Catalina Gomez-Quiles

A Multilevel State Estimation Paradigm for Smart Grids

The main objective of this paper is to describe a multilevel framework that facilitates seamless integration of existing state estimators (SEs) that are designed to function at different levels of modeling hierarchy in order to accomplish very large-scale monitoring of interconnected power systems. This has been a major challenge for decades as power systems grew pretty much independently in different areas, which had to operate in an interconnected and synchronized fashion. The paper initially provides a brief historical perspective which also explains the existing state estimation paradigm. This is followed by a review of the recent technological and regulatory drivers that are responsible for the new developments in the energy management functions. The paper then shows that a common theoretical framework can be used to implement a hierarchical scheme by which even very large-scale power systems can be efficiently and accurately monitored. This is illustrated for substation level, transmission system level as well as for a level between different transmission system operators in a given power system. Finally, the paper describes the use and benefits of phasor measurements when incorporated at these different levels of the proposed infrastructure. Numerical examples are included to illustrate performance of the proposed multilevel schemes.

State Estimation in Two Time Scales for Smart Distribution Systems

The monitoring of distribution systems relies on a critical set of pseudomeasurements and a varying but low number of redundant measurements. In the light of the different refreshing rates of both types of information, this paper considers a state estimation model structured in two time scales. Possibilities and limitations of the proposed model are discussed, and illustrated on a real distribution system comprising a diversity of load patterns.

State Estimation for Smart Distribution Substations

Summary form only given. In the upcoming smart grid environment many more measurements will be available, which can be locally processed by the so-called substation state estimator (SSE). Distribution substations serve energy to a large set of feeders, each one delivering power to a certain number of secondary transformers. In this context, the SSE may have to deal with a huge network model, comprising several hundred or even thousand buses. Taking advantage of the weak electrical coupling existing among the set of feeders connected to the same or adjacent substations, a two-stage procedure is proposed in this paper to efficiently solve the SSE. In the first stage the overall SE is decomposed into f + s WLS subproblems (f and s being the total number of feeders and substations, respectively), which are then solved in a decoupled manner. The second stage, involving a linear WLS problem, consists of coordinating the solution provided by each subsystem (feeder or substation). The proposed solution scheme has a number of advantages, as shown by the case studies.

Bilinear Power System State Estimation

This paper presents a three-stage state estimation methodology based on the sequential solution of two weighted least squares (WLS) linear problems with a nonlinear explicit transformation in between. This requires that appropriate sets of auxiliary variables be introduced so that the resulting measurement models become linear. Simulation results show that the proposed approach yields, in a non-iterative manner, virtually the same solution as that provided by the Gauss-Newton iterative scheme arising in the conventional WLS method.

A Factorized Approach to WLS State Estimation

This paper presents a factorized state estimation methodology based on the solution of two successive WLS problems. In the proposed scheme, a minimal set of intermediate variables is first introduced so that the resulting measurement model is linear. Estimates of those variables are then used as pseudo-measurements of a subsequent nonlinear estimator, along with the associated covariance matrix. The aim of the preliminary step is to reduce the size of the raw measurement vector to the maximum extent, without losing any relevant statistical information. Simulation results show that the proposed approach converges faster, is computationally more efficient, and provides accurate estimates after the first linear stage.

Factorized Load Flow

This paper extends to the load flow problem the factorized solution methodology recently developed for equality-constrained state estimation. This is done by considering a redundant set of initial conditions in order to transform the undetermined system arising in the first linear stage into an overdetermined one. The second nonlinear stage proceeds exactly like in the state estimation case. Experimental results are included showing that the factorized load flow is more robust than the standard NR method, while remaining computationally competitive.

Price and Resource-Related Uncertainty in the Estimation of the Revenue of a Wind Farm

The revenue that wind farms produce is subject to the inherent uncertainty of the wind resource in the short-run and the long-term. This revenue is subject to an additional price-related uncertainty in jurisdictions where the output of the wind farms is paid at the prices cleared at the local electricity market. An econometric model is developed to estimate the risks of using limited information in the estimation of the annual revenue of a wind farm. Sensitivities that measure the influence of each uncertainty factor in the overall risks are also developed. An application example is shown by which investors or policy-makers may determine how typical wind farm capital costs may influence financial project feasibility under a predetermined risk.

Forecasting Prices in Electricity Markets: Needs, Tools and Limitations

Electricity is a fundamental good for society. The price at which it is sold as a commodity influences all levels of economic activity and determines the profits and benefits that generators and consumers reap from participating in the electricity markets. Forecasting the electricity prices at different time-frames, namely in the short-run (daily), medium-term (seasons) or long-term (years), is of foremost importance for all industry stakeholders for cash flow analysis, capital budgeting and financial procurement as well as regulatory rule-making and integrated resource planning, among others. On the other hand, the process of price formation in competitive electricity markets is unique in terms of the different factors that come into play in the settlement process. These factors, which may be endogenous or exogenous to the market, bring about uncertainty and volatility to the electricity prices. This uncertainty hinders the forecast user’s ability to estimate the prices with accuracy at the different time-frames. This chapter explores the different reasons why forecasting electricity prices is necessary in electricity markets, the most widely used methodologies for short-term electricity price forecasting and their fundamental common limitations. This analysis is carried out using actual electricity price datasets.

Computation of Maximum Loading Points via the Factored Load Flow

This paper presents a fast and straightforward algorithm to obtain the maximum loading points of power systems by simply performing bisection searches between feasible and infeasible load flow cases. The proposed method exploits the ability and robustness of the factored load flow solution procedure to converge to complex solutions well beyond the maximum loadability points. Test cases on a diversity of benchmark cases show that the new method is computationally attractive when compared with existing continuation power flow methods.

The Value of Wind Resource Geographic Diversity for Wind Farm Profitability

Portfolio analysis theory and an econometric wind farm revenue estimation model under limited information are combined for the quantification of the value of the geographic diversity of the wind resource in the profitability of diversified wind farm investments. Investment decisions are driven by a compromise between risk and return. The proposed model draws on actual data to estimate the extent under which, by diversifying a portfolio of wind farms, revenue per MW-installed may be increased or risk may be reduced in comparison to investing all available capital on a single site. Results show that for the particular geographical setting explored, estimated benefits may provide pivotal competitiveness for wind farm investors in the estimation of optimal rates in Request for Proposal bidding processes or bilateral fixed-rate negotiation with local utilities.