show that the proposed method can effectively improve the unbalanced load of distribution lines. Compared with the loss of each phase line and center line before loss reduction, the loss value after loss reduction shows a significant downward trend, and the bus loss rate of the proposed method is relatively low. The line loss of each phase is controlled within 2%. [ABSTRACT FROM AUTHOR]

In order to solve the problem of low voltage caused by unbalanced load in the distribution network, a transformer loss intelligent prediction model under unbalanced load is proposed. Firstly, the mathematical model of a transformer with an unbalanced load is established. The zero-sequence impedance and neutral line current of the transformer are calculated by using the Chaos Game Optimization algorithm (CGO), and the correctness of the mathematical model is proved by using actual data. Then, the correlation among network input variables is eliminated by using Principal Component Analysis (PCA), so the number of network input variables is decreased. At the same time, Sparrow Search Algorithm (SSA) is used to optimize the initial weight and threshold of the BP network, and an accurate transformer loss prediction model based on the PCA-SSA-BP is established. Finally, compared with the transformer loss prediction model based on BP network, Genetic Algorithm optimized BP network (GA-BP), Particle Swarm optimized BP network (PSO-BP) and Sparrow Search Algorithm optimized BP network (SSA-BP), the transformer loss prediction model based on PCA-SSA-BP network has been proven to be accurate by using actual data and it is helpful for low-voltage recovery in the distribution network. [ABSTRACT FROM AUTHOR]

Permanent Magnet Synchronous Motors (PMSM) have important features such as high torque, high power density, high acceleration, small volume, low noise and high efficiency. With these features, is widely used in the industry. One of the negativities that occur during the operation of electric motors is speed fluctuations and vibrations due to the unbalanced loads. Unbalanced loading can be caused by the character of the load, as well as the poor mounting of the motor to the load, the misalignment on the shaft and the load itself being an eccentric load. Especially at high speeds, this causes permanent damage to the motors. Specification and elimination of these fluctuations, which occur for different reasons, are very important for a reliable operation. In this study, unbalanced load situations are investigated in an unbalanced PMSM and the speed ripples in the unbalanced load of the motor are attempted to be decreased by the proposed Adaptive Harmonic Injection approach. The simulation is carried out under various operating conditions by abruptly and linearly changing the motor speed under unbalanced load. It is observed that speed fluctuations in the motor can be effectively suppressed under different operating condition. [ABSTRACT FROM AUTHOR]

Power electronics converters can be applied as emulators to mimic different grid components used for system behavior analyses and control validation. Synchronous generators (SGs) are the major sources of electric grids. Converter-based SG emulators have been developed for system stability analysis, fault analysis, and frequency support. However, existing SG emulators have not considered the impacts of load unbalance, which is a common phenomenon in distribution grids and will lead to system-level issues. In this article, a SG emulator considering an actual SG's negative sequence (NS) performance is developed for system analyses under unbalanced load conditions. With different simplifications, a SG can have different orders of electrical models. By deriving the NS performances of different SG electrical models, an appropriate SG electrical model in unbalanced load conditions is selected. Then a novel control diagram is proposed to ensure that the NS performances of the selected model can be fully realized. The derived NS models and the proposed control diagram are verified through simulation first and then validated with a converter-based hardware testbed.

This study introduces a new three-dimensional space vector modulation technique for a four-leg quasi Z-source inverter (4L-qZSI) integrating a qZSN and a two-level four-leg inverter. The proposed method encompasses three variants, namely 3DZSVM2, 3DZSVM4, and 3DZSVM8, designed to enhance steady-state operations and harmonic distortions for 4L-qZSI. One of the main contributions of this research is the establishment of a new modulation technique for the 4L-qZSI. The proposed method amalgamates the benefits of SVMs in both abc and $\alpha \beta \gamma $ coordinates. The design processes of the 3DZSVM algorithm are carried out in the newly proposed $\rho \sigma \tau $ coordinates, while the space vector diagram (SVD) of the 4L-qZSI is utilized in the $\alpha \beta \gamma $ location. The proposed algorithm is applied in a single sector, optimizing time interval calculations and pulse creation without requiring trigonometric functions. Extensive simulation studies were conducted to validate the performance of the introduced modulation scheme for the 4L-qZSI. The simulation results show excellent steady-state performance and benefit over the conventional space vector modulation with zero sequences (CZPWM), including a power loss reduction of 50% and a 50% decrease in the THD of the output voltage. In addition, applying this technique results in enhanced output current quality, reduced power loss by 40%, and decreased inductive current ripple by 50% under unbalanced load conditions. Furthermore, the proposed 3DZSVM control strategy for 4L-qZSI is experimentally verified using the TMS320F28379D kit based on the Hardware-in-the-Loop (HIL) simulator. This demonstrates the practicality and effective performance of the suggested control strategy under unbalanced load conditions.

The propulsion system for underwater vehicles, driven by a counter-rotating permanent magnet synchronous motor (CRPMSM), can enhance the operational stability and efficiency of the vehicle. Due to the influence of complex underwater flows, the load imbalance of CRPMSM’s dual counter-rotating rotors may lead to severe issues of dual-rotor desynchronization rotation. Combining traditional vector control (VC) with master-slave control strategies can address the desynchronization problem when CRPMSM’s load changes. However, it results in significant speed fluctuations and a long transition time during the transition from load disturbance to synchronous rotation. This paper introduces a model predictive control (MPC) strategy to effectively resolve this issue. The incremental MPC model is established based on the mathematical model of CRPMSM in the dq coordinate system. The predictive control system forecasts the d- and q-axis components of stator currents for the next four control cycles. It selects the optimal control increments to minimize the cost function based on current predictions and different inverter voltage states. The obtained optimal d- and q-axis components of stator voltage are used to control CRPMSM under unbalanced load disturbances. Simulation results demonstrate that, compared to the VC strategy, CRPMSM utilizing the MPC strategy exhibits better dynamic performance with faster speed response and reduced torque fluctuations during load and speed variations.

The safe and efficient operation of the shearer is the key to coal mining. However, the walking wheel with wear and short fatigue life seriously restrict the improvement of the shearer’s reliability. And the failure effect of torsion deformation is mostly ignored. Therefore, to reveal the failure mechanism of the walking wheel and improve the haulage reliability of the shearer, the meshing model of the walking wheel and pin track considering torsional deformation was established. The meshing characteristics of the walking wheel and the damage mechanism of the tooth surface caused by the axial unbalanced load were analyzed, and the effects of the roll angle, the velocity, and the traction force were discussed. The results show that the peak force is close to the meshing-in area, the stress concentration on the tooth profile of the walking wheel is significant, but the stress distribution in the axial direction of the pin track is uniform; although the roll angle can restrain the meshing impact of the walking wheel, the axial unbalanced load and the wear on the load-bearing side increases with the appearance of the torsional deformation; with the velocity increasing, the stability of the walking wheel with roll angle decreases, the axial unbalanced load intensifies while the safety factor decreases; with the traction load increasing, the load distribution improves, but the bending fatigue strength of the tooth root and the safety factor decrease, and the plastic deformation and wear on the bearing-load side increase. The results provide a reference for exploring the meshing characteristics and failure mechanism of the walking wheel and improving the traction reliability of the shearer.

Asynchronous loads (AL), because of their low negative-sequence resistance, produce the effect of reduced unbalance at their connection points. Therefore, proper modeling of unbalanced load flows in power supply systems requires properly accounting for AL. Adequate models of the induction motor can be realized in the phase frame of reference. The effective use of such models is possible only if accurate data on the parameters of induction motor equivalent circuits for positive and negative sequences are available. Our analysis shows that the techniques used to determine these parameters on the basis of reference data can yield markedly disparate results. It is possible to overcome this difficulty by applying parameter identification methods that use the phase frame of reference. The paper proposes a technique for parameter identification of models of individual induction motors and asynchronous load nodes. The results of computer-aided simulation allow us to conclude that by using parameter identification, we can obtain an equivalent model of an asynchronous load node, and such a model provides high accuracy for both balanced and unbalanced load flow analysis. By varying load flow parameters, we demonstrate that the model proves valid over a wide range of their values. We have proposed a technique for the identification of asynchronous load nodes with such asynchronous loads, including electrical drives equipped with static frequency converters. With the aid of the AL identification models proposed in this paper, it is possible to solve the following practical tasks of management of electric power systems: increasing the accuracy of modeling their operating conditions; making informed decisions when taking measures to reduce unbalance in power grids while accounting for the balancing adjustment effect of AL. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints. • Optimal operation of dynamic boundary MGs considering network and load unbalance. • Integration of unbalanced power and voltage constraints to ensure stable operation. • Fast and scalable mixed-integer linear programming model. • Mixed-integer semidefinite programming captures unbalanced voltage. • Better renewable utilization and resiliency in dynamic boundary microgrids. [ABSTRACT FROM AUTHOR]

In recent years, with the large-scale new energy grid connection on the power supply side of the new power system and the continuous improvement of its penetration rate, the loads on the user side has become more complex, diversified and nonlinear, resulting in the decline of power quality in the distribution network. In order to solve these problems of unbalanced output voltage, low-voltage direct current (DC) voltage oscillation, and harmonic injection of distribution network under unbalanced load, an optimal control strategy considering positive sequence and negative sequence currents was proposed. Based on the three-level topology of power electronic transformer with T-type three-level output stage, and space vector pulse width modulation (SVPWM) modulation and neutral point potential balance technology was used. The three-phase voltage balance or constant DC voltage can be ensured and the stable operation of distribution network can be realized. Simulation analysis and verification results show that the proposed method is feasible and effective, and can effectively improve the power quality of distribution network under unbalanced load conditions. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model of an electric power system which consists of a three-phase power line with distributed parameters and an equivalent, unbalanced RLC load cooperating with the line. The above model was developed on the basis of the modified Hamilton–Ostrogradsky principle, which extends the classical Lagrangian by adding two more components: the energy of dissipative forces in the system and the work of external non-conservative forces. In the developed model, there are four types of energy and four types of linear energy density. On the basis of Hamilton's principle, the extended action functional was formulated and then minimized. As a result, the extremal of the action functional was derived, which can be treated as a solution of the Euler–Lagrange equation for the subsystem with lumped parameters and the Euler–Poisson equation for the subsystem with distributed parameters. The derived system of differential equations describes the entire physical system and consists of ordinary differential equations and partial differential equations. Such a system can be regarded as a full mathematical model of a dynamic object based on interdisciplinary approaches. The partial derivatives in the derived differential state–space equations of the analyzed object are approximated by means of finite differences, and then these equations are integrated in the time coordinate using the Runge–Kutta method of the fourth order. The results of computer simulation of transient processes in the dynamic system are presented as graphs and then discussed. [ABSTRACT FROM AUTHOR]

The analysis of power quality (PQ) in a large enterprise in the point of common coupling (PCC) of the Power Electronics design department shows that, in order to improve the power quality (PQ), three goals must be achieved: the compensation of the distortion power, the compensation of the reactive power and the compensation of the load unbalance. In order to obtain these goals, a four--wire shunt active power filter (SAPF) with split filtering capacitor was designed and built. The SAPF is controlled by implementing the indirect current control method in an original variant. The control algorithm is substantiated and implemented on dSPACE 1103 controlling board. In order to manage the entire system (start, stop and data acquisition), a graphic interface was built and used in experimental evaluation process. The experimental performances obtained for each goal are presented under graphic form and under numeric form of the synthetic indicators. The results show that all the indicators of power quality respect the standards and regulations and prove the validity of the proposed solution. [ABSTRACT FROM AUTHOR]

Premature failure of a deep-groove ball bearing used in an aeroengine governor took place during service. In this paper, the failure mode and root cause of the bearing were studied by macroscopic and microscopic examination, metallographic analysis, hardness test, calculations of contact stress and L10 life, flatness measurement and comparative experiment. The results show that the failure modes of the inner ring raceway and steel balls are contact fatigue spalling, the failure modes of the outer ring raceway are wear and contact fatigue spalling, and the failure mode of the cage is fatigue fracture. The root cause and direct cause of the bearing failure were the unqualified machining process of the spring end face and the high unbalanced axial load, respectively. The unqualified machining process induced high points of the spring end face, which caused misalignment of the outer ring and inner ring and thereby resulted in the high unbalanced axial load. The characteristic damages induced by high axial load were climbing with the morphology of metal extrusion and accumulation at the border of the raceway for the inner and outer ring, and multiple fatigue fractures with the characteristic of multi origins for the cage. The unqualified machining process can be prevented by adopting the refined grinding process and adding detection requirements of flatness. [ABSTRACT FROM AUTHOR]

In the standalone power generation system based on brushle doubly fed induction generator (BDFIG), the special loads such as unbalanced loads and nonlinear loads will cause negative sequence, fifth and seventh harmonic components in power winding (PW) and the corresponding harmonic components in control winding, which will cause some torque ripple so as to make the machine unable to output stable active power, increase the vibration and noise, and so on. This article will first analyze the harmonic components of the torque in details, and then propose an optimized torque ripple suppression method. Through the low frequency harmonic control method of the line side converter without additional sensors, the negative sequence, and fifth harmonic components of PW voltage are controlled to achieve the suppression of the second and sixth harmonic components of the torque. Compared with traditional active filtration method, the proposed method in this article needs to satisfy fewer constraints and tune fewer parameters, and can be utilized more flexibly. Comprehensive experimental results based on a 5-kVA BDFIG demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Although nonlinear Alternating Current (AC) Optimal Power Flow (OPF) may provide more accurate results compared to linearized OPF models, many ACOPF problems are complex and may require high, sometimes infeasible, computational time. The linear Direct Current OPF (DCOPF) has been widely used in power system analysis; however, it has limitations regarding reactive power analysis, and it may cause significant error in distribution networks with a high R/X ratio of feeders. Moreover, most of the existing formulations for the linear ACOPF do not consider mutual impedance for the lines and simplify the network as a single-phase system, which does not significantly represent unbalanced loads. This paper proposes a novel linear AC three-phase OPF formulation for unbalanced ZIP loads using current injection and considering delta and wye loads. The formulation is extended to include shunt capacitors, voltage regulators, and mutual impedance. The proposed methodology is illustrated using the IEEE 123-bus test system in case studies including/not-including voltage regulators, distributed generation, high R/X ratio, and mutual impedance. The results are very accurate compared with a nonlinear three-phase ACOPF model. The high computational performance and the accuracy of the proposed model considering distributed generation and high R/X ratio show its effectiveness in active distribution networks.

Torque reaction is one of the most critical issues with current aerial and undersea vehicles. Contra‐Rotating Propulsion (CRP) systems are the most popular technique for compensating the torque reaction of floating vehicles. However, the unbalanced load conditions are inescapable in CRP systems, which eliminate the net zero torque reaction and impulse unwanted spinning on vehicle. A new single‐phase dual rotor axial flux induction motor has been investigated in this paper that has the ability of self‐compensate reaction torque against unbalanced loads. The proposed motor can eliminate the requirement for complicated torque reaction control systems. Finite element simulation shows the expected performance of proposed motor under unbalanced conditions. The simulation results have been verified by experimental testing of a motor prototype. [ABSTRACT FROM AUTHOR]

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The safe and efficient operation of the shearer is the key to coal mining. However, the walking wheel with wear and short fatigue life seriously restrict the improvement of the shearer's reliability. And the failure effect of torsion deformation is mostly ignored. Therefore, to reveal the failure mechanism of the walking wheel and improve the haulage reliability of the shearer, the meshing model of the walking wheel and pin track considering torsional deformation was established. The meshing characteristics of the walking wheel and the damage mechanism of the tooth surface caused by the axial unbalanced load were analyzed, and the effects of the roll angle, the velocity, and the traction force were discussed. The results show that the peak force is close to the meshing-in area, the stress concentration on the tooth profile of the walking wheel is significant, but the stress distribution in the axial direction of the pin track is uniform; although the roll angle can restrain the meshing impact of the walking wheel, the axial unbalanced load and the wear on the load-bearing side increases with the appearance of the torsional deformation; with the velocity increasing, the stability of the walking wheel with roll angle decreases, the axial unbalanced load intensifies while the safety factor decreases; with the traction load increasing, the load distribution improves, but the bending fatigue strength of the tooth root and the safety factor decrease, and the plastic deformation and wear on the bearing-load side increase. The results provide a reference for exploring the meshing characteristics and failure mechanism of the walking wheel and improving the traction reliability of the shearer. [ABSTRACT FROM AUTHOR]

In order to solve the problem of low voltage caused by unbalanced load in the distribution network, a transformer loss intelligent prediction model under unbalanced load is proposed. Firstly, the mathematical model of a transformer with an unbalanced load is established. The zero-sequence impedance and neutral line current of the transformer are calculated by using the Chaos Game Optimization algorithm (CGO), and the correctness of the mathematical model is proved by using actual data. Then, the correlation among network input variables is eliminated by using Principal Component Analysis (PCA), so the number of network input variables is decreased. At the same time, Sparrow Search Algorithm (SSA) is used to optimize the initial weight and threshold of the BP network, and an accurate transformer loss prediction model based on the PCA-SSA-BP is established. Finally, compared with the transformer loss prediction model based on BP network, Genetic Algorithm optimized BP network (GA-BP), Particle Swarm optimized BP network (PSO-BP) and Sparrow Search Algorithm optimized BP network (SSA-BP), the transformer loss prediction model based on PCA-SSA-BP network has been proven to be accurate by using actual data and it is helpful for low-voltage recovery in the distribution network.

In general, severe load imbalances in small AC micro-grid systems can degrade their operational performance and their maintenance. This is because the unbalanced load in the micro-grid affects the energy flow and the voltage regulation functions of each phase. In order to solve the voltage imbalance problem, several algorithms for the 3-phase 4-leg CVCF inverter have been proposed, but the control algorithms are not enough to operate the 4-leg CVCF inverter in a stable manner. Therefore, this paper proposes a single-phase voltage and power control algorithm for the 3-phase 4-leg CVCF inverter based on a dq control in order to improve the voltage imbalance problem caused by a severely unbalanced load, where the single phase voltage control algorithm is composed of an αβ-dq and a dq-αβ transformer, a voltage and a current controller, and an off-set controller and a PWM, and the single-phase power control algorithm is also composed of an αβ-dq and a dq-αβ transformer, an active/reactive power and a current controller, and an off-set controller and a PWM. Additionally, this paper performs modeling of the single-phase voltage and the power controller for a 4-leg CVCF inverter using the Matlab/Simulink S/W. From the simulation results, it is confirmed that the transient stability of the proposed single voltage control algorithm can be improved compared to the conventional control algorithm, and voltage control can also be maintained in a stable manner under extremely unbalanced conditions. Further, it is confirmed that 3-phase currents of the proposed single-phase power control algorithm are controlled in a stable manner under extremely unbalanced conditions. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a novel control scheme on AC/DC ring bus islanded microgrid under unbalanced and non‐linear loads. The DC bus is integrated with the fuel cell, one wind turbine, and two batteries. The DC bus can be divided into two sub‐sections, where the first zone is supported by the fuel cell and battery 1, and the second zone is installed with the wind turbine and battery 2. The AC bus is also able to be sectionalized into two sub‐sections where the diesel generator and the unbalanced load are located on the first section and the non‐linear load with one wind turbine are placed on the other section. The DC bus is connected to the AC bus through two parallel three‐phase lines each one configured by three single‐phase inverters. The proposed control scheme in the ringed and separated modes presents several contributions including balancing the unbalanced loads, compensating the harmonics of non‐linear loads, improving the voltage stability and sag/swells, enabling partial operation under outages, and enhancing resilience. In the ring mode, wind turbine 1 and diesel generator inject balanced and linear P‐Q powers to the system as 39 kW/6 kVAr and 7 kW/9 kVAr, respectively. In the separated mode, the P‐Q powers of wind turbine 1 are 36 kW/9 kVAr and they are 15 kW/9 kVAr for diesel generators. In both modes, the unbalanced and non‐linear powers are supplied by the DC bus. The results verify that the developed control strategy efficiently deals with harmonic components, unbalanced currents and voltage issues. [ABSTRACT FROM AUTHOR]

An improved density-based spatial clustering of applications with noise (IDBSCAN) analysis approach based on kurtosis and sample entropy (SE) is presented for the identification of operational state in order to provide accurate monitoring of spindle operation condition. This is because of the low strength of the shock signal created by bearing of precision spindle of misalignment or imbalanced load, and the difficulties in extracting shock features. Wavelet noise reduction begins by dividing the recorded vibration data into equal lengths. Features like kurtosis and entropy in the frequency domain are used to generate feature vectors that indicate the bearing operation state. IDBSCAN cluster analysis is then utilized to establish the ideal neighborhood radius (Eps) and the minimum number of objects contained within the neighborhood radius (MinPts) of the vector set, which are combined to identify the bearing operating condition features. Finally, utilizing data from the University of Cincinnati, the approach was validated and assessed, attaining a condition detection accuracy of 99.2%. As a follow-up, the spindle's vibration characteristics were studied utilizing an unbalanced bearing's load bench. Bearing state recognition accuracy was 98.4%, 98.4%, and 96.7%, respectively, under mild, medium, and overload circumstances, according to the results of the experimental investigation. Moreover, it shows that conditions of bearings under various unbalanced loads can be precisely monitored using the proposed method without picking up on specific sorts of failures. [ABSTRACT FROM AUTHOR]

A study on the capacity increase of a power converter according to the increase in the single capacity of wave energy converters and four-leg topology that can supply stable power even under unbalanced load conditions during independent operation is required. Therefore, in this paper, the performances of various four-leg inverters, from two-level inverters to three-level inverters, which are used as power converters for wave energy converters, are compared respectively. Since the four-leg converter has an unusual structure, the performance of each four-leg inverter was analyzed by applying the model predictive control that can easily and simply configure the controller. To verify the performance of each four-leg inverter, a comparison was performed under balanced load and unbalanced load conditions. Based on this, a suitable four-leg topology of the power converter for wave energy converters was confirmed. [ABSTRACT FROM AUTHOR]

Due to the non-uniformity of the sparse matrix, the calculation of SPMV (sparse matrix vector multiplication) will lead to redundancy in calculation, redundancy in storage, unbalanced load and low GPU utilization. In this study, a new matrix compression method based on CSR and COO is proposed for the above analysis: PBC algorithm. This method considers the load balancing condition in the calculation process of SPMV, and blocks are divided according to the strategy of row main order to ensure the minimum standard deviation between each block, aiming to satisfy the maximum similarity in the number of nonzero elements between each block. This paper preprocesses the original matrix based on block splitting algorithm to meet the conditions of load balancing for each block stored in the form of CSR and COO. Finally, the experimental results show that the time of SPMV preprocessing is within the acceptable range of the algorithm. Compared with the serial code without CSR optimization, the parallel method in this paper has an acceleration ratio of 178x. In addition, compared with the serial code for CSR optimization, the parallel method in this paper has an acceleration ratio of 6x. And a representative matrix compression method is also selected for performing comparative analysis. The experimental results show that the PBC algorithm has a good efficiency improvement compared with the comparison algorithm. [ABSTRACT FROM AUTHOR]

A three-phase five-limb transformer is a potential application form of the Sen Transformer (ST), especially for the scenarios with significantly unbalanced load conditions. This paper proposes a quasi-steady-state model of three-phase five-limb ST (TPFLST) based on duality. Firstly, an equivalent circuit model that takes into account the eddy current effect and the coupling effect involving the magnetic circuit can be derived according to the equivalent magnetic circuit of the TPFLST. The iron-core of the TPFLST may be represented by the parallel combination of the resistances reflecting the power loss of the iron-core and the saturable inductances considering the ferromagnetic hysteresis in virtue of the principle of duality. Subsequently, an electric circuit model of the voltage and current of each winding for the TPFLST is able to be accomplished on the basis of the electrical connection between the TPFLST and the external systems in accordance with Kirchhoff’s voltage and current law. Consequently, a quasi-steady-state model of the TPFLST which considers the coupling relationship involving the magnetic and electric circuits can be formed by combining the equivalent circuit model and the electric circuit model. With the help of MATLAB, the effectiveness of the proposed model may be verified by comparing the results about power flow control including power, voltage, and current with the ones from the existing literature. Furthermore, the TPFLST is found to be better-suited for the unbalanced load condition according to a comparison among the unbalanced degrees of output currents for the STs with different core structures under unbalanced load conditions.

Asynchronous loads (AL), because of their low negative-sequence resistance, produce the effect of reduced unbalance at their connection points. Therefore, proper modeling of unbalanced load flows in power supply systems requires properly accounting for AL. Adequate models of the induction motor can be realized in the phase frame of reference. The effective use of such models is possible only if accurate data on the parameters of induction motor equivalent circuits for positive and negative sequences are available. Our analysis shows that the techniques used to determine these parameters on the basis of reference data can yield markedly disparate results. It is possible to overcome this difficulty by applying parameter identification methods that use the phase frame of reference. The paper proposes a technique for parameter identification of models of individual induction motors and asynchronous load nodes. The results of computer-aided simulation allow us to conclude that by using parameter identification, we can obtain an equivalent model of an asynchronous load node, and such a model provides high accuracy for both balanced and unbalanced load flow analysis. By varying load flow parameters, we demonstrate that the model proves valid over a wide range of their values. We have proposed a technique for the identification of asynchronous load nodes with such asynchronous loads, including electrical drives equipped with static frequency converters. With the aid of the AL identification models proposed in this paper, it is possible to solve the following practical tasks of management of electric power systems: increasing the accuracy of modeling their operating conditions; making informed decisions when taking measures to reduce unbalance in power grids while accounting for the balancing adjustment effect of AL.

Real-time thermal capacity estimation is not only part of prognostics and health management but also determines the dynamic loading capability of the traction transformer. The hot-spot temperature (HST) is the vital parameter for real-time thermal capacity estimation. In high-speed railway, the unbalanced loads of the two phases of the traction transformer cause unbalanced winding losses and therefore affect the top-oil temperature and further influence the HST in each phase. In order to explore the dynamic thermal performance of the transformer under unbalanced load (current), a thermal model for calculating the HST was proposed incorporating thermal interaction between two power supply phases. This model treats the winding loss of each phase independently, considering the temperature dependence of winding ohmic losses and eddy current losses. A thermal circuit topology is presented with independent phase windings sharing the same top-oil temperature, where an improved heat transfer correlation is used to account for the nonlinear thermal convection. The proposed model is verified by the factory temperature rise tests and field operation data for the same batch of transformers. [ABSTRACT FROM AUTHOR]

In this study, a model of a variable refrigerant flow (VRF) heat pump is developed that combines multiple physical equations into only one characteristic equation. The parameters of the characteristic equation are estimated according to the specifications in the manufacturer catalog published based on the definitions established by the Japanese Industrial Standards. This model allows the evaluation of effects that cannot be represented by the conventional models; for example, defrost, unbalanced heat loads, changes in pipe length, and changes in indoor and outdoor temperature, and humidity. The model is sufficiently fast for use in practical applications because it can perform calculation for building with 10,000 m2 floor area in 1 min. The effects of the above-described characteristics on the energy performance vary depending on the local climate. The availability of such a model facilitates the comparison of VRF-system configurations during their design phase, which improves the energy efficiency of buildings. [ABSTRACT FROM AUTHOR]