There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Simulation and the monte carlo method

(1990). ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY. Electric Machines & Power Systems: Vol. 18, No. 2, pp. 209-210.

Energy function analysis for power system stability

With the continuous increase of wind power penetration in power systems, the problems caused by the volatile nature of wind speed and its occurrence in the system operations such as scheduling and dispatching have drawn attention of system operators, utilities and researchers towards the state-of-the-art wind speed and power forecasting methods These methods have the required capability of reducing the influence of the intermittent wind power on system operations as well as of harvesting the wind energy effectively In this context, combining different methodologies in order to circumvent the challenging model selection and take advantage of the unique strength of plausible models have recently emerged as a promising research area Therefore, a comprehensive research about the combined models is called on for how these models are constructed and affect the forecasting performance Aiming to fill the mentioned research gap, this paper outlines the combined forecasting approaches and presents an up-to date annotated bibliography of the wind forecasting literature Furthermore, the paper also points out the possible further research directions of combined techniques so as to help the researchers in the field develop more effective wind speed and power forecasting methods

A review of combined approaches for prediction of short-term wind speed and power

The existence of wind power forecast errors is one of the most challenging issues for wind power system operation. It is difficult to find a reasonable method for the representation of forecast errors and apply it in scheduling. In this paper, a probability distribution model named “versatile distribution” is formulated and developed along with its properties and applications. The model can well represent forecast errors for all forecast timescales and magnitudes. The incorporation of the model in economic dispatch (ED) problems can simplify the wind-induced uncertainties via a few analytical terms in the problem formulation. The ED problem with wind power could hence be solved by the classical optimization methods, such as sequential linear programming which has been widely accepted by industry for solving ED problems. Discussions are also extended on the incorporation of the proposed versatile distribution into unit commitment problems. The results show that the new distribution is more effective than other commonly used distributions (i.e., Gaussian and Beta) with more accurate representation of forecast errors and better formulation and solution of ED problems.

A Versatile Probability Distribution Model for Wind Power Forecast Errors and Its Application in Economic Dispatch

Distributed solar generation has the potential to reach high penetration levels in distribution systems. However, its integration reshapes distribution system power flows and causes rapid-fluctuations in system statuses. The facts challenge major voltage management approaches, nowadays, such as using online load tap changing (OLTC) transformers, voltage regulators (VRs), or shunt capacitors. In this paper, we explore the capability of using vehicle-to-grid (V2G) electric vehicles (EVs) to join distribution system voltage management, and to collaborate with OLTCs to mitigate the voltage problems caused by distribution solar generations. A two-stage control method is proposed for this purpose. The first stage controls the making of rolling schedules for EV charging and OLTC tap positions, while the second controls the EVs to resist the solar generation fluctuation to maintain voltage profiles. A case system with simultaneous overvoltage/undervoltage risks is designed to test the effectiveness of the proposed method. The results demonstrate that both the over/undervoltage risks are mitigated.

Mitigating Voltage Problem in Distribution System With Distributed Solar Generation Using Electric Vehicles

This paper presents a distribution locational marginal pricing (DLMP) method through chance constrained mixed-integer programming (MIP) designed to alleviate the possible congestion in the future distribution network with high penetration of electric vehicles (EVs). In order to represent the stochastic characteristics of the EV driving patterns, a chance constrained optimization of the EV charging is proposed and formulated through MIP. With the chance constraints in the optimization formulations, it guarantees that the failure probability of the EV charging plan fulfilling the driving requirement is below the predetermined confidence parameter. The efficacy of the proposed approach was demonstrated by case studies using a 33-bus distribution system of the Bornholm power system and the Danish driving data. The case study results show that the DLMP method through chance constrained MIP can successfully alleviate the congestion in the distribution network due to the EV charging while keeping the failure probability of EV charging not meeting driving needs below the predefined confidence.

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Distribution Locational Marginal Pricing for Optimal Electric Vehicle Charging Through Chance Constrained Mixed-Integer Programming

Wide-area power system stabilizer (WPSS) is one of the most potentially effective approaches to damp interarea low frequency oscillations in power systems. When WPSS is implemented in a real project, emphasis should be put on feedback signal delay problem. In order to intensively study the delay of phasor measurement unit data, field tests have been carried out in Guizhou power grid (GZPG), and results show that, in the long-term, the delay might change remarkably under some circumstances, such as when route switches or communication load increases. Therefore, this paper proposes an adaptive time delay compensation method to deal with such kind of delay. Bounded random delay is divided into several intervals and compensators are designed for each delay interval. Then appropriate compensators will be selected according to the delay measured online, based on the switching rules that is also demonstrated in this paper. The delay used here is the average delay before the compensator switching. The proposed compensator is demonstrated in a two area power system. Numerical simulation results show the effectiveness and feasibility of the proposed adaptive compensator. A comparison with conventional methods is also presented. Finally, the proposed method is validated on GZPG based on real-time digital simulations.

Adaptive Time Delay Compensator (ATDC) Design for Wide-Area Power System Stabilizer

This paper aims to study the measurement and modeling methods for delays in wide-area closed-loop control systems (WACS). The delays are classified into communication delays and operational delays based on the information flow of WACS. For communication delays, an affine evaluation model is proposed based on previous studies, and this model is verified by the measured communication delays of the Guizhou Power Grid in Southwest China. For operational delays, a real-time digital simulator (RTDS) hardware-in-the-loop measurement method is developed, and the measured operational delays are obtained and analyzed. Finally, an estimation method for the closed-loop delay in actual WACS is proposed, in which the uplink and downlink communication delays are modeled as constants and the operational delay is modeled as a normal distribution. Consequently, the closed-loop delay follows a normal distribution with the calculated parameters by combining the communication delays and operational delay. The measurement results and analysis presented in this paper are important for the development and applications of WACS.

Lin Cheng

Papers

A Versatile Probability Distribution Model for Wind Power Forecast Errors and Its Application in Economic Dispatch

Mitigating Voltage Problem in Distribution System With Distributed Solar Generation Using Electric Vehicles

Distribution Locational Marginal Pricing for Optimal Electric Vehicle Charging Through Chance Constrained Mixed-Integer Programming

Adaptive Time Delay Compensator (ATDC) Design for Wide-Area Power System Stabilizer

Measurement and Modeling of Delays in Wide-Area Closed-Loop Control Systems