Augmented Lagrange Hopfield Network Research Articles

Augmented Lagrange Hopfield Network for Economic Emission Load Dispatch Problem with Quadratic Fuel Cost Function

This paper proposes an augmented Lagrange Hopfield Network (ALHN) based method for solving economic emission dispatch (EELD) problem with quadratic fuel function. The ALHN is the combination of augmented Lagrange function and Hopfield neural network in aim to improve performance in terms of convergence speed and getting global optimization. In addition to minimizing electricity generation fuel cost, emission released into the air from thermal plants is also another main objective needs to be minimized. In order to test the performance of the proposed ALHN two systems including a three unit system with one load case and a six unit system with three load cases are employed. The obtained result by the ALHN compared to that from other methods has revealed that the proposed ALHN is a very promising artificial intelligent algorithm for solving economic emission load dispatch problem.

Multi-Objective Short-Term Fixed Head Hydrothermal Scheduling Using Augmented Lagrange Hopfield Network

This paper proposes an augmented Lagrange Hopfield network (ALHN) based method for solving multi-objective short term fixed head hydrothermal scheduling problem. The main objective of the problem is to minimize both total power generation cost and emissions of NOx, SO₂, and CO₂ over a scheduling period of one day while satisfying power balance, hydraulic, and generator operating limits constraints. The ALHN method is a combination of augmented Lagrange relaxation and continuous Hopfield neural network where the augmented Lagrange function is directly used as the energy function of the network. For implementation of the ALHN based method for solving the problem, ALHN is implemented for obtaining non-dominated solutions and fuzzy set theory is applied for obtaining the best compromise solution. The proposed method has been tested on different systems with different analyses and the obtained results have been compared to those from other methods available in the literature. The result comparisons have indicated that the proposed method is very efficient for solving the problem with good optimal solution and fast computational time. Therefore, the proposed ALHN can be a very favorable method for solving the multi-objective short term fixed head hydrothermal scheduling problems.

Refined augmented Lagrange Hopfield network-based Lagrange relaxation for hydrothermal scheduling

This paper proposes a refined augmented Lagrange Hopfield network-based Lagrange relaxation (ALHN-LR) for solving short term hydrothermal scheduling (HTS) problem with pumped-storage hydro units. ALHN-LR consists of improved Lagrange relaxation (ILR) and augmented Lagrange Hopfield network (ALHN). For solving the HTS problem, the proposed method applies enhanced ILR for finding thermal unit scheduling, ALHN for solving constrained economic dispatch (CED), and heuristic search-based algorithms in earlier papers for committing hydro and pumped-storage units, repairing ramp rate, emission, and transmission constraint violations, and refining the obtained result. The proposed ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrangian function can properly handle both equality and inequality constraints in CED problem. The proposed ALHN-LR is tested on a hydrothermal system with 17 thermal, two hydro and two pumped-storage units, and the IEEE 24-bus reliability test system over the 168-hour schedule time horizon. Test results indicate that the proposed method can obtain less total costs than those from augmented Hopfield network (AHN), hybrid enhanced Lagrangian relaxation and quadratic programming (hybrid LRQP), and augmented Lagrangian relaxation (ALR).

Augmented Lagrange Hopfield network initialized by quadratic programming for economic dispatch with piecewise quadratic cost functions and prohibited zones

This paper proposes a method based on quadratic programming (QP) and augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem with piecewise quadratic cost functions and prohibited zones. The ALHN method is a continuous Hopfield neural network with its energy function based on augmented Lagrange function which can properly deal with constrained optimization problems. In the proposed method, the QP method is firstly used to determine the fuel cost curve for each unit and initialize for the ALHN method, then a heuristic search is used for repairing prohibited zone violations, and the ALHN method is finally applied for solving the problem if any violations found. The proposed method has been tested on different systems and the obtained results are compared to those from many other methods in the literature. The result comparison has indicated that the proposed method has obtained better solution quality than many other methods. Therefore, the proposed QP-ALHN method could be a favorable method for solving the ED problem with piecewise quadratic cost functions and prohibited zones.

Real Power Dispatch on Large Scale Power Systems by Augmented Lagrange Hopfield Network

This paper proposes an augmented Lagrange Hopfield network (ALHN) for real power dispatch on large-scale power systems. The proposed ALHN is a continuous Hopfield network with its energy function based on augmented Lagrange function. For this combination, the ALHN method can easily deal with large-scale problems with nonlinear constraints. The proposed ALHN has been tested on systems from 40 units to 240 units, IEEE 118-bus and IEEE 300-bus systems, and the obtained results have been compared to those from other methods. The test results have shown that the ALHN method can obtain better solutions than the compared methods in a very fast manner. Therefore, the proposed ALHN could be favorable for implementation on the real power dispatch problems for large-scale systems.

Economic dispatch with multiple fuel types by enhanced augmented Lagrange Hopfield network

This paper proposes an enhanced augmented Lagrange Hopfield network (EALHN) for solving economic dispatch (ED) with piecewise quadratic cost functions. The EALHN is an augmented Lagrange Hopfield neural network (ALHN), a continuous Hopfield neural network with its energy function based on augmented Lagrangian function, enhanced by a heuristic search for determination of fuel type. The proposed EALHN solves the ED problem in two phases. In the first phase, a heuristic search based on the average production cost of generating units is used to determine the most suitable fuel type for each unit so that total maximum power generation from all units is sufficient for supplying to load demand. In the last phase, the ALHN is applied to find optimal solution corresponding to the chosen fuel types. The proposed method is tested on several systems with various load demands and the obtained test results are compared to those from many other methods in the literature. Test results have indicated that the proposed method is efficient and fast for the ED problems with multiple fuel types represented by quadratic cost functions.

The augmented Lagrange Hopfield network for economic dispatch with multiple fuel options

This paper proposes an augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem with multiple fuel options. The proposed ALHN method is a continuous Hopfield neural network with its energy function based on augmented Lagrangian function. The advantages of ALHN over the conventional Hopfield neural network are simpler use, more general applications, faster convergence, better optimal solution, and larger scale of problem implementation. The proposed ALHN solves the problem by directly searching the most suitable fuel among the available ones for each unit and finding the optimal solution for the problem based on minimization of the energy function of the continuous Hopfield neural network. The proposed method is tested on systems up to 100 units and the obtained results are compared to those from many other methods in the literature. The results have shown that the proposed method is efficient for solving the ED problem with multiple fuel options and favorable for implementation in large scale problems.

Augmented Lagrange Hopfield network based Lagrangian relaxation for unit commitment

This paper proposes an augmented Lagrange Hopfield network based Lagrangian relaxation (ALHN-LR) for solving unit commitment (UC) problem with ramp rate constraints. ALHN-LR is a combination of improved Lagrangian relaxation (ILR) and augmented Lagrange Hopfield network (ALHN) enhanced by heuristic search. The proposed ALHN-LR method solves the UC problem in three stages. In the first stage, ILR is used to solve unit scheduling satisfying load demand and spinning reserve constraints neglecting minimum up and down time constraints. In the second stage, heuristic search is applied to refine the obtained unit schedule including primary unit de-commitment, unit substitution, minimum up and down time repairing, and de-commitment of excessive units. In the last stage, ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrangian relaxation is applied to solve constrained economic dispatch (ED) problem and a repairing strategy for ramp rate constraint violations is used if a feasible solution is not found. The proposed ALHN-LR is tested on various systems ranging from 17 to 110 units and obtained results are compared to those from many other methods. Test results indicate that the total production costs obtained by the ALHN-LR method are much less than those from other methods in the literature with a faster manner. Therefore, the proposed ALHN-LR is favorable for large-scale UC implementation.

Augmented Lagrange—Hopfield Network for Economic Load Dispatch with Combined Heat and Power

This article proposes an augmented Lagrange–Hopfield network for the combined heat and power economic dispatch problem. The augmented Lagrange–Hopfield network method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation. In the proposed augmented Lagrange–Hopfield network, the energy function is augmented by Hopfield terms from the Hopfield neural network and penalty factors from the augmented Lagrangian function to damp out oscillation of the Hopfield network during the convergence process, leading to a fast convergence. The proposed augmented Lagrange–Hopfield network has been tested on various systems and compared to Lagrangian relaxation, the genetic algorithm, the improved ant colony search algorithm, evolutionary programming, the improved genetic algorithm with multiplier updating, and the harmony search algorithm. Test results indicate that the proposed neural network is better than the other methods due to a lower total cost and faster computational time, especially for large-scale combined heat and power economic dispatch problems.

Improved merit order and augmented Lagrange Hopfield network for short term hydrothermal scheduling

This paper proposes an improved merit order (IMO) combined with an augmented Lagrangian Hopfield network (ALHN) for solving short term hydrothermal scheduling (HTS) with pumped-storage hydro plants. The proposed IMO-ALHN consists of a merit order based on the average production cost of generating units enhanced by heuristic search algorithm for finding unit scheduling and a continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation for solving constrained economic dispatch (CED). The proposed method is applied to solve the HTS problem in five stages including thermal, hydro and pumped-storage unit commitment by IMO and heuristic search, constraint violations repairing by heuristic search and CED by ALHN. The proposed method is tested on the 24-bus IEEE RTS with 32 units including 4 fuel-constrained, 4-hydro, and 2 pumped-storage units scheduled over a 24-h period. Test results indicate that the proposed IMO-ALHN is efficient for hydrothermal systems with various constraints.

Enhanced merit order and augmented Lagrange Hopfield network for hydrothermal scheduling

This paper proposes an enhanced merit order (EMO) and augmented Lagrange Hopfield network (ALHN) for solving hydrothermal scheduling (HTS) problem with pumped-storage units. EMO is a merit order enhanced by heuristic search based algorithms and the ALHN is a continuous Hopfield network with its energy function based on augmented Lagrangian function. EMO is efficient in unit scheduling, whereas ALHN can properly handle generation ramp rate limits, and time coupling constraints such as limited fuel, water discharge for hydro units, and water balance for pumped-storage units. The proposed method solves HTS problem by optimizing step by step of sub-problems in four phases. In the first phase, EMO is applied to solve only thermal unit commitment satisfying power balance, spinning reserve, limited fuel, and minimum up and down time constraints. In the second phase, the enhanced ALHN is used to solve economic dispatch (ED) and commit hydro units based on the obtained unit schedule from the first phase. In the third phase, the enhanced ALHN is applied to handle transmission constraint. In the last phase, the enhanced ALHN is used to commit pumped-storage units and solve final constrained ED. In each phase, heuristic search based algorithms are applied to repair the constraint violations and refine the obtained solution. The proposed EMO–ALHN is tested on a hydrothermal system with 17 thermal, 2 hydro, and 2 pumped-storage hydro units with a scheduling time horizon of 24 h. Test results indicate that the proposed method obtains less costs and faster computational times than those from augmented Hopfield neural network (AHN) and hybrid enhanced Lagrangian relaxation and quadratic programming (Hybrid LRQP) for two test cases.

Ramp rate constrained unit commitment by improved priority list and augmented Lagrange Hopfield network

This paper proposes an improved priority list (IPL) and augmented Hopfield Lagrange neural network (ALH) for solving ramp rate constrained unit commitment (RUC) problem. The proposed IPL-ALH minimizes the total production cost subject to the power balance, 15 min spinning reserve response time constraint, generation ramp limit constraints, and minimum up and down time constraints. The IPL is a priority list enhanced by a heuristic search algorithm based on the average production cost of units, and the ALH is a continuous Hopfield network whose energy function is based on augmented Lagrangian relaxation. The IPL is used to solve unit scheduling problem satisfying spinning reserve, minimum up and down time constraints, and the ALH is used to solve ramp rate constrained economic dispatch (RED) problem by minimizing the operation cost subject to the power balance and new generator operating frame limits. For hours with insufficient power due to ramp rate or 15 min spinning reserve response time constraints, repairing strategy based on heuristic search is used to satisfy the constraints. The proposed IPL-ALH is tested on the 26-unit IEEE reliability test system, 38-unit and 45-unit practical systems and compared to combined artificial neural network with heuristics and dynamic programming (ANN-DP), improved adaptive Lagrangian relaxation (ILR), constraint logic programming (CLP), fuzzy optimization (FO), matrix real coded genetic algorithm (MRCGA), absolutely stochastic simulated annealing (ASSA), and hybrid parallel repair genetic algorithm (HPRGA). The test results indicate that the IPL-ALH obtain less total costs and faster computational times than some other methods.

Improved merit order and augmented Lagrange Hopfield network for unit commitment

This paper proposes an improved merit order (IMO) and augmented Lagrange Hopfield network (ALHN) for unit commitment (UC). IMO is a merit-order method which is based on average production cost of generating units improved by heuristic search algorithms, whereas ALHN is a continuous Hopfield neural network with its energy function based on augmented Lagrange relaxation. The proposed IMO-ALHN solves UC problem in three stages. In the first stage, IMO is applied for unit scheduling. In the second stage, ALHN is used to solve ramp rate constrained economic dispatch (RED) based on the obtained unit schedule, and a strategy for repairing ramp rate constraint violation is performed if a feasible solution is not found. In the last stage, a heuristic search for unit decommitment is applied on the obtained solution from RED for further improvement and ALHN is again applied to solve RED if there is any change in the unit schedule. The proposed method is tested on systems up to 1000 generating units with schedule time horizon up to 168 h. Test results indicate that the proposed method is very attractive and favourable over many other methods due to substantial production cost savings and faster computational times.