Voltage Phase Angle Research Articles

Model for Minimizing Energy Consumption of Electric Power Systems Taking Into Account the Balance of Active and Reactive Power

The work covers the developed model of minimization of active power shortage taking into account the balance of active and reactive power. The motivation for the formation and testing of this model is the need to improve the adequacy of models of this class, as well as the need to implement it in the developed methodology for assessing planned reliability. The article specifies the requirements for the model and the process of its formation, which is based on the models of minimization of active power shortage and the optimal power flow format models. When forming the model, the required set of parameters was specified, namely, the modules of busbar voltages, phase angles of voltages, active and reactive resistance, and balance constraints of active and reactive power were formed. As a result of the analysis of experiments using circuits with 3 nodes, a difference in the result of the minimum power shortage (from 3.05 to 4.46%) was revealed compared to the problem based on the model of minimization of active power shortage without taking into account reactive power in balance constraints.

Taxonomy of Power Converter Control Schemes Based on the Complex Frequency Concept

This paper proposes a taxonomy of power converter control schemes based on the recently proposed concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">complex frequency</i> . This quantity captures local frequency variations due to the change of both the phase angle and amplitude of bus voltages and current injections. The paper derives the analytical expressions of the link between complex power variations and complex frequency of each converter controller as well as the identification of critical control parameters. The main contribution of this work is to provide a general framework that allows classifying converters synchronization mechanisms and controllers. This framework also allows comparing converters with synchronous machines. To validate the theoretical results, extensive simulations are performed using a modified version of the WSCC 9-bus system. Examples of how the theoretical formulations of the paper can be used to improve power converter control in power system applications are showcased.

Conditions for Estimation of Sensitivities of Voltage Magnitudes to Complex Power Injections

Voltage phase angle measurements are often unavailable from sensors in distribution networks and transmission network boundaries. Therefore, this paper addresses the conditions for estimating sensitivities of voltage magnitudes with respect to complex (active and reactive) electric power injections based on sensor measurements. These sensitivities represent submatrices of the inverse power flow Jacobian. We extend previous results to show that the sensitivities of a bus voltage magnitude with respect to active power injections are unique and different from those with respect to reactive power. The classical Newton-Raphson power flow model is used to derive a novel representation of bus voltage magnitudes as an underdetermined linear operator of the active and reactive power injections—parameterized by the bus power factors. Two conditions that ensure the existence of unique complex power injections given voltage magnitudes are established for this underdetermined linear system, thereby compressing the solution space. The first is a sufficient condition based on the bus power factors. The second is a necessary and sufficient condition based on the system eigenvalues. We use matrix completion theory to develop estimation methods for recovering sensitivity matrices with varying levels of sensor availability. Simulations verify the results and demonstrate engineering use of the proposed methods.

The power flow analysis for electric power network: A tutorial article

The power system network is complex. This makes it more challenging to obtain valuable information because of its hundreds of buses and transmission lines. In addition, solving the steady-state equations of the power system network requires substantial mathematical computations. The power flow analysis is a study of the electrical power system. Engineers and utility companies use it for the design, control, planning, and future improvement of the electrical power network. Power flow analysis calculates the voltage magnitude, phase angles, active and reactive power flows, losses of the power system network under various loads, and generation conditions. This paper is a tutorial article aimed to present the power flow analysis techniques of Gauss-Seidel, Newton-Raphson, and Fast-Decoupled approaches. The Power World Simulator is used to demonstrate the software implementation of the approaches. The results show that Newton Raphson and Fast Decoupled have a faster convergence. The Newton Raphson method is the popular technique used for the analysis. An illustrative example for an IEEE 3-bus system on each technique is also presented in the article.

Synchrophasor-Based Out-of-Step Prediction in Large Grids

Out-of-step (OOS) condition is a potential problem in the power system and uncontrolled islanding is one of the severe consequences of out-of-step condition which leads to cascaded tripping of the system. To avoid this undesired cascaded tripping, early prediction of out-of-step condition is essential before losing the synchronization of generators and between the system areas. Controlled islanding is the last emergency action that can be taken by splitting the system intentionally into coherent islands. Conventionally, OOS condition has been detected with impedance-based measurement techniques which have their own limitations. With the implementation of a wide-area measurement system with synchrophasor measurement units (PMUs) in the power system, it is now possible to measure the bus voltage angle at a much faster rate than with SCADA. In this paper, synchrophasor-based bus voltage angle measurement has been used for early prediction of OOS condition in power systems. A new algorithm has been formulated for both generator and tie lines based on the trajectory of first and second derivatives of the bus voltage phase angle for early detection of OOS condition. The prediction speed of proposed method is found to be between 5% and 70% of time to OOS, after disturbance clearance. The proposed algorithm has been mathematically formulated and evaluated with three benchmark systems in real-time simulation environment with an OPAL-RT real-time simulator and a HYPERSIM platform.

Calculation of electric network modes in real-time using the “Rezhym” software suite

The article presents a software suite for calculating the modes of an electrical network. Theoretical foundations of calculation, general information about the software suite, and recommendations for working with it are provided. It is shown that the theoretical basis of the software suite includes nodal equations and modifications of the Newton's method. Nodal equations are used to model various modes of electrical networks (steady-state, post-fault, heavy load). Nonlinear nodal voltage equations describe the steady-state operation of the electrical system with nonlinear current sources specified. The nodal voltage equations are presented in the form of power balance equations and matrix notation. In solving the equations for steady-state operation, the variables used are the magnitude and phase angles of voltage at nodes (U and δ). The article explains how the nonlinear system of steady-state equations is solved using the Newton's method, where a linearized system of equations is solved at each iteration step, with convergence control based on the vector of mismatches. The computer program's algorithm is implemented through input data module, the basic module, and the results output module. The article discusses the main conditions for running the program, which include a minimum requirement for technical resources such as a personal computer. The system software used by the program should be an operating systems starting from Windows 95 and above. The operator using the program should have practical skills in working with the graphical user interface of the operating system. The article highlights the significance of the basic module, which is the main component consisting of initial data processing procedures and information output as per the user's request. The basic module allows for real-time changes in initial data values and calculations with new values. The software suite enables calculations to be conducted in real-time. The program was developed and modernized at the Department of Electrical Power Transmission of the National Technical University “Kharkiv Polytechnic Institute”. The programs have been implemented in the educational process and scientific activities of the department.

Adaptive active and reactive power control strategy for virtual synchronous generator

SummaryWith the increase in the penetration level of renewables into the grid, the virtual synchronous generator (VSG) concept has emerged as an attractive solution for controlling grid‐tied inverters. The variation in reactive power also affects the real power of the system as well. To address the voltage variations and phase angle variations occurring because of the energy storage elements, the control of the reactive power loop (RPL) is important. Also, it is used to maintain voltage regulation and improve the power factor of the VSG system. This paper focuses on the damping of oscillations occurring because of load variation by proper adjustment of the rotational inertia, damping coefficient, droop coefficient, and regulatory coefficient of reactive power with a proposed adaptive control strategy. Small‐signal analysis of the active and reactive power and point of common coupling (PCC) have been derived, and the detailed dynamic performances are analyzed. The influences of parameters perturbation on PCC voltage and reactive power were investigated. Furthermore, adaptive control includes optimizing dynamic indexes such as rise time, delay time, and response settling time. Finally, the performance and improvement in the results of VSG with and without adaptive control are compared.

Enhancement of Power Transfer Capability of Transmission Line Using Thyristor Controlled Series Capacitor (TCSC)

Electricity demand is increasing with the increase in urbanization and industrialization. And to meet this increasing demand, the power generation system has been rapidly increased. But along with increase in generation capacity, transmission capacity also needs to be increased simultaneously. For this, either new transmission line needs to be added in the network or power transfer capability of the existing transmission line needs to be enlarged. Latter is the more preferred choice as it involves less cost and time than to erect the new transmission lines. Power transfer capability of a transmission line can be improved by the adjustment of various parameters of a power system network such as voltage phase angles of the buses connected by the lines, impedance of the lines, etc. For this several power electronics-based FACTS devices have been developed, which are most effective in manipulating these parameters to control the power flow through the lines. In this paper, the use of thyristor-controlled series capacitor (TCSC) is highlighted. In this paper, TCSC is implemented in series with line, connecting two buses, to reduce line series impedance. From the results, it is seen that TCSC implementation increases power transfer capability and stability limit, while improving voltage regulation.

Design and PIL implementation of a new robust backstepping based low-complexity voltage-oriented control method for four-leg rectifiers

This paper proposes a low computational complexity enhanced voltage-oriented control strategy (EVOC) based on robust backstepping controllers (BSC) in the synchronous rotating frame (dq0 frame) for a PWM four-leg voltage-source-rectifier (FLVSR). Unlike traditional VOC strategies, the suggested EVOC approach does not need any synchronization method and Park transformations, and it has the similar architecture and same features as the traditional VOC when it’s synchronization loop for grid voltage phase angle detection is properly operated. In addition to controlling the FLVSR, the suggested EVOC strategy is also used to develop the model of the three phase FLVSR in the dq0 frame using the concepts of direct instantaneous power control (DPC) theory, which combine the benefits of traditional DPC and traditional VOC with less computational complexity. The robust BSC is adopted for accurate regulation of FLVSR input currents and dc bus voltage simultaneously while taking into account the FLVSR parameter uncertainties. It produces sinusoidal currents with lower ripples and has high robustness against parametric variations. It is also simple to implement and has a relatively high grid voltage disturbance rejection ability. Finally, comparisons with both the traditional VOC strategy using PI controllers (VOC-PIC) and the EVOC strategy using PI controllers (EVOC-PIC) under various conditions demonstrate the superiority and benefits of the proposed EVOC-BSC strategy.

A new continuous variables and convex relaxation based formulation for reconfiguration of unbalanced mutually coupled active distribution networks

With the integration of renewable energy-based sources and demand response initiatives, the distribution network has transformed into an active network with bidirectional flows. Network Reconfiguration (NR), i.e., changing network topology, is an alternative to minimize power loss in the distribution network with sectionalizing switches (normally closed) and tie-line switches (normally open). Due to the discrete nature of switches (on or off), the NR formulation is generally a mixed-integer NP-hard nonlinear problem. This paper proposes the first NR formulation for an unbalanced active distribution network with continuous variables to indicate switches’ statuses in NR while considering mutual coupling between line impedances. The obtained solution provides the optimal real power and voltage magnitude settings of dispatchable Distributed Generators (DGs) and network topology for the minimum active power loss in the network. The proposed formulation considers all practical aspects of the distribution network, i.e., mutual coupling, load unbalances, angular unbalance, and the absence of one or two phases in a line section, which, otherwise, have not been considered together in previous formulations. Further, a novel convex relaxation for bus voltage phase angles avoids explicit voltage recovery. Compared to prior formulations, numeric results for unbalanced radial distribution networks showcase the proposed formulation’s effectiveness.

Digitalized Control Algorithm of Bridgeless Totem-Pole PFC with a Simple Control Structure Based on the Phase Angle

Compared to the conventional boost power factor correction (PFC) converter, a totem-pole bridgeless PFC has high efficiency because it does not have an input diode rectifier stage, but a current spike may occur when the polarity of the grid voltage changes. This paper proposes a digital control algorithm for bridgeless totem-pole PFC with a simple control structure based on the phase angle of grid voltage. The proposed algorithm has a PI-based double-loop control structure and performs DC-link voltage and input inductor current control. Rectifying switches operate based on the proposed rectification algorithm using phase angle information calculated through a single-phase phase-locked loop (PLL) to prevent current spikes. The feed-forward duty ratio value is calculated according to the polarity of the grid voltage and added to the double-loop controller to perform appropriate power factor control. The performance and feasibility of the proposed control algorithm are verified through a 3 kW hardware prototype.

Analysis of Radial Distribution Systems by using Particle Swarm Optimization under Uncertain Conditions

Abstract: Losses in the network are one of the most important parts of a power distribution network, and work should be done to lower their value. The research used the Particle Swarm Optimisation (PSO) metaheuristic algorithm to investigate the impact of concurrently optimising phase balance and conductor size on the planning issues and objective functions of an imbalanced distribution system. These objective functions include power loss, voltage unbalance, total neutral current, and complicated power unbalance. Firstly, the optimisation process is applied to each goal function. Then, they are put together with weights to form a multi-objective optimisation problem. In this study, it was tried to find out how to minimise losses in electrical power distribution networks that aren't fair. Power flow and optimal DG placement are two PSO techniques that may be used to reduce losses. These changes may be applied to existing distribution systems using an effective load-flow method for a three-phase imbalanced radial distribution network. Knowing the node voltage, angle, branch current, actual power loss, wattles power loss, branch losses, etc. helps determine the network's true state. Simple formulae may be used to describe the relationship between the voltage at one end of the distribution system, the voltage at the other end, and the voltage drops throughout the whole system. An approach is developed to identify the relevant variables. The voltage's angle at the target is calculated with its magnitude. It's a process that requires time and effort. From the substation to each terminal node, the constant voltage of 1p.u. is considered. Voltage magnitude and phase angle are varied between repetitions, and voltage reductions are computed using the new parameters. The suggested approach has been applied to 19- and 25-node networks with unequal distribution. To demonstrate its efficacy, the recommended approach's speed requirements were compared to those of another recently developed technology. Good outcomes are achieved, and DG proves to be a viable option for reducing costs and improving performance.

The Efficacy of Multi-Period Long-Term Power Transmission Network Expansion Model with Penetration of Renewable Sources

The electrical energy demand increase does evolve rapidly due to several socioeconomic factors such as industrialisation, population growth, urbanisation and, of course, the evolution of modern technologies in this 4th industrial revolution era. Such a rapid increase in energy demand introduces a huge challenge into the power system, which has paved way for network operators to seek alternative energy resources other than the conventional fossil fuel system. Hence, the penetration of renewable energy into the electricity supply mix has evolved rapidly in the past three decades. However, the grid system has to be well planned ahead to accommodate such an increase in energy demand in the long run. Transmission Network Expansion Planning (TNEP) is a well ordered and profitable expansion of power facilities that meets the expected electric energy demand with an allowable degree of reliability. This paper proposes a DC TNEP model that minimises the capital costs of additional transmission lines, network reinforcements, generator operation costs and the costs of renewable energy penetration, while satisfying the increase in demand. The problem is formulated as a mixed integer linear programming (MILP) problem. The developed model was tested in several IEEE test systems in multi-period scenarios. We also carried out a detailed derivation of the new non-negative variables in terms of the power flow magnitudes, the bus voltage phase angles and the lines’ phase angles for proper mixed integer variable decomposition techniques. Moreover, we intend to provide additional recommendations in terms of in which particular year (within a 20 year planning period) can the network operators install new line(s), new corridor(s) and/or additional generation capacity to the respective existing power networks. This is achieved by running incremental period simulations from the base year through the planning horizon. The results show the efficacy of the developed model in solving the TNEP problem with a reduced and acceptable computation time, even for large power grid system.

An algorithm for distance protection based on the change of the voltage phase angle

Conventional distance protection methods usually require additional filtering of the input signals to remove the influence of the DC component and the distortion of sinusoidal signals. The paper shows an algorithm that does not require additional filtering of the input signals. The proposed algorithm uses measured voltages at the beginning of the line and auxiliary voltages as input signals. The auxiliary voltages were calculated from measured currents and voltages at the beginning of the line and known line parameters. The algorithm compares the instantaneous values of the measured and calculated auxiliary voltages and detects a fault on the line based on the change in the phase angle of the voltage. Testing of the presented algorithm was performed with signals obtained from computer simulations of line faults and recordings of faults from protection devices from the real network. The obtained results confirmed that the algorithm represents fast and sensitive protection of transmission lines.

Synchrophasor network-based detection and classification of power system events: A singular value decomposition approach

Timely detection and classification of power system events are essential for situation awareness and reliable electricity grid operation. It is also a crucial step with regard to synchrophasor network data management and archiving. In this paper, an event detection and classification method based on the singular value decomposition (SVD) of synchrophasor data is proposed. The detection algorithm exploits the low-dimensionality characteristics of synchrophasor data and identifies the changes in the dimensionality of a sliding data matrix. The SVD-based method assigns several detection flags indicating events and outliers in voltage magnitude, phase angle and frequency data. The proposed classification algorithm comprises a decision tree employing detection flags and singular values to classify events into several categories, e.g., fault, voltage magnitude and phase angle events, and generation-load mismatch events. Moreover, the proposed algorithm identifies whether events are spatially correlated. Field synchrophasor data collected from a smart grid are used to evaluate the performance of the proposed method. The numerical results show that the proposed method can successfully detect and classify different types of events even in the presence of measurement uncertainty.

CNISOGI and VSSMCLMS Filters for Solving Grid and Load Abnormalities for a Microgrid With Seamless Mode Transfer Capability

A cascaded non-identical second-order generalized integrator (CNISOGI) and a variable step size modified clipped least mean square (VSSMCLMS) adaptive filter are proposed for a microgrid to solve the grid and load abnormalities. The CNISOGI filter estimates the positive sequence components (PSCs) from polluted (unbalanced/distorted) grid voltages. Hence improved quality grid currents are realized even though the grid voltages are polluted. Moreover, the CNISOGI filter estimates the accurate phase angle and frequency of voltages; thus, seamless transition of the microgrid is achieved between different modes. The comparative performance of the CNISOGI filter is studied over different control techniques and it demonstrates the better filtering capability of the proposed control. The microgrid is connected to the grid or a diesel generator (DG) set in subject to the availability of energy sources and the load demand to supply uninterrupted electricity to loads. Therefore, it provides an attractive solution for powering critical loads. The load compensation is achieved with the help of a VSSMCLMS filter. It estimates the active fundamental component of the load currents with faster response and lesser weight oscillations. The comparative performance of the VSSMCLMS filter is studied over conventional filters in MATLAB/Simulink and under laboratory conditions to ascertain its superiority in the filtering process.

Experimental Validation of a Phase Lead-Lag Synchronous Frame Phase-Locked Loop Under Different Voltage Conditions

Due to the rapid increase in single-phase inverters tied to the grid, fast and robust phase-locked loop algorithms have become indispensable. In previous work, a phase lead-lag synchronous reference frame phase-locked loop (PLL) was proposed. The method makes use of two single-tuned filters that perform as a phase detector. They are capable of shifting the phase of the grid voltage to be advanced or delayed by 45∘ with respect to the grid voltage phase. The generated orthogonal signals are transformed by Park transformation. The quadrature voltage is regulated to zero by means of a PI controller, while its output determines the frequency of the grid voltage and the phase angle obtained by integrating the estimated frequency. In this paper, deficiencies in the previous work are addressed. A small signal model of the method which takes into account frequency variation, voltage variation, and harmonic distortion is derived and presented. The design guidelines are discussed and an example illustrated. The method is validated through simulations and experiments under various voltage conditions while the algorithm is implemented on a rapid prototyping MicroLabBox. It is tested under different voltage scenarios, generated by a programmable AC source. The experimental results show that the method can track the phase angle of the grid voltage with nearly zero phase error under normal voltage conditions. It can track the phase of the grid voltage under 45∘ step phase jumps in 2.75 cycles, achieve harmonic attenuation of -15 dB under 15% third harmonic distortion, and attain an adequate phase margin near 45∘. This confirms that the method is fast and robust under adverse voltage conditions.

Distribution System State Estimation Using Hybrid Traditional and Advanced Measurements for Grid Modernization

Distribution System State Estimation (DSSE) techniques have been introduced to monitor and control Active Distribution Networks (ADNs). DSSE calculations are commonly performed using both conventional measurements and pseudo-measurements. Conventional measurements are typically asynchronous and have low update rates, thus leading to inaccurate DSSE results for dynamically changing ADNs. Because of this, smart measurement devices, which are synchronous at high frame rates, have recently been introduced to enhance the monitoring and control of ADNs in modern power networks. However, replacing all traditional measurement devices with smart measurements is not feasible over a short time. Thus, an essential part of the grid modernization process is to use both traditional and advanced measurements to improve DSSE results. In this paper, a new method is proposed to hybridize traditional and advanced measurements using an online machine learning model. In this work, we assume that an ADN has been monitored using traditional measurements and the Weighted Least Square (WLS) method to obtain DSSE results, and the voltage magnitude and phase angle at each bus are considered as state vectors. After a period of time, a network is modified by the installation of advanced measurement devices, such as Phasor Measurement Units (PMUs), to facilitate ADN monitoring and control with a desired performance. Our work proposes a method for taking advantage of all available measurements to improve DSSE results. First, a machine-learning-based regression model was trained from DSSE results obtained using only the traditional measurements available before the installation of smart measurement devices. After smart measurement devices were added to the network, the model predicted traditional measurements when those measurements were not available to enable synchronization between the traditional and smart sensors, despite their different refresh rates. We show that the regression model had improved performance under the condition that it continued to be updated regularly as more data were collected from the measurement devices. In this way, the training model became robust and improved the DSSE performance, even in the presence of more Distributed Generations (DGs). The results of the proposed method were compared to traditional measurements incorporated into the DSSE calculation using a sample-and-hold technique. We present the DSSE results in terms of Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) values for all approaches. The effectiveness of the proposed method was validated using two case studies in the presence of DGs: one using a modified IEEE 33-bus distribution system that considered loads and DGs based on a Monte Carlo simulation and the other using a modified IEEE 69-bus system that considered actual data for loads and DGs. The DSSE results illustrate that the proposed method is better than the sample-and-hold method.

Simulation and Modeling of Detailed Load flow Analysis for the 400kVA and 132kVA Iraqi Grid

A load flow program is developed using MATLAB and based on the Newton–Raphson method,which shows very fast and efficient rate of convergence as well as computationally the proposed method is very efficient and it requires less computer memory through the use of sparsing method and other methods in programming to accelerate the run speed to be near the real time. The designed program computes the voltage magnitudes and phase angles at each bus of the network under steady–state operating conditions. It also computes the power flow and power losses for all equipment, including transformers and transmission lines taking into consideration the effects of off–nominal, tap and phase shift transformers, generators, shunt capacitors, shunt inductors, line reactors and bus reactors. Thus, overloaded transformers and transmission lines are identified, and remedial measure can be designed and implemented. It also provides the ability of tie lines, area splitting, and contingency analysis.Any generator station(s) or busbar(s) that exceeds the specified operation limits will be automatically checked and flagged and then the program will automatically suggest the best solution to the problem. It also automatically checks whether the system is sub divided into sub areas or not. If yes, it will find the solution for each area separately. A complete report about the results and the state of the system (the violated generators, busbars, and transmission lines, the required modifications to overcome the violations, the names of the areas splitted,…) will be displayed in working window as well as generating a text file containing all details . It is important to mention that this program is used by the national control center of the Ministry of Electricity and its efficiency was tested through applying the data of the two major Iraqi networks (400kV and 132kV), the program shows very accurate results and provides efficient notes about the status of the networks

Designing Robust Networks of Coupled Phase Oscillators With Applications to the High Voltage Electric Grid

We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et al. that quantifies the impact of a small perturbation at an individual phase-oscillator's natural frequency to the system's global synchronized frequencies. Given a complex network topology with specific governing dynamics, the proposed framework finds an optimal allocation of edge weights that minimizes such vulnerability measure(s) at the node(s) for which we expect perturbations to occur by solving a tractable semi-definite programming problem. We specify the mathematical model to high voltage electric grids where each node corresponds to a voltage phase angle associated with a bus and edges correspond to transmission lines. Edge weights are determined by the susceptance values along the transmission lines. In this application, frequency synchronization is increasingly challenged by the integration of renewable energy, yet is imperative to the grid's health and functionality. Our framework helps to alleviate this challenge by optimizing the placement of renewable generation and the susceptance values along the transmission lines.