Nonlinear Ac Research Articles

Network-constrained thermal unit commitment for hybrid AC/DC transmission grids under wind power uncertainty

The day-ahead energy and reserve management considering transmission restrictions and voltage security limits is a challenging task for large-scale power systems in the presence of volatile renewable energy sources. In this paper, a two-stage robust optimization model is proposed for the joint scheduling of energy and reserve for hybrid AC/DC transmission grids. The optimal schedule, including the commitment, power dispatch, and reserve allocations is computed subject to the feasibility of nonlinear AC and DC network constraints under a specified set of scenarios. Furthermore, the proposed decomposition approach renders the second stage (network security evaluations) into standard optimal power flow problems, which addresses the scalability issues observed with existing methods. A second-order cone relaxation is applied to nonlinear AC and DC network constraints to improve the computational tractability. In simulations, the proposed robust optimization model is illustrated using a recently proposed hybrid AC/DC transmission grid architecture with a specific topology. The results demonstrate the effective utilization of the grid capacity to accommodate more demand and renewable energy sources. This hybrid AC/DC transmission grid architecture induces exactness of the convex relaxation, supporting the validity of the optimal day-ahead schedule. The efficiency and computational performance of the proposed method is compared to the existing literature and the robustness is verified using an out-of-sample analysis.

Chance-Constrained AC Optimal Power Flow: A Polynomial Chaos Approach

As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chance-constrained optimal power flow while explicitly considering the full nonlinear ac power flow equations and stochastic uncertainties. We use polynomial chaos expansion to model the effects of arbitrary uncertainties of finite variance, which enables to predict and optimize the system state for a range of operating conditions. We apply chance constraints to limit the probability of violations of inequality constraints. Our method incorporates a more detailed and a more flexible description of both the controllable variables and the resulting system state than previous methods. Two case studies highlight the efficacy of the method, with a focus on satisfaction of the ac power flow equations and on the accurate computation of moments of all random variables.

Two-Dimensional Tandem Mass Spectrometry in a Single Scan on a Linear Quadrupole Ion Trap.

A two-dimensional tandem mass spectrometry (2D MS/MS) scan has been developed for the linear quadrupole ion trap. Precursor ions are mass-selectively excited using a nonlinear ac frequency sweep at constant rf voltage, while simultaneously, all product ions of the excited precursor ions are ejected from the ion trap using a broad-band waveform. The fragmentation time of the precursor ions correlates with the precursor m/z value (the first mass dimension) and also with the ejection time of the product ions, allowing the correlation between precursor and product ions. Additionally, the second mass dimension (product ions' m/z values) is recovered through fast Fourier transform of each mass spectral peak, revealing either intentionally introduced "frequency tags" or the product ion micropacket frequencies, both of which can be converted to product ion m/z through the classical Mathieu parameters, thereby revealing a product ion mass spectrum for every precursor ion without prior isolation. We demonstrate the utility of this method for analyzing a broad range of structurally related precursor ions, including chemical warfare agent simulants, fentanyls and other opioids, amphetamines, cathinones, antihistamines, and tetracyclic antidepressants.

Energy Trading and Market Equilibrium in Integrated Heat-Power Distribution Systems

The increasing utilization of cogeneration plants and energy conversion facilities accelerates the integration of energy systems, which introduces both opportunities and challenges into system operation and management. Thorough mathematical models and analytical methods that take into account the energy flow interdependence and strategic behaviors in multi-carrier energy systems are highly desired. This paper studies an integrated heat-power distribution system from the market perspective. The nonlinear AC optimal power flow (OPF) model is used to clear the distribution power market, which exactly accounts for network losses. To facilitate computation, convex relaxation is applied and polyhedral outer approximation of second-order cone is performed, leading to a linear market clearing model. An optimal thermal flow (OTF) model is employed to clear the heat market. Energy consumptions of heating devices are charged according to locational marginal prices. The market equilibrium is interpreted by a fixed point between OPF and OTF and reformulated as a mixed-integer linear program. Dedicated optimization models are set forth to investigate the market impact of strategic providers and elastic demands in which the market equilibrium condition serves as constraint. Case studies validate the effectiveness of the proposed model and method.

Interaction-induced long-time tail of a nonlinear ac absorption in a localized system: A relay-race mechanism

In conventional solid-state electron systems with localized states the ac absorption is linear since the inelastic widths of the energy levels exceeds the drive amplitude. The situation is different in the systems of cold atoms in which phonons are absent. Then even a weak drive leads to saturation of the ac absorption within resonant pairs, so that the population of levels oscillates with the Rabi frequency. We demonstrate that, in the presence of weak dipole-dipole interactions, the response of the system acquires a long-time component which oscillates with frequency much smaller than the Rabi frequency. The underlying mechanism of this long-time behavior is that the fields created in the course of the Rabi oscillations serve as resonant drive for the second-generation Rabi oscillations in pairs with level spacings close to the Rabi frequency. The frequency of the second-generation oscillations is of the order of interaction strength. As these oscillations develop, they can initiate the next-generation Rabi oscillations, and so on. Formation of the second-generation oscillations is facilitated by the non-diagonal component of the dipole-dipole interaction tensor.

Evidence of long-range ferromagnetic order and spin frustration effects in the double perovskite La2CoMnO6

We present a comprehensive study on the magnetic structure, dynamics, and phase evolution in the single-phase double perovskite $La_2CoMnO_6$. The mixed valence state due to oxygen deficiency is verified by X-ray photoelectron spectroscopy, and confirms a double ferromagnetic transition observed in DC magnetization. Neutron diffraction reveals that the magnetic structure is dominated by long-range ferromagnetic ordering, which is further corroborated by a critical exponents analysis of the paramagnetic to ferromagnetic phase transition. An analysis of the magnetization dynamics by means of linear and nonlinear ac magnetic susceptibilities marks the presence of two distinct cluster glass-like states that emerge at low temperatures. The isothermal entropy change as a function of temperature and magnetic field (H) is exploited to investigate the mechanism of stabilization of the magnetic phases across the H-T phase diagram. In the regime of the phase diagram where thermal energy is sufficiently low, regions of competing interactions due to local disorder become stabilized and display glass-like dynamics. The freezing mechanism of clusters is illustrated using a unique probe of transverse susceptibility that isolates the effects of the local anisotropy of the spin clusters. The results are summarized in a new H-T phase diagram of $La_2CoMnO_6$ revealed for the first time from these data.

Cluster-glass dynamics of the Griffiths phase in Tb5−xLaxSi2Ge2

The static magnetization and dynamic susceptibility responses of the cluster system within a Griffiths phase of the magnetocaloric compound ${\mathrm{Tb}}_{5\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Si}}_{2}{\mathrm{Ge}}_{2}$ ($x=0.075$) have been investigated. A novel cluster-glass state within the Griffiths phase is formed at a characteristic freezing temperature where short-range ferromagnetic correlations set in the paramagnetic regime. Ferromagneticlike correlations are built up at around 155 K, which suddenly become frozen at a lower temperature $\ensuremath{\sim}140\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, thus in analogy with a reentrant spin glass behavior. The ac susceptibility near the freezing temperature follows a critical slowing down process characterized by ${\ensuremath{\tau}}_{0}={10}^{\ensuremath{-}13}s$ and dynamic exponents $\mathrm{z}\ensuremath{\nu}\ensuremath{\sim}6$ and $\ensuremath{\beta}\ensuremath{\sim}0.4$, similar to well-known spin glass systems. The nonlinear ac susceptibility analysis shows clearly the existence of a transition associated to the reentrant behavior. The origin of the intermediate cluster-glass phase inside the Griffiths phase is proposed to be the result of a combination of short-ranged RKKY intralayer positive exchange interactions between rare-earth ${\mathrm{Tb}}^{3+}$ ions and antiferromagnetic exchange between adjacent interlayers involving Si and Ge atoms in connection to the ${\mathrm{Tb}}^{3+}$ atoms.

AC load flow based model for transmission expansion planning

This paper proposes an accurate model to solve the transmission network expansion planning (TNEP) problem. The TNEP problem is solved using a linear DC model, a mixed integer linear DC model, and the proposed accurate exact mixed integer non-linear AC model. A 19 bus system which is a part of the 220 kV Egyptian transmission network is used for the verification of the proposed load flow models. The proposed exact non-linear AC load flow based model that considered control of active and reactive power flow in the network and considered the power losses in the system yielded promising results when compared to DC load flow based linear and mixed integer linear models. It provided a planned network with least number of added lines and consecutively with the least cost.

Study of Insulation Material Properties Subjected to Nonlinear AC–DC Composite Electric Field for Converter Transformer

The nonlinear ac-dc composite electric field in the winding area of the converter transformer was studied by considering the frequency and temperature dependence of the insulation materials in this paper. First, the relative permittivity and conductivity of vegetable oils, mineral oils, and insulation papers were measured at different frequencies and temperatures. Then, the oil-paper insulation structure model of one 500 kV converter transformer valve-side winding was established. The nonlinear composite electric field of the converter transformer insulation with vegetable oils and mineral oils was analyzed. The maximum voltage of the converter transformer with mineral oils is 524.9 kV, at -20 °C and that with vegetable oils is 497.1 kV. The results show that the calculation method proposed in this paper is more accurate than the traditional superposition method.

Fully distributed AC power flow (ACPF) algorithm for distribution systems

Power flow is one of the basic tools for system operation and control. Due to its nature, which determines the complex nodal voltages, line flows, currents and losses, it enforces a large computation load on a power system. A distributed/decentralised algorithm unburdens the central controller and shares the total computation load with all agents. Therefore, such algorithms are an effective method for dealing with power flow complexity. In this study, a distributed method based on a linearised AC power system is proposed. First, the linearisation procedure of a comprehensive non-linear AC power flow (ACPF) is detailed. Second, a distributed method is presented based upon the linear ACPF equations. Three case studies are presented to evaluate the overall performance of the proposed method. In the first case study, the accuracy level of both linearised ACPF and distributed ACPF is assessed. In the second case study, the dynamic performance of distributed ACPF is investigated based on the load sudden changes. In the third case study, the scalability of the proposed distributed ACPF is evaluated by applying it to a larger power system.

Look ahead dynamic security-constrained economic dispatch considering frequency stability and smart loads

Conventional economic dispatch models aim to determine the optimal production of generation units under the steady state operation constraints. Due to the growing integration of low inertia power generation technologies (e.g. wind, solar, etc.), considering stability constraints, in particular, frequency stability, a theme of this work, becomes a crucial need in nowadays security-constrained economic dispatch (SCED) programs. This paper develops a new look ahead dynamic (i.e. multi-period) security-constrained economic dispatch model, further considering frequency stability constraints (DSCED-FSC). The aim of the DSCED-FSC is to optimize the cost of power generation subject to operation and frequency stability constraints under normal and contingency conditions. The proposed DSCED-FSC secures N-1 contingencies for both thermal limits and frequency stability. The system frequency response is included in DSCED-FSC model by linearizing the discretized rotor angle swing equation. The dynamic models of governors and load damping are considered in the discretized system frequency response. The safety of system frequency response under generation outages is provided by activating generators' governors, inertial response and load damping as the primary frequency reserve. In addition to primary frequency reserve, the demand elasticity of smart motor loads is utilized to avoid the activation of under frequency load shedding (UFLS) relays under severe generation outages. The proposed DSCED-FSC model is formulated as a mixed integer linear programming (MILP) problem. The nonlinear AC power flow equations are linearized using Taylor series expansions and piecewise linear (PWL) approximation techniques. The efficacy of the proposed DSCED-FSC model in supporting system frequency is investigated using the IEEE 118-bus test system.

Power Grid AC-Based State Estimation: Vulnerability Analysis Against Cyber Attacks

To ensure grid efficiency and reliability, power system operators continuously monitor the operational characteristics of the grid through a critical process called state estimation (SE), which performs the task by filtering and fusing various measurements collected from grid sensors. This study analyzes the vulnerability of the key operation module, namely ac-based SE, against potential cyber attacks on data integrity, also known as false data injection attack (FDIA). A general form of FDIA can be formulated as an optimization problem, whose objective is to find a stealthy and sparse data injection vector on the sensor measurements with the aim of making the state estimate spurious and misleading. Due to the nonlinear ac measurement model and the cardinality constraint, the problem includes both continuous and discrete nonlinearities. To solve the FDIA problem efficiently, we propose a novel convexification framework based on semidefinite programming (SDP). By analyzing a globally optimal SDP solution, we delineate the “attackable region” for any given set of measurement types and grid topology, where the spurious state can be falsified by FDIA. Furthermore, we prove that the attack is stealthy and sparse, and derive performance bounds. Simulation results on various IEEE test cases indicate the efficacy of the proposed convexification approach. From the grid protection point of view, the results of this study can be used to design a security metric for the current practice against cyber attacks, redesign the bad data detection scheme, and inform proposals of grid hardening. From a theoretical point of view, the proposed framework can be used for other nonconvex problems in power systems and beyond.

Linear/quadratic programming-based optimal power flow using linear power flow and absolute loss approximations

This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We consider a linear power flow and branch flow approximation and derive a power loss approximation in the form of absolute value functions that are suitable to cover a broader operating range. The key ideas are (1) to capture power losses and power flows in the full decision variable domain, (2) to combine these approximations to recast the nonlinear constraints of the OPF problem into linear ones, and (3) to solve the approximate OPF problem with off-the-shelf solvers in a non-iterative fashion. In this way, the problem complexity can be reduced significantly. In detail, we present four OPF approximation methods, in which we relax the absolute power loss functions as linear constraints. In a comprehensive case study the usefulness of our OPF methods is analyzed and compared with an existing OPF relaxation and approximation method. As a result, the errors on voltage magnitudes and angles are reasonable, while obtaining near-optimal results for typical scenarios. We find that our methods reduce significantly the computational complexity compared to the nonlinear AC-OPF making them a good choice for power system planning purposes.

Probabilistic Power Flow Analysis Using Multidimensional Holomorphic Embedding and Generalized Cumulants

This paper proposes a new analytical probabilistic power flow (PPF) approach for power systems with high penetration of distributed energy resources. The approach solves probability distributions of system variables about operating conditions. Unlike existing analytical PPF algorithms in literature, this new approach preserves nonlinearities of ac power flow equations and retain more accurate tail effects of the probability distributions. The approach first employs a multidimensional holomorphic embedding method to obtain an analytical nonlinear ac power flow solution for concerned outputs such as bus voltages and line flows. The embedded symbolic variables in the analytical solution are the inputs such as power injections. Then, the approach derives cumulants of the outputs by a generalized cumulant method, and recovers their distributions by Gram–Charlier expansions. This PPF approach can accept both parametric and nonparametric distributions of random inputs and their covariances. Case studies on the IEEE 30-bus system validate the effectiveness of the proposed approach.

AC magnetic response of superconducting single crystals exhibiting a second peak on the DC magnetization curves

The strong modulation of the AC magnetic response in the magnetic field-temperature region of the DC magnetization peak effect (PE) occurring just below the DC irreversibility line (IL) of weakly pinned superconducting single crystals is well known. However, it is not yet clear if the AC magnetic signal registered at usual frequencies and amplitudes is significantly affected by the presence of the second magnetization peak (SMP) in the DC magnetic hysteresis curves, since the SMP appears in specimens with stronger pinning and is located well below the IL. We investigated the AC magnetic response of several La2−xSrxCuO4 and 122-type pnictide superconducting single crystals exhibiting a pronounced DC SMP. It was found that in the case of small demagnetization effects, the AC magnetic signal across the SMP remains in the linear regime, with no detectable distortions in the SMP range (within the high sensitivity of a Physical Property Measurement System). This indicates reduced values of the Campbell penetration depth compared with the London magnetic penetration depth. A clearly nonmonotonic, SMP-related variation has only been obtained for the DC field dependence of the out of phase component of the AC magnetic moment in the nonlinear regime. The nonlinear AC Bean regime far below the IL has been attained in the conditions of enhanced demagnetization effects (plate-like specimens in perpendicular magnetic fields).

Comparing the Effects of Failures in Power Grids Under the AC and DC Power Flow Models

In this paper, we compare the effects of failures in power grids under the nonlinear AC and linearized DC power flow models. First, we numerically demonstrate that when there are no failures and the assumptions underlying the DC model are valid, the DC model approximates the AC model well in four considered test networks. Then, to evaluate the validity of the DC approximation upon failures, we numerically compare the effects of single line failures and the evolution of cascades under the AC and DC flow models using different metrics, such as yield (the ratio of the demand supplied at the end of the cascade to the initial demand). We demonstrate that the effects of a single line failure on the distribution of the flows on other lines are similar under the AC and DC models. However, the cascade simulations demonstrate that the assumptions underlying the DC model (e.g., ignoring power losses, reactive power flows, and voltage magnitude variations) can lead to inaccurate and overly optimistic cascade predictions. Particularly, in large networks the DC model tends to overestimate the yield. Hence, using the DC model for cascade prediction may result in a misrepresentation of the gravity of a cascade.

Antiresonant quantum transport in ac-driven molecular nanojunctions

(Dated: July 17, 2017) We calculate the electric charge current flowing through a vibrating molecular nanojunction, which is driven by an ac voltage, in its regime of nonlinear oscillations. Without loss of generality, we model the junction by a vibrating molecule which is doubly clamped to two metallic leads which are biased by time-periodic ac voltages. Dressed-electron tunneling between the leads and the molecule drives the mechanical degree of freedom out of equilibrium. In the deep quantum regime, where only a few vibrational quanta are excited, the formation of coherent vibrational resonances affects the dressed-electron tunneling. In turn, back action modifies the electronic ac current passing through the junction. The concert of nonlinear vibrations and ac driving induces quantum transport currents which are antiresonant to the applied ac voltage. Quantum back action on the flowing nonequilibriun current allows us to obtain rather sharp spectroscopic information on the population of the mechanical vibrational states.

Stochastic and Chance-Constrained Conic Distribution System Expansion Planning Using Bilinear Benders Decomposition

Second order conic programming (SOCP) has been used to model various applications in power systems, such as operation and expansion planning. In this paper, we present a two-stage stochastic mixed integer SOCP (MISOCP) model for the distribution system expansion planning problem that considers uncertainty and also captures the nonlinear AC power flow. To avoid costly investment plans due to some extreme scenarios, we further present a chance-constrained variant that could lead to cost-effective solutions. To address the computational challenge, we extend the basic Benders decomposition method and develop a bilinear variant to compute stochastic and chance-constrained MISOCP formulations. A set of numerical experiments is performed to illustrate the performance of our models and computational methods. In particular, results show that our Benders decomposition algorithms drastically outperform a professional MISOCP solver in handling stochastic scenarios by orders of magnitude.

The Interconnection of Quadratic Droop Voltage Controllers Is a Lotka-Volterra System: Implications for Stability Analysis

This letter studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs. We show that the voltage dynamics is a Lotka-Volterra system, which is a class of nonlinear positive systems. We study the stability of the closed-loop system by proving a uniform ultimate boundedness result and investigating conditions under which the network is cooperative. We then restrict to study the stability of voltage dynamics under a decoupling assumption (i.e., zero relative angles). We analyze the existence and uniqueness of the equilibrium in the interior of the positive orthant for the system and prove an asymptotic stability result.

Analyzing Cascading Failures in Power Grids under the AC and DC Power Flow Models

In this paper, we study cascading failures in power grids under the nonlinear AC and linearized DC power flow models. We numerically compare the evolution of cascades after single line failures under the two flow models in four test networks. The cascade simulations demonstrate that the assumptions underlying the DC model (e.g., ignoring power losses, reactive power flows, and voltage magnitude variations) can lead to inaccurate and overly optimistic cascade predictions. Particularly, in large networks the DC model tends to overestimate the yield (the ratio of the demand supplied at the end of the cascade to the initial demand). Hence, using the DC model for cascade prediction may result in a misrepresentation of the gravity of a cascade.