Ramp Rate Constraints Research Articles

Power‐based transmission constrained unit commitment formulation with energy‐based reserve

Staircase transmission constrained unit commitment (TCUC) formulations have been used for decades and are considered as energy-based TCUC formulations (EbUC). Recently, it has been reported that EbUC formulations may result in undeliverable energy schedules. Some power-based TCUC formulations (PbUC) have been proposed to address this problem. However, exact continuous time-based power outputs of units are usually approximated in these PbUC formulations and ramp-rate capacities of units are not accurately modelled. Besides, the implicit coupling between ramp-rate constraints and spinning reserves is neglected in both EbUC and PbUC formulations, which may cause that scheduled spinning reserve levels are unavailable in some time periods. To address these problems, a new PbUC formulation is proposed in this study with continuous time-based power outputs. It is found that the formulation can be transformed into an equivalent mathematical program and a Lagrangian relaxation-based approach is presented. Numerical testing is performed for a 10-unit system and an IEEE 24-bus system. Results show that the model and the solution algorithm in this study are effective.

Large Scale Multi-area Static/Dynamic Economic Dispatch using Nature Inspired Optimization

Economic dispatch (ED) ensures that the generation allocation to the power units is carried out such that the total fuel cost is minimized and all the operating equality/inequality constraints are satisfied. Classical ED does not take transmission constraints into consideration, but in the present restructured power systems the tie-line limits play a very important role in deciding operational policies. ED is a dynamic problem which is performed on-line in the central load dispatch centre with changing load scenarios. The dynamic multi-area ED (MAED) problem is more complex due to the additional tie-line, ramp-rate and area-wise power balance constraints. Nature inspired (NI) heuristic optimization methods are gaining popularity over the traditional methods for complex problems. This work presents the modified particle swarm optimization (PSO) based techniques where parameter automation is effectively used for improving the search efficiency by avoiding stagnation to a sub-optimal result. This work validates the performance of the PSO variants with traditional solver GAMS for single as well as multi-area economic dispatch (MAED) on three test cases of a large 140-unit standard test system having complex constraints.

Two-phase mixed integer programming for non-convex economic dispatch problem with spinning reserve constraints

This paper proposes a deterministic two-phase mixed integer programming (TPMIP) approach to solve the non-convex economic dispatch (ED) problem considering ramp rate constraints, valve-point effect (VPE), prohibited operating zones (POZs), transmission loss, and spinning reserve constraints. In the first phase, the non-smooth cost function induced by VPE is piecewise linearized and the POZs constraints are formulated as a set of mathematical formulas via a mixed integer encoding technique. Then, the non-convex ED problem is converted to a mixed integer programming (MIP) problem and can be solved by commercial optimization solvers. In the second phase, based on the solution obtained in the first phase, the range of the power output of each unit is compressed and then solve the MIP problem again to make a further exploitation for an optimal solution in the subspace of the whole solution domain. To demonstrate the effectiveness of TPMIP, it is applied to eight test systems and the simulation results are compared with those obtained by the existing methods cited in this paper. Numerical simulations have verified that the proposed method provides a comprehensive framework in solving the non-convex ED problem.

Gravitational search algorithm-based dynamic economic dispatch by estimating transmission system losses using A-loss coefficients

Dynamic economic dispatch (DED) is an important problem in power system generation, operation, planning, and control. The objective of the DED problem is to schedule power generation for the online units over a time horizon, satisfying the unit and ramp rate constraints. Here, valve point loading effects that cause nonsmoothness of the objective function is also considered while solving the DED. The accuracy of the solution not only depends on the optimal scheduling of generating units, but it also lies in accuracy while estimating transmission system losses. Generally, B-loss coefficients are used in estimating transmission losses. However, in the literature, A-loss coefficients are found to be at par with B-loss coefficients in estimating transmission system losses. Therefore, in this paper, the performance in estimating the transmission system losses using A-loss coefficients are investigated through the solution of the DED problem. Here, a recently evolved heuristic search technique called the gravitational search algorithm is used for solving the DED. The feasibility of the proposed method is tested and validated on standard benchmark test systems such as the IEEE 30-bus system, IEEE 39-bus system, and IEEE 118-bus system. All simulations are carried out using SCILAB 5.4 (www.scilab.org), which is open-source software.

Parallel Augmented Lagrangian Relaxation for Multi- Period Economic Dispatch Using Diagonal Quadratic Approximation Method

Dynamic economic dispatch (DED) over multiple time periods is a large-scale coupled spatial-temporal optimization problem. Therefore, the Lagrangian relaxation method has been widely used to split the large-scale optimization problem with coupled structure into several small sub-problems. In order to bring robustness for updating the dual multipliers and yielding convergence without strong assumptions, the augmented Lagrangian relaxation method is introduced in this paper. However, the added penalty term in an augmented Lagrangian function is non-separable, which leads to the difficulty in achieving full decomposition for parallel computation. To address this problem, a diagonal quadratic approximation method is employed to yield an approximated block separation of the non-separable penalty term. Furthermore, the ramp rate constraints are relaxed in this paper, so that the DED model is decomposed into several single-period economic dispatch models that can be efficiently handled in parallel, called the parallel augmented Lagrangian relaxation method. Particularly, the proposed relaxation strategy has a high separability feature which theoretically leads to sound convergence property. Numerical results on the IEEE 118-bus and a practical Polish 2383-bus test system over a different number of time periods show the effectiveness of the proposed method. In addition, the proposed method can be extended to other coupled spatial-temporal scheduling problems in power systems, such as energy storage dispatch.

A new approach to solve Economic Dispatch problem using a Hybrid ACO–ABC–HS optimization algorithm

Abstract This paper presents a newly developed hybrid optimization algorithm for solving the problem of Economic Dispatch (ED) for a multi-generator system. The hybrid algorithm named ACO–ABC–HS combines the framework of Ant Colony Optimization (ACO), Artificial Bee Colony (ABC) and Harmonic Search (HS) algorithms to find the optimized solution for the system. The ACO algorithm is used to find the initial solution set, the ABC algorithm is employed to test and improve each of the probable solutions provided by the ACO module, while the HS module is used to discard the inferior solutions from the solution set and replace them with better ones. The performance of this hybrid algorithm is compared with those of conventional ED solving techniques like Gradient Search as well as other evolutionary algorithms namely ABC, ACO, HS and Particle Swarm Optimization (PSO). Valve point loading, environmental emissions, line losses and ramping rate constraints have been included in the ED analysis to provide more practical results. The algorithm’s performance is also tested for Multi-Area Economic Dispatch (MAED) with tie-line constraints. The results obtained clearly point out the superiority of the hybrid algorithm in finding out the optimum results, while satisfying the constraints of minimizing the generation costs, reducing the emissions as well as tie-line costs and transmission losses.

Adaptive bacterial foraging and genetic algorithm for unit commitment problem with ramp rate constraint

Summary Solving unit commitment (UC) problem is one of the most critical tasks in electric power system operations. Therefore, proposing an accurate method to solve this problem is of great interest. The original bacterial foraging (BF) algorithm suffers from poor convergence characteristics for larger constrained optimization problems. In addition, the stopping criterion used in the original BF algorithm increases the computation burden of the original algorithm in many cases. To overcome these drawbacks, a hybridized adaptive BF and genetic algorithm (HABFGA) algorithm is proposed in this paper to solve the UC problem with ramp rate constraint. The HABFGA algorithm can be derived by combining adaptive stopping criterion, BF algorithm and genetic algorithm; therefore, the drawbacks of the original BF algorithm can be treated before employing it to solve the complex UC problem. To illustrate the effectiveness of the HABFGA algorithm, several standard and real test systems with different numbers of generating units are used. The results of HABFGA algorithm are compared with the results obtained using other published methods employing same test systems. This comparison shows the effectiveness and the superiority of the proposed method over other published methods. Copyright © 2015 John Wiley & Sons, Ltd.

Assessment of marginal emissions factor in power systems under ramp-rate constraints

Assessment of marginal emissions factor in power systems under ramp-rate constraints

Demand response based and wind farm integrated economic dispatch

Increased penetration of intermittent renewable energy resources is pushing the grid to prepare more reserves to meet the supply and demand balance. Demand response (DR) is an efficient strategy to reduce the overall load at peak times. In order to fully utilize the application of DR and make DR capable of actively supporting grid operations at all times, this paper builds a DR and wind farm integrated economic dispatch model. The objective is to minimize the total operation costs, such as fuel cost, startup cost, greenhouse gas (GHG) emission costs, and DR cost. DR maximum participating time and DR ramp rate constraints are considered. A system with 10 traditional units, one large-scale wind farm, three types of DR, including interruptible load, direct load control, and load as capacity resource are selected to verify the proposed model. Four DR penetration rates are analyzed: 0%, 10%, 20% and 30%. The results indicate that DR penetration can decrease total operation costs. The lower price DR resource gets the priority to be committed. The DR and wind farm integration is indispensable in the future economic dispatch.

Honey Bees Searching Optimization for Non Convex Dynamic Power Dispatch Problem in Thermal Units

Dynamic Power Dispatch (DPD) intends to schedule the online generators output with the forecasted load demand over a certain period of time, in order to operate an electric power system most economically within its operating limits. The behavior and the activity of honey bees during food foraging is implemented as a Honey Bees Searching Optimization (HBSO) technique in solving the DPD problem. The HBSO algorithm provides a balance between exploration and exploitation of a search space. Further, the HBSO is independent of control parameters when compared to other techniques. The DPD formulation includes ramp rate constraint, rectified sinusoidal effect, uniformity and disparity constraint, which normally present in the realistic power system. In order to express the efficacy of the HBSO algorithm a test case of 6 units DPD problem is considered and lower fuel cost is obtained when compared with other algorithm.

Binary fish swarm algorithm for profit‐based unit commitment problem in competitive electricity market with ramp rate constraints

This study presents a new approach based on a binary fish swarm algorithm (BFSA) and dynamic economic dispatch (DED) method for generation companies (GENCOs) profit (PF)-based unit commitment (PBUC) problem considering power and reserve generations simultaneously in a day-ahead competitive electricity markets. BFSA is used to decide the units on/off status, whereas the optimum dispatch solution is determined using DED method with modified unit generation limits because of ramp rate constraints over the complete scheduled time horizon. To avoid the search to get trapped at a local optimal solution, swap move-based local search and cyclic re-initialisation operators are embedded in BFSA. Moreover, two strategies for selling power and reserve are considered in problem formulation and implementation phase. Its effectiveness is validated on 10 and 100 thermal units in a day-ahead electricity market in terms of GENCOs PF and computation time. The results obtained for PBUC problem with BFSA method have been compared with those obtained with priority list, dynamic programming, Lagrange relaxation, genetic algorithm and binary artificial bee colony algorithm, and BFSA has been found effective to achieve quality solutions in reasonable computation time.

The application of one rank cuckoo search algorithm for solving economic load dispatch problems

In this paper, a one rank cuckoo search algorithm (ORCSA) is proposed for solving economic load dispatch (ELD) problems. The main objective of the ELD problem is to minimize total cost of thermal generators while satisfying power balance constraint, prohibited operating zones, ramp rate constraints and operating limits of generators. Moreover, the generating units considered in this paper have different characteristics such as quadratic fuel cost function, nonconvex fuel cost function and multiple fuel options. The proposed ORCSA method has been developed by performing two modifications on the original cuckoo search algorithm (CSA) to improve optimal solution quality and computational time. The first modification is to merge new solution generated from both Lévy flights and replacement a fraction of egg together and to evaluate and rank the solutions at once only. A bound by best solution mechanism has been used in the second modification for properly handling the inequality constraints. The proposed ORCSA method has been tested on different systems with different characteristics of thermal units and constraints. The results obtained by ORCSA have been compared to those from other methods available in the literature and the result comparison has indicated that the ORCSA method can obtain better solution quality than many other methods. Therefore, the proposed ORCSA can be a very effective and efficient method for solving ELD problems.

Evaluating the effectiveness of normal boundary intersection method for short-term environmental/economic hydrothermal self-scheduling

The problem of the optimal scheduling of available hydro and thermal generating units considering a short scheduling period (one day-one week) in order to maximize the total profit is denoted as short-term hydro thermal self-scheduling (SHTSS). Mixed-integer linear programming (MILP) method is proposed to model the SHTSS problem in the day-ahead energy and reserve markets. MILP formulation allows for considering a precise model for the prohibited working zones, dynamic ramp rate constraints and operating services of thermal generating units, as well as the characteristics of multi-head power discharge for hydro generating units and reservoirs’ spillage. This problem is modelled as a multi-objective (MO) optimization one, having two objectives, i.e. maximization of the profit of Generation Company's (GENCO's) and minimization of emissions from thermal units. In order to solve the problem and generate the non-inferior solutions, normal boundary intersection (NBI) method is applied. The main advantage is the provision of set of uniformly distributed non-dominated solutions regardless of the scales of objective functions values. Then, a fuzzy based decision maker is employed in order to select a non-inferior solution. In order to demonstrate the effectiveness of the presented method, several numerical simulations are presented. Furthermore, the obtained results are compared with those obtained considering different methods for obtaining non-inferior solutions, such as weighted sum method, evolutionary programming-based interactive fuzzy satisfying method, differential evolution, particle swarm optimization and hybrid multi-objective cultural algorithm.

A Novel Strategy-Based Hybrid Binary Artificial Bee Colony Algorithm for Unit Commitment Problem

In this paper, a hybrid approach based on a novel binary artificial bee colony (NBABC) algorithm and local search (LS) is developed to solve the unit commitment problem (UCP). Also, the ramp rate constraints are taken into account in the solution of UCP by performing conventional economic dispatch with modifying unit generating capacities over the entire scheduling time horizon. The proposed NBABC–LS method differs from its counterparts in three main aspects: (i) it utilizes a novel strategy which measures the dissimilarity between two binary strings for generating the new binary strings for UCP; (ii) it uses an intelligent scout bee phase; (iii) A LS module is hybridized with the NBABC algorithm. These modifications result in three major advantages: (i) it avoids the problem of slow and premature convergence and thus does not fall into the local optimum solutions; (ii) it can quickly find the near global optimum solution for UCP; (iii) accuracy and robustness of the solution are achieved. The proposed approach is successfully applied to the test systems up to 100 thermal units over 24-h scheduling time horizon and the real Turkish interconnected power system consisting of eight thermal units over 8-h scheduling time horizon. The obtained results confirm the quality solution in terms of total generation cost compared with the other methods reported in the literature.

Improved Optimal Operation Planning Method Based on Tabu Search for Residential PEFC-CGS Considering Ramping Rate

This paper proposes an improved optimal operation planning method for residential PEFC-CGS (Polymer Electrolyte Fuel CellCo-Generation System). Residential PEFC-CGS has recently been gathering attention as one of the distributed power sources with high efficiency and low environmental impacts. Previous research pointed out that the output variations of PEFC adversely affect the durability. It can be surmised that smaller output variations will be desired to extend durability years. However, in this field, ramping rate have not been sufficiently considered. For local search and tabu search, ramping rate constraint makes our operation planning difficult because it restricts the search for feasible neighborhood solutions. Therefore, the authors proposed a method to deal with typical and harsher ramping rate constraints in comparison with conventional methods. There are two key points for the improvement. One is the reinforcement of the search along the output power axis; the other is to make use of the strategy of tabu search which avoids the local optimal solutions. The simulation results show the effectiveness of the proposed method in the daily operation planning. Furthermore, in the case using typical ramping rate parameter, it is confirmed that tabu search doesn’t contribute the reduction of daily operational cost due to the above stated restriction of the search area.

An improved priority list and neighborhood search method for unit commitment

This paper presents an improved priority list and neighborhood search (IPL-NS) method for ramp rate constrained unit commitment (RUC). The IPL-NS consists of two steps. At the first step, an IPL based on a mixed integer linear programming (MILP) formulation for UC is proposed to get unit status for UC without ramp rate constraints. At the second step, a neighborhood search (NS) algorithm based on three neighborhoods is produced to get unit status for RUC. The IPL-NS approach is applied to solve several popular test systems of up to 1000 units and the simulation results confirm the superiority of the proposed method. At the same time, the numerical results show that the proposed IPL can commit the most economic unit first much better than other existing PL methods. The results also indicate that the presented NS can handle the ramp rate constraints efficiently.

Multi-objective dynamic economic emission dispatch of electric power generation integrated with game theory based demand response programs

The dynamic economic emission dispatch (DEED) of electric power generation is a multi-objective mathematical optimization problem with two objective functions. The first objective is to minimize all the fuel costs of the generators in the power system, whilst the second objective seeks to minimize the emissions cost. Both objective functions are subject to constraints such as load demand constraint, ramp rate constraint, amongst other constraints. In this work, we integrate a game theory based demand response program into the DEED problem. The game theory based demand response program determines the optimal hourly incentive to be offered to customers who sign up for load curtailment. The game theory model has in built mechanisms to ensure that the incentive offered the customers is greater than the cost of interruption while simultaneously being beneficial to the utility. The combined DEED and game theoretic demand response model presented in this work, minimizes fuel and emissions costs and simultaneously determines the optimal incentive and load curtailment customers have to perform for maximal power system relief. The developed model is tested on two test systems with industrial customers and obtained results indicate the practical benefits of the proposed model.

Solution of economic load dispatch using hybrid chemical reaction optimization approach

In this paper, a new and efficient optimization technique based on hybridization of chemical reaction optimization (CRO) with differential evolution (DE) is developed and demonstrated to solve the ELD problem with thermal cost function having valve point loading effect together with and without multiple fuel options and with and without considering prohibited operating zone and ramp rate constraint. When valve-point effects, multi-fuel operations and the constraints of prohibited operating zone and ramp rate are taken into account, ELD problem become more complex than conventional ELD problem. To show the priority of the proposed algorithm, it is implemented on six different test systems for solving ELD problems. Comparative studies are carried out to examine the effectiveness of the proposed HCRO-DE approach with conventional DE, CRO and the other algorithms reported in the literature. The simulation results show that the proposed HCRO-DE method is capable of obtaining better quality solutions than DE, CRO and the other well popular optimization techniques.

A Model Predictive Control Approach to Combined Heat and Power Dynamic Economic Dispatch Problem

Combined heat and power dynamic economic dispatch (CHPDED) problem is a nonlinear constrained optimization problem, which determines the optimal heat and power schedule of committed generating units by minimizing the fuel cost and satisfying both the predicted heat and power load demands, ramp rate constraints, and other constraints over a time horizon. We assume that both the heat and power demands are periodic. In this paper, we first extend the CHPDED problem in such a way that its optimal solution can be periodically implemented. Then, we present a model predictive control (MPC) approach for the periodic implementation of the optimal solutions of the CHPDED problem. We assume that there are certain disturbances or uncertainties in the execution of the optimal controller. The convergence and robustness of the MPC algorithm are demonstrated through the application of MPC to the CHPDED problem with an eleven-unit system.

Incorporating short-term operational plant constraints into assessments of future electricity generation portfolios

This paper presents a post-processing extension to a Monte-Carlo based generation portfolio planning tool in order to assess the short-term operational implications of different possible future generation portfolios. This extension involves running promising portfolios through a year of economic dispatch at 30-minute intervals whilst considering operational constraints and associated costs including minimum operating levels, ramp rate constraints and generator start-up costs. A case study of a power system with coal, combined cycle gas turbine (CCGT), open cycle gas turbine (OCGT) and wind generation options highlights that incorporating operational criteria into the long-term generation investment and planning analysis can have operating, economic and emissions implications for the different generation portfolios. The extent of the impacts depends on the dispatch strategies; the carbon price; and the mix of technologies within the portfolio. As intermittent generation within power systems increases and carbon pricing begins to change the merit order, such short-term operational considerations will become more significant for long-term generation investment frameworks.