This essay performs a reliability constraint stochastic model for unit commitment problem by considering generation and transmission constraints with high wind penetration and volatility of load demands. This query is expressed as a MILP that is based on the linear direct current model. The proposed approach models uncertainty of wind generators output power, load demand fluctuations and stochastic elements outage of the system like generators and transmission lines. In this paper, stochastic interdependence between random variables like wind speed and load demand is recognized. To establish the probability distribution of these correlated random variables, Copula theory is applied. Correlation structure between wind speed of different locations and a group of loads existing in the same area is investigated and studied based on historical data. For representing these uncertainties in the stochastic unit commitment problem, possible scenarios are generated with Monte Carlo simulation method. The reliability constraints are utilized in each scenario to evaluate the feasibility of solutions from a reliability point. The introduced stochastic UC is executed on the RTS 96-bus test system. Numerical results demonstrate the advantages of implementing stochastic programming on the UC problem by taking into account the intermittent behavior of wind energy and load inconstancy.

Reliability constraint stochastic UC by considering the correlation of random variables with Copula theory

Evaluating rotational inertia as a component of grid reliability with high penetrations of variable renewable energy

In this paper, the Unit Commitment (UC) problem in a power network with low levels of rotational inertia is studied. Frequency-related constraints, namely the limitation on Rate-of-Change-of-Frequency (RoCoF), frequency nadir and steady-state frequency error, are derived from a uniform system frequency response model that incorporates dynamics and controls of both synchronous generators and grid-forming inverters. These constraints are then included into a stochastic UC formulation that accounts for wind power and equipment contingency uncertainties using a scenario-tree approach. In contrast to the linear RoCoF and steady-state frequency error constraints, the nadir constraint is highly nonlinear. To preserve the mixed-integer linear formulation of the stochastic UC model, we propose a computationally efficient approach that allows to recast the nadir constraint by introducing appropriate bounds on relevant decision variables of the UC model. This method is shown to be generally more accurate and computationally more efficient for medium-sized networks than a piece-wise linearization method adapted from the literature. Simulation results for a modified IEEE RTS-96 system revealed that the inclusion of inertia-related constraints significantly influences the UC decisions and increases total costs, as more synchronous machines are forced to be online to provide inertial response.

Stochastic Unit Commitment in Low-Inertia Grids

Understanding the impact of non-synchronous wind and solar generation on grid stability and identifying mitigation pathways

Day-ahead stochastic coordinated scheduling for thermal-hydro-wind-photovoltaic systems

An increased use of variable generation technologies such as wind power and photovoltaic generation can have important effects on system frequency performance during normal operation as well as contingencies. The main reasons are the operational principles and inherent characteristics of these power plants like operation at maximum power point and no inertial response during power system imbalances. This has led to new challenges for Transmission System Operators in terms of ensuring system security during contingencies. In this context, this paper proposes a Robust Unit Commitment including a set of additional frequency stability constraints. To do this, a simplified dynamic model of the initial system frequency response is used in combination with historical frequency nadir data during contingencies. The proposed approach is especially suitable for power systems with cost-based economic dispatch like those in most Latin American countries. The study is done considering the Northern Interconnected System of Chile, a 50-Hz medium size isolated power system. The results obtained were validated by means of dynamic simulations of different system contingencies.

https://www.mdpi.com/1996-1073/9/11/957/pdf

Robust Unit Commitment Including Frequency Stability Constraints

Two-stage robust UC including a novel scenario-based uncertainty model for wind power applications

In recent years, a wide range of techniques has been developed to predict electoral results and to measure the influence of different factors in these results. In this paper, we analyze the influence of the political profile of candidates (characterized by personal and political features) and their campaign effort (characterized by electoral expenditure and by territorial deployment strategies retrieved from social networks activity) on the electoral results. This analysis is carried out by using three of the most frequent data analyitcs algorithms in the literature. For our analysis, we consider the 2017 Parliamentary elections in Chile, which are the first elections after a major reform of the electoral system, that encompassed a transition from a binomial to a proportional system, a modification of the districts’ structure, an increase in the number of seats, and the requirement of gender parity in the lists of the different coalitions. The obtained results reveal that, regardless of the political coalition, the electoral experience of candidates, in particular in the same seat they are running for (even when the corresponding district is modified), is by large the most influential factor to explain the electoral results. However, the attained results show that the influence of other features, such as campaign expenditures, depends on the political coalition. Additionally, by means of a simulation procedure, we show how different levels of territorial deployment efforts might impact on the results of candidates. This procedure could be used by parties and coalitions when planning their campaign strategies.

https://www.mdpi.com/2227-7390/9/8/902/pdf

The Impact of Candidates’ Profile and Campaign Decisions in Electoral Results: A Data Analytics Approach

Electoral systems are modified by individuals who have incentives to bias the rules for their political advantage (i.e., gerrymandering). To prevent gerrymandering, legislative institutions can rely on mathematical tools to guarantee democratic fairness and territorial contiguity. These tools have been successfully used in the past; however, there is a need to accommodate additional meanings of the term fairness within the electoral systems of modern democracies. In this paper, we present an optimization framework that considers multiple criteria for drawing districts and assigning the number of representatives. Besides some typical districting criteria (malapportionment and contiguity), we introduce novel criteria for ensuring territorial equilibrium and incentives for candidates to deploy their representation efforts fairly during their campaign and period in office. We test the method, which we denote as Multi-criteria Pen, in a recent and a forthcoming reform of the Chilean electoral system. The results show the potential of our tool to improve the current territorial design and offers insights on the motivations, objectives, and deficiencies of both reform plans.

Camilo Campos-Valdés

Papers

Robust Unit Commitment Including Frequency Stability Constraints

Two-stage robust UC including a novel scenario-based uncertainty model for wind power applications

The Impact of Candidates’ Profile and Campaign Decisions in Electoral Results: A Data Analytics Approach

A Multi-Criteria Pen for Drawing Fair Districts: When Democratic and Demographic Fairness Matter