C. Byron Winn

Optimal dispatch strategy in remote hybrid power systems

Abstract For small villages in developing countries, local stand-alone power systems are often more cost-effective than utility grid extension. Various combinations of wind turbine generators, photovoltaic arrays, diesel gensets, and batteries—remote hybrid power systems—may be preferred to diesel-only systems. Dispatch strategy is the aspect of control strategy that pertains to energy flows among components. In systems with both batteries and diesel genset(s), dispatch affects the life-cycle cost through both the fuel usage and the battery life. In this study, dispatch strategies are compared using (1) an analysis of cost trade-offs, (2) a simple, quasi-steady-state time-series model, and finally (3) HYBRID2, a more sophisticated stochastic time-series model. An idealized predictive dispatch strategy, based on assumed perfect knowledge of future load and wind conditions, is developed and used as a benchmark in evaluating simple, non-predictive strategies. The results illustrate the nature of the optimal strategy and indicate that one of two simple diesel dispatch strategies—either load-following or full power for a minimum run time—can, in conjunction with the frugal use of stored energy (the Frugal Discharge Strategy), be virtually as cost-effective as the Ideal Predictive Strategy. The optimal choice of these two simple charging strategies is correlated to three dimensionless parameters, yielding a generalized dispatch design chart for an important class of systems.

Optimal sizing of solar collectors by the method of relative areas

Abstract A method is presented for calculating directly, without iteration, the approximate collector area which minimizes the total life-cycle cost of an active solar space and/or domestic hot water heating system. The method is based on an empirical relationship between annual solar load fraction and relative collector area. This relationship was determined by correlating data that were generated by the Klein, Beckman and Duffie F-Chart program, which in turn is based on a correlation of digital computer simulation results. The calculations may be performed in a few minutes using a hand-held calculator. Required data are tabulated for 170 locations, and a solved example is included. Compared to results from the F-chart program, deviations of total life-cycle costs from the minima are typically less than 3 per cent. Uncertainty of future energy prices is regarded as the limiting factor in the accuracy of the optimization calculations. A detailed economic analysis is included.

Optimal controllers of the second kind

Abstract An approximate analytical solution to the problem of determining the optimal flow rate through solar collectors so as to maximize the integral of the difference between the useful energy and the pumping costs incurred in collecting the solar energy has been obtained. The solution that is presented is an optimal feedback controller that is based upon measurable states of the system. The solution technique that was employed was that of the Pontryagin maximum principle and an approximate analytical solution to the resulting two-point boundary value problem was obtained by means of a transformation that involved using the heat removal factor as the control. The optimal control (the mass flow rate) is then recoverable from the heat removal factor. The derivation of the optimal control law is presented. Also presented is a discussion of implementation of the optimal control law. Finally, comparisons between these results and those presented in an earlier paper in which a numerical solution was obtained are presented.

Controls in Solar Energy Systems

The characteristics of bang-bang, proportional, integral, derivative, and PID controllers, and their applications to solar energy systems, are presented. Also included is a determination of the effects of temperature settings on cycling rates in systems using bang-bang controllers. A phase-plane representation is developed and an analytical representation for the number of cycles as a function of temperature settings, solar radiation, and physical parameters is presented.

Modern Control Concepts in Hydrology

Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time-invariant or time-dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and confirm the results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

A sequential filter used for parameter estimation in a passive solar system

Abstract The use of a sequential least squares filter for estimating passive solar system parameters is presented as it applies to certain types of systems. The method given is used to identify parameters in a particular existing system, and the results are given. A discussion is also included on a comparison of various sampling rates used by the filter, with a view toward selecting a “reasonable” sampling rate.

The Application of Optimal Linear Regulator Theory to a Problem in Water Pollution

At present, many metropolitan sewer systems do not meet existing and proposed standards on water pollution. Existing systems were designed to overflow at prescribed locations in order to protect the sewage treatment plants whenever severe overload conditions exist (usually during storms). This discharge of untreated overflows into natural receiving waters is of growing concern to water pollution control authorities. The model considered in this paper is representative of the combined storm-sewer systems in cities such as Minneapolis-St. Paul, Minn., Seattle, Wash., and San Francisco, Calif. The objective is to utilize the total storage capacity available in the system in such a manner as to minimize the water pollution resulting from overflows at individual points within the system. In addition, it is required that no abrupt changes in control be admitted, as this is likely to lead to undesirable surges. The nonlinear model is shown to fit within the framework of an optimal regulator problem with derivative constraints. The optimal feedback control law is derived and compared with the optimal bang-bang controller. The solution technique that is presented may be applied to many combined storm-sewer systems in which the flows through the systems to the treatment plants may be controlled. It may be used by city engineers to determine necessary modifications to existing systems in order to meet the new standards regarding water pollution.

Dynamic effects of bang-bang control on the thermal performance of walls of various constructions

The problem of energy consumption during heating and cooling with bang-bang control based upon room air temperature is studied. An analytical model is solved using the Laplace Transform technique, yielding an exact solution to the system. TMY weather data are used from four locations during the months of August and January to assess climatological effects. Approximate models are developed to explain the time lags observed during free response, and the observed chattering rate under bang-bang control. Results indicate the presence of a thermal mass effect due to the nonlinear interaction between the thermal wave penetrating the wall and the control function, with a greater effect for walls of massive construction, and in moderate weather conditions.

SIMSHAC: a simulation program for solar heating and cooling of buildings

A dynamic simulation model for use in analyzing the performance of specific designs of solar-heated-and- cooled buildings has been developed. The name of the program is SIMSHAC, an acronym for SImulation Model for Solar-Heated-And-Cooled buildings. To use the design program, one has merely to specify the components (that is, each subsystem; for example, collectors, storage units, splitting and mixing valves, house heating and cooling loads, auxiliary heating, auxiliary cooling, heat exchanger, etc.), and the manner in which they are connected and all initial conditions. Program SIMSHAC then writes the program for the specific system to be analyzed. Each subsystem is described by a set of time-dependent differential equations or, possibly, algebraic equations. System state variables include tempera ture, mass flow rate, and enthalpy. The model can handle three types of incident solar radiation data models. These are (1) deterministic (e.g., an algebraic-equation sun model), (2) random simulation (e.g., a model based upon cloud-cover statistics), and (3) actual tabulated input information based upon collected solar data for a specific site. The model has been used for the analysis of five different types of buildings in five locations within the United States. The types include single-family residences, small businesses, three-story apartments, schools, and mobile homes. The locations considered are Atlanta, Georgia; Madison, Wisconsin; Wilmington, Delaware; Mobile, Alabama; and Santa Maria, California. The program has also been used to simulate the solar- heated-and-cooled experimental laboratory presently being built by the National Science Foundation on the campus at Colorado State University.

Orbit Determination by Range-Only Data

The determination of satellite orbits for use in geodesy using range-only data has been examined. A recently developed recursive algorithm for rectification of the nominal orbit after processing each observation has been tested. It is shown that when a synchronous satellite is tracked simultaneously with a subsynchronous geodetic target satellite, the orbits of each may be readily determined by processing the range information. Random data errors and satellite perturbations are included in the examples presented.