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In this paper, an adaptive admittance control scheme is developed for robots to interact with time-varying environments. Admittance control is adopted to achieve a compliant physical robot-environment interaction, and the uncertain environment with time-varying dynamics is defined as a linear system. A critic learning method is used to obtain the desired admittance parameters based on the cost function composed of interaction force and trajectory tracking without the knowledge of the environmental dynamics. To deal with dynamic uncertainties in the control system, a neural-network (NN)-based adaptive controller with a dynamic learning framework is developed to guarantee the trajectory tracking performance. Experiments are conducted and the results have verified the effectiveness of the proposed method.

In single-phase voltage source inverters (VSI) under a weak grid, the frequency coupling, caused by the asymmetrical system structure, poses a challenge to system modeling and controller design. In this article, a frequency coupling suppression control strategy is presented, where all the frequency coupling components in the current reference are eliminated. As a result, the single-phase grid-tied inverter is directly modeled as a simple single-input single-output (SISO) admittance rather than a complicated multiple-input multiple-output (MIMO) admittance matrix. The SISO admittance model is simple, compact, and accurate, which facilitates design-oriented analysis. The admittance characteristic analysis shows that the Sym-PLL has a critical impact on the system stability under weak grid conditions. To improve the system stability, a prefilter-based impedance-shaping control strategy is proposed by mitigating the negative resistor behavior of the Sym-PLL. Finally, simulations and experimental results validate the effectiveness of the frequency-coupling suppression control strategy.

The need for accurate assessment of the geomagnetic hazard to power systems is driving a requirement to model geomagnetically induced currents (GIC) in multiple voltage levels of a power network. The Lehtinen–Pirjola method for modelling GIC is widely used but was developed when the main aim was to model GIC in only the highest voltage level of a power network. Here we present a modification to the Lehtinen–Pirjola (LP) method designed to provide an efficient method for modelling GIC in multiple voltage levels. The LP method calculates the GIC flow to ground from each node. However, with a network involving multiple voltage levels, many of the nodes are ungrounded, i.e. have infinite resistance to ground, which is numerically inconvenient. The new modified Lehtinen–Pirjola (LPm) method replaces the earthing impedance matrix [Ze] with the corresponding earthing admittance matrix [Ye] in which the ungrounded nodes have zero admittance to ground. This is combined with the network admittance matrix [Yn] to give a combined matrix ([Yn] + [Ye]), which is a sparse symmetric positive definite matrix allowing efficient techniques, such as Cholesky decomposition, to be used to provide the nodal voltages. The nodal voltages are then used to calculate the GIC in the transformer windings and the transmission lines of the power network. The LPm method with Cholesky decomposition also provides an efficient method for calculating GIC at multiple time steps. Finally, the paper shows how software for the LP method can be easily converted to the LPm method and provides examples of calculations using the LPm method.

Increasing renewable penetration in distribution grids calls for improved monitoring and control, where power flow (PF) model is the basis for many advanced functionalities. However, unobservability makes the traditional way infeasible to construct PF analysis via admittance matrix for many distribution grids. While data-driven approaches can approximate PF mapping, direct machine learning (ML) applications may suffer from several drawbacks. First, complex ML models like deep neural networks lack the degradability and explainability to the true system model, leading to overfitting. There are also asynchronization issues among different meters without GPS chips. Last but not least, bad data is quite common in the distribution grids. To resolve these problems all at once, we propose a variational support matrix regression (SMR). It provides structural learning to (1) embed kernels to regularize physical form in observable area while achieving good approximation at unobservable area, (2) integrate temporal information into matrix regression for asynchronized data imputation, and (3) define support matrix for margins to be robust against bad data. We test the performance for mapping rule learning via IEEE test systems and a utility distribution grid. Simulation results show high accuracy, degradability from data-driven model to physical model, and robustness to data quality issues.

This paper develops a grey-box approach to small-signal stability analysis of complex power systems that facilitates root-cause tracing without requiring disclosure of the full details of the internal control structure of apparatus connected to the system. The grey-box enables participation analysis in impedance models, which is popular in power electronics and increasingly accepted in power systems for stability analysis. The Impedance participation factor is proposed and defined in terms of the residue of the whole-system admittance matrix. It is proved that, the so defined impedance participation factor equals the sensitivity of the whole-system eigenvalue with respect to apparatus impedance. The classic state participation factor is related to the impedance participation factor via a chain-rule. Based on the chain-rule, a three-layer grey-box approach, with three degrees of transparency, is proposed for root-cause tracing to different depths, i.e. apparatus, states, and parameters, according to the available information. The association of impedance participation factor with eigenvalue sensitivity points to the re-tuning that would stabilize the system. The impedance participation factor can be measured in the field or calculated from the black-box impedance spectra with little prior knowledge required.

To analyze oscillation phenomenon caused by the interaction between converters and an AC grid, the impedance/admittance analysis method is a popular solution, in which each electrical component is represented by an external impedance/admittance matrix and a lumped matrix is formed for stability analysis. However, for converter-integrated power systems considering typical collector subsystems (e.g., the radial and the ring collector subsystems in wind farms and PV stations), the impedance network reduction to form the lumped impedance/admittance matrix (LIM/LAM) becomes complicated particularly for a ring collector subsystem, which affects the efficiency of the oscillation analysis. To address this problem, this paper proposes a method that can transform a typical topology of collector subsystems into a pure-parallel topology so that lumped admittance matrix is much easier to be derived. Algorithm complexity analysis confirms its computational advantages. A fifty-converter system is used to verify the effectiveness of the proposed method.

A stabilization method is presented for the Boltzmann equation (BE) that is based on Godunov’s approach applied directly in the phase space. This makes it possible to perform transient simulations under quasiballistic conditions and to include the Pauli principle in the scattering integral without further approximations. The method ensures positive distribution functions by construction. The BE is solved self-consistently together with the Poisson and Schrodinger equations by the Newton–Raphson method for a nanowire silicon nMOSFET, for which the stationary ${I}$ – ${V}$ characteristics, the small-signal admittance parameters, and the switching behavior are calculated. The large-signal behavior of the MOSFET as an amplifier is evaluated by cyclostationary simulations including power gain and the output power at higher harmonics. The current responsivity of the MOSFET operated as a passive mixer is simulated up to terahertz (THz) frequencies including the quasiballistic case with negligible scattering.

The RC bridge-T Circuit are sometimes preferred for radio frequency applications as it does not require transformer (inductive coupling). The uses of the resistance-capacitance form of the network permits a wide tuning range. The article aims to develop a band pass filter's mathematical model using the Floating Admittance Matrix (FAM) approach. Both types of RC bridge-T network form the band-pass filters. The use of the conventional methods of analysis such as KCL, KVL, Thevenin's, Norton's depends on its suitability for the type of the particular circuit. The proposed mathematical modeling scheme using the floating admittance matrix approach is unique, and the same can be used for all types of circuits. This method is suitable to use the partitioning technique for large network. The sum property of all the elements of any row or any column equal to zero provides the assurance to proceed further for analysis or re-observe the very first equation. This saves time and energy. The FAM method presented here is so simple that anybody with slight knowledge of electronics but understating the matrix maneuvering, can analyze any circuit to derive all types of its transfer functions. The mathematical modeling using the FAM approach provides leverage to the designer to comfortably adjust their design at any stage of analysis. These statements provide compelling reasons for the adoption of the proposed process and demonstrate its benefits. The theoretically obtained equations meet the expected result for the RC bridge-T network. Its response peaks at the theoretically obtained value of the frequency. The simulated results are in agreement with the topological explanations and expectations.

Topology identification and parameter estimation form the basis for the operation and control of the distribution network with little or no observability. This paper proposes a method to estimate the admittance matrix for open-loop distribution networks based only on active/reactive power injection and voltage magnitude data. We derive the linear relationship between the admittance matrix and the measurements based on decoupled linear power flow (DLPF) equations. A total least squares regression method is proposed based on analysis of the characteristics of the open-loop grid admittance matrix. Case studies on the IEEE 33-bus system demonstrate the proposed method's effectiveness, accuracy, and efficiency.

The extensive application of the power electronic transformers (PETs) in power systems poses a challenge as the accurate and high-speed electromagnetic transient (EMT) simulation of PET has been a critical issue. The computational time of the detailed EMT simulation of PET on EMT programs is unacceptable due to the large electrical node count, microsecond-range simulation steps, and high switching frequency of the devices and transformers. This article proposes a hierarchical modeling scheme for PET. Unlike the existing modeling methods, the proposed technique recursively decreases the dimension order of the admittance matrix to obtain the generalized Norton equivalent of each phase leg. The final admittance matrix overlaid onto the external system admittance matrix has a dimension order of magnitude remarkably smaller than that of the unreduced structure. By comparison with a detailed EMT model of a medium-voltage dc system, the performance of the proposed scheme has been assessed in PSCAD/EMTDC under various working conditions. With negligible loss of accuracy, approximately one to two orders of magnitude speedup over a straightforward EMT program is achieved.

This article aims to develop a band pass filter's mathematical model using the Floating Admittance Matrix (FAM) method. The use of the conventional methods of analysis based KCL, KVL, Thevenin's, Norton's depends on the type of the particular circuit. The proposed mathematical modeling using the floating admittance matrix method is unique, and the same can be used for all types of circuits. This method uses the partitioning technique for large network. The sum property of all the elements of any row or any column equal to zero provides the assurance to proceed further for analysis or re-observe the very first equation. This saves time and energy. The FAM method presented here is so simple that anybody with slight knowledge of electronics but understating the matrix maneuvering, can analyze any circuit to derive all types of transfer functions. The mathematical modeling using the FAM method provides leverage to the designer to comfortably adjust their design at any stage of analysis. These statements provide compelling reasons for the adoption of the proposed process and demonstrate its benefits

A simulation tool for modeling harmonic propagation in low voltage distribution networks with manifold nonlinear equipment is developed. The tool is based on a hybrid domain approach representing each nonlinear household device with accurate and fast white box model and the supply network – with the harmonic admittance matrix in the frequency domain. Proposed tool features significant reduction of simulation time compared with the brute force time domain (BFTD) simulation, high level of accuracy as opposed to the traditional frequency domain methods, and improved convergence under weak grid conditions in respect to conventional iterative harmonic analysis. Eventually this preconditions the use of the proposed approach in computationally intensive simulations, e.g. in stochastic harmonic modeling with the Monte Carlo method. Additionally two application examples of the developed tool are provided demonstrating its effectiveness compared to the BFTD modeling.

For the dc-link busbar in a high-capacity converter, the large-size laminated busbar is not adoptable due to the machining difficulty and limitation in current capability. In contrast, the regular nonlaminated busbar solution guarantees the required power capacity with a lower cost and easier installation. The main challenges exist in the large stray inductance and corresponding resonance phenomenon. Related analysis and accurate synthesis theory have not been reported. In this article, a matrix analysis method is proposed for the formed multiport and high-order network in a dc-link busbar. First, the multiport interaction and coupling are mathematically derived based on the subnetwork admittance matrix combination. The multipeak resonance phenomena are explained in detail. Meanwhile, it is manifested that proposed matrix method can be applied with the positive and negative sequence current analysis. Then accurate resonate currents can be obtained under the nonsinusoidal busbar current consideration. Finally, a resonance current gain (RCG) value is formed for the quantitative capacitor current evaluation and busbar design guidance. Proposed design and evaluation method is verified in a 315-kW converter system. More than 49% resonant current in the capacitor gets depressed by the enhancement. Its effect is close to the laminated busbar solution.

When the control parameters and operating conditions remain unchanged, it is usually believed that the admittance characteristic of grid-connected inverter is time-invariant. However, considering the effect of frequency-coupling, an abnormal phenomenon is observed in the admittance measurement of the grid-connected inverter: the phase of the off-diagonal elements Y12 and Y21 in the admittance matrix is always changed with time, which presents a time-varying admittance characteristic. To explore this phenomenon, the theoretical analyses based on the traditional frequency-coupling admittance measurement method are made. Because the initial phase of the signal cannot be obtained from Fast Fourier Transform (FFT) in experiments and the disturbance frequency and coupling frequency are different, the phase difference between the two frequency components changes with time. However, the influence is not considered in the traditional frequency-coupling admittance measurement method, which makes the measurement results exhibit the confusing time-varying characteristic. The phenomenon is defined as pseudotime-varying admittance characteristic in this letter. To accurately measure the admittance characteristic of the grid-connected inverter, a frequency-coupling admittance measurement method based on phase correction is proposed, which corrects the phase of disturbance frequency components and coupling frequency components. Finally, the effectiveness of the proposed measurement method is verified by experiments.

In this paper, a photovoltaic (PV) generator is represented as a lumped-parameters network equivalent. This equivalent can be readily integrated into a power flow algorithm. The PV generator is initially modeled via its harmonic domain admittance matrix (HDAM). The HDAM is obtained by using the flexible harmonic domain (FHD) which permits to include frequency coupling. Reduction of the HDAM to fundamental power frequency quantities provides the lumped-parameters π-shaped circuit of the PV generator, amenable for power flow algorithm. It is demonstrated that multiple π-equivalents, emulating solar farms with distinct switching frequencies of the involved power electronics devices, can be integrated into the power flow solution algorithm.

The Alternating Direction Method of Multipliers (ADMM) is widely utilized to solve the distributed Optimal Power Flow (OPF) problem, providing convergence under certain assumptions. ADMM relies on a penalty parameter $\rho$ to accelerate its convergence. The selection of appropriate values of $\rho$ is crucial for the quality of the final solution and for the efficiency of the iterative process. In this paper, we propose a weighted- $\rho$ ADMM, with its weights automatically determined by leveraging the nature of the optimal power flow problem. Specifically, the affinity matrix, a combination of the admittance matrix and Hessian matrix of the Lagrangian function of the associated OPF problem, is utilized to determine the penalty parameters. The convergence of the iterative scheme is analyzed and the effectiveness of the proposed methodology is validated through simulation experiments which show that the weighted- $\rho$ ADMM overcomes the necessity for suitable initial parameter selection.

The controller for the power assist robot that is in constant contact with the user requires to be sensitively controlled as per the user"s intention and maintain control stability to ensure the user"s safety. Admittance control is generally used for human intention-based force control. By setting the parameters of the admittance control at a low level it is possible to sensitively control according to the user"s intention. However, too sensitive settings make the system unstable. Therefore, it is difficult to set a fixed admittance parameter in a power assist robot in which dynamics change with an increase in load mass. Consequently, we propose a variable admittance control strategy according to the load mass. The proposed method responds sensitively to the user"s intention by setting the admittance parameters at low during no-load action and ensures stability by setting the admittance parameter high when transmitting high loads. In simulation with a carrying load of 30 kg, the proposed method requires half the interaction force compared with a fixed admittance control when decelerating and has twice faster settling time when stopped. In addition, through experimental verifications, the variable admittance control was proven to reduce the user"s load by 70% compared to load mass.

In this study, a humanoid prototype of 2-DOF (degrees of freedom) lower limb exoskeleton is introduced to evaluate the wearable comfortable effect between person and exoskeleton. To improve the detection accuracy of the human-robot interaction torque, a BPNN (backpropagation neural networks) is proposed to estimate this interaction force and to compensate for the measurement error of the 3D-force/torque sensor. Meanwhile, the backstepping controller is designed to realize the exoskeleton's passive position control, which means that the person passively adapts to the exoskeleton. On the other hand, a variable admittance controller is used to implement the exoskeleton's active follow-up control, which means that the person's motion is motivated by his/her intention and the exoskeleton control tries best to improve the human-robot wearable comfortable performance. To improve the wearable comfortable effect, serval regular gait tasks with different admittance parameters and step frequencies are statistically performed to obtain the optimal admittance control parameters. Finally, the BPNN compensation algorithm and two controllers are verified by the experimental exoskeleton prototype with human-robot cooperative motion.

High-energy neutral and charged Drell--Yan differential cross-section measurements are powerful probes of quark-lepton contact interactions that produce growing-with-energy effects. This paper provides theoretical predictions of the new physics effects at the Next-to-Leading order in QCD and including one-loop EW corrections at the single-logarithm accuracy. The predictions are obtained from SM Monte Carlo simulations through analytic reweighting. This eliminates the need of performing a scan on the new physics parameter space, enabling the global exploration of all the relevant interactions. Furthermore, our strategy produces consistently showered events to be employed for a direct comparison of the new physics predictions with the data, or to validate the unfolding procedure than underlies the cross-section measurements. Two particularly relevant interactions, associated with the W and Y parameters of EW precision tests, are selected for illustration. Projections are presented for the sensitivity of the LHC and of the HL-LHC measurements. The impact on the sensitivity of several sources of uncertainties is quantified., 32 page, 10 figures, 3 tables; v2: several plots have been updated to fix a problem in the code, the overall discussion has been slightly improved, and few typos have been corrected; v3: typos corrected, preprint added

Cables with cross-bonded cable sheaths are predominantly used in high-voltage ac systems. Existing frequency-domain models of such cables use ABCD-parameters, which may cause numerical problems in the high-frequency region, or Y-parameters. The existing Y-parameters model excludes bonding wire impedances which may result in inaccurate estimates of the magnitude or frequency of the cable input impedance at resonant frequencies. This letter extends the formulation of an existing Y-parameters model to include bonding wire impedances. The proposed extended formulation is validated against a cable model in commercially available EMT-type software, in frequency- and time domain. For a certain bonding wire impedance model, the proposed Y-parameters model is shown to have a lower magnitude of the cable input impedance at resonant frequencies compared with a model excluding bonding wire and grounding impedances.

Sharing corridors between high voltage alternating current (HVAC) power lines and metallic pipelines has become quite common. Voltages can be induced on pipelines from HV power lines, which may cause a risk of electric shock to the operator and serious corrosion damage on metallic pipelines. This paper aims to examine the capacitive coupling between aerial metallic pipelines and HV power lines in perfect parallelism case and in general situation which is formed by parallelism, approaches and crossings, using a combination of charge simulation method and Artificial Bee Colony (ABC) algorithm. The electric field at the pipeline's surface and the induced voltage on the pipeline are strongly affected by the pipeline separation distance. The presented simulation results are compared with those obtained from the admittance matrix analysis, a good agreement has been obtained.

This paper presents an analytical model for intrinsic short-circuit admittance (Y) parameters of DH-DD-TM-SG MOSFET. Y parameters have been modeled using different small-signal equivalent circuit parameter which is used to find the Scattering parameters. These Y parameters have further been employed for computing S-parameters. These parameters are further used to investigate the microwave performance parameters of the proposed device. The Unilateral Power Gain and the maximum oscillation frequency is determined to evaluatethe microwave performance. The proposed device shows a higher cut-off frequency (f_T) and maximum oscillation frequency as to TM-SG MOSFET. The proposed device exhibits a 4.2% improvement in U_T 2.81% in G_ms and 6.9% improvement in G_MTPG as compared to TMSG. The analytical result of DH-DD-TM-SG MOSFET is in accordance with the simulated results.

The convergence of the iterative harmonic analysis (IHA) of networks with nonlinear loads can be improved if the Gauss algorithm is replaced by the modular decoupled Newton solution (M-DNS). The core of the M-DNS is the harmonically coupled admittance matrix (HCAM) of each nonlinear load. HCAM of high-power converters has received special attention. However, the HCAM of single-phase uncontrolled rectifiers (SPUR) with capacitive smoothing has only been developed under certain simplifications for the SPUR. A reference model for the SPUR is extensively accepted and a detailed analytical procedure (DAP) is the fastest way to obtain the steady state of the SPUR. The main object of this paper is to present a HCAM for the reference model of SPUR with capacitive smoothing. This HCAM is directly derived from a DAP for the converter. Convergence properties of the IHA with this HCAM are studied.

The impedance parameters of transmission wires in the traction network are subjected to current-carrying capacity, environment conditions, which will lead to the change of calculation results. In this paper, firstly, the influence of environment conditions on the resistance, reactance, conductivity and admittance parameters of transmission wire is analyzed; Secondly, the calculation method that considers the variation parameters in the traction network is proposed. In the process of calculation, the conductor resistance is taken as the state variable, and the conductor temperature, conductor resistance and power flow are corrected in the process of iterative inverse solution The results show that the change of transmission wire parameters has considerable influence on the results, and the change of impedance parameters should be considered in the process of power flow calculation in the traction network.

Starting from the device physics, we construct the model of light-emitting transistors (LETs) for the simulation and application in optoelectronic integrated circuits and electronic design automation. Our model contains the essential features of LETs relevant to the device operation and can properly describe the electrical-to-electrical and electrical-to-optical properties of LETs. An admittance matrix is also presented for general simulations of modulation responses, such as scattering parameters and current gains in common-emitter, common-collector, and common-base configurations. The large-signal eye diagrams of LETs on circuit simulator are also demonstrated for the simulation program with integrated circuit emphasis (SPICE) compatibility. Our model can help circuit designers to evaluate the circuit performance and speed up the design process.

We present a new approach to the study of the stability of vacuum electronic devices (VEDs) using the Naval Research Laboratory (NRL) large-signal code TESLA-Z. The approach combines a precomputed complex impedance matrix, $\hat {Z}$ , describing the structure with a TESLA-Z computed admittance matrix, $\hat {Y}_{ \boldsymbol {bt}}$ , characterizing the electron beam and beam tunnel. The gain matrix $\hat {G}$ for a given device then can be found as the product of the reduced $Z$ -matrix of the structure and admittance matrix $\hat {Y}_{ \boldsymbol {bt}}$ of the beam tunnel. Subsequent analysis of the eigenvalues of the gain matrix $\hat {G}$ using Nyquist’s method determines the stability of the device. We discuss the details of the new algorithm and illustrate its application to an experimental G-band serpentine TWT.

This article presents a new method for accurately designing and analyzing an antenna or array. The proposed technique operates solely on the transfer admittance matrix of a perfect electrically conducting antenna fabric that is obtained using a full-wave simulator only once. The desired antenna, which must be a subset of the fabric, is then synthesized by progressively loading the fabric and applying a computationally efficient iterative postprocessing technique that transforms the stored admittance matrix into one that corresponds to the desired antenna or array. Given that the admittance matrix of the fabric is used as the basis for all subsequent antennas that can be represented by the fabric, it contains the solutions to an entire class of antennas. The proposed method is demonstrated by applying it to the class of colinear antennas up to five wavelengths long, arranged along a single axis. The method is validated by comparing its results to those obtained using a conventional full-wave simulator. The proposed method is applied first to the case of multiple loads located at arbitrary port locations along the fabric. Then, open-circuited loads are used to decimate the tips of a linear antenna to demonstrate that the method accurately predicts the response of an electrically shorter antenna. Finally, decimation is used to transform the fabric into an array of smaller antennas, where it is shown that mutual coupling effects are accurately predicted.

This paper presents four centrality measurements applied to an alternating current (AC) microgrid (MG) modeled as a multiplex network. The MG secondary control is separated into a frequency and a power-sharing layers, each one with a different adjacency matrix. A physical layer is also considered with an admittance matrix representing the impedances among the inverters. Centrality measures are used to determine the importance of nodes in separate layers, thereafter adjacency and Laplacian matrices are redefined to calculate the role of nodes in the multiplex system. First, a global adjacency matrix is calculated by the matrix sum of each adjacency matrix. Second, the adjacency matrix is calculated by a supra-Laplacian matrix. The first eigenvalue of the perturbed matrix is used to determine the diffusivity in the network using as leaders the sets obtained by the centrality measures. The role of the nodes in the system is verified in a simulated MG model of 37 nodes. Degree centrality and energy Laplacian measures present similar sets of nodes; however, the fastest set of nodes is found using the Eigenvector measurements for uniform and supra Laplacian approach.

Background: The primary motive of an electrical power system is to generate and supply electric power efficiently and reliably to the consumer-end. Transmission losses, system instability and increasing cost in proportion to demand are the main challenges faced in this process. Power flow analysis is required to robustly predict the active / reactive power within the buses, voltage magnitude / phase angles at each bus, cost of transmission and losses well before the practical installation of the power network. Methods/Statistical Analysis: In this paper, we employ power flow analysis using Newton Raphson method and Fast Decoupled method to minimize cost of the electricity and finding optimum active and reactive powers without affecting the voltage regulation. The power flow algorithms are applied for solving the aforementioned load flow problem for ring distribution network of Bahawalpur. We carried out the modeling by obtaining realistic data for constructing bus admittance matrix and specifications of generation units and loads which are connected at the buses. Findings: As a result, optimum flow of power along with the voltage values among different regions of Bahawalpur is obtained. The results from both the algorithms successfully converge and there is an absolute match to validate the accuracy. Novelty: These novel results are of paramount importance since the proposed architecture of Bahawalpur is ring distribution network to replace the existing radial network for improved performance. Furthermore, this research will pave the way for power system planning of Bahawalpur region where all the electrical parameters are known beforehand to design the components according to the requirement. Keywords: Electric power system; voltage magnitude; phase angle; power flow analysis; Newton Raphson method; ring distribution network; active power; reactive power

Although the low-frequency/harmonic oscillation of grid-tied inverters under weak grids has been widely researched, the classical impedance-based approach focuses more on the identification of stable operating points and the stability margin of return-ratio matrix. Furthermore, it cannot provide stability regions of system parameters. Therefore, this paper proposes a line impedance cooperative stability region identification method. Firstly, the output impedance matrix and the input admittance matrix are respectively built in $d-q$ axis. Secondly, a novel stability forbidden region is proposed. It is less conservative than the forbidden region criteria in existing literatures. Based on the stability forbidden region, the stability operation region is established via mirror, translation and rotation mappings. It is less conservative compared with the norm-based stability criteria. The solving of stability operation region is first transformed into the eigenvalue identification problem in this paper. Furthermore, the detailed line impedance cooperative stability region is solved by guardian map theory. It can provide guidance for system planning and stabilization method researches with simplified computational process. Finally, the simulation and experimental results show that the proposed line impedance cooperative stability region identification method is more effective and less conservative.

A waveguide fed transverse slot has been analysed using the Method of Moments (MoM) formulation, wherein the internal admittance matrix elements have been evaluated from image theory and using the images of the slot due to waveguide walls. The contribution from all the images not in the same row as the slot has been evaluated using a closed-form expression and a rapidly converging series with negligible contribution. The contribution from the row containing the reference slot has been evaluated by adding the mutual admittance between a few images and the reference slot using some recently developed simple and accurate approximations. The formulation has been extended to transverse slots radiating between the baffles. The results calculated using this simple, efficient and intuitive method are in excellent agreement with other theoretical as well as measured results. The technique can be extended to other slot configurations such as an inclined slot and for other slot aperture distributions such as with an edge condition in configurations permitting image formation.

Purpose The purpose of this paper is to implement a passive compliance training strategy for our newly designed 2-UPS/RRR parallel ankle rehabilitation robot (PARR) to enhance its rehabilitation training safety. Design/methodology/approach First, a kinematic analysis of the PARR is introduced, and the mechanism ensures that the rotation centre of the ankle joint complex (AJC) coincides with robot’s rotation centre. Then, a passive compliance training strategy based on admittance control is described in detail and is implemented on our PARR. Findings Experiments involving healthy subjects were conducted, and the performance of trajectory tracking was quantitatively evaluated, with the results showing excellent compliance and trajectory tracking accuracy, which can ensure that a secondary injury to the AJC during passive rehabilitation training is avoided. The influence of different admittance parameters was also simulated and analysed, which can contribute to the development of adaptive parameter adjustment research. Originality/value The paper can be used to improve the effectiveness of ankle rehabilitation, to alleviate manual therapy problems in terms of labour intensiveness, precision and subjectivity and to ensure safety and comfort during rehabilitation sessions.