Renewable power forecast to scheduling of thermal units

In this work is discussed the importance of the renewable production forecast in an island environment. A probabilistic forecast based on kernel density estimators is proposed. The aggregation of these forecasts, allows the determination of thermal generation amount needed to schedule and operating a power grid of an island with high penetration of renewable generation. A case study based on electric system of S. Miguel Island is presented. The results show that the forecast techniques are an imperative tool help the grid management.

Self-scheduling and bidding strategies of thermal units with stochastic emission constraints

This paper is on the self-scheduling problem for a thermal power producer taking part in a pool-based electricity market as a price-taker, having bilateral contracts and emission-constrained. An approach based on stochastic mixed-integer linear programming approach is proposed for solving the self-scheduling problem. Uncertainty regarding electricity price is considered through a set of scenarios computed by simulation and scenario-reduction. Thermal units are modelled by variable costs, start-up costs and technical operating constraints, such as: forbidden operating zones, ramp up/down limits and minimum up/down time limits. A requirement on emission allowances to mitigate carbon footprint is modelled by a stochastic constraint. Supply functions for different emission allowance levels are accessed in order to establish the optimal bidding strategy. A case study is presented to illustrate the usefulness and the proficiency of the proposed approach in supporting biding strategies. (C) 2014 Elsevier Ltd. All rights reserved.

Growth and development of honey weed based on days or thermal units

This work was carried out with the objective of evaluating the growth and development of honey weed (Leonurus sibiricus) based on days or thermal units (growing degree days). Thus, two independent trials were developed to quantify the phenological development and total dry mass accumulation in increasing or decreasing photoperiod conditions. Considering only one growing season, honey weed phenological development was perfectly fit to day scale or growing degree days, but with no equivalence between seasons, with the plants developing faster at increasing photoperiods, and flowering 100 days after seeding. Even day-time scale or thermal units were not able to estimate general honey weed phenology during the different seasons of the year. In any growing condition, honey weed plants were able to accumulate a total dry mass of over 50 g per plant. Dry mass accumulation was adequately fit to the growing degree days, with highlights to a base temperature of 10 ºC. Therefore, a higher environmental influence on species phenology and a lower environmental influence on growth (dry mass) were observed, showing thereby that other variables, such as the photoperiod, may potentially complement the mathematical models.

Initial growth and development of southern sandbur based on thermal units

Availability of basic information on weed biology is an essential tool for designing integrated management programs for agricultural systems. Thus, this study was carried out in order to calculate the base temperature (Tb) of southern sandbur (Cenchrus echinatus), as well as fit the initial growth and development of the species to accumulated thermal units (growing degree days - GDD). For that purpose, experimental populations were sown six times in summer/autumn conditions (decreasing photoperiod) and six times in winter/spring condition (increasing photoperiod). Southern sandbur phenological evaluations were carried out, on alternate days, and total dry matter was measured when plants reached the flowering stage. All the growth and development fits were performed based on thermal units by assessing five base temperatures, as well as the absence of it. Southern sandbur development was best fit with Tb = 12 ºC, with equation y = 0,0993x, where y is the scale of phenological stage and x is the GDD. On average, flowering was reached at 518 GDD. Southern sandbur phenology may be predicted by using mathematical models based on accumulated thermal units, adopting Tb = 12 ºC. However, other environmental variables may also interfere with species development, particularly photoperiod.

Growth and development of sourgrass based on days or thermal units

This work was carried out with the objective of evaluating growth and development of sourgrass (Digitaris insularis) based on days or thermal units (growing degree days - GDD). Two independent trials were developed aiming to quantify the species' phenological development and total dry matter accumulation in increasing or decreasing photoperiod conditions. Plants were grown in 4 L plastic pots, filled with commercial substrate, adequately fertilized. In each trial, nine growth evaluations were carried out, with three replicates. Phenological development of sourgrass was correctly fit to time scale in days or GDD, through linear equation of first degree. Sourgrass has slow initial growth, followed by exponential dry matter accumulation, in increasing photoperiod condition. Maximum total dry matter was 75 and 6 g per plant for increasing and decreasing photoperiod conditions, respectively. Thus, phenological development of sourgrass may be predicted by mathematical models based on days or GDD; however, it should be noted that other environmental variables interfere on the species' growth (mass accumulation), especially photoperiod.

Growth and Development of Purple Nutsedge Based on Days or Thermal Units

This work was carried out with the objective of elaborating mathematical models to predict growth and development of purple nutsedge (Cyperus rotundus) based on days or accumulated thermal units (growing degree days). Thus, two independent trials were developed, the first with a decreasing photoperiod (March to July) and the second with an increasing photoperiod (August to November). In each trial, ten assessments of plant growth and development were performed, quantifying total dry matter and the species phenology. After that, phenology was fit to first degree equations, considering individual trials or their grouping. In the same way, the total dry matter was fit to logistic-type models. In all regressions four temporal scales possibilities were assessed for the x axis: accumulated days or growing degree days (GDD) with base temperatures (Tb) of 10, 12 and 15 oC. For both photoperiod conditions, growth and development of purple nutsedge were adequately fit to prediction mathematical models based on accumulated thermal units, highlighting Tb = 12 oC. Considering GDD calculated with Tb = 12 oC, purple nutsedge phenology may be predicted by y = 0.113x, while species growth may be predicted by y = 37.678/(1+(x/509.353)-7.047).

Determination of the critical period of weed control in corn using a thermal basis

Field studies were conducted over 3 years in southeast Buenos Aires, Argentina, to determine the critical period of weed control in maize (Zea mays L.). The treatments consisted of two different periods of weed interference, a critical weed-free period, and a critical time of weed removal. The Gompertz and logistic equations were fitted to relative yields representing the critical weed-free and the critical time of weed removal, respectively. Accumulated thermal units were used to describe each period of weed-free or weed removal. The critical weed-free period and the critical time of weed removal ranged from 222 to 416 and 128 to 261 accumulated thermal units respectively, to prevent yield losses of 2.5%. Weed biomass proved to be inverse to the crop yield for all the years studied. When weeds competed with the crop from emergence, a large increase in weed biomass was achieved 10 days after crop emergence. However, few weed seedlings emerged and prospered after the 5-6 leaf maize stage (10-20 days after emergence).

Coordinated Scheduling of Wind-Thermal Gencos in Day-Ahead Markets

This paper presents a stochastic mixed-integer linear programming approach for solving the self-scheduling problem of a price-taker thermal and wind power producer taking part in a pool-based electricity market. Uncertainty on electricity price and wind power is considered through a set of scenarios. Thermal units are modeled by variable costs, start-up costs and technical operating constraints, such as: ramp up/down limits and minimum up/down time limits. An efficient mixed-integer linear program is presented to develop the offering strategies of the coordinated production of thermal and wind energy generation, aiming to maximize the expected profit. A case study with data from the Iberian Electricity Market is presented and results are discussed to show the effectiveness of the proposed approach.

Bidding Decision of Wind-Thermal GenCo in Day-Ahead Market

This paper deals with the self-scheduling problem of a price-taker having wind and thermal power production and assisted by a cyber-physical system for supporting management decisions in a day-ahead electric energy market. The self-scheduling is regarded as a stochastic mixed-integer linear programming problem. Uncertainties on electricity price and wind power are considered through a set of scenarios. Thermal units are modelled by start-up and variable costs, furthermore constraints are considered, such as: ramp up/down and minimum up/down time limits. The stochastic mixed-integer linear programming problem allows a decision support for strategies advantaging from an effective wind and thermal mixed bidding. A case study is presented using data from the Iberian electricity market.

Bidding strategy of wind-thermal energy producers

This paper presents a stochastic mixed-integer linear programming approach for solving the self-scheduling problem of a price-taker thermal and wind power producer taking part in a pool-based electricity market. Uncertainty on electricity price and wind power is considered through a set of scenarios. Thermal units are modelled by variable costs, start-up costs and technical operating constraints, such as: forbidden operating zones, ramp up/down limits and minimum up/down time limits. An efficient mixed-integer linear program is presented to develop the offering strategies of the coordinated production of thermal and wind energy generation, having as a goal the maximization of profit. A case study with data from the Iberian Electricity Market is presented and results are discussed to show the effectiveness of the proposed approach.

A practical approach for profit-based unit commitment with emission limitations

This paper proposes a practical approach for profit-based unit commitment (PBUC) with emission limitations. Under deregulation, unit commitment has evolved from a minimum-cost optimisation problem to a profit-based optimisation problem. However, as a consequence of growing environmental concern, the impact of fossil-fuelled power plants must be considered, giving rise to emission limitations. The simultaneous address of the profit with the emission is taken into account in our practical approach by a multiobjective optimisation (MO) problem. Hence, trade-off Curves between profit and emission are obtained for different energy price profiles, in a way to aid decision-makers concerning emission allowance trading. Moreover, a new parameter is presented, ratio of change, and the corresponding gradient angle, enabling the proper selection of a compromise commitment for the units. A case study based on the standard IEEE 30-bus system is presented to illustrate the proficiency Of Our practical approach for the new competitive and environmentally constrained electricity supply industry.

Nonlinear optimization method for short-term hydro scheduling considering head-dependency

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent reservoirs under competitive environment. We propose a new nonlinear optimization method to consider hydroelectric power generation as a function of water discharge and also of the head. Head-dependency is considered on short-term hydro scheduling in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems, providing a higher profit at a negligible additional computation time in comparison with a linear optimization method that ignores head-dependency.

Spinning reserve and emission unit commitment through stochastic optimization

This paper proposes a stochastic mixed-integer linear approach to deal with a short-term unit commitment problem with uncertainty on a deregulated electricity market that includes day-ahead bidding and bilateral contracts. The proposed approach considers the typically operation constraints on the thermal units and a spinning reserve. The uncertainty is due to the electricity prices, which are modeled by a scenario set, allowing an acceptable computation. Moreover, emission allowances are considered in a manner to allow for the consideration of environmental constraints. A case study to illustrate the usefulness of the proposed approach is presented and an assessment of the cost for the spinning reserve is obtained by a comparison between the situation with and without spinning reserve.

Spinning reserve and emission unit commitment through stochastic optimization

This paper proposes a stochastic mixed-integer linear approach to deal with a short-term unit commitment problem with uncertainty on a deregulated electricity market that includes day-ahead bidding and bilateral contracts. The proposed approach considers the typically operation constraints on the thermal units and a spinning reserve. The uncertainty is due to the electricity prices, which are modeled by a scenario set, allowing an acceptable computation. Moreover, emission allowances are considered in a manner to allow for the consideration of environmental constraints. A case study to illustrate the usefulness of the proposed approach is presented and an assessment of the cost for the spinning reserve is obtained by a comparison between the situation with and without spinning reserve.

Esclonamento de máquinas de cogeração utilzando programação inteira mista

As centrais termoelétricas convencionais convertem apenas parte do combustível consumido na produção de energia elétrica, sendo que outra parte resulta em perdas sob a forma de calor. Neste sentido, surgiram as unidades de cogeração, ou Combined Heat and Power (CHP), que permitem reaproveitar a energia dissipada sob a forma de energia térmica e disponibilizá-la, em conjunto com a energia elétrica gerada, para consumo doméstico ou industrial, tornando-as mais eficientes que as unidades convencionais Os custos de produção de energia elétrica e de calor das unidades CHP são representados por uma função não-linear e apresentam uma região de operação admissível que pode ser convexa ou não-convexa, dependendo das caraterísticas de cada unidade. Por estas razões, a modelação de unidades CHP no âmbito do escalonamento de geradores elétricos (na literatura inglesa Unit Commitment Problem (UCP)) tem especial relevância para as empresas que possuem, também, este tipo de unidades. Estas empresas têm como objetivo definir, entre as unidades CHP e as unidades que apenas geram energia elétrica ou calor, quais devem ser ligadas e os respetivos níveis de produção para satisfazer a procura de energia elétrica e de calor a um custo mínimo. Neste documento são propostos dois modelos de programação inteira mista para o UCP com inclusão de unidades de cogeração: um modelo não-linear que inclui a função real de custo de produção das unidades CHP e um modelo que propõe uma linearização da referida função baseada na combinação convexa de um número pré-definido de pontos extremos. Em ambos os modelos a região de operação admissível não-convexa é modelada através da divisão desta àrea em duas àreas convexas distintas. Testes computacionais efetuados com ambos os modelos para várias instâncias permitiram verificar a eficiência do modelo linear proposto. Este modelo permitiu obter as soluções ótimas do modelo não-linear com tempos computationais significativamente menores. Para além disso, ambos os modelos foram testados com e sem a inclusão de restrições de tomada e deslastre de carga, permitindo concluir que este tipo de restrições aumenta a complexidade do problema sendo que o tempo computacional exigido para a resolução do mesmo cresce significativamente.