Common-Mode Frequency in Inverter-Penetrated Power Systems: Definition, Analysis, and Quantitative Evaluation

<p>As synchronous generators (SGs) are extensively replaced by inverter-based generators (IBGs), modern power systems are facing complicated frequency stability problems. Conventionally, the frequency nadir and the rate of change of frequency (RoCoF) are the two main factors concerned by power system operators. However, these two factors heavily rely on simulations or experiments, especially in a power system with high-penetration IBGs, which offer limited theoretical insight into how the frequency response characteristics are affected by the devices. This paper aims at filling this gap. Firstly, we derive a formulation of the global frequency for an IBG-penetrated power system, referred to as common-mode frequency (CMF). The derived CMF is demonstrated to be more accurate than existing frequency definitions, e.g., the average system frequency (ASF). Then, a unified transfer function structure (UTFS) is proposed to approximate the frequency responses of different types of devices by focusing on three key parameters<a>, which dramatically reduces the complexity of frequency analysis. </a>On this basis, we introduce two evaluation indices, i.e., frequency drop depth coefficient (FDDC) and frequency drop slope coefficient (FDSC), to theoretically quantify the frequency nadir and the average RoCoF, respectively. Instead of relying on simulations or experiments, our method rigorously links the system’s frequency characteristics to the characteristics of heterogeneous devices, which enables an in-depth understanding regarding how devices affect the system frequency. Finally, the proposed indices are verified through simulations on a modified IEEE 39-bus test system. </p>

Common-Mode Frequency in Inverter-Penetrated Power Systems: Definition, Analysis, and Quantitative Evaluation

<p>As synchronous generators (SGs) are extensively replaced by inverter-based generators (IBGs), modern power systems are facing complicated frequency stability problems. Conventionally, the frequency nadir and the rate of change of frequency (RoCoF) are the two main factors concerned by power system operators. However, these two factors heavily rely on simulations or experiments, especially in a power system with high-penetration IBGs, which offer limited theoretical insight into how the frequency response characteristics are affected by the devices. This paper aims at filling this gap. Firstly, we derive a formulation of the global frequency for an IBG-penetrated power system, referred to as common-mode frequency (CMF). The derived CMF is demonstrated to be more accurate than existing frequency definitions, e.g., the average system frequency (ASF). Then, a unified transfer function structure (UTFS) is proposed to approximate the frequency responses of different types of devices by focusing on three key parameters<a>, which dramatically reduces the complexity of frequency analysis. </a>On this basis, we introduce two evaluation indices, i.e., frequency drop depth coefficient (FDDC) and frequency drop slope coefficient (FDSC), to theoretically quantify the frequency nadir and the average RoCoF, respectively. Instead of relying on simulations or experiments, our method rigorously links the system’s frequency characteristics to the characteristics of heterogeneous devices, which enables an in-depth understanding regarding how devices affect the system frequency. Finally, the proposed indices are verified through simulations on a modified IEEE 39-bus test system. </p>

Optimization of synchronized frequency and voltage control for a distributed generation system using the Black Widow Optimization algorithm

A distributed generation network could be a hybrid power system that includes wind–diesel power generation based on induction generators (IGs) and synchronous generators (SGs). The main advantage of these systems is the possibility of using renewable energy in their structures. The most important challenge is to design the voltage-control loop with the frequency-control loop to obtain optimal responses for voltage and frequency deviations. In this work, the voltage-control loop is designed by an automatic voltage regulator. A linear model of the hybrid system has also been developed with coordinated voltage and frequency control. Dynamic frequency response and voltage deviations are compared for different load disturbances and different reactive loads. The gains of the SG and the static volt-ampere reactive compensator (SVC) controllers in the IG terminal are calculated using the Black Widow Optimization (BWO) algorithm to insure low frequency and voltage deviations. The BWO optimization algorithm is one of the newest and most powerful optimization methods to have been introduced so far. The results showed that the BWO algorithm has a good speed in solving the proposed objective function. A 22% improvement in time adjustment was observed in the use of an optimal SVC. Also, an 18% improvement was observed in the transitory values.

Analysis of Synchronous Generators’ Local Mode Eigenvalues in Modern Power Systems

New energy sources, storage facilities, power electronics devices, advanced and complex control concepts, economic operating doctrines, and cost-optimized construction and production of machines and equipment in power systems adversely affect small-signal stability associated with local oscillations. The objective of the article is to analyze local oscillations and the causes that affect them in order to reduce their negative impact. There are no recognized analyses of the oscillations of modern operating synchronous generators exposed to new conditions in power systems. The basic idea is to perform a numerical analysis of local oscillations of a large number of synchronous generators in the power system. The paper represents the local mode data obtained from a systematic analysis of synchronous generators in the Slovenian power system. Analyzed were 74 synchronous generators of the Slovenian power system, plus many additional synchronous generators for which data were accessible in references. The mathematical models convenient for the study of local oscillations are described first in the paper. Next, the influences of transmission lines, size of the synchronous generators, operating conditions, and control systems were investigated. The paper’s merit is the applicable rules that have been defined to help power plant operators avoid stability-problematic situations. Consequently, boundaries were estimated of the eigenvalues of local modes. Finally, experiments were performed with a laboratory-size synchronous generator to assess the regularity of the numerically obtained conclusions. The obtained results enable the prediction of local oscillations’ frequencies and dampings and will be useful in PSS planning.

Development of mechanical coupling and exciter system in synchronous generators

Power is generated in a variety of ways, including renewable energy, nuclear power, and burning of fossil fuels. The majority of our power is currently generated by burning fossil fuels, mostly natural gas and coal, to spin turbines attached to an electromagnetic generator. The main advantage of AC generation is that the voltage levels can be altered up and down with transformers, allowing electricity to be sent across long distances to the loads that demand it. The excitation system demand for large synchronous generators with a few hundred-megawatt ratings becomes very enormous. The challenge of transmitting such a big amount of power through high-speed sliding contacts becomes daunting. Mechanical coupling with exciter for synchronous generators is essential to mitigate such problems as the corrected output is linked directly to the field winding. This paper aims to develop a simulation of a 3-phase diesel engine-based 2 MVA/400 V synchronous generator with mechanical coupling and an exciter system. The developed simulation of the synchronous machine is set to deliver 25 % of its rating value (500 kW) till the time of 3 sec. Then, additional power of 1 MW is switched at t=3 sec via a 3-phase circuit breaker. The dynamic response of field current and field voltage of the simulation shows reasonable step performance as the steady-state time is less than 3 sec. The control of the excitation system allows the generator to maintain voltage, control reactive power flow, and assist in maintaining power system stability. The simulation was accurate when measuring the voltage and current under these changes. This analysis can help to investigate further integration with renewable energy sources.

Voltage stabilization of a controlled autonomous magnetoelectric generator with a magnetic shunt and permanent magnet excitation

The paper presents the results of testing and research of the characteristics of a controlled autonomous magnetoelectric synchronous generator with a magnetic shunt. Structurally, the studied generator is a modified asynchronous machine in which the rotor is made with permanent magnets and an additional system in the form of a magnetic shunt. By adjusting the winding current of the magnetic shunt, the output voltage of the generator is regulated. The following characteristics were investigated: the no-load characteristic during operation with permanent magnets and when the winding current of the magnetic shunt changes with forward and reverse polarity. Also, the external characteristic for active and active-inductive loads; the control characteristic when the load current changes at a constant generator voltage. Analysis of the obtained characteristics makes it possible to determine the limits of regulation of the external characteristic, which is ≈40 % relative to the main magnetic flux. The obtained regulation depth allows maintaining the stability of the external characteristic for power factors not exceeding 0.9, which is the usual passport value for autonomous power plants based on synchronous generators. Comparison of the data of research conducted on the experimental setup shows sufficient convergence for engineering and practical tasks. The maximum quantitative difference is 9.3 %, which suggests the adequacy of the previously developed mathematical model. The control characteristic, constructed experimentally at constant generator voltage, is the control law of the magnetic shunt winding for the studied generator. The investigated version of a synchronous generator with a magnetic shunt should be used for autonomous power plants, renewable energy systems, and autonomous power supply systems.

A comparative study of wind turbine-generator modeling techniques: Physical modeling, subspace identification, and dynamic neural networks

The increase of the favorable impacts of wind energy on the environment and the global energy requires overall understanding of the modeling methods that are commonly used for time-based simulation of wind energy systems. This paper introduces a comprehensive comparison of three salient modeling techniques of wind energy conversion systems, which are: the physical modeling, subspace system identification, and Dynamic Neural Network (ANN). The models have been created with the different modeling philosophies with the aid of historical data-sets representing four apart days of operation. The real system incorporates (TWT-1.65) type Wind-Turbine intergated with Multi-Pole Synchronous Generators (MPSG). The compariosn provides some crucial answers to the concerns of which technique is suited for an application, consequently, the comparison includes quantitative and qualitative measures. This article can be considered as a brief guide for future researchers to have thorough understanding of the modeling concepts in the field of wind engineering.

Decentralized Frequency Regulation of Hybrid MTDC-linked Grids

This paper proposes a new strategy for optimal grid frequency regulation (FR) in an interconnected power system where regional ac grids and an offshore wind farm are linked via a multi-terminal high voltage direct<em>-</em>current (MTDC) network. In the proposed strategy, decentralized <i>H</i>_∞ controllers are developed to coordinate the operations of ac synchronous generators and hybrid MTDC converters, thus achieving optimal power sharing of interconnected ac grids and minimizing frequency deviations in each grid. To develop the controllers, robust optimization problems are formulated and solved using a dynamic model of the hybrid MTDC-linked grids with model parameter uncertainty and decentralized control inputs and outputs. The model orders of the resulting controllers are then reduced using a balanced truncation algorithm to eliminate unobservable and uncontrollable state variables while preserving their dominant response characteristics. Sensitivity and eigenvalue analyses are conducted focusing on the effects of grid measurements, parameter uncertainty levels, and communication time delays. Comparative case studies are also carried out to verify that the proposed strategy improves the effectiveness, stability, and robustness of real-time FR in MTDC-linked grids under various conditions characterized mainly by load demands, communications systems, and weighting functions.

Decentralized Frequency Regulation of Hybrid MTDC-linked Grids

This paper proposes a new strategy for optimal grid frequency regulation (FR) in an interconnected power system where regional ac grids and an offshore wind farm are linked via a multi-terminal high voltage direct<em>-</em>current (MTDC) network. In the proposed strategy, decentralized <i>H</i>_∞ controllers are developed to coordinate the operations of ac synchronous generators and hybrid MTDC converters, thus achieving optimal power sharing of interconnected ac grids and minimizing frequency deviations in each grid. To develop the controllers, robust optimization problems are formulated and solved using a dynamic model of the hybrid MTDC-linked grids with model parameter uncertainty and decentralized control inputs and outputs. The model orders of the resulting controllers are then reduced using a balanced truncation algorithm to eliminate unobservable and uncontrollable state variables while preserving their dominant response characteristics. Sensitivity and eigenvalue analyses are conducted focusing on the effects of grid measurements, parameter uncertainty levels, and communication time delays. Comparative case studies are also carried out to verify that the proposed strategy improves the effectiveness, stability, and robustness of real-time FR in MTDC-linked grids under various conditions characterized mainly by load demands, communications systems, and weighting functions.