OPTIMAL OPERATION OF INTERCONNECTED HYDRO POWER PLANTS

Abstract

With the enormous growth in energy requirements during recent years, the power production utilities are under great pressure to generate more and more power. In view of the fact that available resources are limited, their optimum utilization has become increasingly important. As such, optimizing the operations of interconnected hydropower plants is vital in the era of water and energy shortage. The solution of this problem is notable component in the planning and operation of a power system where the hydroelectric generation constitutes a significant portion of the installed capacity. The determination of optimal schedules for hydro generation is essentially a key assignment in water resource management. The aim of hydro system scheduling problem is to find out the periodic water releases from each reservoir and through each power house so as to optimize the total benefit of hydro generated energy. The constraints that must be considered include load balance, flow balance or continuity equation, the boundary condition on the total available quantity of water, reservoir storage limits and the turbine discharge rate limits. The solution of this problem has been recognized as a formidable task on account of limited volume of stored water in system reservoirs. This is because water discharge rate in an earlier interval affects the future discharge rates and thus influences the overall operation of the hydropower system. Furthermore, the presence of multiple interconnected reservoirs and the need for multi-period optimization characterize the problem as large-scale problem. All these features when combined makes the solution of Abstract a large-scale constrained nonlinear programming problem for the determination of optimal schedules for hydro generation quite complex. Various computational procedures concerning the optimal operation of multi-reservoir hydro systems have been developed by many researchers. In the past, computational methods used for solving this problem have been maximum principal, variational calculus, dynamic programming, nonlinear programming, decomposition methods and network flow programming. But these methods suffer from various computational difficulties such as dimensionality difficulty, large memory requirement, non-optimal results and large computational time. Due to the presence of large number of variables and nonlinear nature of the scheduling problem step size calculation also creates computational difficulties. In the present work, firstly, the hydro generation scheduling problem using a decomposition method is considered. In this problem, the objective is to maximize annual hydropower generation of interconnected hydropower plants. In the proposed technique, coupling constraints on reservoir storage at the end of planning horizon are V augmented in the objective function using coordinating multipliers. This facilitates interval-wise decomposition of the overall problem into a subproblem for each interval. Water discharge rate variables are expressed as a function of storage variables for each interval using flow balance equation. This eliminates the constraints on flow balance and reduces by half the number of variables in the subproblems. The constrained nonlinear programming subproblems are converted into unconstrained nonlinear programming subproblems and solved sequentially by variable metric method. This method does not require single dimensional search. The next step is to update the coordinating multipliers. The determination of adaptive updating step size requires the evaluation of feasible solution to the overall problem. For this purpose Heuristic Rule based approach has been developed to find feasible solution. After the evaluation of the feasible solution the coordinating multipliers are updated using a subgradient algorithm. Computer time Abstract and memory requirements for this method are greatly reduced due to the decomposed problem formulation. The results from this method are compared with those obtained from decomposition method based on constant step size and the proposed method shows the potential of achieving improved performance. In recent years there has been some promising applications of ANN models in the field of hydro scheduling. One such application is based on linear programming neural network. The linear programming neural network is an analog computational circuit. The major feature of this network is that, once designed, it can easily be implemented through hardware and thus is capable of providing much rapid solutions. However the network is limited mainly by two shortcomings. Firstly, it cannot handle nonlinear objective function and secondly at steady state it converges in the infeasible region. A hybrid method based on decomposition and two-phase neural network is developed for hydro scheduling problem mentioned in the previous section. The twophase optimization neural network is an extension of linear programming neural network in that it provides exact solution to convex constrained nonlinear programming problems. In this formulation, the objective function is expressed in terms of reservoir releases instead of storages using flow balance equation. Then interval-wise decomposition is carried out in the same manner as explained in the previous section. A two-phase optimization neural network is employed to solve each subproblem separately. The network operates in two phases and provides fast, efficient and accurate solutions. In phase 1, whenever constraint violation occurs, its magnitude and direction are fed back to adjust the states of the neurons. This brings the problem variables near to the boundary of the feasible region. In second phase, the directional vector of the constraints is gradually replaced by the corresponding lagrange multipliers and this moves the Abstract solution trajectory to the feasible region. In this way the overall energy of the network continuously decreases until it attains a minimum. Corresponding to this minimum energy, the states of the neurons are considered to be a minimizer of the original problem. The results from this method are compared with the former decomposition methods and the new method is found to have better performance. Some of the water resource projects are constructed to serve more than one objective. These may include municipal and industrial water supply, hydropower generation, irrigation, fish and wildlife maintenance, flood control, recreations and navigation. In such a situation the problem of hydro scheduling is of multiobjective nature. A basic problem is that the objectives may be conflicting. Such a problem has been addressed by a number of researchers in the past using a constraint method and weighted objective function method. While the extensive computational burden is the main drawback of the constraint method, the evaluation of weighting factors in order to assess a preferred compromise between objectives is the prominent difficulty with the weighted objective approach. An effective solution technique based on neural nets is developed to solve the multiobjective hydro scheduling problem. Here the objectives are to maximize the annual hydropower generation and to satisfy the irrigation requirements as far as possible. Scheduling indicators are introduced to help the reservoir operators in making a judicious compromise between the conflicting objectives. The neural nets used in this work are of two types. The first kind is the trainable multi layer feed forward network that identifies the weighting parameters and the second one is the feedback dynamical system evolving in time, which optimizes the constrained, nonlinear hydro scheduling problem. While the primary advantage of the multilayer perceptron is fast computation and the capability to generalize from training examples, the two-phase neural network on the IV Abstract other hand is well suited for hardware implementation that will then be capable of solving large-scale multiobjective hydro scheduling problem almost instantaneously. The inflows to reservoirs are usually uncertain and thus the hydro scheduling becomes a stochastic optimization problem. A major difficulty encountered in operating even a single stochastic long-term hydroelectric reservoir is its large dimensionality. Over the past several years, a number of mathematical procedures have been evolved for operation scheduling of reservoirs with random inflows. In general, the large-scale stochastic optimization problem is broken down into smaller subproblems. Mainly two kinds of models namely explicit stochastic and implicit stochastic are reported in literature. In the past few years' ANNs have been applied to stochastic hydro scheduling problem. However widely used backpropagation neural net suffers from well-known problems of slow convergence and local minima especially for large size problems. In this work a fuzzy-neural model is formulated for operating a reservoir type hydro plant with random inflows. Inflow sequences with specified mean and standard deviation are randomly generated using normal distribution. Further, to meet the objective that is to maximize annual hydropower generation, monthly reservoir releases with different inflow scenarios are determined for large number of years using non-linear programming technique. Fuzzy partitions are used in this work to build a fuzzy rule based system for hydro scheduling by dynamically dividing the input space of reservoir inflows and releases into a set of subspaces. This partition is used to determine a set of fuzzy rules that model the relationship between reservoir inflows and releases. Significant input features are identified using fuzzy partitions. Fuzzy rules based system developed from fuzzy partitions is employed to find the structure of the fuzzy neural network and set its initial weights. The network is trained by backpropagation algorithm Abstract to increase the accuracy that is initially obtained using fuzzy rule based model. The training with backpropagation algorithm is very fast. The problem of short term hydrothermal scheduling is to find out the water release from each reservoir and through each power house over all the planning period so as to minimize thermal generation cost. The governing constraints of the short term scheduling problem are demand-supply balance, flow balance, bounds on storage, discharge and thermal generation, and coupling constraint. The common assumption is that load demand and river inflows are known. Finally, two short-term scheduling examples are solved using two-phase neural network. First problem is concerned with a test system that is composed of a cascaded multi reservoir hydropower system interconnected to neighboring systems with transmission lines through which energy can be imported or exported. The second problem on the other hand is a hydrothermal scheduling problem, which consists of multi-chain cascaded hydropower system and a thermal system. The intent here is not to devise the constrained nonlinear optimization technique, but rather to verify the optimal scheduling results obtained by the proposed method with those from conventional and rigorous nonlinear optimization procedure. In both the cases the comparison has been carried out with the conjugate gradient method based on augmented lagrangian procedure. The comparison has shown the promise of the proposed approach in reaching optimal hydro and hydrothermal schedules.