Chilean Central Interconnected System Research Articles

Optimizing Hydrothermal Scheduling with Non-Convex Irrigation Constraints: Case on the Chilean Electricity System

Water stored in large reservoirs can support various economic activities, such as electricity generation and agriculture, that need to be efficiently coordinated. Such coordination is usually undertaken through optimization models that use hydro plants to minimize total electricity production cost subject to an array of prescribed constraints that ensure delivery of sufficient volumes of water to further sectors. In this context, we present a sub-optimal approach based on SDDP method to schedule power plants in a hydro-thermal system that presents non-convex irrigation constraints. We show applicability of this approach in the Chilean Central Interconnected System (SIC), where we accurately model current prescribed rules that coordinate water uses between electricity and agriculture sectors. We demonstrate that the presented SDDP-based approach determines feasible and near-optimal solutions with costs reasonably close to those optimally determined through alternative MILP formulation (that can properly capture non-convexity). We also found, however, that there may be issues associated with the levels of security of supply of the near-optimal solution since its stored water volumes tend to be lower than those associated with the optimum MILP solution.

Short-term Hydrothermal Generation Scheduling Using a Parallelized Stochastic Mixed-integer Linear Programming Algorithm

Short-term hydrothermal generation scheduling (STHTGS) is the optimization process through which decisions are made about the commitments of thermal generators and the allocation of hydro energy resources in the planning horizon (1 day to 1 week), while satisfying a large set of technical constraints. Uncertainty in this problem may appear in different modelling parameters, but the extended stochastic version of the STHTGS problem may lead to impractical solution times. This paper discusses the application of a parallelized stochastic mixed-integer linear program (SMILP) to solve the stochastic STHTGS problem. In order to decrease simulation time a scenario-based decomposition approach based on the progressive hedging (PH) algorithm is proposed. Computational experiments are conducted in two multi-processor nodes of a cluster for different numbers of stochastic scenarios. The algorithm is tested in the Chilean Central Interconnected System using a problem instance considering a weekly horizon with hourly resolution. Results show that the PH algorithm has good convergence properties, needing only a few iterations to converge. Furthermore, as PH generates similarly sized sub-problems, the parallel version of the algorithm scales up quite well as the number of scenarios is increased.

Generation Capacity Expansion Planning Under Hydro Uncertainty Using Stochastic Mixed Integer Programming and Scenario Reduction

Generation capacity expansion planning (GCEP) is the process of deciding on a set of optimal new investments in generation capacity to adequately supply future loads, while satisfying technical and reliability constraints. This paper shows the application of stochastic mixed-integer programming (SMIP) to account for hydrological uncertainty in GCEP for the Chilean Central Interconnected System, using a two-stage SMIP multi-period model with investments and optimal power flow (OPF). The substantial computational challenges posed by GCEP imply compromising between the detail of the stochastic hydrological variables and the detail of the OPF. We selected a subset of hydrological scenarios to represent the historical hydro variability using moment-based scenario reduction techniques. The tradeoff between modeling accuracy and computational complexity was explored both regarding the simplification of the MIP problem and the differences in the variables of interest. Using a simplified OPF model, we found the difference of using a subset of hydro scenarios to be small when compared with using a full representation of the stochastic variable. Overall, SMIP with scenario reduction provided optimal capacity expansion plans whose investment plus expected operational costs were between 1.3% and 1.9% cheaper than using a deterministic approach and proved to be more robust to hydro variability.

Hydrological scenario reduction for stochastic optimization in hydrothermal power systems

AbstractMost of the methods developed for hydrothermal power system planning are based on scenario‐based stochastic programming and therefore represent the stochastic hydro variable (water inflows) as a finite set of hydrological scenarios. As the level of detail in the models grows and the associated optimization problems become more complex, the need to reduce the number of scenarios without distorting the nature of the stochastic variable is arising. In this paper, we propose a scenario reduction method for discrete multivariate distributions based on transforming the moment‐matching technique into a combinatorial optimization problem. The method is applied to hydro inflow data from the Chilean Central Interconnected System and is benchmarked against results for the optimal operation of the Chilean Central Interconnected System determined with the selected subsets and the complete set of historical hydrological scenarios. Simulation results show that the proposed scenario‐reduction method could adequately approximate the probability distribution of the objective function of the operational planning problem. Copyright © 2014 John Wiley & Sons, Ltd.

Iterative Heuristic Response Surface Method for Transmission Expansion Planning

Transmission expansion planning has become a central challenge in the design of competitive electricity markets. The underlying optimization/decision problem exhibits a high level of complexity, being nonconvex, dynamic, and nonlinear, with multiple objective functions and a wide range of uncertainties. In this paper we propose a methodology for handling the expansion problem that involves a novel adaptation of an iterative optimization method based on response surface models already used successfully in the design and manufacture of integrated circuits. It is implemented in a distributed environment using Web services, and is validated and compared with a genetic algorithm based methodology. An application of the proposed methodology to the Chilean Central Interconnected System is then presented and analyzed. The results demonstrate its potential in the fields of risk analysis and decision support systems in power markets.

Primary and secondary frequency regulation in a longitudinal hydrothermal system by Liapunov method

The problem of primary and secondary frequency regulation of a multi-machine power system is analysed with a Liapunov function method based on a quadratic performance index. The main purpose is to determine the best set of parameters of primary and secondary regulation according to an optimisation criterion. The objective consists of achieving a settling time as short as possible which is relevant in a longitudinal system, whose structure includes long transmission lines with a reduced number of loops. Frequency and turbine valve positions are used as state variables, and optimal control parameters for primary and secondary regulation are used as control variables. Performance index behaviour under different frequency control schemes is then used to determine the optimal values to set the droops and gains of primary and secondary regulation. Tests for different disturbance locations and selection of regulating units are simulated on a model of the Chilean Central Interconnected System (CIS). It is shown that significant improvements can be achieved with the proposed method.

Congestion Management and Transmission Rights in Centralized Electric Markets

A new congestion management system is proposed, applied under nodal and zonal dispatches with implementation of fixed transmission rights (FTR) and flowgate rights (FGR), respectively. The FTR model proves to be especially suitable for congestion management in deregulated centralized market structures with nodal dispatch, while the FGR is suitable for decentralized markets. The main contribution of this work is a nontraditional valuation of FGR under a centralized market, such as those present in Latin America, that builds a link between both transmission rights under the same market structure. To accomplish that, a computational model is developed, implementing marginal theory where congestion components are introduced in the pricing model. An application to the Chilean Central Interconnected System indicates that FGR presents advantages over FTR regarding signals on grid use, but its application results in complications that make its implementation unattractive.

A scenario simulation approach for market power analysis in hydrothermal systems

This paper focuses on markets based on physical bilateral contracts combined with a power exchange (PX). The main feature to be analyzed is the behavior of the hydrothermal system where one or more companies have a big reservoir with capacity for inter annual regulation. In this work, inter annual regulation means the ability of a reservoir to allocate water from consecutive years. The use of the reservoirs in a context of a power exchange market with competition is the main objective of this study. Results on the Chilean Central Interconnected System using stochastic dynamic programming are presented and discussed.

A Scenario Simulation Approach for Market Power Analysis in Hydrothermal Systems

This paper focuses on markets based on physical bilateral contracts combined with a power exchange (PX). The main feature to be analyzed is the behavior of the hydrothermal system where one or more companies have a big reservoir with capacity for interannual regulation. In this work, interannual regulation means the ability of a reservoir to allocate water from consecutive years. The use of the reservoirs in a context of a power exchange market with competition is the main objective of this study. Results on the Chilean central interconnected system using stochastic dynamic programming are presented and discussed.

Electromechanical Transients Simulation on a Multicomputer via the VDHN-Maclaurin Method

This paper reports simulations of power systems electromechanical transients on a multicomputer, formulated as a nonlinear algebraic problem by using the time parallelization concept. The bi-factorized inversion, which is the most time consuming stage of the simulation, is solved by the Very Dishonest Newton (VDHN)-Maclaurin method, a fully parallel indirect method based on the decomposition of the nonupdated Jacobian matrix. This proposal is made to orient the search for the decomposition based on a sufficient condition for the convergence of the Maclaurin series, which is a desirable situation for the design of more robust algorithms for power system simulation. Such condition keeps a close relation with a physical coupling property exhibited by power systems, and the characteristics of the simulation method. Theoretical and numerical results show that a successful implementation of this method can be better reached when the Jacobian matrix is decomposed as a block diagonal matrix plus a matrix with off diagonal blocks elements, the latter representing weak couplings between the diagonal blocks. The /spl epsiv/ Decomposition is used to satisfy the sufficient condition for convergence and the Longest Path Scheduling Method to prevent the uneven loading of processors, permitting to adapt the method in a efficient way on a coarse grain computer. The parallel simulation was written in C language and implemented on a Parsytec PowerXplorer multicomputer. Tests using electromechanical models of the Chilean Central interconnected system and the IEEE300 test system were made to evaluate the advantages and drawbacks of the parallel method.

Electromechanical transients simulation on a multicomputer via the VDHN-Maclaurin method

This paper reports simulations of power systems electromechanical transients on a multicomputer, formulated as a nonlinear algebraic problem by using the time parallelization concept. The bi-factorized inversion, which is the most time consuming stage of the simulation, is solved by the "Very Dishonest Newton (VDHN)-Maclaurin" method, a fully parallel indirect method based on the decomposition of the nonupdated Jacobian matrix. This proposal is made to orient the search for the decomposition based on a sufficient condition for the convergence of the Maclaurin series, which is a desirable situation for the design of more robust algorithms for power system simulation. Such condition keeps a close relation with a physical coupling property exhibited by power systems, and the characteristics of the simulation method. Theoretical and numerical results show that a successful implementation of this method can be better reached when the Jacobian matrix is decomposed as a block diagonal matrix plus a matrix with off diagonal blocks elements, the latter representing weak couplings between the diagonal blocks. The /spl epsiv/ Decomposition is used to satisfy the sufficient condition for convergence and the Longest Path Scheduling Method to prevent the uneven loading of processors, permitting to adapt the method in a efficient way on a coarse grain computer. The parallel simulation was written in C language and implemented on a Parsytec PowerXplorer multicomputer. Tests using electromechanical models of the Chilean Central interconnected system and the IEEE300 test system were made to evaluate the advantages and drawbacks of the parallel method.