Small Signal Stability Research Articles

Programmable Crypto-Control for IoT Networks: An Application in Networked Microgrids

In collaborative networked microgrids (NMs), distributed energy resources (DERs) utilize intelligent IoT based controllers to coordinately support various smart community functions. Meanwhile, privacy and security issues occur when IoT-based controllers interact with each other. This paper presents a cryptography-based, programmable control (crypto-control) scheme to provably preserve the privacy of DERs while ensuring fast, flexible distributed control in NMs. Specifically, it makes the following contributions: 1) a programmable crypto-control-based NMs (PCNMs) architecture, where crypto-controllers are fully virtualized, is devised; 2) a novel dynamic encrypted weight addition (DEWA) approach, which integrates an enhanced partial homomorphic encryption and a secret sharing scheme, is devised to ensure privacy preserving of distributed controls; 3) the DEWA privacy-preserving property is mathematically analyzed; and 4) a real-time DEWA-based PCNMs testbed is deployed by incorporating DEWA, real software defined networking switches, and IoT devices. The deployable crypto-control scheme is interfaced with and thoroughly verified in a Real-Time Digital Simulator environment, and the experimental results validate the effectiveness, benefits, and superiority of DEWA-based PCNMs. The inherent resilience of the DEWA-based PCNMs is validated by small signal stability analyses.

Quantifying fluctuations for dynamical power systems with stochastic excitations: A power spectral density-based method.

Fluctuations of state variables play a pivotal role in analyzing small signal stability of the power system due to the integration of renewable energy sources. This paper develops a theoretical analysis methodology by using the power spectral density (PSD) for capturing the frequency and amplitude of state variable fluctuations in heterogeneous power systems with stochastic excitations. The fluctuations in generation and consumption occurring simultaneously are modeled by stochastic Ornstein-Uhlenbeck processes. The PSDs of the state variable fluctuations can be analytically calculated. PSD-based quantities have been proposed to evaluate angle and frequency deviations. Moreover, a global performance metric has been presented to measure the synchronization stability and calculated using the PSDs of frequency deviations. The underlying mathematical relationship between the metric and the primary control effort mimicking the H2-norm performance is explained in detail. Finally, the proposed analysis methodology is numerically illustrated on the IEEE RTS-96 test case. We investigate the impact of auto-correlations of stochastic processes on stability. Our results show the metric can be an alternative quantitative index of stability. We further find that the inertia allocation does not provide significant grid stability gain under small stochastic power fluctuations.

A New Current Limiting Strategy Based on Id − ω and Iq − V Droop Characteristics for Grid-Connected Distributed Generations

Background: Increase in the output current of inverter-based Distributed Generations (DGs), which are connected to Upstream Grid (UG) and equipped with droop controller, due to UG frequency and/or voltage magnitude drop is a conventional event. The first solution to limit the output currents is using current limiter circuits at the output side of the grid-connected droop-controlled DG. Suppose the increasing output currents of this DG in continuous UG frequency drop exceeds their maximum. In that case, the current limiter circuits limit them to their maximum values. This limitation is based on the P-ω droop characteristic due to instability because the DG frequency will be greater than the UG frequency. This difference leads to sending and receiving power between DG and UG. To overcome this problem, different methods have been presented in the literature. Methods: This paper proposes a method based on a floating droop controller. In this method in order to limit output currents strictly, I_od-ω and I_oq-v droop characteristics are used instead of P-ω and Q-v characteristics, respectively. In the proposed method, instead of increasing the droop coefficients to limit currents, the droop curves are moved downward. Also, two transient supplementary signals are proposed to ensure that instantaneous currents do not have overshoot in the transient state. Results: Small-signal stability analysis shows that the system remains stable under the proposed controller. Moreover, the proposed strategy performance is indicated by time-domain simulation results using MATLAB/Simulink software under different case studies. Conclusion: The proposed new method limits the output currents of grid-connected droop-controlled DG without using current limiter circuits and performs a stable operation under the abnormal conditions of the grid.

Smooth switching control strategy with complete process of frequency support for photovoltaic grid-connected converter

The continuous increase in the penetration of renewable energy sources such as photovoltaics (PV) brings operational challenges to the traditional distribution network. With a large-scale PV integration, the power system behaves as a weak grid, which leads to more frequent and wider changes in system strength. In order to improve the system stability, the PV system is required to operate stably while providing necessary system support under different operating conditions. However, there are two issues for the PV system needs to address to satisfy this requirement. Nowadays, there are two types of control strategies for PV systems: the grid-following (GFL) control and the grid-forming (GFM) control. The two control strategies differ in inertia support capability and control stability under different operating conditions. To guarantee the grid connection stability as well as the operating stability under AC systems with different strengths, the smooth switching between the GFL and GFM is an urgent topic. In addition, how to maintain the system frequency support performance during the control switching of the PV system is also a challenge. In this paper, an advanced smooth switching control strategy is proposed to enhance the operational stability and flexibility of the PV system while maintaining the frequency support performance during the switching process. Firstly, the small-signal stability of typical control strategies of GFL and GFM under different system strengths is compared to analyze the necessity of the control switching between the two control modes. Then, a smooth switching control strategy is proposed to realize the smooth switching when AC grid strength changes. More importantly, to improve the system frequency performance and realize continuous frequency support during the switching process, a power correction function is developed on the smooth switching control strategy. The effectiveness and universality of the proposed control strategy are verified by case studies on a modified IEEE 33 bus distribution network with high PV system integration.

Passivity-Based Decentralized Criteria for Small-Signal Stability of Power Systems With Converter-Interfaced Generation

With the increasing penetration of converter-interfaced generation, it would be advantageous to specify local grid-connectivity criteria to ensure small-signal stability of the interconnected system, rather than carrying out centralized stability studies every time the connection of a new device is contemplated. Passivity of the device admittance, which is an example of a local criterion, has been used previously to avoid resonances between converter-interfaced systems and the lightly damped oscillatory modes of the network, but it is unsuitable in general due to the conservative nature of passivity. Therefore, a composite set of criteria are proposed in this paper, which include time-scale separation (slow-fast clustering) constraints on the transient behaviour, and distinct passivity constraints for the slow and fast clusters. The application of these criteria is demonstrated using a case study.

Small signal stability constrained optimal power flow model based on trajectory optimization

The essence of traditional power system’s small signal stability analysis model using the eigenvalue analysis method is to analyze the time-invariant system obtained after the approximate linearization of the system, because it only considers the equilibrium state and therefore cannot consider the power system nonlinearity. In contrast, time-domain simulation can fully consider the system nonlinearity from the whole small signal dynamic period, because it considers not only the equilibrium state but also the state after the equilibrium point. On the basis of the time-domain simulation idea, this paper proposes an SSSC-OPF (small signal stability constrained-optimal power flow) based on optimizing the rotor angle trajectory. The objective function and the SSS constraint (small signal stability constraint) of the model are extracted from rotor angle curves of each generator, and the system stability is ensured by both in concert. Compared with the general SSSC-OPF model using the SSS constraint based on the eigenvalues, the proposed model can consider nonlinearity while avoiding the errors caused by the approximate linearization in the general SSSC-OPF model, and has a higher degree of generalizability. Finally, this paper performs the simulations in three test systems, the IEEE 9-bus test system, the IEEE 39-bus test system, and the IEEE 118-bus test system, and verifies the proposed model’s effectiveness by comparing the simulation results.

Modified virtual frequency‐voltage frame control scheme with zero sharing error for islanded AC microgrids

AbstractThe active power‐virtual frequency (P‐ω′) and reactive power‐virtual voltage (Q‐V′) droop control scheme has been suggested for coordinated control of distributed energy resources (DERs) in islanded microgrids. While this method mitigates the issue of active and reactive power coupling in the droop controller, its main limitation is power‐sharing error. Due to the local property of the virtual frequency and voltage, significant steady‐state errors occur for both active and reactive power sharing. In this paper, a decentralized method is proposed to eliminate the mentioned errors without utilization of communication links. In the proposed scheme, P‐ω′ and Q‐V′ droops are realized at the microgrid point of common coupling (PCC). By employing the PCC virtual frequency/voltage for the active/reactive power sharing of all DERs, the sharing errors caused by the local property are eliminated. Small signal stability of the proposed scheme is studied, and Hardware‐in‐the‐Loop (HIL) experimental results are presented to validate the proposed method and highlight the improvements compared with the conventional P‐ω′/Q‐V′ scheme. The results verify the efficacy of the proposed method for providing accurate active and reactive power sharing while regulating the frequency and voltage close to the rated values.

A simplified model of flexible power point tracking algorithms in double-stage photovoltaic systems

Traditionally, photovoltaic (PV) systems have been operated using maximum power point tracking algorithms, which force the PV arrays to produce the maximum available power at all times. Nevertheless, distribution system operators are increasingly asking for flexible power point tracking (FPPT) algorithms, which allow the regulation of the PV power to a predefined reference value. FPPTs are difficult to tune and often have non-linear behavior. It complicates the modeling of PV systems for power system stability studies. This paper proposes a simplified model that reproduces the dc-side dynamics of a double-stage FPPT-controlled PV system. In addition to its simple tuning, the key advantage of the proposed model is that it can be easily translated into differential equations, which can be used in stability analyses. The proposed model is validated on a temporal simulation as well as a small-signal stability study.

Dynamic Security Assessment of Small-Signal Stability for Power Grids Using Windowed Online Gaussian Process

The online small-signal stability assessment of electrical power grids is typically a challenging problem due to uncertainties and parameter variations of power system dynamics as well as the incurred high computational complexity. This paper proposes a novel theoretical framework for dynamic small-signal stability assessment of power grids by estimating the region of attraction (ROA) for operating states in real time. By analyzing the latest sampling data of power grids in a fixed time window, an up-to-date training set is constructed with the aid of converse Lyapunov function, which enables us to develop an online learning approach based on Gaussian Process (GP) to assess the stability level of power grids. As a result, an iteration algorithm is designed to update the assessment parameters by learning the input-output pairs in the training set. Theoretical analysis is conducted to ensure the existence of converse Lyapunov function for differential-algebraic system that serves to describe power system dynamics, as well as to estimate the region of attraction for operating states with a given confidence level. In particular, a practical method is proposed to leverage time series of phasor measurement unit (PMU) measurements including voltage/current magnitude, phase and frequency (i.e., PMU data) of real power grids for validating the online GP approach. Moreover, validations are taken to substantiate the proposed approach by using PMU data of real smart-grid infrastructure and IEEE test cases. The proposed assessment approach contributes to situational awareness of human operators in the control station, thereby taking proactive remedial actions prior to emergencies. Note to Practitioners—This paper was motivated by the problem of online assessment of power systems security but it also applies to other industrial control systems that have stable state trajectories. Existing approaches to security assessment of power systems generally focus on the adoption of various machine-learning algorithms by treating power grid as a “black box,” which ignores the intrinsic characteristics of power systems and thus restricts the inference performance. This paper proposes a new approach using limited sampling data and system dynamics to construct a domain of stability for power grids, which can reflect the evolution of security zones and provide more accurate predictions. In this work, we mathematically characterize the domain of stability for a practical power grid by analyzing and learning its state trajectories. Then we show how the proposed approach can be efficiently implemented online, which can timely alert human operators to abnormalities. Preliminary validations suggest that this approach is feasible and effective. In future research, we will incorporate it into an energy management system and test it in other industrial processes.

Improvement of power system stability in wind connected generator by using PSAT

Voltage stability in power systems is a major problem that receives international attention. An open and free source piece of software, Power System Analysis Toolbox (PSAT) is used in this study to create a model of modified IEEE 14 bus system. Models of two recently created wind turbines—the Squirrel Cage Induction Generator (SCIG) and Doubly Fed Induction Generator (DFIG)—are connected to a modified IEEE 14 bus system. The stability of the power system is examined in this work in relation to the effects of Squirrel Cage Induction Generator (SCIG) and Doubly Fed Induction Generators (DFIG). Here, both DFIG and SCIG, which have variable speeds, are regarded as wind generators. In this work, a small signal stability investigation using SCIG and DFIG wind turbine systems was carried out on a modified IEEE 14 bus system. The results of their simulation were analysed.

Ambient data driven sensitivity-based active power scheduling for enhancing the small-signal stability of large-scale interconnected power systems

Ambient data driven sensitivity-based active power scheduling for enhancing the small-signal stability of large-scale interconnected power systems

Small-Signal Stability Assessment and Interaction Analysis for Bipolar DC Microgrids

Bipolarity in dc microgrids is desirable as it enhances the system's reliability and efficiency. However, the stability assessment for a bipolar dc microgrid is challenging due to the integration of a three-wire dc distribution line and numerous connected power converters, which is different from the stability analysis of a conventional unipolar dc microgrid. In this article, the basic form is arranged by a generalized voltage source or current source, and the simplified form is derived by looking into the different bus ports of a bipolar system in detail. Then, an impedance sum criteria-based stability conditions of different bus ports in the bipolar dc microgrid are proposed. To explore the mutual influence of the stability among different bus ports and investigate the stability issues caused by unbalanced loads connected to the symmetrical bus port, three cases are studied: 1) ± <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> bus ports are connected with balanced and unbalanced loads; 2) − <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> bus port introduces the photovoltaic unit and the energy storage unit; and 3) the 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dc</sub> bus port introduces the photovoltaic unit and the energy storage unit. Finally, a ±24 V bipolar dc microgrid platform is set up to conduct experiments, verifying the accuracy and effectiveness of the stability evaluation method.

Impedance Modeling and Mechanism Analysis of Low-Frequency Oscillations in Single-Phase MMC-RPC Integrated Vehicle-Grid Coupling System

The single-phase modular multilevel converter-based railway static power conditioner (MMC-RPC) has significant advantages in governing the power quality problems in the traction power supply system. The mechanism analysis of low-frequency oscillations (LFOs) in the MMC-RPC integrated vehicle-grid coupling system when electric multiple units are put into operation is a critical issue, which has been investigated in this article. The third-order ac admittance models of single-phase MMC-RPC and vehicle rectifiers are developed for the first time. To comprehensively study the small-signal stability of the MMC-RPC integrated vehicle-grid coupling system, this article proposes a modal analysis method based on modal phase margin and parameter sensitivity and combined with the generalized Nyquist stability criterion. It is found that LFOs around 10 Hz or 48 Hz are prone to occur due to the interactions of MMC-RPC or vehicle rectifiers with the traction power grid. To reveal the LFO mechanism, dominant modes and key parameters leading to LFOs in different working scenarios are clarified, and a series of guidelines are proposed for LFO elimination. Furthermore, the effects of control loops and power flow of MMC-RPC on system stability are revealed in detail. Finally, real-time hardware-in-the-loop experimental results validate the theoretical analysis.

Grid-tie Inverter Control Based on a Virtual Synchronous Generator with a Variable Electric Grid Density

The paper presents the results of analyzing the effectiveness of the proposed structure of a system for automatically controlling the grid-tie inverter of renewable energy sources based on a current-controlled virtual synchronous generator (CC-VSG) carried out using the developed linearized model of the proposed system and the small-signal stability analysis. The developed model has been verified, and the presented study results reflect the specific features of the proposed control system in comparison with the conventional structure of a voltage-controlled VSG (VC-VSG). It has been proven that the proposed CC-VSG model shows stable operation under small perturbations of the operating parameters over a wide range of network density variations. At the same time, an effective response speed and damping level that ensure an acceptable inertial response have been achieved. It has also been determined that the improvement of damping by tuning makes it possible to more rapidly increase the power output and has a favorable effect on the inertial response of the CC-VSG model over the entire network density variation range considered, which cannot be achieved by using the conventional VC-VSG structure.

Investigation of Oscillation and Resonance in the Renewable Integrated DC-Microgrid

This paper assessed the small-signal stability performance of a multi-converter-based direct current microgrid (DCMG). The oscillation and potential interactions between critical modes are evaluated. First, the complete analytical model of the DCMG is developed with the converter and associated controllers. Three methodologies, impedance scanning, eigenvalue analysis, and time-domain simulation, along with the fast Fourier transform (FFT) analysis, have been used to comprehensively investigate the oscillations and interactions. The simulation results show inherent weak modes, with a wide range of oscillations in the studied DCMG, which may destabilize the system under disturbances. Based on the sensitivity analysis, controller gains and DC-link capacitance are identified as the most critical parameters and substantially influence the weak modes leading to oscillations, interactions, and resonance. Finally, the performance of the various control synthesis methods is compared. This examination would help the researchers, planning, and design engineers to design and stably operate a multi converter-based DC microgrid.

A unified distributed hierarchal control of a microgrid operating in islanded and grid connected modes

AbstractTo guarantee an uninterruptable power supply, a microgrid must be able to operate in both islanded and grid‐connected modes. Hence, it is required to synchronize the voltage phasor of the point of common coupling of the microgrid with the utility grid. Therefore, a distributed cooperative hierarchal control structure is proposed that seamlessly synchronized an islanded microgrid with the utility grid. A proposed method uses a leader‐follower based consensus to regulate the voltage phasor while ensuring proportionate load sharing. A synchronization controller is designed that uses an adjustable parameter to eliminate the voltage magnitude and phase mismatch, and transmit the regulated compensation signal to the leader DGs. The leader DGs transmits these signals to the follower DGs through a cyber‐channels. Moreover, a Massachusetts Institute of Technology rule and Lyapunov function based adaptive controllers are designed to update the secondary control law parameters in case of any disturbance or uncertainty. These adaptive techniques do not require prior knowledge about the microgrid topology, loads, and impedances thus enhancing the system performance. Furthermore, a small signal stability analysis is presented to facilitate the controller parameter design criteria. Finally, the robustness and effectiveness of proposed structure is verified through simulation results in different scenarios.

Generic security-constrained inertia emulation scheme for VSI-based DC system using supercapacitor

The large-scale grid integration of renewable energy source via a voltage source inverter (VSI)-based DC system results in a continuous reduction in system kinetic inertia, deteriorating grid frequency stability. To mitigate this problem, this paper proposes a generic security-constrained inertia emulation (SIE) scheme, which integrates an appropriately-sized supercapacitor (SC) bank with a VSI-based DC system via a bidirectional DC/DC converter. Inertial response provision is enabled by an SIE control loop developed for the DC/DC converter controller to adjust the SC voltage along with the grid frequency. It is further underpinned by adding an inertia adjustment algorithm to cope with potential security risks of VSI overcurrent and DC system overvoltage. The SIE scheme features a plug-and-play advantage without modifying the original system. The SIE controller parameter optimization is also carried out through the small-signal stability analysis. The effectiveness of the SIE scheme is evaluated using a modified IEEE 39-bus test system in the presence of generator outage and grid fault.

Power system stabilizer design for ideal AVR using local measurements

In this work, the application of an Ideal automatic voltage regulator is presented for an interconnected power system. The Ideal AVR is designed using the feedback linearization technique and it is shown that the voltage regulation response with the Ideal AVR is superior to conventional linear AVR. Subsequently, a power system stabilizer is added to improve the small signal stability. The proposed control scheme is demonstrated to provide vastly superior voltage regulation and damping of the rotor mode compared to conventional control. Simulation results are presented using a sub-transient (6th order) model of the IEEE 14 generator 59 bus system.

Small-signal stability of AC/DC capacity and MMC controller voltage loop dominated systems

Small-signal stability of AC/DC capacity and MMC controller voltage loop dominated systems

Small-Signal System Frequency Stability Analysis of the Power Grid Integrated With Type-II Doubly-Fed Variable Speed Pumped Storage

This article proposes a structurally distinctive doubly-fed variable speed pumped storage (VSPS), denoted as the Type-II VSPS. Where, the speed is controlled by a back-to-back (BTB) converter while the power is controlled by a speed governor, which is the exact opposite of the control method for conventional VSPS. The small-signal frequency stability analysis of a power grid integrated with the Type-II VSPS is carried out to investigate the influence of this type of VSPS on power grid stability. Firstly, the transfer function models of hydraulic and electric subsystems of the Type-II VSPS are established, and the system small-signal stability analysis is carried out based on the obtained models and Nyquist stability criterion. Secondly, an improved system frequency response (SFR) model for the power grid integrated with Type-II VSPS is presented. Such a model is applied to investigate the frequency response of the modern power grid integrated with a large-scale VSPS (the current single unit capacity has reached 450 MW). Furthermore, the small-signal stability of the modern power grid is analyzed based on the Nyquist stability criterion. Finally, time-domain simulations and experiments are conducted to validate the effectiveness of the small-signal stability analysis.