Power Transfer Limit Research Articles

Comparative Analysis of the Power Output Capabilities of Grid-Following and Grid-Forming Inverters Considering Static, Dynamic, and Thermal Limitations

This paper investigates the maximum transferable power (MTP) of inverter-based resources (IBRs) and provides the output capability curves (OCCs) of grid-tied grid-following inverters (GFLIs) and grid-forming inverters (GFMIs). To this end, in the first part of the paper, mathematical equations for GFLI static, thermal, and phase-locked loop (PLL)-induced power transfer limits are derived in terms of the grid short-circuit ratio (SCR) and its X/R ratio. Then, considering other operational limitations, such as the IBR AC- and DC-side voltage limits, the OCC of the GFLI is obtained. Additionally, the impact of the reactive current and the reactive control mode on the OCC is further studied, and accordingly, an auxiliary control loop is proposed to maximize the GFLI MTP. In the second part of the paper, a similar approach is employed to derive mathematical equations for GFMI static and thermal limits, and accordingly, the OCC of a GFMI is obtained. The effects of the variation of the voltage set-point of the GFMI on its OCC are then studied, and the superiority of GFMIs compared to GFLIs is shown in terms of the MTP capability. Eventually, several simulation and experimental cases are conducted to validate the obtained equations and OCCs for both grid-following and grid-forming control modes.

Coupled-Inductor-Based Bidirectional Resonant Converter With Reduced Component Count and Load-Independent Voltage Gain

The bidirectional DC/DC converter (BDC) is a critical part to interface the DC-bus with energy storage system (ESS) in DC microgrid. This paper proposes a coupled-inductor based bidirectional resonant converter with center-aligned pulse width modulation (PWM) modulation method and reduced component count. The structure of dual half-bridges with coupled inductor makes the current analysis more complex than the full-bridge PWM resonant converter. Hence, a method of performance analysis based on the symmetrical pi model is proposed and the corresponding parameter design process is introduced. In addition, fixed switching frequency operation, load-independent voltage gain, full-load range zero-voltage-switching (ZVS), automatic bidirectional power transfer and bidirectional power limitation can be realized in the proposed PWM converter. An experimental prototype with rated power of 1000W is built to demonstrate the operation and performance of the proposed converter.

A Loadability Study of 30 kV Misurata Distribution Network

Due to the expansion of power distribution networks, the power delivered to the loads might get through corridors which limits their capability of transmitting the power. This concept is termed as the loadability. An unplanned increase in power consumption in the Libyan network, especially after 2011, led to major problems at different levels of the power network. For instance, these issues are addressed at the generation level as power shortages and load shedding while at the distribution level presented as under voltages and loadability issues. In this paper, a study of the loadability of 30 kV Misurata electrical distribution network (MDN) is carried out using the NEPLAN software. Even though the MDN is considered one of the largest distribution networks in Libya, a lack of data is found which makes an ambiguous vision about this network and the necessary developments required in the future as well as adds some difficulties to making studies. The work presents the steady state operation of MDN under the existence of the current and estimated loads up to the year 2026. The results show significant loading problems in Misurata distribution network which should be considered to avoid the anticipated future power transfer limitations. Some visible solutions are proposed toensure the optimal operation of the distribution network.

Genetic Algorithm Optimization of Power Transfer Limit for Enhancement of Stability of Power System

The work presents the Genetic Algorithm (GA) as an innovative method for optimizing power transfer limits to improve the stability of power systems. This is especially important given the increasing integration of renewable energy and the growing complexity of power networks. Traditional static threshold methods often lead to inefficiencies and instability during periods of high demand or fluctuating renewable generation. The GA tackles these challenges by representing potential solutions as chromosomes that evolve over successive generations through processes inspired by natural selection. These processes include initialization, fitness evaluation, selection, crossover, mutation, and replacement. The results of the genetic algorithm optimization indicate the optimal threshold value of 1.0564602 for the power transfer limit of the power systems. This dynamic adaptation ensures robust and efficient solutions, ultimately improving power transfer efficiency and meeting constraints to prevent overloads and voltage instability. Ultimately, the GA enhances overall power system performance by ensuring efficient and reliable operation in the face of modern challenges.

A Scenario-classification Hybrid-based Banding Method for Power Transfer Limits of Critical Inter-corridors

A Scenario-classification Hybrid-based Banding Method for Power Transfer Limits of Critical Inter-corridors

Capacity Assessment for Wind-Storage Integration System Considering Electro-Thermal Coupling of Overhead Transmission Line

The high uncertainty of wind power generation generally makes the low utilization rate of dedicated overhead transmission lines (OTL) which carry fluctuated power flow transferred from wind farms to main system. Energy storage systems deployed in large scale wind farms to support system power balance creates the opportunities to treat such problem. Therefore, this study proposes an OTL power transfer limit calculation method by solving the electro-thermal coupling equations for dynamic heat exchange process affected by multiple varying ambient conditions. Accordingly, the wind power transmission is optimized and maximized by energy storage operation on the condition that the conductor temperature is maintained under allowable maximum value. Furthermore, the simulation based on proposed method show the coordinated operation of wind farm, related energy storage system and dedicated OTL, which are defined as the wind-storage integration system (WSIS). Finally, case studies demonstrate the effectiveness of the proposed method in analyzing the optimal scales of wind farm and energy storage, with the consideration of dynamic electro-thermal behavior of dedicated transmission line in carrying wind power.

Enhancement of power transfer capacity of transmission network using multilevel multifunction inverter

This article presents a multilevel multifunction inverter (MLMFI) with a novel controller for the grid-connection of a solar array. The aim of this work is to improve the technology of the power transfer capacity of existing transmission lines in order to alleviate the current energy crisis. An effective mathematical modelling of an MLMFI configuration having two series-connected H-bridges per phase with isolated solar arrays is presented. A novel closed-loop controller is proposed for reference signal generation using the PWM technique. With the proposed controller, the power flow in a transmission line is analysed for daytime and nighttime conditions. The proposed controller performance was tested on a realistic single-machine infinite-bus power system with midpoint MLMFI using MATLAB simulation software. The proposed MLMFI-based solar array enhanced the stable power transfer limit of a transmission line. A comparative analysis between conventional and proposed controllers for power flow and transient stability studies was also presented. The proposed MLMFI results were validated by developing an experimental model.

A series inductance based three-port isolated hybrid DC–DC converter for microgrid applications

The paper proposes a series inductance based three-port isolated hybrid converter (3PIHC) for wide change in voltage transformation ratio (VTR) which supports DC microgrid applications. Three-ports in the proposed converter is integrated by means of a three-winding high frequency transformer (HFT). The leakage inductance of three-winding HFT acts as an energy transfer element between the ports. The factors which need to be considered for designing the leakage inductance are power transfer flexibility and limits of current transfer at wide change in VTR. In a feasible scenario, the intricate aspects such as inconsistency of leakage inductance, requirements of power flow variability and current restrictions necessitates auxiliary inductors in series with the three-winding HFT. This paper focuses on selecting appropriate value of series inductance for 3PIHC based on the application demand and minimized converter losses. Study and analysis are carried out to evaluate the converter performance at certain values of series inductance which is the sum of leakage inductance of HFT and auxiliary inductance. A hybrid configuration is adopted in the proposed converter where the primary port holds multi-level half bridge structure which reduces the voltage stress across the transformer primary winding and semiconductor switches. The secondary and tertiary port occupies H-bridge circuit topology. Converter analysis is presented for both conventional phase-shift modulation (CPM) and dual phase shift modulation (DPM). A simple computational method for obtaining the phase-shift variables at minimum value of current stress is developed. Evaluated the converter current stress for various values of series inductance and at wide change in VTR. A prototype of the proposed converter is implemented and examined. The experimental results demonstrated authenticates the accuracy of theoretical analysis.

Physics-Constrained Robustness Evaluation of Intelligent Security Assessment for Power Systems

Machine learning (ML) algorithms have been widely developed to enable real-time security assessment for large-scale electricity grids. However, it also has been extensively recognized that the ML models are vulnerable to adversarial examples, which are slightly perturbed instances that can mislead the classifications but cannot be distinguished by human eyes. Considering the adversarial examples against the ML-based security assessment, they must not only cause misclassification but also follow the power balance and transfer limits and bypass the bad data detection. To this end, this paper proposes a novel concept named physics-constrained robustness that aims to computing a lower-bound of adversarial perturbations, evaluating the vulnerability of the ML-based intelligent security assessment (ISA) for power systems. A general optimization problem is formulated to compute the physics-constrained robustness of ISA with the mislabeling, power balance, power limitation, and invisible constraints. The analytical results and comparing relationship of ISA’s robustness with different constraints are provided. By using the static security assessment as an example, we provide explicit formulations to evaluate the physics-constrained robustness of. Finally, extensive experiments are conducted to evaluate the physics-constrained robustness of ISA in static and dynamic cases with the real-world load profiles from New York State and provide suggestions to select the ML models and parameters.

Static Voltage Stability Assessment of Ethiopian power System Using Normalized Active Power Margin Index

Voltage stability assessments, made so far on the Ethiopian electric power system (EEP), are limited both in number and in methodology. Here, in this paper the static voltage stability of the Ethiopian power system is investigated using an index called normalized active power margin. The methodology starts from determining Thevenin equivalent of a system as viewed from the load buses. The Thevenin equivalent parameters help to determine the load bus maximum active power transfer limit and to draw the PV relation curves. The approach avoids the time-consuming method of PV curve based maximum active power transfer determination, which requires large number of power flow computations. The resulting maximum active power transfer and current operating active power load are used for the index calculation. The index is tested using IEEE 30 bus system and produced results matching with other previously established indices. The index is capable of ranking vulnerability of load buses to voltage instability. Then, scenarios of heavy load and light load EEP cases, with and without system reactive power compensation, are investigated. Results reveal weakest buses are supplied from 66kV transmission lines, load bus 232 being the weakest of all. On the other hand, the most stable buses are supplied from 132 kV transmission lines, bus 149 being the most stable bus. PV curves drawn, also, reveal the improvement that come with reactive power compensation and with operating in light load condition.

Optimized design of power loops for virtual synchronous generator to enhance transient stability

AbstractVirtual synchronous generator (VSG) control is an attractive method to solve the stability issues of future renewables (e.g. photovoltaic [PV])‐dominated power system. Unfortunately, a VSG is prone to transient instability under grid faults, and the existing work ignores the instability issues caused by current limitation and reactive power loop (RPL). To tackle with the problem, this article analyzes the transient stability of VSG considering the impact of current limitation and RPL. It indicates that the roots of transient instability can be attributed to two aspects, that is, (1) the positive feedback and continuous phase angle integration in active power loop (APL) which are caused by the P‐f control structure, (2) the decline of active power transfer limit which is caused by the Qvsg‐vcd‐iod‐Pvsg control structure. Based on it, an optimized VSG control method is proposed to improve the transient stability, by optimizing the design of power loops for VSG. Compared with other stability control methods, the proposed method avoids the use of frequency detection, and it is simple in design and implementation. Finally, the proposed method is validated by the experiments.

Bifurcation Analysis of Active Electrical Distribution Networks Considering Load Tap Changers and Power Converter Capacity Limits

The aim of this article is to analyze the parameter stability and power transfer limits of active distribution networks with power converters and load tap changers by using bifurcation theory.First, the nonlinear model of a representative distribution grid with mixed loads and power converters is derived. Frequently neglected effects of converter capacity limits and transformers with load tap changers are considered, and for this purpose, static and dynamic saturations are modeled by using approximations based on smooth functions. In addition, a solution based on an antiwindup scheme is provided to model load tap changers without numerical convergence problems. These methods allow their integration to the model in a comprehensive way. Results show the impact of converter parameters and its limits on system stability as well as the impact of weak grid conditions. Moreover, they show that these effects can destabilize the system under, seemingly, safe operating conditions. The results indicate that reactive power support from converters can improve stability margins and the performed analysis can help in the design of the converter control parameters. Experimental results obtained from the laboratory environment comprising two distributed generators and a grid emulator are used for the validation of the contributions of this article.

Adaptive Tuning of PV Generator Control to Improve Stability Constrained Power Transfer Capability Limit

The stability of power systems can largely limit the power transfer capability limit of transmission lines. The PV generator control is different from synchronous generator control. The impact of PV generator dynamics on the power transfer limit constrained by stability is not well explored in the literature. This paper focuses on improving the stability constrained power transfer capability limit of transmission lines emanating from PV generators. The PV generator is provided with dc link voltage and reactive power control and is equipped with low voltage ride through capability, voltage and frequency support functionalities. In this paper, Lyapunov function analysis based adaptive tuning laws are proposed for PV generator control parameters to improve the power transfer capability limit (constrained by stability) of transmission lines connecting PV generators to grid. The tuning laws are proposed for Phase Locked Loop (PLL), outer and inner control loop parameters. The effectiveness of the proposed method is validated on a Single PV-Synchronous Machine system, modified IEEE-39 and IEEE-118 bus system. Comparison with existing method shows that the proposed tuning method can achieve higher power transfer capability limit considering stability.

A Distributed Power Transfer Limit Calculation Method for Multi-Area Interconnection Power Networks

For multi-area interconnected power networks, each subarea may be operated by independent regulator, who oppose to open the access of private information such as network topology to the others. For this case, this study proposes a decomposition-coordination strategy to calculate power transfer limit (PTL) considering both saddle node bifurcation (SNB) and limit-induced bifurcation (LIB). The external coordination equations are derived based on the sensitivity analysis of boundary buses at tie-lines, to express the power exchange of subareas and the consistent boundary state variables. Power Flow (PF) results for each subarea system are separately calculated followed by the adjustment of tie-lines' PF injected into boundary buses according to the external coordination. Then the alternation between internal and external iterations, for which operators of subareas are not required to share private network information, could generate the same results as conventional PF that relies on the complete information. Moreover, an improved Continuation PF (CPF) model that includes the prediction of the PF of area tie-lines is proposed. The point of collapse (POC) method is employed to calculate PTL involving the SNB of the interconnected networks to improve the accuracy of the algorithm. Case studies demonstrate the effectiveness and reliability of the proposed method.

Stability Analysis of Droop-Based Converter Using SISO Method From DC Side Perturbation

Droop-based converter plays an important role in future multi-terminal DC (MTDC) system due to its control flexibility, which imposes a great challenge on the stability of the DC grid. Traditional input impedance and eigenvalue analysis methods fail to build the mathematical relationship between the system operating points and the related critical parameters that keep the system stable. The main objective of the paper is to examine the DC side stability of the single grid-connected VSC with the single input single output (SISO) method. The transfer function between the small perturbation of DC-link voltage and DC current at the end of transmission line is firstly constructed considering the control impacts of droop-based converter and the dynamics of DC networks. Based on SISO model, the stability criteria of single VSC converter under different control modes is further proposed by using the classical Routh Judgement. In addition, the sufficient stabilizing conditions and DC side stability boundary are accordingly obtained based on the derived stability criteria. It is worth mentioning that, a critical operation index, namely, DC power transfer limit (DCPTL) is firstly defined for the droop-based converter operating as an inverter, and DC system instability might occur when the transmitted power exceeds this limit. Finally, numerical simulation results of two-terminal HVDC system validate the accuracy of the proposed stability analysis and the criteria for the droop-based converter.

Analysis of Controller Bandwidth Interactions for Vector-Controlled VSC Connected to Very Weak AC Grids

Stability assessment of conventional vector current control (VCC) of voltage-source converters (VSCs) in weak grids has not been standardized. In this article, a small-signal model is derived to quantify the maximum active power transfer in a very weak grid across a much wider range of controller bandwidths than has previously been investigated. A novel investigation of the VCC-VSC controller bandwidth interactions between inner and outer control loops, including the phase-locked loop (PLL) dynamics, is demonstrated, and a stability bubble of safe operating points is established. Robustness of the stability bubble under different short circuit ratios is investigated, and dynamic performance considerations are introduced to form a reduced operating region with good transient performance. The controller gains within this region allow rated power transfer in inverting mode and good dynamic performance with no modifications to the conventional VCC structure. For very weak grids, it is recommended that PLL bandwidths between 5 and 30 Hz are avoided. If a slow PLL bandwidth is chosen, the outer loop <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis should have a fast bandwidth; with a fast PLL, the outer loop <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis control bandwidth should be reduced. In all cases, the outer loop <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -axis should be slowed down to reach the power transfer limit.

Power transfer limit calculation for multi-area interconnected power networks

Multi-area interconnected schemes are beneficial for power networks to coordinate energy resources and have created the need to identify the critical conditions for transferring power among multiple subareas. This study proposes an improved continuation power flow (CPF) model to calculate the power transfer limits (PTL) among interconnected networks corresponding to either saddle node bifurcation (SNB) or limit-induced bifurcation (LIB). Formulations of the cooperation in multi-area automatic generation control (AGC) systems are proposed to express the power balance in each subarea and the adjustments of power exchange. The predictor-corrector scheme for the improved CPF is derived and restated. Moreover, a practical step size control method is proposed in accordance with polynomial fitting analysis with the relevant computational variables to enhance the performance and efficiency of CPF steps. Case studies based on an IEEE 5-bus, IEEE 118-bus and Polish 2383-bus test system demonstrate the efficiency of the proposed CPF model and its ability to generate reliable PTL results.

Research on Additional Control Technology Based on Energy Storage System for Improving Power Transfer Capacity of Multi-Terminal AC/DC System with Low Cost

The multi-terminal AC/DC system will become one of the important forms of the future power grid. The negative impedance characteristic caused by the constant power load in the DC network will reduce the power transfer capacity between the terminals, especially when a grid fault occurs in AC system at any terminal. Energy storage has played an important role in improving the stability of AC and DC systems. This paper proposes an additional control method based on an energy storage system to improve system power transfer capacity with low cost. The state space model of two-terminal AC/DC system is established, and the feedback laws for additional control are further designed by Lyapunov theory. Furthermore, the additional control strategies based on the energy storage system is built, without changing the existing control system of each control object. Finally, the corresponding system simulation model is established by Matlab/Simulink for analysis and verification. The research results show that the proposed additional control method is effective. The power transfer limitation can be overcome by only adding small damping energy with the stable DC voltages under large disturbances, and the power transfer capacity between the terminals can be significantly improved with low control cost.

Effect of stochasticity on voltage stability support provided by wind farms: Application to the Hellenic interconnected system

This paper focuses on the effect of wind farm stochastic power variability on the voltage stability support to a real power system. An emergency maximum reactive support (EMRS) control strategy is considered, with the help of which wind farms can contribute in increasing the power transfer limit in a weak part of a transmission system. In order to generate realistic synthetic wind power data, a Markov model with low complexity is chosen and implemented to simulate wind power generation. Wind farm feeder characteristics and MV/HV substation controls, such as feeder resistance and reactance, switched capacitor banks and load tap changer controls, as well as wind farm converter voltage and current limitations are modeled in detail. Different scenarios, initiating from a historic insecure snapshot in an area of the Hellenic interconnected system, are used to assess the impact of stochastic wind farm generation on the contribution of the maximum reactive support control scheme on voltage stability.

Steady-state Analysis of Voltage Source Converter (VSC) Connected to Weak AC System and Optimal Control Strategies

The power transfer limitation of voltage source converter (VSC) connected to weak AC system is restricted by three main elements: steady-state characteristic, small signal stability, and transient stability. In this paper, according to steady-state analysis, constraint condition and mathematical model of VSC system are established to figure out the appropriate operating point. A novel outer-loop control diagram is proposed. Meanwhile, a small signal model of VSC system is established. Based on participation factor analysis, the dynamic performance of phase-locked loop (PLL) have significant impacts on the system stability assessment. Therefore, an advanced PLL control appending damping factor is proposed. Simulations validated the following conclusions: 1) The optimal AC voltage of point of common coupling is associated with the equivalent AC system voltage, impedance, and the current limitation. The novel outer-loop controller can enhance the power transfer limitations. 2) The small signal stability of VSC can be enhanced by appending an alternative damping factor control on PLL. The advanced PLL has robustness which can endure a great active power disturbance in AC system. Simulations and calculations have been performed to validate the findings.