Presence Of Constant Power Loads Research Articles

Dynamic stability analysis of the aircraft electrical power system in the more electric aircraft concept

This paper presents the modelling and analysis process of the electrical power management system on board an electrified aircraft conforming to the More/All Electric Aircraft concept. The main objective of the study is to assess the stability of the Electric Power Distribution System under different operational conditions, including the aspect of constant power loads. The paper describes the structure of the system, in which the key role is played by a synchronous generator and a three-phase rectifier converting alternating current AC into direct current DC. To solve the problem, modeling methods in the Matlab/Simulink environment were used, which enabled the analysis of the dynamic properties of the system and the assessment of stability under various types of loads. The obtained test results show that the presence of constant power loads can lead to instability in the EPDS system, manifested by voltage and current oscillations exceeding the standards specified in the MIL-STD-704E standard. The paper also provides tools for predicting system stability without the need to conduct full stability tests, which is important for the design of modern aviation power systems. The final section of the work presents the research results obtained and the resulting significant insights and practical conclusions.

Experimental Evaluation of the Robust Controllers Applied on a Single Inductor Multiple Output DC-DC Buck Converter to Minimize Cross Regulation Considering Parametric Uncertainties and CPL Power Variations

This paper presents two control design strategies for voltage regulation in a single inductor dual-output DC-DC buck converter system. Based on a nominal multiple input multiple output plant model and performance requirements, both a Linear Quadratic Regulator and a Decoupled PI control law are designed to control the power converter system under parametric uncertainties such as voltage source variation, constant power load variation, and load resistance variation. Therefore, the converter can cascade operation, which may cause the undesired effects of voltage oscillation and reduce the system’s stability margin. The control performance was assessed under both the uncertainties of resistive loading and the power variation in a constant power load. A single inductor dual-output DC-DC buck converter board was developed for experimental tests. The experimental results show that the Linear Quadratic Regulator strategy, compared to the PI strategy, presented a robust performance in the presence of parametric uncertainties in the resistive load-bearing; however, it was sensitive to uncertainties due to the presence of constant power loads.

A long-horizon move-blocking based direct power model predictive control for dynamic enhancement of DC microgrids

This research paper presents a novel long-horizon move-blocking based direct power model predictive control (DPMPC) strategy, uniquely designed to enhance the dynamic performance of boost converters in the grid-connected mode within DC microgrids. A precise dynamic model is developed considering a boost converter connected to a DC-link supplying constant power and resistive loads. To predict the system's dynamic behavior over an extended interval and enhance its performance in the presence of constant power loads, the long-horizon based finite control set model predictive control (FCS-MPC) method is introduced. To address the computational complexity associated with the conventional long-horizon DPMPC approach, a move-blocking (MB) strategy is incorporated into FCS-MPC, reducing the computational burden while improving the dynamic performance of the boost converter. Unlike recent studies that utilize DPMPC with short prediction interval, this paper presents evidence that a longer prediction interval is crucial for maintaining system stable and enhancing the dynamic response and also utilizing MB to make the control implementable in the real-time. The simulation results conducted using MATLAB/Simulink demonstrate the effective performance of the proposed strategy across various operating conditions of the boost converter. Experimental results further validate the strategy's capability to enhance the dynamic performance of the boost converter. Importantly, the experimental findings confirm the feasibility of implementing the proposed long-horizon move-blocking DPMPC strategy in real-time applications.

Dynamic Analysis, Stability and Design of Grid Forming Converters With PI-Based Voltage Control in DC and 3-Phase AC Microgrids

This paper analyzes the dynamic behavior of the voltage control loop based on proportional-integral regulators, commonly used for grid-forming converters in 3-phase AC and DC Microgrids and applications that involve a DC-link voltage control. The paper proposes a simple and accurate generalized analysis useful both for the system characterization and design. Two different control schemes, based on linear (Direct Voltage Control, DVC) and quadratic voltage feedback (Quadratic Voltage Control, QVC), are analytically studied, simulated and experimentally tested, demonstrating a superior performance of the QVC under the presence of constant power loads. The operation limits, the system stability and the disturbance rejection capability are analyzed considering the effect of control and plant parameters and the effect of the different types of disturbances and the operating point, taking into account the non-linearities of the system. The analysis is mainly focused on the effect of constant power loads given their negative impact on the system performance. The study provides a generic procedure for the analysis and design of proportional-integral voltage controllers, including the selection of the system capacitance for meeting specific dynamic specifications while considering system characteristics as the load level, the stability margins and the maximum voltage deviation under disturbances.

A move blocking based direct voltage model predictive control to enhance the dynamic performance of DC microgrids containing constant power loads

AbstractHere, a move blocking (MB) based direct voltage model predictive control (DVMPC) strategy is introduced to enhance the dynamic performance of a DC microgrid in presence of constant power loads (CPLs). For this aim, an automatic discrete dynamic model is first developed for a boost converter. Considering the CPL effects on the dynamic model of the boost converter, a model predictive control is then designed to directly regulate the output voltage of the converter. Move blocking strategy is finally integrated into DVMPC in order to extend the prediction horizon, and consequently, dealing with the non‐minimum phase characteristic of the boost converter. The dynamic performance of the boost converter with a CPL load in both continuous conduction mode (CCM) and discontinuous conduction mode (DCM) is evaluated using MB‐based DVMPC and traditional control strategies. The simulation results conducted using MATLAB/Simulink demonstrate that the proposed approach not only enhances the dynamic performance of the DC microgrid, but also reduces the computational burden on the processor. Moreover, experimental results have been performed to validate the proposed strategy. Finally, the stability analysis of the proposed direct voltage control is provided.

Impact of Virtual Inertia on DC Grid Stability With Constant Power Loads

Virtual inertia is an effective control approach to attenuate sudden voltage changes during transient events in low-inertia DC grids. While methods have been proposed to implement virtual inertia, its impact on DC grid stability in the presence of constant power loads (CPLs) remains unclear. In this paper, we perform a rigorous stability analysis for DC grids with CPLs powered by virtual-inertia-enhanced converters. We derive a closed-form stability criterion that can be used to evaluate the impact of virtual inertia on the system stability, and demonstrate that, given a set of system parameters, the stability of a DC grid powering CPLs can be improved for a range of virtual inertia designs. We provide analytical expressions for the optimal virtual inertia that improves stability and for the maximum virtual inertia that does not deteriorate stability. In addition, we present a step-by-step guideline to design a stable DC grid with virtual inertia. Test results are presented to validate the analysis.

Effect of Endogenous Failure Events on the Survivability of Turboelectric Distributed Propulsion System

Recent advancements in aircraft electrification have led to the introduction of turboelectric distributed propulsion (TeDP). For instance, NASA's N3X airplane aims to curb jet fuel emissions with the aid of TeDP. However, it is crucial to analyze the survivability of the TeDP system during extreme conditions. The endogenous failure events are of specific interest as they were found to cause a significant number of accidents for commercial aircraft. While the distribution reconfiguration is necessary to meet the critical load demands under extreme failure events, it can also create a transient overload condition in the turboshaft engine. The power system survivability is further deteriorated in the presence of constant power loads. In this article, a mathematical analysis of the survivability of the system is presented to make the aircraft power system highly resilient to endogenous failure events. A power system collapse mitigation strategy is proposed by adding an energy storage system. Moreover, the analytical expressions are formulated to size the energy storage unit to prevent the system collapse. Various failure conditions are modeled using PSCAD/EMTDC to study the minimum energy storage required to prevent system collapse.

Distributed resilient control against denial of service attacks in DC microgrids with constant power load

Recent events have shown that cyber attacks are becoming real threats to the power system reliability and resiliency, and there is no exception to the DC microgrids which would become popular in the future. Currently, most secondary controls in DC microgrids heavily rely on communications, making them specifically vulnerable to cyber attacks. This paper presents a resilient distributed control based on the average consensus algorithm and the proportional-integral (PI) consensus algorithm to enhance the system resilience against denial of service attacks and improve the microgrid stability, particularly in the presence of constant power loads. The proposed control casts the average voltage restoration problem into an optimization problem, and because of this, the voltage control is immune to the communication damage caused by malicious denial of service attacks. Moreover, the small-signal stability model of the DC microgrid with distributed energy storages and constant power loads is established, and the impacts of varying constant power loads, controller parameters and communication topology on the system stability are analyzed. Simulations are conducted to verify the effectiveness of the proposed method.

Dynamic Stability Performance of Autonomous Microgrid Involving High Penetration Level of Constant Power Loads

Nowadays, behaving as constant power loads (CPLs), rectifiers and voltage regulators are extensively used in microgrids (MGs). The MG dynamic behavior challenges both stability and control effectiveness in the presence of CPLs. CPLs characteristics such as negative incremental resistance, synchronization, and control loop dynamic with similar frequency range of the inverter disturb severely the MG stability. Additionally, the MG stability problem will be more sophisticated with a high penetration level of CPLs in MGs. The stability analysis becomes more essential especially with high-penetrated CPLs. In this paper, the dynamic stability performance of an MG involving a high penetration level of CPLs is analyzed and investigated. An autonomous MG engaging a number of CPLs and inverter distributed generations (DGs) is modeled and designed using MATLAB. Voltage, current, and power controllers are optimally designed, controlling the inverter DGs output. A power droop controller is implemented to share the output DGs powers. Meanwhile, the current and voltage controllers are employed to control the output voltage and current of all DGs. A phase-locked loop (PLL) is essentially utilized to synchronize the CPLs with the MG. The controller gains of the inverters, CPLs, power sharing control, and PLL are optimally devised using particle swarm optimization (PSO). As a weighted objective function, the error in the DC voltage of the CPL and active power of the DG is minimized in the optimal problem based on the time-domain simulation. Under the presence of high penetrated CPLs, all controllers are coordinately tuned to ensure an enhanced dynamic stability of the MG. The impact of the highly penetrated CPLs on the MG dynamic stability is investigated. To confirm the effectiveness of the proposed technique, different disturbances are applied. The analysis shows that the MG system experiences the instability challenges due to the high penetrated CPLs. The simulation results confirm the effectiveness of the proposed method to improve the MG dynamic stability performance.

Decentralized Voltage Control of Autonomous DC Microgrids With Robust Performance Approach

In this article, we propose an optimal decentralized robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control system for the voltage control problem of autonomous uncertain dc microgrids consisting of multiple distributed generations (DGs) with general topology. The one-degree-of-freedom (DoF) structure of the developed control system guarantees the robust performance of the system as well as its robust stability against various sources of uncertainty, such as plug-and-play (PnP) operation of the DGs, topology changes, large load perturbations, different subsequent system changes, and the presence of constant power loads (CPLs). To that end, the uncertain dc microgrid is modeled as a Linear Time-Invariant (LTI) polytopic state-space system. Then, a state-feedback control technique based on linear matrix inequality (LMI) with linearly parameter-dependent (LPD) Lyapunov matrices is implemented on the uncertain dc microgrids. The proposed controller does not require any sort of communications, and the robust performance property of the controller eliminates the need for prefilter design. The efficiency of the proposed controller is analyzed by simulating different case studies through SimPowerSystems Toolbox in MATLAB. Finally, the performance of the proposed control method is validated via experimental studies.

Energy management and damping improvement of a DC microgrid with constant power load using interconnection and damping assignment-passivity based control

This paper deals with (i) damping improvement and (ii) energy management of a DC microgrid for improvement of its stability. The direct current (DC) microgrid has a solar-photovoltaic system as a renewable source and fuel cell-battery combination as a backup system to supply power to constant power loads (CPLs). The presence of CPLs in a DC microgrid makes the stability problem more challenging since the negative impedance characteristics of CPLs bring instability into the system. A control approach using interconnection and damping assignment-passivity based control (IDA-PBC) is proposed in this paper to address both the objectives. The proposed control approach provides an efficient energy management, the required damping and also maintains the stability by making the system passive. The tuning parameters of the control laws are adapted incorporating the state of charge (SoC) for the effective energy management. In addition, an integral action is added with the proposed control laws to eliminate the steady-state error in the voltage level of the DC bus and load bus. The proposed IDA-PBC control along with an integral action is compared with four other control approaches, and reveals its better performances. The MATLAB/Simulink results show that the proposed control technique provides better responses in terms of providing damping and effective energy management.

Second-Order Cone Approximation for Voltage Stability Analysis in Direct-Current Networks

In this study, the voltage stability margin for direct current (DC) networks in the presence of constant power loads is analyzed using a proposed convex mathematical reformulation. This convex model is developed by employing a second-order cone programming (SOCP) optimization that transforms the non-linear non-convex original formulation by reformulating the power balance constraint. The main advantage of the SOCP model is that the optimal global solution of a problem can be obtained by transforming hyperbolic constraints into norm constraints. Two test systems are considered to validate the proposed SOCP model. Both systems have been reported in specialized literature with 6 and 69 nodes. Three comparative methods are considered: (a) the Newton-Raphson approximation based on the determinants of the Jacobian matrices, (b) semidefinite programming models, and (c) the exact non-linear formulation. All the numerical simulations are conducted using the MATLAB and GAMS software. The effectiveness of the proposed SOCP model in addressing the voltage stability problem in DC grids is verified by comparing the objective function values and processing time.

Improved DC-Link Voltage Regulation Strategy for Grid-Connected Converters

In this article, an improved dc-link voltage regulation strategy is proposed for grid-connected converters applied in dc microgrids. For the inner loop of the grid-connected converter, a voltage modulated direct power control is employed to obtain two second-order linear time-invariant systems, which guarantees that the closed-loop system is globally exponentially stable. For the outer loop, a sliding mode control strategy with a load current sensor is employed to maintain a constant dc-link voltage even in the presence of constant power loads at the dc-side, which adversely affect the system stability. Furthermore, an observer for the dc-link current is designed to remove the dc current sensor at the same time improving the reliability and decreasing the cost. From both simulation and experimental results obtained from a 15-kVA prototype setup, the proposed method is demonstrated to improve the transient performance of the system and has robustness properties to handle parameter mismatches compared with the input-output linearization method.

Nonlinear Model Predictive Stabilization of DC–DC Boost Converters With Constant Power Loads

This article addresses the problem of stabilization of dc–dc converters feeding constant power loads (CPLs). An explicit model predictive control is developed based on an average model of a boost converter. The optimal control law is obtained offline by solving a multiparametric nonlinear programming problem over a simplex partition of the state space. The performance is validated through simulation and experimental studies. A delay compensation scheme is included for online implementation. The control is able to drive the output voltage to the desired level and stabilize it despite the instability effects produced by the presence of CPLs. It also features robustness against abrupt changes on the input voltage and the load.

Distributed Event-Triggered $H_\infty$ Consensus Based Current Sharing Control of DC Microgrids Considering Uncertainties

The uncertainties caused by sources [such as wind power and photovoltaic (PV)], load switchings, and the equivalent negative impedance of constant power loads (CPLs) commonly exist in microgrids and often undermine the system stability and damping. In this article, a distributed secondary $H_\infty$ consensus approach with an event-triggered communication scheme is proposed for dc microgrids to achieve accurate current sharing and satisfactory performance in the presence of CPLs and uncertainties. Different from many existing works, the proposed event-triggered communication scheme only requires the information at every fixed sampled interval without the Zeno-behavior and continuous-time information. Then, global large-signal stability of the dc microgrid with CPLs and uncertainties under the proposed distributed control is analyzed, where a primary plug-and-play (PnP) voltage controller is considered for each distributed generator (DG). Furthermore, effects of key controller parameters and CPLs on the dynamic performance is analyzed, and a PnP design method is presented for the primary–secondary controllers. With the proposed method, full PnP operation of the dc microgrid can be realized and communication burden can be considerably reduced. Finally, simulation results are presented to validate the proposed method.

Admittance matrix computation and stability analysis of droop controlled DC micro-grids with CPL

In this paper, an analytical method of computing the admittance matrix is introduced that facilitates the stability analysis of DC micro-grid systems, in presence of constant power loads (CPLs). Due to their nonlinear behaviour, CPLs can yield instability in DC micro-grids; an effect referred to as ‘negative impedance instability’. The proposed method is particularly useful when a typical controller (droop control, voltage regulation) is designed to control the DC bus voltage of the micro-grid, as it allows the factorisation of the admittance matrix separating singular matrices. In doing so, the closed-loop stability proof can be more easily approached by isolating the singularities and, then employing straightforward linear algebra tools to arrive at the stability conditions. In order to validate the proposed approach, compute the admittance matrix and test the stability conditions, a DC micro-grid with n DC/DC power converters connected to a CPL is considered. Simulation results are also displayed to demonstrate the desired operation of the DC micro-grid control and design framework.

Power flow approximation for DC networks with constant power loads via logarithmic transform of voltage magnitudes

This paper proposes a logarithmic transformation of voltages (LTVM) for the power flow in DC grids. This problem is non-linear due to the presence of constant power loads (CPLs), which also introduce a negative resistance effect that can create numerical instability for conventional algorithms. The proposed methodology is applied to dc-microgrids, dc-distribution and multi-terminal high voltage DC transmission (MT-HVDC). Two main approximations are presented and compared in terms of computational performance and the accuracy of the solution. Simulation results performed in Matlab/Octave demonstrate the advantages of the proposed methodology using a complete set of test systems, from low to high voltage applications. The proposed methodology does not require any consideration about the topology of the grid (radial or meshed) or the number of constant power loads.

Decentralised robust T‐S fuzzy controller for a parallel islanded AC microgrid

This study proposes a decentralised robust fuzzy control strategy for islanded operation of an AC microgrid with voltage source inverters. The objective is to design a robust controller for regulating the load voltage and sharing power among distributed generators (DGs) in the presence of uncertainties in the system and non-linear loads. The AC microgrid consists of parallel DGs connected to a main AC bus. A Takagi-Sugeno fuzzy approach is developed in this article to achieve stability and desired performance in dealing with non-linearities in the islanded microgrid and H ∞ criterion is used to obtain a robust control strategy in presence of uncertainties raised by unmodelled and high frequency dynamics. Therefore, a non-convex condition in H ∞ optimisation problem is converted to a convex linear matrix inequality (LMI) condition and is solved by MATLAB LMI toolbox. In order to develop a decentralized system, P–f and Q–V droop controllers are used to specify set-points for local inverter controllers in each DG. The effectiveness of the proposed control strategy in presence of constant power load and DG accidental outage is validated by the simulation of a microgrid test system in MATLAB SimPowerSystems toolbox. Comparison with cascaded proportional integral controller shows advantages of robust T-S controller.

Decentralized monotonicity-based voltage control of DC microgrids with ZIP loads

In this paper we propose a monotonicity-based approach for decentralized voltage control of dominantly resistive DC microgrids with ZIP loads. For this purpose, we introduce the notion of set of assignable robust controlled decentralized invariants for the system. Then, upon selection of a desired invariant, an inner decentralized voltage control is designed and a criteria for convergence of the system’s trajectories to an equilibrium point—in presence of constant power loads (CPLs)—is established. Interestingly, a simple realization of the proposed controller corresponds to a piece-wise voltage droop control, the gain of which are determined by the control specifications. A discussion on the selection of appropriate invariants is also carried out and the obtained theoretical results are validated on a 8-terminal benchmark.

Passivity-Based Control of Switched Reluctance-Based Wind System Supplying Constant Power Load

This paper presents a passivity-based control (PBC) scheme for the switched reluctance generator (SRG) in small-scale wind energy conversion systems for dc microgrid applications. The main objective is to stabilize the output voltage in case the system supplies constant power loads (CPLs) and operates with maximum power point tracking (MPPT). Stability improvement and dc-link ripple reduction in the presence of CPLs is achieved using system-level modeling of SRG-based dc microgrid through the Euler-Lagrange system (ELS) from the viewpoint of the machine physical structure. Compared with other control methods, the proposed MPPT method based on passivity-based speed controller employs the back electromotive force (EMF) in the generation process as a position-dependent voltage source to overcome the major challenge of SRG complicated uncertain dynamic model. To deal with the time-varying inductance and back EMF of SRG, an adaptation mechanism is incorporated in the proposed adaptive PBC and the control design is constructed by using the Lyapunov theorem where the closed-loop stability is ensured. The effectiveness of the proposed method in avoiding instability effects of SRG and CPL with voltage ripple reduction and precise wind turbine speed tracking is investigated with simulation results and validated with experimental by using a four-phase, 8/6 SRG drive system.