Robert E. Larson

A Dynamic Estimator for Tracking the State of a Power System

The problem of real-time estimation of the state of a power system is treated from the point of view of the theory of least-squares estimation (Kalman-Bucy filtering). Since under normal operating conditions, the power system behaves in a quasi- static manner, a simple model for the time behavior of the power system is derived. This model, together with the real-time measurement system, enables the design of a tracking state-estimator algorithm. The proposed algorithm has several advantages over the previously suggested static estimator algorithm in regard to its computational aspects, real-time implementation, and the accuracy of the estimated state.

State Estimation in Power Systems Part I: Theory and Feasibility

State estimation is a digital processing scheme which provides a real-time data base for many of the central control and dispatch functions in a power system. The estimator processes the imperfect information available and produces the best possible estimate of the true state of the system. The basic theory and computational requirements of static state estimation are presented, and their impact on the evolution of the data-acquisition, data- processing, and control subsystems are discussed. The feasibility of this technique is demonstrated on network examples.

A survey of dynamic programming computational procedures

Although dynamic programming has long provided a powerful approach to optimization problems, its applicability has been somewhat limited because of the large computational requirements of the standard computational algorithm. In recent years a number of new procedures with greatly reduced computational requirements have been developed. The purpose of this paper is to survey a number of the more promising of those techniques. A review of the theory of dynamic programming and the standard computational algorithm is included. Several applications of the new techniques are discussed.

Applications of dynamic programming to the control of water resource systems

The complexity and expense of water system projects have made optimum operation and design by computer-based techniques of increasing interest in recent years. Dynamic programming offers a powerful approach to a wide variety of these problems. Most water system problems can be classed as one of the following three types: 1.(1) Optimum operation during a short period, such as 24 hours, when all quantities are known; 2.(2) Monthly or yearly policy optimization when some system parameters, such as stream inflows, are not known exactly; 3.(3) Long-range planning or resource allocation when demands may or may not be known exactly. Realistic water resource problems have many decision and state variable constraints. There are also nonlinearities or stochastic variations in both the state equations and the return function. This paper describes how dynamic programming can handle these difficulties. Several specialized dynamic programming techniques applicable to water system problems are also introduced. These include successive approximations, forward dynamic programming, dynamic programming for stochastic control, and iteration in policy space. Four examples are solved and discussed-short-term optimization of a two-reservoir system is solved with forward dynamic programming; short-term optimization of a four-reservoir system is treated by successive approximations; optimum operation over a year, when stream-flows are stochastic variables, is found by iteration in policy spaces; and optimum long-term planning of system additions given projected demand is treated by forward dynamic programming.

State Estimation in Power Systems Part II: Implementation and Applications

State estimation is a digital processing scheme which provides a real-time data base for many of the central control and dispatch functions in a power system. Its purpose is to permit improvements in system security and data accuracy and to reduce measurement and telemetry cost. The on-line implementation of an efficient state-estimator algorithm is discussed, and its feasibility is demonstrated on a 400-node network. The main motivations for and potential applications of on-line state estimation are listed, and the tradeoffs between measurement, estimation, and on-line load- flow computation are briefly discussed.

Optimization of tree-structured natural-gas transmission networks

As natural gas pipeline systems have become more complex, the natural gas pipeline industries have increasingly used modern optimization techniques in the planning and operation of such systems. The problem considered in this paper is the optimization of a single-source natural-gas transmission network operating in steady-state and having a tree (loop-free) structure similar to Fig. 1.l Specifically, an operating policy for the compressors of the network is desired that minimizes the total compressor horsepower expended while delivering the specified steady-state flow of gas, meeting pressure constraints along the network, and meeting constraints on the operating characteristics of each compressor. The optimization of a single source tree structured network is considered in three stages. First, the optimization of a single pipeline with numerous compressors in series is shown to be a one-dimensional dynamic programming problem. Second, the optimization of a single junction network is decomposed into the sequential optimization of single pipelines. Third, the optimization of a multiple junction network is decomposed into the sequential solution of single junction networks. Consequently, the overall result is to decompose the optimization of networks into the sequential solution of one-dimensional dynamic programming problems. Since the computational requirements of one-dimensional dynamic programming problems are modest, the entire network can be optimized on moderate size computers.

Optimum quantization in dynamic systems

In this paper the problem of optimally designing a quantizer imbedded in a closed-loop dynamic system is considered. The criterion for the design is that the overall system performance as expressed by a variational criterion is optimized. The function of quantization is thus related to the functions of control and estimation that are performed in the system. First, a procedure is described for optimally designing a quantizer in a static open-loop system, where the design criterion is the expected value of a function of the instantaneous error between the input and output of the quantizer. This procedure reduces the search over all quantizer parameters to an iterative search over a single parameter. Next, the existing methods for finding the optimal design of a quantizer imbedded in a dynamic system are reviewed. The most general method found in the literature involves a combination of dynamic programming with an exhaustive search for all quantizer parameters. The computational requirements of this procedure are quite large even for low-order systems with few quantizer parameters. Finally, a new result is presented that leads to greatly reduced computational requirements for the dynamic system case. It is shown that under certain conditions an overall optimum system design is obtained by first optimizing the system with all quantizers removed and then applying the procedure for the static open-loop case mentioned above. This result is analogous to the separation of the functions of estimation and control that occurs under similar conditions. The computational savings over the existing procedures are very extensive, and the new procedure is computationally feasible for a large class of practical systems.

Optimum adaptive control in an unknown environment

This correspondence describes the formulation and solution of a nonlinear, non-Gaussian stochastic control problem. Dynamic programming is used to obtain the solution to the problem of optimally controlling a robot, equipped with sensors, that is operating in an unknown environment.

Foreword [Intro. to the Bellman Special Issue]

The Bellman Special Issue of the Transactions on Automatic Control is a first in the history of the Control Systems Society. Never before has the Society dedicated a special issue to an individual - and especially an individual who is a mathematician rather than an engineer. The papers appearing in the special issue deal with a variety of topics which in one way or another reflect the influence of Bellmans ideas-ideas contained in over six hundred papers, thirty-six books, and seven monographs. All of the papers in the special issue have beenc ontributed and all have been subjected to a rigorous review process. In addition, a brief biography of Richard E. Bellman is given highlighting his professional achievements.

Application of combined optimum control and estimation theory to direct digital control

This paper demonstrates methods for applying combined optimum control and estimation theory to serial systems with time delay. The case of serial linear systems with time delay is considered in detail; a result analogous to the separation theorem of linear systems is presented. Illustrative examples of serial chemical reactors, rolling mills, and second-order plus dead-time approximations of higher order systems are discussed. Numerical results for a second-order plus dead-time system are presented: these results are compared with a suboptimal feedback controller (modified Smith predictor) and the open-loop response. It is shown that, in this case, the optimum estimation and control gains may be approximated by constants which further simplify the DDC algorithm. In the second-order plus dead-time approximation to higher order overdamped systems, the optimum algorithm can be reduced to recursive estimation with constant gain and linear state variable feed forward control. This algorithm may be used as a direct replacement for digital controllers used in the process industries.