Rodrigo Novaes, UFJF – BSc

This work deals with the long-term hydrothermal scheduling problem, also called energy planning. It investigates the cost impacts when the thermal dispatch is determined based on the expected inflow scenario, comparing it with an unusual (in this context) stochastic programming approach that considers multiple scenarios in the problem formulation, called here-and-now approach. A conceptual analysis based on fundamental concepts of stochastic programming is presented alongside the text, pointing out two conceptual errors possibly committed by the models currently used for policy and dispatch calculations. A case study is also presented, showing the benefits of using the stochastic model and of correctly representing the uncertainties or, in other words, of building a mathematical model that honestly represents the physical phenomenon reality.

Document only available in Portuguese. For further information, please directly contact the author or email PSR (psr@psr-inc.com).

Celso Dall'Orto, UNIFEI – MSc

The dispatch decisions along with the definition of the electricity market prices of the Brazilian power system are made based on stochastic optimization models. In these models, the goal is to minimize the expected value of operating costs over a period of study considering future uncertainties mainly associated with river flows. The medium-term model uses a planning horizon of five years plus five additional years as a “buffer”, to avoid the fast depletion of reservoirs in the end of the study horizon. The reduction in the study period and post-period-study, if it does not affect the short-term dispatch decisions, can bring gains such as reducing the size of the mathematical problems to be solved and thus reducing the simulations' computational time. The aim of this study is to analyze the possibility of such horizon reduction in the current simulations with the Brazilian system.

Document only available in Portuguese. For further information, please directly contact the author or email PSR (psr@psr-inc.com).

Mateus Cavaliere, UFRJ – BSc

The present work presents a methodology based on market equilibrium to predict future electricity prices in the environment of free market for contracts with duration of one and three years. In this approach, generators offer their contracting levels according to market prices (contracting supply curve) and the loads, in turn, stipulate their contracting levels for each market price (contracting demand curve), in the meeting point of the curves the equilibrium price is obtained in the contract market. The methodology is based on bi-level optimization with equilibrium constraints where scenarios represent the uncertainty of short-term market prices. The risk measure for generators and loads is a weighted average of expected value and the expected value within a confidence interval (known as Conditonal Value at Risk), of revenue and expenditure, reflecting their degrees of risk aversion.

Document only available in Portuguese. For further information, please directly contact the author or email PSR (psr@psr-inc.com).

Igor Carvalho, UFRJ – BSc

The origin of electric power systems expansion problem is based on new investments necessity on generation and transmission systems due to constant load growth in order to fulfill the expansion plan predicted. Also, to adequately provide reactive power through the electric network, it is necessary an adequate shunt equipment allocation equipment. This must be done in order to keep voltage magnitude levels between acceptable boundaries, which guarantees a safe operation of the system. To do so, it is necessary to make an reactive power expansion analysis of the system which consists in solving a non-linear and non-convex power flow optimization problem. Due to problem’s high complexity aforementioned, which has a large number of variables, the state of art commercial software tools used for generation and transmission planning are still in need of using heuristics to generate potentially robust and economically efficient solutions for the system analyzed. Once the state of art solution is based on a superposition of the expansion plans found in each scenario, any investment cost reduction due to an application of a method considering all the scenarios can result in huge savings. Therefore, in the present work, it is proposed the application of the decomposition method called Progressive Hedging to the problem of expansion planning of reactive power equipment. The main goal is to obtain cost reductions on reactive investment plans for electric power systems.

Document only available in Portuguese. For further information, please directly contact the author or email PSR (psr@psr-inc.com).

Lucas Okamura, UFRJ – BSc

The transmission expansion planning of electrical systems is a key component to ensure a long-term equilibrium between the demand and supply of electrical energy. If the objective is to seek the plan with minimum investment costs, optimization techniques applied by computational models are normally used. However, if the transmission system has too many circuits, those models can require big computation efforts to find the optimal solution. This course conclusion work presents a methodology to calculate the optimal transmission expansion plan for transmission systems composed by multiples subsystem or countries, without requiring representative computation efforts. Firstly, a quick literature review about transmission expansion planning techniques will be presented. After that, the proposed methodology will be explained and applied in a case that represents the Central America transmission system.

Document only available in Portuguese. For further information, please directly contact the author or email PSR (psr@psr-inc.com).

Daniela Bayma, UFRJ – BSc

This course completion assignment presents the Beneficiary Methodology and its mathematical formulation as a proposal for transmission cost allocation. It is characterized by splitting circuit costs among agents who get economic benefit from these circuits existence/construction. The benefit evaluation is made through an analysis on demand marginal costs and generators dispatch with and without the circuit construction. Beneficiaries are defined as generators and consumers who, respectively, increase their revenues and reduce their payments with a transmission line existence. In this undergraduate thesis, a python script was made to perform simulations of adding and removing circuits. This script works with the software SDDP developed by PSR that determines the minimum cost dispatches for the system operation. Intending to validate and demonstrate the applicability of the methodology case studies are also presented. Furthermore, this study highlights other existing cost allocation methodologies and evaluates the state of art in which they are found. Besides, it stands out advantages and downsides of each method compared to the proposed methodology.

Document only available in Portuguese. For further information, please directly contact the author or email PSR (psr@psr-inc.com).