Linear Approximation Method Research Articles

An Efficient Algorithm for Power Flow Optimization in PV Inverters Systems

Aiming at the problem of optimal power flow in photovoltaic (PV) Inverters, this paper proposes a real-time algorithm for optimal power flow (OPF) in distributed PV inverters with sophisticated communication technologies and measurement. A higher accuracy and computation speed are obtained by proposing a linear, time-varying optimization method, and the objective function and constraints were linearized using the Taylor expansion under the premise of small variable changes during the short control period. By comparing with the constant linearization method, the proposed time-varying linear approximation method is more accurate and efficient. The problems faced by the centralized calculation is overcome by proposing a distributed control method which utilizes the alternating direction method of multipliers. The proposed distributed control method enables the distributed PV inverters to optimize their own power setpoints with only a little information required from neighbor nodes. Case study results demonstrate that the proposed algorithm makes the distributed PV Inverters more efficient and economical than the other methods.

Drone routing with energy function: Formulation and exact algorithm

Drone delivery is known as a potential contributor in improving efficiency and alleviating last-mile delivery problems. For this reason, drone routing and scheduling has become a highly active area of research in recent years. Unlike the vehicle routing problem, however, designing drones’ routes is challenging due to multiple operational characteristics including multi-trip operations, recharge planning, and energy consumption calculation. To fill some important gaps in the literature, this paper solves a multi-trip drone routing problem, where drones’ energy consumption is modeled as a nonlinear function of payload and travel distance. We propose adding logical cuts and subgradient cuts in the solution process to tackle the more complex nonlinear (convex) energy function, instead of using the linear approximation method as in the literature, which can fail to detect infeasible routes due to excess energy consumption. We use a 2-index formulation to model the problem and develop a branch-and-cut algorithm for the formulation. Benchmark instances are first generated for this problem. Numerical tests indicate that even though the original model is nonlinear, the proposed approach can solve large problems to optimality. In addition, in multiple instances, the linear approximation model yields routes that under the nonlinear energy model would be energy infeasible. Use of a linear approximation for drone energy leads to differences in energy consumption of about 9% on average compared to the nonlinear energy model.

A Blood Bank Network Design Problem with Integrated Facility Location, Inventory and Routing Decisions

We aim to design an effective supply chain network for a blood distribution system to satisfy the needs of hospitals in a certain region. In the analyzed current system, each hospital keeps a certain level of inventory, received at certain time periods by the shipments from a main blood bank. We propose an alternative system, in which some of the hospitals are selected as local blood banks (LBB) and all other hospitals will be assigned to an LBB. More frequent shipments will be made from LBBs to these hospitals, leading to lower inventory levels to be kept at each hospital. The inventories kept separately at the hospitals in the current system will be pooled at the selected LBBs in the proposed system. We develop a mixed integer nonlinear programming (MINLP) model to determine the optimal selection of LBBs, assignment of hospitals to LBBs, optimal inventory levels at each LBB and routing decisions among the facilities in order to minimize total system costs. We also propose a piecewise linear approximation method and a simulated annealing heuristic approach to find the solution of this problem. The proposed model and the solution techniques are applied on a real life case study for the blood distribution network in Istanbul. It is observed that significant improvements can be obtained by the proposed system when compared to the current design. Performances of the solution methods are also compared and a sensitivity analysis related to system parameters is presented via detailed numerical experiments.

Compact block boundary value methods for semi‐linear delay‐reaction–diffusion equations with algebraic constraints

AbstractIn the present paper, we study a class of linear approximation methods for solving semi‐linear delay‐reaction–diffusion equations with algebraic constraint (SDEACs). By combining a fourth‐order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and order p in time, where p is the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated.

Power Allocation Based on Reinforcement Learning for MIMO System With Energy Harvesting

This paper focuses on the use of a reinforcement learning (RL) approach to find two online power allocation policies in a point to point EH-MIMO wireless communication system. In our study, we train the power allocation policies in order to learn the map between the environment and the agent. Particularly, in order to avoid “dimension disaster” problem which may happen in our proposed SARSA power allocation policy, we introduce a linear approximation method to get an approximate SARSA power allocation policy. The linear approximation can handle infinite number of states and trade-off between complexity and performance of power allocation is significantly improved. The simulation results show that the proposed SARSA and approximate SARSA power allocation policies have a considerable throughput increase compared with the benchmark policies, such as greedy, random and conservative policies.

Model reduction-based initialization methods for solving the Poisson-Nernst-Plank equations in three-dimensional ion channel simulations

The Poisson-Nernst-Planck (PNP) model is frequently-used in simulating ion transport through ion channel systems. Due to the nonlinearity and coupling of PNP model, choosing appropriate initial values is crucial to obtaining a convergent result or accelerating the convergence rate of finite element solution, especially for large channel systems. Continuation is an effective and commonly adopted strategy to provide good initial guesses for the solution procedure. However, this method needs multiple times to solve the whole system at different conditions. We utilize a reduced model describing a near-or partial-equilibrium state as an approximation of the original PNP system (describing a non-equilibrium process in general). Based on the reduced model, we design three initialization methods for the solution of PNP equations under general conditions. These methods provide the initial guess of the PNP system by solving a specifically designed Poisson-Boltzmann-like model, Smoluchowski-Poisson-Boltzmann-like model, and linear approximation model. Simulations of potassium channels 1BL8 and 2JK4 demonstrate that these methods can effectively reduce the number of Gummel iteration steps and the total CPU time in the solution of the PNP equations, and especially do not need the continuation approach anymore. The reason is that these initial guesses can approximate the PNP solution well in the channel region. Besides, our numerical experiments demonstrate that as one of the initialization methods, the linear approximation method can even produce very close results such as current-voltage curves to that from the PNP model when the membrane potential is not high.

Approximate feedback linearization based optimal robust control for an inverted pendulum system with time-varying uncertainties

In the present study, to attain an approximate feedback linearization based optimal robust control of an under-actuated cart-type inverted pendulum system with two-degree-of-freedom (2DOF) having time-varying uncertainties is desirable. To reach such a goal, at first, the governing dynamical equations of the cart-type inverted pendulum are presented. Then, using an approximate feedback linearization method, the dynamics of the nonlinear system are changed to those of the linear one. In order to simultaneously stabilize the both degrees of freedom, a robust sliding mode controller is designed for this under-actuated system. Finally, the control law is improved with aid of a novel adaptive approach based on an approximating function found via a multiple-crossover genetic algorithm so that the system always will be optimally robust against time-varying parametric uncertainties. The results are displayed to show how the proposed controller improves the settling time and overshoot of the system outputs. In addition, such an improvement in the values of the selected objective functions is clearly evident.

A bi-level programing for wildfire self-evacuation network design

A non-linear bi-level problem is suggested in this paper for wildfire self-evacuation planning, the upper problem of which includes binary variables and the lower problem includes continuous variables. In this model, the upper problem selects a number of links and adds them to the available evacuation network. It, moreover, predicts the traffic balance, and the time window of the links in the lower problem. A part of the objective function in the bi-level problem is non-linear which is linearized with a linear approximation method that does not require binary variables. Then the linear bi-level model is reformulated as a non- linear single level problem. This model is linearized and transferred into Mixed Integer Programing. The model is then used for the real case study of the Beechworth fire in 2009. The resulted outputs of the model are beneficial in planning design schemes for emergency evacuation to use the maximum potential of the available transportation network.

Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional programming problem through nonlinear membership function. The proposed approach defines a fuzzy goal for each objective through a nonlinear membership function. By means of nonlinear membership function, the multi-objective linear plus linear fractional programming problem transformed into a multi-objective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multi-objective linear programming problem, the fuzzy goal programming model is formulated by minimizing the negative deviational variables. The proposed procedure is illustrated through numerical examples and a real-life application problem. Further, it is compared with the existing methods. Finally, the Euclidean distance function has been used to prove the efficiency of the proposed method.

EEG Self-Adjusting Data Analysis Based on Optimized Sampling for Robot Control

Research on electroencephalography (EEG) signals and their data analysis have drawn much attention in recent years. Data mining techniques have been extensively applied as efficient solutions for non-invasive brain–computer interface (BCI) research. Previous research has indicated that human brains produce recognizable EEG signals associated with specific activities. This paper proposes an optimized data sampling model to identify the status of the human brain and further discover brain activity patterns. The sampling methods used in the proposed model include the segmented EEG graph using piecewise linear approximation (SEGPA) method, which incorporates optimized data sampling methods; and the EEG-based weighted network for EEG data analysis, which can be used for machinery control. The data sampling and segmentation techniques combine normal distribution approximation (NDA), Poisson distribution approximation (PDA), and related sampling methods. This research also proposes an efficient method for recognizing human thinking and brain signals with entropy-based frequent patterns (FPs). The obtained recognition system provides a foundation that could to be useful in machinery or robot control. The experimental results indicate that the NDA–PDA segments with less than 10% of the original data size can achieve 98% accuracy, as compared with original data sets. The FP method identifies more than 12 common patterns for EEG data analysis based on the optimized sampling methods.

Comparisons of mechanical and electromyographical muscular utilization ratios.

The physical loading of a muscle during functional activities can be estimated by the muscular utilization ratio. This ratio is defined as the percentage of muscular involvement relative to the maximal capacity. Either mechanical or electromyographical approaches can be used to obtain the muscle utilization ratio. However, the non-linear relationship between electromyographical activity and muscle force, as well as the non-equivalence between agonist muscles, may create differences between the mechanical muscle utilization ratio calculated from joint moments and the electromyographical muscle utilization ratio calculated from electromyographical data. The aim of this study was to compare, during a squat test, the mechanical muscle utilization ratio and the electromyographical muscle utilization ratio estimated by three different methods; direct linear approximation, second order polynomial regression and linear interpolation. The knee extensor moment and electromyographical data of rectus femoris and vastus medialis of 11 subjects were recorded during both knee extension and squat. Both tests were performed with the knee maintained at 90 degrees of flexion. The results showed that: a) the electromyographical muscle utilization ratio, calculated from the average of vastus medialis and rectus femoris, significantly underestimates the mechanical muscle utilization ratio (ANOVA, p < 0.01), b) the differences between the mechanical muscle utilization ratio and the electromyographical muscle utilization ratio are larger for the direct linear approximation method than for the second order polynomial regression (ANOVA, p < 0.01) or the linear interpolation method (ANOVA, p < 0.01), and c) independent of the method utilized, there is no difference between the electromyographical muscle utilization ratio predicted by the vastus medialis as compared with the rectus femoris (ANOVA, p > 0.01).

Cost-optimal evaluation of centralized and distributed microgrid topologies considering voltage constraints

Optimal design of hybrid renewable mini-grids requires both economic and power quality considerations. Existing modeling approaches address these considerations via separate or loosely coupled models. Here, we extend REopt—a techno-economic optimization model developed at the National Renewable Energy Laboratory—to consider both within a single model. REopt formulates the design problem as a mixed-integer linear program that solves for a site's optimal technology mix, sizing, and operation to minimize life cycle cost. REopt has traditionally assumed a single node system. In the work presented here, we expand the REopt platform to consider multiple connected nodes with associated voltage constraints. In order to do this, we model power flow using a fixed-point linear approximation method. We then use the model to explore design considerations of mini-grids in Sub-Saharan Africa. Specifically, we evaluate under what combinations of transmission line distance and capacity it is technically viable and economically preferable to build multiple isolated mini-grids versus an interconnected, centralized system.

Environmental Modelling through Chaotic Approach for Malaysian West Coast Sea Level.

Sea level forecasting is an essential task for coastal engineering, geodetic application, navigation, and recreational activities. Predicting the behavior of future sea level is important for monitoring and forecasting of changes in fishery and marine ecosystems as well as for protection of coastal. This research is focused on the analysis and prediction of hourly sea level time series data at the benchmark station located in Penang by using chaotic approach. The purpose of this research was to identify the presence of chaotic behavior by the phase space reconstruction and Cao methods, and also a local linear approximation method is applied for prediction purposes. The results notified that the value of correlation coefficient between the observed and predicted time series is 0.8838 which is near to one. This reveals that the local linear approximation method can be used to predict the sea level time series in Malaysia. Certainly, the result of this research is expected to help stakeholder such as Department of Survey and Mapping Malaysia (JUPEM) in having a better sea level management.

Double-channel resistance-to-voltage converter for cable teraohmmeters

The paper considers a teraohmmeter resistance converter to monitor cable insulation with an additional input amplifier that emits a low-frequency interference signal. Adaptive algorithms for a double-channel converter circuit to compensate for low-frequency interference are proposed. There are considered algorithms using minimax criteria and linear approximation method for estimation of interference influence. It is shown classification of algorithms according to industrial frequency interference filtering method and signal observation interval. There were investigated two ways of interference application: step signal from a DC voltage source up to 300 V and fading harmonic signal from an AC voltage source and amplifier up to 300 V. A doublechannel circuit of the resistance-to-voltage converter is found to provide a 2-fold increase in the signal-tonoise ratio in comparison with a single-channel circuit. It is shown that the maximum deviation of readings for the single-channel circuit exceeds 20 % (up to 32 %) in short-term exposure to interference with amplitude of up to 300 V. At the same time, the maximum deviation for the double-channel circuit can attain 17 %, but it does not exceed 20 %. According to GOST 3345–76, the insulation resistance measuring error in therange of 10 GΩ to 100 TΩ should not exceed 20 %.The advantage of the proposed double-channel converter is the possibility to develop new algorithms to eliminate the dependence of readings on interference effects.

Risk-Loss Coordinated Admissibility Assessment of Wind Generation for Integrated Electric-Gas Systems

Due to the widely deployment of gas-fired units and the emerging power-to-gas (P2G) technologies, the interdependencies between power systems and gas systems have been enhanced, yet the impacts on the ability of accommodating the uncertain and variable wind generation are unclear. On one hand, the regulation capability of gas-fired units might be restricted due to pipeline congestion or gas supply shortage; on the other hand, the P2G facilities could operate as interruptible electrical loads to enhance the operational flexibility of the power network. This paper aims to revisit the wind generation admissibility assessment problem in view of integrated electric-gas systems. The overall model is established according to the two-stage robust optimization framework. By introducing the stepwise penalty coefficients for power shortage and surplus, the risk preference of the operator can be reflected. The mixed integer linear programming-based approximation methods is adopted to tackle the computational challenging Weymouth equation in the gas network, which requires an additional column-and-constraint (C&CG) loop to solve the second-stage max-min problem, other than the common one to coordinate the first- and second-stage problems, resulting in a nested C&CG algorithmic structure. The effectiveness of the proposed model and solution methods are validated by the simulation results.

Confidence Interval Based Distributionally Robust Real-Time Economic Dispatch Approach Considering Wind Power Accommodation Risk

This article proposes a confidence interval based distributionally robust real-time economic dispatch (CI-DRED) approach, which considers the risk related to accommodating wind power. In this article, only the wind power curtailment and load shedding due to wind power disturbances are evaluated in the operational risk. The proposed approach can strike a balance between the operational costs and risk even when the wind power probability distribution cannot be precisely estimated. A novel ambiguity set is developed based on the imprecise probability theory, which can be constructed based on the point-wise or family-wise confidence intervals. The worst pair of distributions in the established ambiguity set is then identified, and the original CI-DRED problem is transformed into a determined nonlinear dispatch problem accordingly. By using the sequential convex optimization method and piecewise linear approximation method, the nonlinear dispatch model is reformulated as a mixed integer linear programming problem, for which off-the-shelf solvers are available. A fast inactive constraint filtration method is also applied to further relieve the computational burden. Numerical results on the IEEE 118-bus system and a real 445-bus system verify the effectiveness and efficiency of the proposed approach.

A Linear Spline Markov Approximation Method for Random Maps with Position Dependent Probabilities

We present a rigorous convergence analysis of a linear spline Markov finite approximation method for computing stationary densities of random maps with position dependent probabilities, which consist of several chaotic maps. The whole analysis is based on a new Lasota–Yorke-type inequality for the Markov operator associated with the random map, which is better than the previous one in the literature and much simpler to obtain. We also present numerical results to support our theoretical analysis.

Block-oriented system identification for nonlinear modeling of all-solid-state Li-ion battery technology

The high energy density characteristic of the all-solid-state battery technology makes it one of the promising competitors of current liquid electrolyte-based lithium-ion batteries. However, due to the low ionic conductivity of solid materials and existing issues in active material-solid electrolyte interfaces, all-solid-state batteries show strong nonlinear behavior when the amplitude of input current is relatively high. In this paper, we have developed a methodology based on block-oriented nonlinear systems that can detect, quantize, and model the battery behavior, accurately. For this purpose, two solid-state coin cells, which have different ionic conductivity at the cathode interface are manufactured and excited with multisine input current. The Best Linear Approximation (BLA) method has been used to separate linear frequency response function (FRF) from nonlinear distortion. Then, a Hammerstein-Wiener system has been developed and parametrized to model the nonlinear distortions caused by ionic conductivity variation of the solid electrolyte at the cathode layer. Furthermore, the developed model has been utilized to detect possible faults in the electrode-electrolyte interface based on the nonlinearity level of the measured voltage.

Solution of non linear Fredholm integral equation involving constant delay by BEM with piecewise linear approximation

This paper provides a methodology to solve a non linear Fredholm integral equation involving constant delay. Hybridization of boundary element method (BEM) along with piecewise linear approximation method is considered to resolve the nonlinearity. This simple technique provides a good approximation to non linear integral equations involving constant delay. Variation of constant delay term and efficiency of the method is also discussed via few suitable numerical examples.

A Method of Local Linear Approximation for the Nonlinear Discrete Equations

We obtain new conditions for the existence of bounded solutions of nonlinear discrete equations with the use of local linear approximation of these equations.