Hydrothermal Coordination Problem Research Articles

A Data-Driven Representation of Aggregate Efficiency Curves of Hydro Units for the Mid-Term Hydrothermal Coordination Problem

A crucial aspect of the mid-term hydrothermal coordination problem is the nonlinear variation of hydro power with the water head, which can be computed through forebay and tailrace curves of the reservoirs. More accurate representations may also include turbine efficiency curves as a function of head and discharge, and penstock head losses as a function of turbined outflow. Based on large set of historical data for the operation of hydro plants, we propose a data-driven model to obtain such curves, which comprises: interpolation/extrapolation procedures to fill missing data and extreme regions of the curve; computation of average weekly values to avoid an optimistic behavior when using instantaneous curves for larger time intervals; an additive model with polynomial splines for curve fitting. The methodology was applied to the real Brazilian system, showing a significant improvement in the accuracy of the hydro production function, without sensitive changes on CPU time.

A modified incremental gravitational search algorithm for short-term hydrothermal scheduling with variable head

In this study, the solution of short-term hydrothermal coordination problem (STHCP) with variable head was performed. In the manuscript, incremental gravitational search algorithm (IGSA) which was developed as a new method has been applied to two different power problems. One of the systems used as an example is a variable head STHCP which has previously been solved in the literature by neglecting transmission line losses. The second is a lossy system designed as a variable head STHCP, with the purpose of contributing to the literature. In the lossy system, Newton–Raphson AC power flow method was used to calculate transmission line losses. Possible electrical and hydraulic constraints in the solution of the problem were satisfied using the penalty function method. The results obtained from the solutions of the sample systems were compared and discussed.

A Reservoir Operation Policy Using Inter-Basin Water Transfer for Maximizing Hydroelectric Benefits in Brazil

The Hydrothermal Coordination problem consists of determining an operation policy for hydroelectric and thermoelectric plants within a given planning horizon. In systems with a predominance of hydraulic generation, the operation policy to be adopted should specify the operation of hydroelectric plants, so that hydroelectric resources are used economically and reliably. This work proposes the implementation of reservoir operation rules, using inter-basin water transfer through an optimization model based on Network Flow and Particle Swarm Optimization (PSO). The proposed algorithm aims to obtain an optimized operation policy of power generation reservoirs and consequently to maximize the hydroelectric benefits of the hydrothermal generation system, to reduce the use of thermoelectric plants, the importation and/or energy deficit and to reduce the cost associated with meeting the demand and reduce CO2 emissions from combustion of fossil fuels used by thermoelectric plants. In order to illustrate the efficiency and effectiveness of the proposed approach, it was evaluated by optimizing two case studies using a system with four hydroelectric plants. The first case study does not consider transfer and water and the second case study uses water transfer between rivers. The obtained results illustrate that the proposed model allowed to maximize the hydroelectric resources of a hydrothermal generation system with economy and reliability.

A hydrothermal coordination model for electricity markets: theory and practice in the case of the Greek electricity market regulatory framework

The generation portfolio of the Greek Mainland Electricity System mainly consists of various types of thermoelectric (using fossil fuels: natural gas and lignite) as well as hydroelectric units (impoundment, pumped storage, run of river). Regarding their fuel consumption, thermoelectric units have a large variable cost compared to hydroelectric, which is almost zero, as derived by their advantage of fueling their operation with water. Moreover, as fossil fuel price variation does not correlate to water’s value a significant trade-off is created. Due to that trade-off the use of energy sources (natural gas, lignite or water), without consideration of cost minimization, may always lead to waste and to significant losses. Demand’s variation along with its sudden peaks, as well as the uncertainty of water availability, impose the use of a specialized mathematical model for the optimal handling of the generation portfolio. Load cover should be achieved by a non-constant portfolio over time, of hydro and thermals, coordinated by an algorithm in such a way as to achieve cost minimization. The main target of such a model is the normality of operation, safeguarded by specific technical, operational and economic constraints fulfilling the objective of cost minimization. Optimization of this type can be characterized as hydrothermal coordination problem, which in our case takes the form of a Mixed Integer Programming Model. The innovative character of this model, is that in a time efficient way, it finds the optimal solution, while keeping complexity at very low level, forcing hydroelectric units to maximize production at the peaks of the load, when marginal cost of thermal’s is at the highest point, making the most economical utilization of water resources. Such an algorithm while it achieves significant economies regarding the cash flows and the fuel-quantities (fossils, water for agricultural purposes), delivers heavy support to management for market policy and operational decision-making.

Gravitational search algorithm applied to fixed head hydrothermal power system with transmission line security constraints

Optimal operation and production planning are important problems for electric power generation systems. Optimal operation of an energy generation system conventionally refers to the minimization of total thermal fuel cost (TTFC). However, the presence of thermal and hydraulic generation units in a power system requires that hydraulic as well as thermal constraints be added to a problem, which is referred to as a short term hydrothermal coordination problem (STHCP). STHCPs assume that the amount of water in the reservoirs of a hydraulic generation unit has no effect on power generation when its net heads are fixed. This study applied a gravitational search algorithm (GSA) for the solution of a STHCP with fixed head. The probable electrical and hydraulic constraints of the problem have been provided by punishment function method. Line losses of the power system were calculated using the Newton-Raphson load flow method. Two different cases, where transfer capacities of transmission lines were neglected and included, were set up, and the problem was solved for both cases. Transfer capacities of transmission lines were included to make the problem more complex and realistic. Solutions for both cases were discussed.

Short-term hydrothermal coordination using water cycle algorithm with evaporation rate

Summary The demand of electrical energy is increasing and so is its cost. The conventional means of generation of electrical are the hydel and thermal. Their optimized mutual operation results in the most economic electrical energy for the end user. Therefore, the optimized operation of hydel and thermal plants known as hydrothermal coordination (HTC) is one of the important and challenging tasks in the field of power system operation. This paper investigates a modified version of a new nature inspired algorithm, water cycle algorithm called as evaporation rate–based water cycle algorithm (ERWCA) for the solution of HTC. This algorithm has its roots from the natural water cycle. The raindrops form streams, which flow to the rivers and eventually into the sea. The streams either merge into rivers and sea or they are too slow to reach the rivers or sea; the evaporation process occurs, which again causes the rainfall. Hence, new streams will be created. In this paper, ERWCA has been successfully applied to the problem of HTC. The complex constraints of the hydel and thermal network especially the prohibited discharge zones of hydel plants and the ramp rates of thermal plants, which are rarely taken into account, have been incorporated. The comparison of the results with other nature inspired techniques already available in the literature like particle swarm optimization and differential evolution shows the strength and potential of this new technique ERWCA in obtaining the better quality result.

Application of CVaR risk aversion approach in the expansion and operation planning and for setting the spot price in the Brazilian hydrothermal interconnected system

Traditionally, long-term power generation planning problems has been performed with the main objective of minimizing the expected value of generation and load curtailment costs. However, more recently there has been a need to apply some risk measure in order to avoid large amounts of load curtailment in critical inflow scenarios. This paper describes a direct approach for the implementation of a Conditional Value-at-Risk (CVaR) version for the long term hydrothermal coordination problem under a stochastic dual dynamic programming solving strategy. We also present an actual analysis that was made to validate and determine the key parameters of this model for a real application to the Brazilian system, where since September 2013 the proposed methodology has been officially used for operation planning and dispatch, to set the spot prices in the market and to perform expansion planning studies.

Hydrothermal coordination by bi-level optimization and composite constraint handling method

This paper presents a new adaptive bi-level optimization approach to solve short-term hydrothermal coordination (STHTC) problem with AC network constraints. The proposed bi-level approach is composed of an integer coded genetic algorithm (ICGA) to solve unit commitment (UC) in the upper level and a new modified chaotic simulated annealing (MCSA) technique to determine economic dispatch (ED) for each time interval in the lower level. Moreover, a new composite constraint handling method is also presented, which enhances the efficiency of the proposed approach to solve STHTC problem with AC constraints. The proposed methodology is tested on the 9-bus and IEEE 118-bus test systems. The obtained results confirm the validity of the developed approach.

Stabilization of the Generalized Benders Decomposition applied to Short-Term Hydrothermal Coordination Problem

Solving the Short Term Hydrothermal Coordination (STHTC) Problem considers the resolution of both the Unit Commitment (UC) and the Economic Dispatch (ED) for thermal and hydraulic units. In order to avoid post-dispatch corrections, the transmission network is modeled with a high level of detail considering an AC power flow. These facts lead to a very complex optimization problem which is solved by using a novel decomposition approach which combines Generalized Benders Decomposition (GBD) with Bundle methods presented in [LS97]. This proposed method resembles a stabilized version of the cutting planes method, which drastically reduces the well-known tailing-off effect that Benders methods have. The approach presented in this work allows the decomposition of the whole problem in a quadratic mixed integer master problem, and in a non-linear subproblem which should be separable. The former defines the state and the active power dispatched by each unit whereas the latter determines the reactive power to meet the electrical constraints through a modified AC optimal power flow (OPF). These approaches were applied to a 9-bus test case, and to the IEEE 24-bus test case. The problem is solved for a time horizon of a day with a one-hour step.

HYDROTHERMAL COORDINATION FOR SHORT RANGE FIXED HEAD STATIONS USING FAST GENETIC ALGORITHM

This paper presents a Fast genetic algorithm for solving Hydrothermal coordination (HTC) problem. Genetic Algorithms (GAs) perform powerful global searches, but their long computation times, put a limitation when solving large scale optimization problems. The present paper describes a Fast GA (FGA) to overcome this limitation, by starting with random solutions within the search space and narrowing down the search space byconsidering the minimum and maximum errors of the population members. Since the search space is restricted to a small region within the available search space the algorithm works very fast. This algorithm reduces the computational burden and number of generations to converge. The proposed algorithm has been demonstrated for HTC of various combinations of Hydro thermal systems. In all the cases Fast GA shows reliable convergence. The final results obtained using Fast GA are compared with simple (conventional) GA and found to be encouraging.

A hydro power system operation using Genetic Algorithms and mixed-integer nonlinear programming

A hydro power system operation using Genetic Algorithms and mixed-integer nonlinear programmingThis paper proposes a new hybrid optimization method for solving a hydrothermal coordination problem. In general, the problem is decomposed into smaller hydro and thermal sub-problems which are solved separately. The hydro sub-problem is solved by the peak shaving method using the proposed hybrid optimization method. It combines genetic algorithms with the traditional numerical optimization method. The hybrid method has been applied to a real hydrothermal system, i.e., the Slovak power system. The results have proved the efficiency of the proposed method.

Optimization methods applied for solving the short-term hydrothermal coordination problem

Short-term hydrothermal coordination (STHTC) is a very complicated optimization problem. It is a dynamic large-scale non-linear problem and requires solving unit commitment and economic power load dispatch problems. From this perspective, many successful and powerful optimization methods and algorithms have been employed to solve this problem. These optimization methodologies and techniques are widely diverse and have been the subject of ongoing enhancements over the years. This paper presents a survey of literature on the various optimization methods applied to solve the STHTC problem. A review and a methodology-based classification of most of the publications on the topic are presented.

Analysis of stochastic problem decomposition algorithms in computational grids

Stochastic programming usually represents uncertainty discretely by means of a scenario tree. This representation leads to an exponential growth of the size of stochastic mathematical problems when better accuracy is needed. Trying to solve the problem as a whole, considering all scenarios together, yields to huge memory requirements that surpass the capabilities of current computers. Thus, decomposition algorithms are employed to divide the problem into several smaller subproblems and to coordinate their solution in order to obtain the global optimum. This paper analyzes several decomposition strategies based on the classical Benders decomposition algorithm, and applies them in the emerging computational grid environments. Most decomposition algorithms are not able to take full advantage of all the computing power available in a grid system because of unavoidable dependencies inherent to the algorithms. However, a special decomposition method presented in this paper aims at reducing dependency among subproblems, to the point where all the subproblems can be sent simultaneously to the grid. All algorithms have been tested in a grid system, measuring execution times required to solve standard optimization problems and a real-size hydrothermal coordination problem. Numerical results are shown to confirm that this new method outperforms the classical ones when used in grid computing environments.

Hydrothermal coordination using modified mixed integer hybrid differential evolution

This work presents a novel modified Mixed Integer Hybrid Differential Evolution (MIHDE) algorithm, for solving the unit commitment problem of a hydrothermal power system. Hydrothermal scheduling involves the optimisation of a non-linear objective function with a set of system and hydraulic constraints. Discrete and dynamic constraints such as unit start-up/shutdown and minimum-up/minimum-downtime limits are also included in the hydro unit commitment. The problem of hydrothermal coordination is a mixed integer non-linear optimisation problem, which is well-suited for the use of MIHDE. In this paper, the MIHDE algorithm is modified in order to handle the reservoir end-volume and load balance constraints in the hydrothermal scheduling. The performance of the proposed approach is validated by illustration with standard test systems. The results of the proposed approach are compared with those techniques reported in literature. From the numerical results, it is found that the modified MIHDE-based approach is able to provide better solution at a relatively lesser computational effort.

On centralized power pool auction: a novel multipliers stabilization procedure

This paper addresses the Short-Term Hydro-Thermal Coordination (STHTC) problem. It is a large-scale, combinatorial and nonlinear optimization problem. It is usually solved using a Lagrangian Relaxation (LR) approach. LR procedure is based on the solution of the dual problem of the original one. The dual problem variables are the Lagrange multipliers. These multipliers have an economic meaning: electric energy hourly prices. This paper focuses in an efficient solution of the dual problem of the STHTC problem. A novel multiplier stabilization technique, which significantly improves the quality of the solution, is presented. The provided method could be the optimization tool used by the Independent System Operator of a centralized Power Pool. The solution procedure diminishes the conflict of interest in determining energy prices. A realistic large-scale case study illustrates the behavior of the presented approach.

A Genetic Algorithm Solution Approach to the Hydrothermal Coordination Problem

In this paper, a genetic algorithm solution to the hydrothermal coordination problem is presented. The generation scheduling of the hydro production system is formulated as a mixed-integer, nonlinear optimization problem and solved with an enhanced genetic algorithm featuring a set of problem-specific genetic operators. The thermal subproblem is solved by means of a priority list method, incorporating the majority of thermal unit constraints. The results of the application of the proposed solution approach to the operation scheduling of the Greek Power System, comprising 13 hydroplants and 28 thermal units, demonstrate the effectiveness of the proposed algorithm.

A nonlinear optimization package for long-term hydrothermal coordination

Long-term hydrothermal coordination is one of the main problems to be solved by an electric utility. Its solution provides the optimal allocation of hydraulic, thermal and nuclear resources at the different intervals of the planning horizon. The purpose of the paper is two-fold. Firstly, it presents a new package for solving the hydrothermal coordination problem. The model implemented accurately describes both the hydraulic and thermal subsystems. The resulting large-scale nonlinear and nonconvex problem is solved through either Minos or Snopt, two state-of-the-art nonlinear optimization packages. The second objective of the paper is to deliver to the optimization community the package. Since it implements a difficult, real, and large-scale problem, it can be considered a good test for new nonlinear optimization solvers. Computational results of the package in the solution of a set of real instances of up to 32,000 nonlinear variables, 13,000 linear and 2500 nonlinear constraints are reported.

Medium-term hydrothermal coordination by semidefinite programming

Hydrothermal coordination (HTC) is a problem that has been solved using direct and decomposition solution methods. The latter has shown shorter solution times than the former. A direct solution method for the HTC problem that is based in semidefinite programming (SDP) is presented in this paper. SDP is a convex programming method with polynomial solution time. The variables of the problem are arranged in a vector, which is used to construct a positive-definite matrix; the optimal solution is then found in the cone defined by the set of positive-definite matrices. An HTC problem can be formulated as a convex optimization problem without explicitly stating the integer value requirements for the thermal-plants discrete variables. Thus, it is possible to replace the nonconvex integer-value constraints by convex quadratic constraints, and then use SDP. Due to its polynomial complexity, it is not necessary to use decomposition or other tools for discrete optimization, such as enumeration schemes or other exponential-time procedures. No initial relaxation is necessary when applying a SDP algorithm; the solution shows only minor mismatches in the integer variables, which are easily corrected by a heuristic method. Different size test cases are presented. The solution quality is assessed by comparing with that produced by a Lagrangian relaxation method.

Wheeling cost influence in hydrothermal dispatch and series compensation allocation

This paper presents a methodology for optimizing both the transmission tariff and the thermal generation costs, considering the series compensation (SC) allocation problem in a multiperiod dispatch. The inclusion of the tariff cost in the objective function of the hydrothermal coordination problem can change the dispatch of remote hydro plants, especially if the SC is considered. The proposed methodology is important because the transmission cost tariff can affect the network users in a competitive environment. The OPF problem is based on the nonlinear primal-dual interior point technique associated with the Benders decomposition approach. The algorithm is tested using an equivalent of the southern system of Brazil and compared with existing techniques.

Medium-Term Hydro-Thermal Coordination by Semidefimite Programming

Hydrothermal coordination (HTC) is a problem that has been solved using direct and decomposition solution methods. The latter has shown shorter solution times than the former. A direct solution method for the HTC problem that is based in semidefinite programming (SDP) is presented. SDP is a convex programming method with polynomial solution time. The variables of the problem are arranged in a vector, which is used to construct a positive-definite matrix; the optimal solution is then found in the cone defined by the set of positive-definite matrices. An HTC problem can be formulated as a convex optimization problem without explicitly stating the integer value requirements for the thermal-plants discrete variables. Thus, it is possible to replace the nonconvex integer-value constraints by convex quadratic constraints and then use SDP. Due to its polynomial complexity, it is not necessary to use decomposition or other tools for discrete optimization, such as enumeration schemes or other exponential-time procedures. No initial relaxation is necessary when applying a SDP algorithm; the solution shows only minor mismatches in the integer variables, which are easily corrected by a heuristic method. Different size test cases are presented. The solution quality is assessed by comparing with that produced by a Lagrangian relaxation method.