Showing papers by "Federico Milano published in 2016"

Generalized Model of VSC-Based Energy Storage Systems for Transient Stability Analysis

Abstract: This paper presents a generalized energy storage system model for voltage and angle stability analysis. The proposed solution allows modeling most common energy storage technologies through a given set of linear differential algebraic equations (DAEs). In particular, the paper considers, but is not limited to, compressed air, superconducting magnetic, electrochemical capacitor and battery energy storage devices. While able to cope with a variety of different technologies, the proposed generalized model proves to be accurate for angle and voltage stability analysis, as it includes a balanced, fundamental-frequency model of the voltage source converter (VSC) and the dynamics of the dc link. Regulators with inclusion of hard limits are also taken into account. The transient behavior of the generalized model is compared with detailed fundamental-frequency balanced models as well as commonly-used simplified models of energy storage devices. A comprehensive case study based on the WSCC 9-bus test system is presented and discussed.

Design of Robust Distributed Control for Interconnected Microgrids

Abstract: This paper proposes a distributed control scheme to regulate the power flows among multiple microgrids operating in islanded mode. Each microgrid controller gathers information from neighboring microgrids and reduces dynamic interactions. Modal analysis and time-domain simulations are used to identify critical issues that degrade the stability of microgrids under different operating conditions. A case study comprising three interconnected microgrids is considered. Each microgrid includes distributed generation and is described through a detailed dynamic model. Time-domain analyses are carried out considering different scenarios and large disturbances. Simulation results indicate that, while conventional controllers can lead to poorly damped power oscillations among the interconnected microgrids, the proposed control scheme guarantees stability in the postdisturbance operating conditions.

Small-Signal Stability Analysis of Large Power Systems With Inclusion of Multiple Delays

Abstract: The paper focuses on the small-signal stability analysis of large power systems with inclusion of multiple delayed signals. The following four techniques are compared: 1) a Chebyshev discretization scheme of an equivalent partial differential equations that resembles the original delay differential-algebraic equations (DDAEs); 2) an approximation of the time integration operator; 3) a linear multistep discretization of the DDAEs based on an high-order implicit time-integration scheme; and 4) the well-known Pade approximants. These techniques are compared using a GPU-based parallel implementation of the Shur method and QR factorization and tested through a real-world transmission system.

Small-Signal Stability Analysis for Non-Index 1 Hessenberg Form Systems of Delay Differential-Algebraic Equations

Abstract: This paper focuses on the small-signal stability analysis of systems modelled as differential-algebraic equations and with inclusions of delays in both differential equations and algebraic constraints. The paper considers the general case for which the characteristic equation of the system is a series of infinite terms corresponding to an infinite number of delays. The expression of such a series and the conditions for its convergence are first derived analytically. Then, the effect on small-signal stability analysis is evaluated numerically through a Chebyshev discretization of the characteristic equations. Numerical appraisals focus on hybrid control systems recast into delay algebraic-differential equations as well as a benchmark dynamic power system model with inclusion of long transmission lines.

Semi-Implicit Formulation of Differential-Algebraic Equations for Transient Stability Analysis

Abstract: The paper proposes a semi-implicit formulation of the differential-algebraic equations (DAEs) describing power system models for transient stability analysis. This formulation, if coupled to an implicit integration scheme, shows two relevant advantages with respect to the conventional explicit formulation: (i) reduce the computational burden; and (ii) increase the sparsity of the Jacobian matrix of the system. The proposed model also allows using null time constants and thus simplifies the computer implementation of the DAEs. The properties and the performance of the proposed semi-implicit formulation and the conventional explicit one are compared through a dynamic 21,177-bus model of the European transmission system.

Analogy and Convergence of Levenberg’s and Lyapunov-Based Methods for Power Flow Analysis

Abstract: This letter focuses on the power flow problem and shows the formal analogy between the Levenberg’s method and a fictitious ODE built using Lyapunov’s second stability criterion. The letter also illustrates theoretical caveats and numerical issues of both methods. In particular, the case study, based on a 2383-bus system, shows that the fixed points of these methods are not necessarily a solution of the power flow problem.

SDE-based wind speed models with Weibull distribution and exponential autocorrelation

Abstract: This paper discusses three approaches to construct wind speed models based on Stochastic Differential Equations (SDEs). The methods are applied to construct models able to simulate wind speed trajectories that are statistically described by means of the Weibull distribution and the exponential autocorrelation. The ability of the three models to reproduce stochastic processes with the above indicated statistical properties is duly studied and compared. With this aim, wind speed measurements recorded in a weather station located in Ireland are analyzed. The parameters obtained in this analysis are used to set up the developed models. Finally, the statistical properties of the trajectories generated by the three models are compared with the statistical properties of the considered wind speed data set.

Comparison of bus frequency estimators for power system transient stability analysis

Abstract: The paper presents a study on the dynamic response of power system frequency control devices considering different approaches to estimate bus frequencies in power system simulators. The frequency signals considered in this paper are obtained based on the center of inertia, a commonly-used washout filter that approximates the derivative of the bus voltage phase angle, and a frequency divider formula developed by the authors. The dynamic behavior of frequency control devices such as thermostatically regulated loads is compared considering the three signals above. Different scenarios are discussed based on the IEEE 14-bus and New England 39-bus, 10-machine test systems.

Validation of the Ornstein-Uhlenbeck process for load modeling based on µPMU measurements

Abstract: This paper investigates the suitability of the Ornstein-Uhlenbeck process, driven by various Levy processes, for load modeling at the distribution network level. An indepth description outlining the procedure for estimating the required parameters is given. Both the statistical properties of the simulated processes and its auto-correlation is compared to that of the field measured data to demonstrate the suitability of the proposed methodology. The development of such stochastic models is facilitated by measures obtained from micro-synchrophasors (µPMU's). The data from these devices serves to demonstrate the need to model the volatility along with validating a model attempting to model said volatility.

Impact of variability, uncertainty and frequency regulation on power system frequency distribution

Abstract: This work originates from the observation of the frequency distribution of the Irish system as obtained from a Frequency Disturbance Recorder lent to the last author by the University of Tennessee. The probability density function of such a distribution appears to be bimodal. The paper first investigates how stochastic sources, in particular, load and wind power estimation errors, impact on the distribution of the frequency of a high-voltage transmission system. Then, possible routes to obtain a bimodal distribution of the frequency are explored and the most likely cause that leads to the observed behaviour of the Irish system is identified. Finally, the paper presents a comparison of different frequency regulation strategies and their impact on the distribution of the frequency. A sensitivity analysis of wind speed and load parameters is presented and discussed based on the IEEE-14 bus system.

The Probe-Insertion Technique for the Detection of Limit Cycles in Power Systems

Abstract: The paper proposes a technique to accurately and efficiently locate periodic steady-state solutions of electric power systems. This technique is based on an enhanced version of the time-domain shooting method (TDSM) and the probe-insertion technique (PIT). The latter has been successfully applied to low-power electronic circuits but it is innovative for the study of electromechanical steady-state periodic behavior of power systems. With this aim, the paper discusses the inherent criticalities of the conventional formulation of power system models (PSMs). Then, a novel formulation is proposed to accommodate the hypotheses and mathematical requirements of the TDSM and PIT. The effectiveness and numerical efficiency of the proposed model and technique are discussed through two case studies based on the IEEE 14-bus and WSCC 9-bus systems.

Automatic voltage and reactive power control in distribution systems: Dynamic coupling analysis

Abstract: The paper focuses on the dynamic response of a secondary voltage control scheme for distribution networks. The proposed control is based on a hierarchical architecture and is similar to the hierarchical voltage control implemented in some countries in high voltage transmission systems. The objective of the paper is to show a possible undesired dynamic coupling of different reactive power control loops of network generators. The effect of an algebraic decoupling matrix of the secondary voltage control as well as its effects simulated on a real-world case study are also duly discussed.

Comparison of different control strategies for energy storage devices

Abstract: This paper compares three control strategies for energy storage devices. Detailed formulations and implementation procedures of PI, sliding mode, and H-infinity controllers are presented and discussed. The dynamic performance of each control technique is also studied and compared. With this aim, the paper duly discusses a comprehensive case study based on the IEEE 14-bus test system with inclusion of a wind power plant and an energy storage device.

On Current and Power Injection Models for Angle and Voltage Stability Analysis of Power Systems

Abstract: This letter provides a comparison between the current and power injection models for angle and voltage stability analysis of power systems. Traditionally, it is believed that the current injection model is computationally more efficient. On the other hand, the power injection model requires computing the products of currents and voltages and, hence, is expected to be computationally more demanding than the current injection one. This letter compares the two approaches using a unique framework. The two formulations are compared through a dynamic 1479-bus model of the all-island Irish transmission system.

An Efficient Representation Format for Fuzzy Intervals Based on Symmetric Membership Functions

Abstract: This article addresses the execution cost of arithmetic operations with a focus on fuzzy arithmetic. Thanks to an appropriate representation format for fuzzy intervals, we show that it is possible to halve the number of operations and divide by 2 to 8 the memory requirements compared to conventional solutions. In addition, we demonstrate the benefit of some hardware features encountered in today’s accelerators (GPU) such as static rounding, memory usage, instruction-level parallelism (ILP), and thread-level parallelism (TLP). We then describe a library of fuzzy arithmetic operations written in CUDA and C++. The library is evaluated against traditional approaches using compute-bound and memory-bound benchmarks on Nvidia GPUs, with an observed performance gain of 2 to 20.

Periodic small-signal analysis as a tool to build transient stability models of VSC-based devices

Abstract: The paper introduces a novel approach to derive a dynamic model of devices with inclusion of Voltage Source Converter (VSC) devices suitable for transient angle and voltage stability analysis of power systems. With this aim, we treat the VSC as a nonlinear switched set of equations and apply a time-domain shooting method to define the behaviour of such model at the fundamental frequency of the system. Then the time-varying small-signal model of the VSC is derived through periodic small-signal analysis. The resulting model is defined in terms of a transfer function from which we can define a lumped equivalent circuit of the original device. The proposed approach is discussed and tested through the study of the transient response of a Static VAR Compensator (STATCOM) device connected to the well-known IEEE 14-bus system.

Delay-based numerical stability of the partitioned-solution approach

Abstract: This paper proposes a technique to evaluate the numerical stability and accuracy of the Partitioned-Solution Method (PSA) for the time domain integration of the Differential Algebraic Equations (DAEs) that are used for power system angle and voltage stability analyses. The partitioned approach consists in solving differential equations and algebraic constraints separately. While efficient, this technique introduces a “mismatch” between state and algebraic variables. The paper states the formal analogy of such a mismatch with a time delay of algebraic variables. Then a Small-signal Stability Analysis (SSSA) for Delay Differential Algebraic Equation (DDAE) is applied to define the numerical stability of the PSA as a function of the integration time step. Results are tested using the IEEE 14-bus system as well as a 1,479-bus model of the all-island Irish system.

Model Predictive Control based AGC for multi-terminal DC grids

Abstract: With increasing DC grid connections between non-synchronous AC systems it is desirable that DC connections would take a role in frequency regulation for connected AC grids. A number of primary and secondary P and PI based controllers have been designed previously for this purpose. Here Model Predictive Control is proposed for including DC power controllers in the provision of Automatic Generation Control.

On the Modelling of Zero Impedance Branches for Power Flow Analysis

Abstract: This letter compares three models of zero impedance branches for power system analysis and proposes a new, simple yet reliable model of such a component based on a steady-state droop control approach. The proposed model proves to be numerically robust and allows representing both short lines as well as the internal electrical nodes that compose substations. Parallel and lossy zero impedance branches can also be straightforwardly defined. A detailed discussion of the features and numerical performance of all models considered in this letter is carried out by means of the a 21,177-bus model of the European ENTSO-E transmission.

On the stochastic nature of deterministic power system models for dynamic analysis

Abstract: The paper presents a study on the impact of uncertainty on the dynamic response of electric power systems. Three sources of uncertainty are considered, namely, (i) uncertainty in the values of the parameters of physical devices; (ii) uncertainty in the models of dynamic devices; and (iii) variations of the parameters and the numerical scheme to integrate the differential algebraic equations that describe the system. A Monte Carlo analysis is used to define the impact of each source of uncertainty as well as all sources together on the dynamic response of the well-known IEEE 14-bus system.

Stability-constrained unit commitment with water network loads

Abstract: The paper presents an analysis of the economical and technical impact of Water Network Loads (WNLs) on the operation of power systems. The paper also proposes an iterative technique to solve both a unit commitment problem with the inclusion of conventional power generation, wind power and WNLs and a N-1 contingency analysis based on time-domain simulations. At each iteration, if the WNLs schedule in a given period is not acceptable for some of the considered contingencies, the unit commitment problem is solved again constraining the amount of dispatchable WNLs. The proposed technique is tested using the New England 39-bus 10-machine system adapted to include wind generation and WNLs.

Design of MPC-based controller for a Generalized Energy Storage system model

Abstract: This paper presents a control strategy based on Model Predictive Control for Energy Storage Systems. The mathematical formulation of this controller is outlined, and the procedure for applying this controller to a Generalized Energy Storage model is then documented. The dynamic performance of the control strategy presented is compared with that of a PI-based control technique. A comprehensive case study based on the New England 39-bus 10-machine test system with the inclusion of Energy Storage Systems is presented and discussed.

Shooting-based stability analysis of power system oscillations

Abstract: This chapter shows an application of TDSM and PIT for the determination of limit cycles in power systems. The main advantage of the proposed technique is the ability to determine both stable and unstable periodic orbits in a unique framework. The proposed technique can also cope with hard limits and/or discontinuities, such as switched capacitor banks, on the right-hand side of differential equations. Moreover, the technique shows a lower computational burden than other techniques proposed in the literature, e.g., Reference 21. This chapter also discusses an unconventional formulation of the PSM to cope with the requirements of the TDSM. The main feature of the proposed model concerns the representation of the speed reference of synchronous machines. This model is basically a generalized COI and involves a recast of the variables to avoid aperiodic drifting of machine angles. The proposed generalization of the COI indicates that a proper reformulation of synchronous machine equations allows applying techniques that are well assessed in circuit analysis. Rethinking PSMs based on rigorous formalism appears as a challenging field of research.

Accuracy and Precision in Computer-Assisted Methods for Orthopaedic Surgery

Abstract: This chapter reviews the major approaches to the definition of bone cutting accuracy in the field of computer-assisted orthopaedic surgery. The first part of the chapter reviews the different concepts of accuracy found in literature, from localization in image-guided systems to osteotomy accuracy evaluation both using navigation systems and in patient-specific instruments. The second part of the chapter focuses in the efforts toward the standardization of different computer-assisted accuracy measurements in orthopaedic surgery.