Unit Commitment and Economic Dispatch

Unit Commitment (UC) problem plays a key role in power systems' operations. Due to the strong modeling capacity of robust optimization to capture various complicated uncertainties in power systems, including those in renewable generation, load realization, demand response, and contingencies, two-stage robust UC has gained intensive attentions from both academic scholars and industry practitioners. However, such tri-level optimization problem is very challenging to solve, considering large-scale real power grids. In this research, we study new computational methods and strategies to address this challenge, including incorporating strong formulations for basic UC model, deriving new valid inequalities considering network constraints, and designing and implementing a decomposition procedure. On large-scale test instances, our solution approach leads to significantly better computational performance, compared to existing formulations or methods.

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.

This paper discusses a consensus-based alternating direction method of multipliers (ADMM) approach to solve the multi-area coordinated network-constrained unit commitment (NCUC) problem in a distributed manner. Due to political and technical difficulties, it is neither practical nor feasible to solve the multi-area coordination problem in a centralized fashion, which requires full access to all data of individual areas. In comparison, in the proposed fully-distributed approach, local NCUC problems of individual areas can be solved independently, and only limited information is exchanged among adjacent areas for facilitating multi-area coordination. Furthermore, as traditional ADMM can only guarantee convergence for convex problems, this paper discusses several strategies to mitigate oscillations, enhance convergence performance, and derive good-enough feasible solutions, including: (i) A tie-line power flow based area coordination strategy is designed to reduce the number of global consensus variables; (ii) Different penalty parameters \r{ho} are assigned to individual consensus variables and are updated via certain rules during the iterative procedure, which would reduce the impact of initial values of \r{ho} on convergence performance; (iii) Heuristic rules are adopted to fix certain unit commitment variables for avoiding oscillations during the iterative procedure; and (iv) An asynchronous distributed strategy is studied, which solves NCUC subproblems of small areas multiple times and exchanges information with adjacent areas more frequently within one complete run of slower NCUC subproblems of large areas. Numerical cases illustrate effectiveness of the proposed asynchronous fully-distributed NCUC approach, and investigate key factors that would affect its convergence performance.

Many different methods have been presented to solve unit commitment (UC) problem in literature with different advantages and disadvantages. The need for multiple runs, huge computational burden and time, and poor convergence are some of the disadvantages, where are especially considerable in large scale systems. In this paper, a new analytical and non-iterative method is presented to solve UC problem. In the proposed method, improved pre-prepared power demand (IPPD) table is used to solve UC problem, and then analytical “λ-logic” algorithm is used to solve economic dispatch (ED) sub-problem. The analytical and non-iterative nature of the mentioned methods results in simplification of the UC problem solution. Obtaining minimum cost in very small time with only one run is the major advantage of the proposed method. The proposed method has been tested on 10 unit and 40-100 unit systems with consideration of different constraints, such as: power generation limit of units, reserve constraints, minimum up and down times of generating units. Comparing the simulation results of the proposed method with other methods in literature shows that in large scale systems, the proposed method achieves minimum operational cost within minimum computational time.

Stochastic Hopfield artificial neural network for unit commitment and economic power dispatch

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.

Using suitable solution techniques to the unit commitment (UC) and economic load dispatch (ELD) problems play major role on finding an optimal power scheduling in electrical power system. The UC and ELD problems are to decide when and which generating units to commit and decommit, in order to minimize the total fuel cost over specified period subject to a large number of difficult constraints. Lagrangian relaxation (LR) has been widely used to solve UC and ELD. Recently bundling method (BM) has appeared to be one of the best multipliers updated techniques for LR. This method has promising and the fastest convergence characteristics for UC and ELD problems. For that reason, this paper is to solve the UC and ELD problems via LR, BM and interior point method. This paper explores also the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

The increasing penetration levels and stochastic characteristics of renewable energies and aging of transmission equipment bring potential negative impact on the economic and reliable operation of power grid. Therefore, the realistic and cost-effective choice for the utilities is to tap the potential of existing transmission infrastructures. Some smart grid technologies can leverage the potential transmission capacity and offer a flexible way for the power system operation. The dynamic thermal rating can evaluate the maximum transmission capacity of lines dynamically based on the environmental data. The optimal transmission switching can change the transmission topology and remove the transmission congestions. These technologies should be considered in the network-constrained unit commitment problem systematically to study their impact on the power system scheduling. However, the dynamic thermal rating incorporated network-constrained unit commitment studies are all based on the fixed transmission topology. So the overall influence of dynamic thermal rating and transmission line switching on network-constrained unit commitment has not been studied as yet. In this paper, the line switching technology and dynamic line rating according to multi-regional environmental information are incorporated in the network-constrained unit commitment framework. Case studies are implemented on a modified RTS-79 system. The simulation results verify the effectiveness of the coordination of two technologies in the reduction of generation cost and wind curtailment.

A layered matrix encoding cascade genetic algorithm and particle swarm optimization approach (GA-PSO) for unit commitment and economic load dispatch problem in a thermal power system is presented in this paper. The tasks of determining and allocating power generation to different thermal units in a way that the total power production cost is at the minimum subject to equality and inequality constraints makes unit commitment and economic load dispatch challenging. A case study, based on the thermal power generation problem presented in [1], is used to demonstrate the effectiveness of the proposed method in generating a cost-effective power generation schedule. The schedule obtained is compared with that of Linear Programming (LP) as reported in [1]. The results show that the proposed GA-PSO approach outperforms LP in solving the unit commitment and economic load dispatch problem for thermal power generation system in this case study.

An optimal solution to the unit commitment (UC) and economic load dispatch (ELD) problems lead to remarkable saving in the power system operational cost. UC and ELD main problems are to find the maximum profit and fast computation simulation time for the scheduling program. Lagrangian relaxation (LR) has become one of the best solution methods in solving the UC and ELD problems. The approach is claimed to be more efficient and easier than other methods in solving large-scale problems. When applying LR, the dual function needed to be updated at the higher level. Lately, bundling method (BM) is one of the best solution methods to Lagrangian dual problem. This paper presents LR technique, BM and interior point method for solving the UC and ELD problems. It will also explore the best possible way of updating Lagrangian multipliers with minimum computation time using fast programming techniques.

Objectives: The main objective of this paper is to solve the Cost Based Unit Commitment (CBIC) problem considering Renewable Energy Sources (RES) and Plug-in Electric vehicles (PEVs). The proposed problem minimizes the total operating of the interconnected system. Methods: A novel and recently developed successful optimization tool of Cat and Mouse Based Optimizer (CMBO) is proposed for optimal solution of Cost Based UC problem. The proposed CMBO approach is having two groups such as Cat group and Mice group for searching the global optimal solution with less computational time. It contains two phases like Cat’s movement towards Mice and Mice escape to a safe place is effectively updating the new position of Cat and Mice to easily reaching the best solutions. The control parameter of CMBO is number of agents is 50, number of variables is 10 and maximum number of iteration is 500. MATLAB 14.0 platform is utilized for the projected problem. Findings: The method tested on standard IEEE-39 bus system (10 generators and 24 hour) with an equivalent PEV and Wind farm. The CMBO approach minimize the total operating cost with various test cases. The outcomes such as UC schedule, Real power output of thermal, wind and PEV units, fuel cost, startup cost and total operating cost of the interconnected system are numerically and graphically reported. The total operating cost is 4.11 % minimized when compared with base case approach and 0.73 % reduced than the other existing method viz. Parallel UCs-RP method. Novelty: The CMBO is recently developed powerful optimizer and parameter free algorithm, so easily reaches the global optimal solutions. The obtained simulated results are compared with other mathematical and intelligent computational approaches for proving the efficiency and performance of the proposed CNBO technique. Keywords: Unit Commitment, Plug­in Electric Vehicles, Renewable Energy Sources, Cost minimization, Cat and Mouse Based Optimizer

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.

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 proposes an improved model predictive control (MPC) based approach for managing distributed energy resources (DER) of a microgrid. MPC based energy management systems are computationally intensive and can become too slow for online optimization. The main aim of this approach is to improve on the computational time and scalability of the current MPC based control schemes. This is done by decoupling the unit commitment (UC) and economic dispatch (ED) problems, and solving them separately. The control scheme takes into account the current and predicted prices of electricity, the forecasts of loads and availability of renewable energy. The proposed approach is compared to an MPC approach commonly found in literature. It performed better in terms of computation time and scalability, with a slight trade-off in cost minimization while respecting the constraints of the microgrid. The effectiveness of this approach is demonstrated using a mathematical model of a microgrid within the MATLAB environment.