Load sampling for scuc based on principal component analysis and kernel density estimation

Unified solution of a non-convex SCUC problem using combination of modified Branch-and-Bound method with Quadratic Programming

In this paper, Security Constrained Unit Commitment (SCUC) problem with combined Thermal- Solar generating units is solved using Artificial Bee Colony (ABC) algorithm. SCUC problem aims to obtain minimum generation cost while satisfying the system, network and security constraints. The SCUC problem is divided into Unit Commitment Problem (UCP) which is considered as the master problem and Security Constrained Economic Dispatch (SCED) is considered as the sub problem. Here, both thermal and solar generations are considered in UCP and SCED solutions. Binary Coded ABC Algorithm is used to solve the UCP and Real Coded ABC Algorithm is used for solving the SCED problem. The constraints such as spinning reserves, hourly load demands, ramp up/ramp down limits of generators, minimum up/down limits, line flow and voltage limits are considered in the problem formulation. Beta distribution function is employed to forecast the solar power generation in different seasons. The comparison is carried out with and without incorporating solar generation. The proposed method is validated on a 6 bus system and a South Indian 86 bus utility.

Day-ahead unit commitment (UC) solution methods seek to determine the status and output of all available generators. In a world with an increasing integration of renewable energy sources such as wind electric generators (WEG), the UC solution process must model and include WEGs too in the decision-making process. Power output of WEGs in a day-ahead decision-making process are usually modeled using a short-term probabilistic forecast. Inclusion of WEGs introduces uncertainty in the solution that may be quantified through an imbalance risk function. Thus a UC solution method should seek a solution to minimize cost and risk in schedule. Two strategies are proposed in this paper to minimize costs and handle risks introduced due to WEGs. These formulations are posed as fuzzy optimization models and are solved using the mixed integer linear programming (MILP) technique. The proposed strategies are tested on a 26- and a 100-generator systems with associated transmission networks that have three and six wind generators each. The results with two strategies of handling WEGs are discussed.

In recent years, high penetration of variable generating sources, such as wind power, has challenged independent system operators (ISO) in keeping a cheap and reliable power system operation. Any deviation between expected and real wind production must be absorbed by the power system resources (reserves), which must be available and ready to be deployed in real time. To guarantee this resource availability, the system resources must be committed in advance, usually the day-ahead, by solving the so-called unit commitment (UC) problem. If the quantity of committed resources is extremely low, there will be devastating and costly consequences in the system, such as significant load shedding. On the other hand, if this quantity is extremely high, the system operation will be excessively expensive, mainly because facilities will not be fully exploited. This thesis proposes computationally efficient models for optimal day-ahead planning in (thermal) power systems to adequately face the stochastic nature of wind production in the real-time system operation. The models can support ISOs to face the new challenges in short-term planning as uncertainty increases dramatically due to the integration of variable generating resources. This thesis then tackles the UC problem in the following aspects: Power system representation: This thesis identifies drawbacks of the traditional energy-block scheduling approach, which make it unable to adequately prepare the power system to face deterministic and perfectly known events. To overcome those drawbacks, we propose the ramp-based scheduling approach that more accurately describes the system operation, thus better exploiting the system flexibility. UC computational performance: Developing more accurate models would be pointless if these models considerably increase the computational burden of the UC problem, which is already a complex integer and non-convex problem. We then devise simultaneously tight and compact formulations under the mixed-integer programming (MIP) approach. This simultaneous characteristic reinforces the convergence speed by reducing the search space (tightness) and simultaneously increasing the searching speed (compactness) with which solvers explore that reduced space. Uncertainty management in UC: By putting together the improvements in the previous two aspects, this thesis contributes to a better management of wind uncertainty in UC, even though these two aspects are in conflict and improving one often means harming the other. If compared with a traditional energy-block UC model under the stochastic (deterministic) paradigm, a stochastic (deterministic) ramp-based UC model: 1) leads to more economic operation, due to a better and more detailed system representation, while 2) being solved significantly faster, because the core of the model is built upon simultaneously tight and compact MIP formulations. To further improve the uncertainty management in the proposed ramp-based UC, we extend the formulation to a network-constrained UC with robust reserve modelling. Based on robust optimization insights, the UC solution guarantees feasibility for any realization of the uncertain wind production, within the considered uncertainty ranges. This final model remains as a pure linear MIP problem whose size does not depend on the uncertainty representation, thus avoiding the inherent computational complications of the stochastic and robust UCs commonly found in the literature.

Unit Commitment solution using an optimized genetic system

Optimal scheduling of distributed battery storage for enhancing the security and the economics of electric power systems with emission constraints

Due to increasing integration of renewable generation into the electrical framework in last decades, the mathematical techniques required for the optimal day-ahead scheduling needs to be continuously improved, specifically for modeling the variability of these sources. In this paper, a method for producing a new solution for the stochastic unit commitment (UC) problem from the analysis of each scenario is developed. The methodology described in this paper can deal with a large number of scenario sets with a reasonable computational effort, by finding the common and feasible solutions for the scenario set under analysis.

Out of step with the rapid growth of China's electricity load demand, the infrastructure of power grid in many areas is not strong enough to insure the security of power system operation. In this case, considering the strict N-1 conditions of lines and transformers, the situation that there is no feasible solution for the security-constrained unit commitment (SCUC) might occasionally occur. In order to address this issue, a homogenized-overload model based on SCUC is proposed in this paper. The homogenized-overload model could obtain a reasonable, suboptimal solution reducing the security risks by lowering the average overload level and reducing the number of overload lines without sacrificing the economy of unit commitment. To identify the overload line set, an identifying method based on the Benders decomposition algorithm is also proposed. The homogenized-overload model and the identifying method are tested respectively in a 6-bus system case and a real provincial power system in China. Simulation results show the validity of the model and the method.

The ISO implements Security Constraint Unit Commitment (SCUC) for clearing of day-ahead market. In this paper, SCUC is also used for simultaneous clearing of energy and reserve market. Spinning reserve and of generating units and Demand Response Programs (DRPs) are considered as system operating reserves in the proposed model. A Mixed Integer Programming model is proposed for power system modeling along with DRPs. The proposed model is applied to the IEEE RTS to demonstrate its effectiveness. The results show that the use of DRPs' reserve, reduce the system operation costs and have high impact in reliability improvement and reduction in market clearing price in critical or peak hours.

This paper proposes an innovative genetic algorithm (GA) approach to solve the thermal unit commitment (UC) problem in power generation industry through a constraint satisfaction technique. Due to a large variety of constraints to be satisfied, the solution space of the UC problem is highly nonconvex, and therefore the UC problem can not be solved efficiently by the standard GA. To effectively deal with the constraints of the problem and greatly reduce the search space of the GA, the minimum up- and down-time constraints are embedded in the binary strings that are coded to represent the on-off states of the generating units. The violations of the other constraints are handled by integrating penalty factors into the cost function. Numerical results on the practical Taiwan Power (Taipower) system of 38 thermal units over a 24-hour period show that the features of easy implementation, fast convergence, and highly near-optimal solution in solving the UC problem can be achieved by the proposed GA approach. >

This paper presents the solving unit commitment (UC) problem using Modified Subgradient Method (MSG) method combined with Simulated Annealing (SA) algorithm. UC problem is one of the important power system engineering hard-solving problems. The Lagrangian relaxation (LR) based methods are commonly used to solve the UC problem. The main disadvantage of this group of methods is the difference between the dual and the primal solution which gives some significant problems on the quality of the feasible solution. In this paper, MSG method which does not require any convexity and differentiability assumptions is used for solving the UC problem. MSG method depending on the initial value reaches zero duality gap. SA algorithm is used in order to assign the appropriate initial value for MSG method. The major advantage of the proposed approach is that it guarantees the zero duality gap independently from the size of the problem. In order to show the advantages of this proposed approach, the four-unit Tuncbilek thermal plant and ten-unit thermal plant which is usually used in literature are chosen as test systems. Penalty function (PF) method is also used to compare with our proposed method in terms of total cost and UC schedule.

This paper presents centralized control for a wind farm using model predictive control (MPC) method. In order to solve intra-day unit commitment (UC) problem, the UC problem is solved by using the MPC method with short-term wind power forecasting. We introduce a new dynamics model for the UC with some constraints to utilize the benefits of the MPC method. The objective function considering the operation and maintenance costs is formulated by adding a new variable in order to average the operating time of each wind turbine (WT) within the whole time. The proposed method could solve the UC problems on-line using the prediction time horizon that could be selected flexibly considering time horizon based on wind power forecasting errors. From the simulation study using 10 WTs, we observed that the proposed dynamics model of UC effectively provided the optimal solution to each scenario. Numerical study will validate that the proposed method can be applied to solving the UC problem of a large scale wind farm by aggregating WTs.

A heuristic solution for short-term thermal unit commitment is presented. The algorithm has been developed as a FORTRAN-based production-type program. Tests of this algorithm on data provided by a midwest utility have demonstrated satisfactory results. The proposed algorithm produces the same unit commitment schedule as a standard dynamic programming (DP)-based algorithm in one fourth the computation time for the DP-based algorithm. The algorithm is nearly linear with the number of unit periods. A unit period is defined as the online duration time versus operation level for each unit. Operating system restrictions limit the prototype to 30 thermal power units as implemented on a PS/2 model 50 personal computer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents an algorithm for integrating and managing electrochemical energy storage systems (ESSs) on unit commitment (UC) problem. As some elements required for integrating electrochemical ESS, such as the power converter, have non-linear characteristics, its corresponding linear modeling could be difficult to be developed and included on the UC problem, which could lead to unfeasible solutions or unexpected results. In order to incorporate full models of ESS and its interface with the power system, in this paper an algorithm to incorporate electrochemical ESS management on the UC problem is presented. An insular power system of 10-units is analyzed, and conclusions are duly drawn.

In traditional electricity market unit commitment (UC) is done only for the reduction of operating cost. In the deregulated electricity market, for a secure and economical hourly generation schedule of the day ahead market, independent system operator (ISO) executes the security constrained unit commitment (SCUC) problem. The objective of the paper is to develop scheduling algorithm using hybrid particle swarm optimization (PSO) for electric generation that accounts directly for system security requirements. The proposed SCUC formulation includes constraints, such as hourly power demand, system reserves, ramp up/down limits, minimum ON/OFF duration limits. The innovation of our approach is to capture the system security requirements within a network flow sub-problem that is solved in conjunction with the unit commitment problem. To solve such SCUC model, a binary coded particle swarm optimization (BPSO) is used for unit commitment master problem and real coded particle swarm optimization (RPSO) is used for the economic dispatch sub-problem. The effectiveness of the suggested method to solve the SCUC problem is validated on different test systems.