Maria Teresa Vespucci

A stochastic model for the daily coordination of pumped storage hydro plants and wind power plants

We propose a stochastic model for the daily operation scheduling of a generation system including pumped storage hydro plants and wind power plants, where the uncertainty is represented by the hourly wind power production. In order to assess the value of the stochastic modeling, we discuss two case studies: in the former the scenario tree is built so as to include both low and high wind power production scenarios, in the latter the scenario tree is built on historical wind speed data covering a time span of one and a half year. The Value of the Stochastic Solution, computed by a modified new procedure, shows that in scenarios with low wind power production the stochastic solution allows the producer to obtain a profit which is greater than the one associated to the deterministic solution. In-sample stability of the optimal function values for increasing number of scenarios is reported.

Handbook of risk management in energy production and trading

In the past decade there have been multiple high-profile cases of cascading blackouts, often resulting in the disconnection of tens of millions of consumers in large areas. It appears that in hindsight many of these disturbances could have been prevented by timely interventive action. In the actual cases, however, lack of complete knowledge about the state of the system undergoing a blackout event has prevented such action. This chapter reviews approaches to the problem of finding optimal interventions for a power system in the early stages of a cascading blackout. Conceptually the problem is one of optimization under uncertainty or robust optimization: the goal is to find a set of corrective actions that will guarantee power supply to as many customers as possible, in all, or at least most, of the possible states that the system may be in. To tackle the problem directly as a stochastic or robust optimization problem is intractable due to the complexities involved, foremost the number of possible states that would have to be considered. We argue, guided by example, that a robust response is to disconnect lines in such a manner as to create an island containing the affected part of the network. We give an overview of such approaches, notably those involving mixed-integer programming to directly design islands that admit a stable steady-state operating point.

A mixed integer nonlinear optimization model for gas sale company

In this paper the authors propose an optimisation model, called OMoGaS (Optimisation Modelling for Gas Seller), to assist companies dealing with gas retail commercialisation. The model takes into account the limits on price imposed by law on small consumers as well as the gas company policies in order to explore the commercial consequences of different policies. The GAMS framework is used for the optimisation of the defined MINLP model where the profit function is based on the number of contracts with the final consumers, on the tipology of consumers and on the cost supported to meet the final demand while the constraints include information on a maximum daily gas consumption, on yearly maximum and minimum comsumption in order to avoid penalties and on consumption profiles. A case study is presented.

Two-stage stochastic mixed integer optimization models for power generation capacity expansion with risk measures

We present two-stage stochastic risk averse optimization models for the power generation mix capacity expansion planning in the long run under uncertainty. Uncertainty is described by a set of possible scenarios in the second stage and uncertain parameters are the unit production costs of the existing power plants as well as those of the candidate plants of new technologies among which to choose, the market electricity price, the price of green certificates and the emission permits and the potential market share of the producer. The problem is expressed as a two-stage stochastic integer optimization model subject to technical constraints, market opportunities and budget constraints. First stage variables represent the number of new power plants for each candidate technology to be added to the existing generation mix every year of the planning horizon. Second stage variables are the continuous operation variables of all power plants in the generation mix along the time horizon. We solve the problem of the maximization of the net present value of the expected profits along the time horizon using both a risk neutral approach and different risk averse strategies (conditional value at risk, shortfall probability, expected shortage and first- and second-order stochastic dominance), under different hypotheses of the available budget, analysing the impact of each risk averse strategy on the expected profit. Results show that risk control strongly reduces the possibility of reaching unwanted scenarios as well as providing consistent solutions under different strategies.

A stochastic model for investments in different technologies for electricity production in the long period

We present a single stage stochastic mixed integer linear model for determining the optimal mix of different technologies for electricity generation, ranging from coal, nuclear and combined cycle gas turbine to hydroelectric, wind and photovoltaic, taking into account the existing plants, the cost of investment in new plants, maintenance costs, purchase and sale of

Models for the generation expansion problem in the Italian electricity market

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A GAS RETAIL STOCHASTIC OPTIMIZATION MODEL BY MEAN REVERTING TEMPERATURE SCENARIOS

CO2 emission trading certificates and green certificates, in order to satisfy regulatory requirements. The power producer is assumed to be a price-taker. Stochasticity of future fuel prices, which affect the generation variable costs, is included in the model by means of a set of scenarios. The main contribution of the paper, beyond considering stochasticity in the future fuel prices, is the introduction of CVaR risk measure in the objective function in order to limit the possibility of low profits in bad scenarios with a fixed confidence level.

Hedging Electricity Portfolio for a Hydro-energy Producer via Stochastic Programming

We introduce a model for analyzing the upgrade of the national transmission grid that explicitly accounts for responses given by the power producers in terms of generation unit expansion. The problem is modeled as a bilevel program with a mixed integer structure in both upper and lower level. The upper level is defined by the transmission company problem which has to decide on how to upgrade the network. The lower level models the reactions of both power producers, who take a decision on new facilities and power output, and Market Operator, which strikes a new balance between demand and supply, providing new Locational Marginal Prices. We illustrate our methodology by means of an example based on the Garver’s 6-bus Network.