Parameter Estimation and Grid Synchronization Using a First-Order Frequency-Locked Loop

Author(s):  
Abdullahi Bamigbade ◽  
Vinod Khadkikar
1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo

Abstract An automatic history-matching algorithm based onan optimal control approach has been formulated forjoint estimation of spatially varying permeability andporosity and coefficients of relative permeabilityfunctions in two-phase reservoirs. The algorithm usespressure and production rate data simultaneously. The performance of the algorithm for thewaterflooding of one- and two-dimensional hypotheticalreservoirs is examined, and properties associatedwith the parameter estimation problem are discussed. Introduction There has been considerable interest in thedevelopment of automatic history-matchingalgorithms. Most of the published work to date onautomatic history matching has been devoted tosingle-phase reservoirs in which the unknownparameters to be estimated are often the reservoirporosity (or storage) and absolute permeability (ortransmissibility). In the single-phase problem, theobjective function usually consists of the deviationsbetween the predicted and measured reservoirpressures at the wells. Parameter estimation, orhistory matching, in multiphase reservoirs isfundamentally more difficult than in single-phasereservoirs. The multiphase equations are nonlinear, and in addition to the porosity and absolutepermeability, the relative permeabilities of each phasemay be unknown and subject to estimation. Measurements of the relative rates of flow of oil, water, and gas at the wells also may be available forthe objective function. The aspect of the reservoir history-matchingproblem that distinguishes it from other parameterestimation problems in science and engineering is thelarge dimensionality of both the system state and theunknown parameters. As a result of this largedimensionality, computational efficiency becomes aprime consideration in the implementation of anautomatic history-matching method. In all parameterestimation methods, a trade-off exists between theamount of computation performed per iteration andthe speed of convergence of the method. Animportant saving in computing time was realized insingle-phase automatic history matching through theintroduction of optimal control theory as a methodfor calculating the gradient of the objective functionwith respect to the unknown parameters. Thistechnique currently is limited to first-order gradientmethods. First-order gradient methods generallyconverge more slowly than those of higher order.Nevertheless, the amount of computation requiredper iteration is significantly less than that requiredfor higher-order optimization methods; thus, first-order methods are attractive for automatic historymatching. The optimal control algorithm forautomatic history matching has been shown toproduce excellent results when applied to field problems. Therefore, the first approach to thedevelopment of a general automatic history-matchingalgorithm for multiphase reservoirs wouldseem to proceed through the development of anoptimal control approach for calculating the gradientof the objective function with respect to theparameters for use in a first-order method. SPEJ P. 521^


2008 ◽  
Vol 41 (2) ◽  
pp. 14078-14083 ◽  
Author(s):  
J.W.C. Van Lint ◽  
Serge P. Hoogendoorn ◽  
A. Hegyi

1980 ◽  
Vol 12 (3) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive scheme Xn = pXn-1 + ∊n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.


1980 ◽  
Vol 12 (03) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis

It is shown that there is an innovation process {∊ n } such that the sequence of random variables {X n } generated by the linear, additive first-order autoregressive scheme X n = pXn-1 + ∊ n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.


2011 ◽  
Vol 64 (4) ◽  
pp. 880-886 ◽  
Author(s):  
P. D. Jensen ◽  
H. Ge ◽  
D. J. Batstone

The biodegradability and bioavailability of hydrolysis-limited substrates under anaerobic (and aerobic) conditions can be represented by two key parameters – degradability (fd), or the percentage that can be effectively be destroyed during digestion, and first order hydrolysis coefficient (khyd), or the speed at which material breaks down. Biochemical methane potential (BMP) testing uses a batch test (in triplicate), and by fitting against a first order model, can fit both parameters in the same test. BMP testing is now being widely used for anaerobic process feasibility and design purposes, and standardisation efforts are ongoing. In this paper, we address a number of key issues relating to the test method and its analysis. This includes proposal of a new fitting and parameter estimation method, evaluation of the impact of inoculum to substrate ratio on fitted parameters, and comparison to performance in continuous systems. The new parameter estimation technique provides an estimate of parameter uncertainty and correlation, and is clearly more suitable than model transformation and linear regression. An inoculum volume ratio of at least 50% (2:1 on VS basis) was required on a cellulose substrate to use methane production as primary indicator, as found by comparing methane production and solubilisation of cellulose. Finally, on a typical material, waste activated sludge, the batch test was slightly conservative in terms of degradability and rate, indicating a bias in the BMP test. The test is a cost-effective and capable method to evaluate potential substrates, but it should be noted that it is generally conservative, especially if sub-optimal inoculum is used.


1977 ◽  
Vol 4 (4) ◽  
pp. 462-470 ◽  
Author(s):  
Thomas W. Constable ◽  
Edward A. McBean

Two nonlinear parameter estimation techniques are used to obtain expected values, variances, and covariance estimates for L and k in the first-order BOD equation. The techniques are compared with a number of other BOD parameter estimation methods with respect to both estimated values of L and k and necessary assumptions about the measurement error structure of BOD analyses. The techniques that historically have been used to estimate the parameters in the first-order BOD equation are shown to often give erroneous answers because of their use of an incorrect error structure.A case study application of the methodology to the raw influent and primary effluent of the Waterloo Pollution Control Plant is included.


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