Per-unit System Research Articles

Bench Testing for Power Flow Management in AC/DC Hybrid Microgrids Using Per-Unit System: Study and Design

This article presents an in-depth study and the design of a test bench dedicated to assessing the performance of power flow management within an AC/DC hybrid microgrid. With a focus on utilizing the per-unit system, our approach aims to accurately emulate the operational conditions of a real microgrid. We delve into the theoretical aspects of power flow management, implementing key concepts such as per-unit (PU) power. The design of the test bench includes the faithful modeling of renewable sources, loads, energy storage, and other constituents of the microgrid. Detailed simulation results and performance analyses are presented, demonstrating the Effectiveness and robustness of our testing approach. This test bench provides a versatile platform for evaluating and enhancing power flow management strategies in hybrid microgrids, thereby contributing to the ongoing development of decentralized and sustainable energy systems.

Pareto Local Search Function for Optimal Placement of DG and Capacitors Banks in Distribution Systems

DGs and capacitor banks are installed to optimize the performance of many distribution networks. Typically, the problem of optimizing the overall performance of the distribution network is examined with multi-objective purposes. Network optimization purposes are usually varied and sometimes contradictory. Therefore, the problem search space is very large due to the variety of purposes. This paper presents a modified Pareto local search function for optimal placement of DGs and capacitor banks. To limit the search space and find Pareto points, a new combination method including Pareto chart and a weight function has been used. The optimal operation of the distribution network is performed by three single objective functions related to the voltage stability index, voltage profile of buses and power loss. In this method, a modified per-unit system is presented to align single objective functions and their weighting coefficients. The network is studied with three different loads. So that, the network is examined in the final stage by increasing the load and reaching bus voltage stability margins. The particle swarm optimization method is applied to solving placement problems. In addition, locating and sizing DG and capacitor banks, tap setting of on load tap changer transformer is adjusted by the proposed method. To show the effectiveness of the purposed method, simulations are applied to 69 bus radial system. The results indicated the favorable advantage of the proposed method to improve the overall performance of the distribution network.

Artificial Neural Network based Solar Energy Integrated Unified Power Quality Conditioner

ABSTRACT The utility grid is prone to power quality issues due to the advent of power electronic devices and integration of Distributed Energy Resources. The power quality has to be maintained despite variation in load under steady and fault conditions. Unified Power Quality Conditioner is a FACTS device that improves the power quality at the Distribution side of the utility grid. In Unified Power Quality Conditioner, reactive and real power compensation is carried out simultaneously improving the power quality. The proposed control algorithm for Unified Power Quality Conditioner is a hybrid combination of Reactive Power Control and Unit Vector Template. The Unified Power Quality Conditioner is integrated with Distributed Energy Resources like solar energy to minimize the power rating of converters and meet the power demand. The reinforced learning algorithms have been effectively increasing the performance of the power electronic devices; among them, the most commonly used is the Neural-Network algorithm. The Artificial Neural Network controller for the solar integrated Unified Power Quality Conditioner system improves the power quality when compared to the conventional controllers by self-adapting themselves to the environmental needs. The system is tested under both balanced and unbalanced load conditions with MATLAB-SIMULINK. The per-unit system has been used for the analysis purpose to minimize the complexity. The hybrid control of the series and shunt converters supported by solar integration at the DC link proves to eliminate distortion caused by the non-linear load. The system is subjected to a momentary voltage sag/swell as per IEEE 1159 standards. The momentary sag/swell that varies between 0.5 seconds to 3 seconds has been made to ride through less than 50 milliseconds as per the Computer and Business Equipment Manufacture Association curve. The load side current harmonics have been minimized inevitably by the proposed control methodology to ensure reliability and good power factor at the Distribution side. A comparative analysis between the conventional Proportional-Integral controller and Artificial Neural Network controller in solar integrated Unified Power Quality Conditioner proved the Artificial Neural Network controller improved the harmonic reduction of various orders by an average of 12.72%. The Total Harmonic Distortion minimization for various harmonic orders was brought under the limits of IEEE 519 standards with Artificial Neural Network controller.

A Novel Per Unit (P.U.) Integer Format Applied to the Control of a Grid-Tied Solar PV Inverter

In advanced power electronic applications such as a grid-tied solar photovoltaic (PV) inverter, control algorithms demand high-level computational support, typically provided by an expensive 32-bit digital-signal-processor (DSP) or microcontroller. In cost-sensitive markets, this may prove to be a significant component of the overall cost of the system. Using a low-cost 16-bit microcontroller is, therefore, highly desirable. However, it poses certain challenges such as fewer bits for the mathematical and logical operations, computations in the fixed-point environment, and lower speeds. In this article, a novel per-unit integer system is proposed towards using a low-cost microcontroller for complex computations, which overcomes the above limitations while maintaining the core functionality in a fixed-point environment. An improved hybrid phase locked loop implementation scheme, that uses the p.u. integer system has also been presented, which significantly reduces the execution time for grid-synchronization. To demonstrate the performance of the proposed concepts, control of a grid-tied PV inverter has been implemented on a low-cost fixed-point microcontroller (dsPIC33FJ16GS402) as well as on an advanced DSP microcontroller (TMS320F28069). Timing analysis and experimental results for a 1 kW grid-tied PV system confirm that the performance of the system using a low-cost microcontroller is comparable to that of the advanced microcontroller.

Maximum Torque per Voltage Flux-Weakening Strategy With Speed Limiter for PMSM Drives

This article presents an enhanced flux weakening (FW) control scheme for permanent magnet synchronous motors, focused on electric vehicle applications. The novelty of the proposed algorithm is the integration in a unified scheme of both the accelerator pedal as torque reference and the cruise speed limiter as speed limit, without interfering between them until this limit is achieved. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis current references are calculated from the proposed algorithm by using a polar coordinate system and a per-unit system. The latter is based on the characteristic machine parameters, which aim to ease and simplify the algorithm implementation. Moreover, it takes advantage of the smooth transition between the low back electromotive force zone and the FW zone thanks to a voltage loop, which changes the current-vector angle. Another fundamental merit of the proposed scheme is its capacity to work in all the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> plane throughout the maximum torque per ampere, constant torque, current and voltage limit, maximum torque per voltage, and constant speed strategies without switching the algorithm. Simulations and experimental results from a real exterior-rotor interior permanent magnet synchronous motor direct-drive e-motorbike verify the effectiveness of the proposed method.

Bond Graph as a formal methodology for obtaining a wind turbine drive train model in the per-unit system

In this paper, the Bond Graph methodology is originally employed to obtain a per-unitized dynamic model for a wind turbine two-mass drive train. Bond Graph is a formal multi-domain methodology that strongly enforces the energy conserving property. A natural outcome of applying this methodology is a reliable and dimensionally homogeneous per-unit dynamic model. This methodology is utilized to address the lack of dimensional homogeneity in some drive train models that are being used in the wind energy literature.

High-Order Filter Design for High-Power Voltage-Source Converters

This paper proposes an analytical design procedure for the LLCL and the LCCL filters for grid integration of high-power voltage-source converters. The low switching frequency and stringent limits on grid-injected harmonics in high-power applications lead to large smoothing filters. In order to reduce the size and weight, high-order filters are already proposed and wise design procedures with the main goal of minimizing the overall filter size are being suggested. In this paper, the parameters of the LLCL and the LCCL filters are designed in the per-unit system to satisfy the requirements on the injected grid current and at the same time minimize the overall filter size through minimizing the total energy stored in the filter components. The experimental results of a downscaled laboratory prototype with a low switching frequency prove the effectiveness of the proposed design procedure.

Implementation methodology of powertrain for series-hybrid military vehicles applications equipped with hybrid energy storage

This paper investigates a component-sizing method and a power-control algorithm for series-hybrid military vehicles equipped with hybrid energy storages that comprise batteries and super-capacitors. Component sizing of the powertrain is determined by the performance specification that is related to mission profiles and power-flow control methods. In order to minimize the effects of mission profiles and power-flow control methods, the linear programming (LP) technique is employed. The LP problem for minimizing the output energy from the engine under different conditions of driving cycles and capacities of the energy storage system (ESS) is solved to eliminate the effect of the power distribution. Through analyzing the effects of different power and energy ratings of the ESS, the optimal values of power and energy capacities of the ESS are determined. The design approaches are extensively verified with simulations and experimental results of a reduced-scale per-unit equivalent system of the 10-ton series-hybrid electric vehicle (SHEV).

Steady-state analysis of the integrated natural gas and electric power system with bi-directional energy conversion

Nowadays, the electric power system and natural gas network are becoming increasingly coupled and interdependent. A harmonized integration of natural gas and electricity network with bi-directional energy conversion is expected to accommodate high penetration levels of renewables in terms of system flexibility. This work focuses on the steady-state analysis of the integrated natural gas and electric power system with bi-directional energy conversion. A unified energy flow formulation is developed to describe the nodal balance and branch flow in both systems and it is solved with the Newton–Raphson method. Both the unification of units and the per-unit system are proposed to simplify the system description and to enhance the computation efficiency. The applicability of the proposed method is demonstrated by analyzing an IEEE-9 test system integrated with a 7-node natural gas network. Later, time series of wind power and power load are used to investigate the mitigation effect of the integrated energy system. At last, the effect of wind power and power demand on the output of Power to Gas (P2G) and gas-fired power generation (GPG) has also been investigated.

Impact of selection of DC base values and DC link control strategies on sequential AC-DC power-flow convergence

This paper demonstrates the convergence of the integrated AC-DC power-flow algorithm as affected by the selection of different base values for the DC quantities and adoption of different control strategies for the DC link. For power-flow modeling of integrated AC-DC systems, the base values of the various DC quantities can be defined in several ways, giving rise to different sets of per-unit system equations. It is observed that different per-unit system models affect the convergence of the power-flow algorithm differently. In a similar manner, the control strategy adopted for the DC link also affects the powerflow convergence. The sequential method is used to solve the DC variables in the Newton Raphson (NR) power flow model, where AC and DC systems are solved separately and are coupled by injecting an equivalent amount of real and reactive power at the terminal AC buses. Now, for a majority of the possible control strategies, the equivalent real and reactive power injections at the concerned buses can be computed a-priori and are independent of the NR iterative loop. However, for a few of the control strategies, the equivalent reactive power injections cannot be computed a-priori and need to be computed in every NR iteration. This affects the performance of the iterative process. Two different per-unit system models and six typical control strategies are taken into consideration. This is validated by numerous case studies conducted on the IEEE 118-bus and 300-bus test systems.

Research on the Differential Protection Algorithm of Multi-Tap Special Transformer

Compared with conventional transformers, the rectiformer is special in connection mode, which is multi-tap and not equipped with the differential protection. In this paper, the differential protection algorithm for Multi-tap special transformer was derived. The regulating methods for the rectiformer were studied first, and then the rectiformer model of one electrolytic aluminium plant was built by PSCAD/EMTDC, characteristics of the rectiformer bank were also analyzed. The algorithm was derived on the basis of the per-unit system, and the processing methods of the regulating transformer’s tap position information were proposed. Finally, a contrast of differential protection algorithm between the multi-tap special transformer and the conventional transformer was made.

Equivalence of Large Scale Wind Farm Based on Per-Unit System on RTDS

The paper introduces per-unit system for single Doubly-fed induction generator (DFIG) and large scale wind farm (LSWF) equivalence, based on which their modeling, including main circuit, linkage equation, power equation and rotor motion equation, are built, and equivalence method of LSWF are present. The single DFIG wind farm system and LSWF are built respectively on Real time digital simulator (RTDS). Comparing simulating results of single DFIG with those of LSWF, conclusion shows per-unit value system is correct, equivalent method is feasible.

Control of DFIG Based on Per-Unit System on RTDS

The paper introduces modeling of Doubly-fed induction machine (DFIG) on orthogonal dq rotating coordinates based on per-unit value system and designs control part on space-vector-orientation, for which relative modules, in RTDS (Real time digital simulator) library, are introduced. Whole single-machine DFIG wind farm is built on RTDS and the maximal wind energy tracking is realized. Simulating results show control is correct and effective.

State-of-Charge Estimation and State-of-Health Prediction of a Li-Ion Degraded Battery Based on an EKF Combined With a Per-Unit System

This paper describes the application of an extended Kalman filter (EKF) combined with a per-unit (p.u.) system to the identification of suitable battery model parameters for the high-accuracy state-of-charge (SOC) estimation and state-of-health (SOH) prediction of a Li-Ion degraded battery. Variances in electrochemical characteristics among Li-Ion batteries caused by aging differences result in erroneous SOC estimation and SOH prediction when using the existing EKF algorithm. To apply the battery model parameters varied by the aging effect, based on the p.u. system, the absolute values of the parameters in the equivalent circuit model in addition to the discharging/charging voltage and current are converted into dimensionless values relative to a set of base value. The converted values are applied to dynamic and measurement models in the EKF algorithm. In particular, based on two methods such as direct current internal resistance measurement and the statistical analysis of voltage pattern, each diffusion resistance <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(R_{\rm Diff})$</tex></formula> can be measured and used for offline and online SOC estimations, respectively. All SOC estimates are within <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\pm$</tex></formula> 5% of the values estimated by ampere-hour counting. Moreover, it is shown that <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$R_{\rm Diff}$</tex></formula> is more sensitive than other model parameters under identical experimental conditions and, hence, implementable for SOH prediction.

Introduction to the Space Vector Modeling of the Brushless Doubly Fed Reluctance Machine

The brushless doubly fed reluctance machine (BDFRM) is the least known of a group of electrical machines that include the classic cascaded induction machine, the brushless doubly-fed induction machine (BDFIM), and the double-fed slip ring induction machine (DFSRIM). Since its initial development some 30 years ago, the BDFRM has been largely ignored because of the performance limitations imposed by the reluctance rotor design. However, improvements in reluctance rotors, a by-product of the development of the synchronous reluctance machine, have resulted in renewed interest in the BDFRM. This together with the promise of higher efficiency and simpler control compared to the BDFIM means that further investigation of the BDFRM is warranted.This paper is designed to be a starting point for research into the BDFRM. It develops the fundamental modelling equations that are required to carry out research into its dynamics and control. The approach is partly tutorial in nature as it presents some “well-known” analysis techniques that are scattered throughout the literature on the machine. It develops from first principles the space vector model of the machine, which is then used to derive the steady-state BDFRM equations. Standard sinusoidal spatial variation and linearity assumptions are used throughout the analysis. Where relevant, the physical concepts behind the machine’s operation are emphasized. In addition to the full dynamic model of the machine, the paper also introduces a per-unit system that forms the basis for machine-independent performance expressions.

Performance Prediction of a Stand-Alone Permanent-Magnet Induction Generator

A permanent-magnet induction generator (PMIG) is a special induction machine self-excited from the inside of the squirrel-cage rotor by a permanent-magnet (PM) rotor. The PMIG can be made to operate as a stand-alone generator when the squirrel-cage rotor is driven by an external prime mover. Moreover, if the capacitors are connected across the stator terminals, adjusting their values can control the output voltage. This paper presents a method for predicting the steady-state performance of such a stand-alone PMIG theoretically. By introducing the per-unit system, a nonlinear equivalent circuit, which can include the variation of the circuit parameters, is derived. Based on this equivalent circuit, the steady-state performance is theoretically calculated, and its validity is confirmed through experiments.

Effective identification of induction motor parameters based on fewer measurements

This paper applies genetic algorithms (GAs) to the problem of parameter identification for field orientation control (FOC) induction motors. Kron's two-axis dynamic model in per-unit system is given, and the model's parameters are estimated by a GA using the motor's dynamic response to a direct on line start. Results with different levels of measurement noise are presented for the model both in the per-unit system and in actual values. For comparison, the results of a simple random search (SRS) method under the same condition are also given. The results show that the parameter identification accuracy, the convergence speed and the practicality of the algorithm have been improved significantly by use of the model in the per-unit system. The results also show that fewer measurements are required to identify the induction motor parameters accurately.

Effective Identification of FOC Induction Motor Parameters Based on Few Measurements

This paper applies genetic algorithms (GAs) to the problem of parameter identification for field orientation control (FOC) induction motors. Kron's two-axis dynamic model in per-unit system is given, and the model's parameters are estimated by a GA using the motor's dynamic response to a direct on-line start. Results with different levels of measurement noise are presented for the model both in the per-unit system and in actual values. For comparison, the results of a simple random search (SRS) method under the same condition are also given. The parameter identification accuracy, convergence speed, and practicality of the algorithm have been improved significantly by use of the model in the per-unit system. Fewer measurements are required to identify the induction motor parameters accurately.

The performance of a medium ring transmission line at steady state

Abstract This paper presents the performance of the ring connection in transmission systems for medium lengths of a line under steady state operation. This will have more significant value especially if the transmitted power is a bulk amount. The ring connection between the phases of single circuit transmission in the form of cumulative connection (capacitive/inductive) impedance is accounted. The mathematical analysis is derived on the basis of Π equivalent circuit. The improvement of transmission performance is tried concerning the power factor either leading or lagging and loads. The earth path effect on transmission line parameters (resistance, inductance and capacitance) is included through the phase shift control. The medium length for such lines on the basis of sequential ring connection impedances is tested. The effect of load variation is investigated with the appearance of the shunt capacitive stray currents due to the increased length of the line. The ring allocation as a ratio of the total line length is tested. The node voltages and branch currents of the sending (first) and ring as well as the receiving (second) circuits are computed. Active and reactive powers at both sending and receiving ends of the proposed system are evaluated and then the transmission efficiency is determined. The effect of load impedance in the per-unit system is studied and resulting variation in the transmission capability is deduced.

Transient stability of power systems: theory and practice

The transient stability of power systems is an extremely intricate and highly nonlinear problem. Traditionally confined to the planning and design of power systems, transient stability studies are now increasingly important in operational planning and real-time operation. This comprehensive text: provides the reader with an in-depth account of the transient stability problem, its physical description, its theoretical formulation and assessment; discusses issues of practical interest; in particular, synchronous machine and load modeling, evaluation of machine parameters and saturation effects, tools to improve stability; provides an extensive coverage of both conventional and nonconventional methods of analysis; practical examples and simulation results illustrate the range of techniques available; includes three appendices that incorporate the per-unit system, equivalent circuit parameters, and excitation systems. Written by two experts in the field, this self-contained book will appeal to practicing power system engineers and planners. The text is also ideal for professionals and advanced students in electrical and electronic engineering and computer science, who require a comprehensive introduction to the problem of power system transient stability.