SYSTEM AND METHOD FOR CLOSED-LOOP DISSOLVED OXYGEN MONITORING AND CONTROL

Abstract

A computer-implemented method of closed-loop dissolved oxygen monitoring and control at a hydroelectric plant includes: regulating at least one aeration valve coupled to a turbine using pattern recognition; wherein a target parameter for the regulating is a dissolved oxygen concentration of water downstream of the hydroelectric plant. The dissolved oxygen concentration may be at least 5.0 milligrams per liter. The pattern recognition may be performed using a neural network.

Claims

1. A computer-implemented method of closed-loop dissolved oxygen monitoring and control at a hydroelectric plant comprising: regulating at least one aeration valve coupled to a turbine using pattern recognition; wherein a target parameter for the regulating is a dissolved oxygen concentration of water downstream of the hydroelectric plant.

2. The method of claim 1, wherein the dissolved oxygen concentration is at least 5.0 milligrams per liter.

3. The method of claim 1, wherein the pattern recognition is performed using a neural network.

4. The method of claim 1, wherein the regulating sets a degree of opening the at least one aeration valve.

5. The method of claim 1, wherein the pattern recognition comprises at least one machine learning algorithm.

6. The method of claim 5, wherein the at least one machine learning algorithm is provided with data inputs including at least one of: (a) dissolved oxygen concentration, water level, and water temperature upstream of the hydroelectric plant; (b) dissolved oxygen concentration, water level, and water temperature downstream of the hydroelectric plant; (c) unit power output and quality; (d) required dissolved oxygen concentration; (e) atmospheric temperature and humidity; and (f) time of day and day of year.

7. The method of claim 6, further comprising: analyzing the data inputs using a four layer, four output neural network that outputs an optimal valve position of each of four intake air valves that minimizes efficiency loss while ensuring the hydroelectric plant satisfies the target parameter.

8. The method of claim 1, wherein the hydroelectric plant comprises a plurality of turbines and the pattern recognition is performed using a single neural network for each turbine.

9. The method of claim 1, wherein the hydroelectric plant comprises a plurality of turbines and the pattern recognition is performed using a single neural network for at least two of the plurality of turbines.

10. The method of claim 1, wherein the at least one aeration valve comprises a plurality of runner blades of the turbine.

11. The method of claim 1, wherein the at least one aeration valve discharges air via through-blade aeration of the turbine.

12. The method of claim 1, wherein the at least one aeration valve discharges air via a passage within at least one runner blade of the turbine.

13. The method of claim 1, wherein the at least one aeration valve discharges air through a crown portion of the turbine.

14. The method of claim 1, wherein the at least one aeration valve discharges air via central aeration of the turbine.

15. The method of claim 1, wherein the at least one aeration valve discharges air via (a) through-blade aeration of the turbine and (b) central aeration of the turbine.

16. A computer-implemented method of closed-loop dissolved oxygen monitoring and control at a hydroelectric plant comprising: using closed-loop control to regulate at least one aeration valve coupled to a turbine and at least one cone valve coupled to a water-retaining structure of the hydroelectric plant; wherein a target parameter for the regulating is a dissolved oxygen concentration of water downstream of the hydroelectric plant.

17. The method of claim 16, wherein the dissolved oxygen concentration is at least 5.0 milligrams per liter.

18. The method of claim 16, wherein the closed-loop control comprises pattern recognition performed using a neural network.

19. The method of claim 18, wherein the pattern recognition comprises at least one machine learning algorithm.

20. The method of claim 16, wherein the closed-loop control is used to set a degree of opening the at least one aeration valve.

21. The method of claim 16, wherein the closed-loop control is used to set a degree of opening the at least one cone valve.

22. The method of claim 16, wherein the closed-loop control is provided with data inputs including at least one of: (a) dissolved oxygen concentration, water level, and water temperature upstream of the hydroelectric plant; (b) dissolved oxygen concentration, water level, and water temperature downstream of the hydroelectric plant; (c) unit power output and quality; (d) required dissolved oxygen concentration; (e) atmospheric temperature and humidity; and (f) time of day and day of year.

23. The method of claim 22, further comprising: analyzing the data inputs using a four layer, four output neural network that outputs an optimal valve position of each of four intake air valves that minimizes efficiency loss while ensuring the hydroelectric plant satisfies the target parameter.

24. The method of claim 16, wherein the hydroelectric plant comprises a plurality of turbines and the closed-loop control is performed using a single neural network for each turbine.

25. The method of claim 16, wherein the hydroelectric plant comprises a plurality of turbines and the closed-loop control is performed using a single neural network for at least two of the plurality of turbines.

26. The method of claim 16, wherein the at least one aeration valve comprises a plurality of runner blades of the turbine.

27. The method of claim 16, wherein the at least one aeration valve discharges air via through-blade aeration of the turbine.

28. The method of claim 16, wherein the at least one aeration valve discharges air via a passage within at least one runner blade of the turbine.

29. The method of claim 16, wherein the at least one aeration valve discharges air through a crown portion of the turbine.

30. The method of claim 16, wherein the at least one aeration valve discharges air via central aeration of the turbine.

31. The method of claim 16, wherein the at least one aeration valve discharges air via (a) through-blade aeration of the turbine and (b) central aeration of the turbine.

32. The method of claim 16, wherein the at least one cone valve comprises a fixed cone valve.

33. The method of claim 16, wherein the at least one cone valve comprises a linear aerating valve.

34. A computer-implemented method of closed-loop dissolved oxygen monitoring and control at a hydroelectric plant comprising a turbine, the method comprising: regulating at least one aeration valve coupled to a turbine by at least one machine learning algorithm; wherein a target parameter for the regulating is a dissolved oxygen concentration of water downstream of the hydroelectric plant.

35. The method of claim 34, wherein the at least one machine learning algorithm comprises a neural network.

36. The medium of claim 35, wherein the dissolved oxygen concentration is at least 5.0 milligrams per liter.

37. A non-transitory computer-readable medium having computer readable instructions that, when executed by a processor of a computer, cause the computer to perform closed-loop dissolved oxygen monitoring and control at a hydroelectric plant comprising: regulating at least one aeration valve coupled to a turbine using pattern recognition; wherein a target parameter for the regulating is a dissolved oxygen concentration of water downstream of the hydroelectric plant.

38. The medium of claim 37, wherein the dissolved oxygen concentration is at least 5.0 milligrams per liter.

39. The medium of claim 37, wherein the pattern recognition is performed using a neural network.

40. A system comprising: a processor; memory including instructions that when executed by the processor, cause the system to perform closed-loop dissolved oxygen monitoring and control at a hydroelectric plant comprising: regulating at least one aeration valve coupled to a turbine using pattern recognition; wherein a target parameter for the regulating is a dissolved oxygen concentration of water downstream of the hydroelectric plant.

41. The system of claim 40, wherein the dissolved oxygen concentration is at least 5.0 milligrams per liter.

42. The system of claim 41, wherein the pattern recognition is performed using a neural network.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Preferred features of the inventions are disclosed in the accompanying drawing, wherein:

[0031] FIG. 1 is a schematic showing operation of a neural net for setting valve position.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0032] In an exemplary embodiment, closed-loop dissolved oxygen monitoring and control is applied with respect to the High Rock Development located in Davie, Davidson, and Rowan counties, North Carolina on the Yadkin River and opened in 1927. The reservoir is impounded by a 936-foot-long, 101-foot-high dam that comprises (1) a 58-foor long non-overflow section, (2) a 550-foot-long gated spillway section with ten 45-foot-wide by 30-foot-high stoney gates, (3) a 178-foot-long, 125-foot-high powerhouse intake, and (4) a 150-foot-long non-overflow section. The concrete powerhouse is integral with the dam and comprises three vertical Francis turbine/generator units with a total installed capacity of 32.91 MW.

[0033] In the exemplary embodiment, it is desired that the dissolved oxygen concentration downstream of the High Rock hydroelectric plant is at least 6.0 milligrams per liter (6 ppm). For example, Title 15A (Environmental Quality) of the North Carolina Administrative Code (NCAC) assigns classifications and water quality standards to surface waters and wetlands in the state. Class C freshwaters are defined in 15A NCAC 02B.0101(c)(1) as freshwaters protected for secondary recreation, fishing, aquatic life including propagation and survival, and wildlife. All freshwaters shall be classified to protect these uses at a minimum. As for fresh surface water standards for Class C waters, 15A NCAC 02B.0211(6) requires: Dissolved oxygen: not less than 6.0 mg/l for trout waters; for non-trout waters, not less than a daily average of 5.0 mg/l with a minimum instantaneous value of not less than 4.0 mg/l; swamp waters, lake coves, or backwaters, and lake bottom waters may have lower values if caused by natural conditions.

[0034] Thus, for regulatory, environmental, and compliance reasons, operators of dams such as High Rock may need to install and operate equipment to adjust the dissolved oxygen content of water that passes through their facilities.

[0035] In order to monitor dissolved oxygen, sensor units for example may be mounted to floats positioned downstream of the dam, with each of the sensor units having a power supply that may include solar cells and batteries, as well as temperature and dissolved oxygen sensors, and a control system for capturing and reporting relevant data. For example, the sensor units preferably are wireless. Each float may be provided with a programmable logic controller (PLC) which is coupled to a cellular modem that transmits sensor data to a server.

[0036] In the exemplary embodiment, in order to meet dissolved oxygen targets at High Rock, controllable valve intake openings are provided with respect to the aerating runners of the turbines. The runners, which rely on the natural creation of a vacuum below the turbine (as water passes through), use the vacuum to pull negative pressure on the headcover of the turbine. The water passing through the turbine incorporates air, of course with oxygen, that is supplied through the runners. The water then is released into the reservoir below, thereby improving dissolved oxygen concentrations below the dam.

[0037] An exemplary aerating system for the runner of a hydraulic turbine that may be adapted for dissolved oxygen monitoring and control is disclosed in U.S. Patent Application Publication No. 2016/0327012 A1 to Beaulieu, which is incorporated in its entirety herein by reference.

[0038] By varying the degree of opening of the valve intakes, operators may vary in a precise manner how much air (with oxygen) is incorporated into the water passing through the turbines, in furtherance of meeting dissolved oxygen requirements.

[0039] The incorporation of dissolved oxygen in the water expelled from the impoundment downstream of the dam, however, can present issues. For example, the disruption and the turbulence induced in the water flow may reduce the efficiency of the turbines and reduce the maximum power output of the facility. Accordingly, the system and method closed-loop dissolved oxygen monitoring and control preferably is operated in a manner that facilitates efficiency. In other words, it is desirable to ensure effective oxygenation of water expelled from the impoundment while minimizing impacts upon turbine operation and power generation.

[0040] Given a set of hydrological conditions upstream of the dam (e.g., current dissolved oxygen concentration, water level, and temperature), a set of hydrological conditions downstream of the dam (e.g., required or desired dissolved oxygen concentration, current dissolved oxygen concentration, water level, and temperature), and a set of desired power characteristics (e.g., power output, power quality, and turbine units in operation), an optimal amount of oxygen intake may be set to meet dissolved oxygen requirements while minimizing impacts upon efficiency. The system and method thus may receive data from in-stream dissolved oxygen sensors upstream and downstream of the dam (e.g., both in the stream and at the dam such as in the intake and draft tube) and use that data along with required or desired dissolved oxygen concentrations, and desired unit power output, and then determine the appropriate air intake valve openings.

[0041] In one exemplary embodiment, the degree of opening the air intake valves may be determined by machine learning algorithm(s). For example, a neural network may be provided with data including: upstream reservoir dissolved oxygen concentration, water level, and temperature; downstream reservoir dissolved oxygen concentrations, water level, and temperature; unit power outputs and qualities; required dissolved oxygen concentration; atmospheric temperature, and humidity; and the time of day and day of the year. In a preferred exemplary embodiment, these inputs may be taken into a four layer, four output neural network that outputs the optimal valve position of each of four intake air valves that minimizes efficiency loss while ensuring the dam satisfies mandated or desired dissolved oxygen targets.

[0042] The control parameterthe air intake valve positionis the independent variable that is adjusted.

[0043] In some embodiments, air temperature (a climate predictor) may be used to predict changes in water temperature.

[0044] In some embodiments, data analyzed to determine how much to open/close the air intake valves may be limited based on the degree of influence of a particular condition on the overall determination. For example, data for air temperature and humidity may not be used in some embodiments.

[0045] In some embodiments, the target parameterthe required or desired dissolved oxygen concentration is at least 6.0 milligrams per liter (6 ppm). When a neural network is trained, for example, this target parameter becomes particularly relevant.

[0046] For example, a valve may be opened 50% while achieving 5.8 milligrams per liter (5.8 ppm) dissolved oxygen concentration in water downstream of the dam. Comparing that concentration to the target, a greater amount of valve opening may be needed to achieve at least 6.0 milligrams per liter (6 ppm).

[0047] In a preferred embodiment, the process parameter is the dissolved oxygen concentration downstream of the dam, which preferably is actual data collected from the water downstream of the dam (e.g., 6.4 ppm or 5.8 ppm). The process parameter represents what the control parameter is adjusted to control. In addition, auxiliary parameters may help predict how the system and method may perform, and include, for example, temperature of air (which may only have a small effect on the calculations, but may help predict how much oxygen will be taken up at what rate), humidity or relative humidity (which also may only have a small effect on the calculations, but may serve as a climate predictor and may influence the amount of oxygen the water will take up), the temperature of the water downstream and upstream of the dam (which impacts the solubility of oxygen in water), dissolved oxygen content upstream, the amount of power desired to be generated, the quality of power (e.g., how much reactive power is produced), head levels upsteam and downstream (e.g., the level of the water, such as depth of the reservoir/impoundment, head water elevation and tail water elevation) which may influence turbine performance (e.g., the larger the difference between those elevations, the more energy may be generated because the energy is a function of the difference between those elevations), the time of day (e.g., dissolved oxygen levels bottom out at nighttime at least in part because plant life in the water is not photosynthesizing and producing oxygen), and the day of the year (e.g., there are seasonal differences in how dissolved oxygen concentration changes, for example because water temperature changes so slowly that the season is a big predictor of water behavior).

[0048] For example, at 9:00 p.m. at night, turbine valve(s) used for aeration may need to be further opened because photosynthesis is not occurring and thus dissolved oxygen levels in downstream water may be low and thus need to be increased.

[0049] In some embodiments, additional parameter(s) (data) may include dissolved oxygen concentrations downstream of additional dam(s) that may be above or below the system in operation, such as a second dam downstream of the first dam.

[0050] In some embodiments, other data that may be provided for use in determining the degree of valve opening/closing includes, for example, rain fall (actual or predicted), barometric pressure, and inflows of rivers upstream (e.g., using gauges/sensors on such rivers upstream for providing data concerning the flow of water coming downstream).

[0051] The system and method disclosed herein advantageously permits operators to better manage the aeration of water while still permitting desired power to be generated. In other words, as stated previously, the performance of the turbine may be impacted by the amount of aeration that is occurring. For example, the operator may start generating 12 MW, but then open valve(s) to provide aeration and the resulting drop in efficiency may decrease the power production to 11.2 MW.

[0052] In some embodiments, aeration is provided by bubbling air in the impoundment and without any aeration using a turbine.

[0053] Turbine efficiency curves may indicate efficiency dependent on (1) flow through the turbine and net head which is (2) headwater elevation minus (3) tailwater elevation. Both flow and net head may be nonlinear.

[0054] For aerating turbines, a fourth dimension may be added: air intake, which also may be nonlinear. Thus, operation of the hydroelectric plant may be based on three independent variables (flow, head, and air intake) and one dependent variable (power output, e.g., efficiency).

[0055] In the preferred embodiment, the process and auxiliary parameters are fed into a neural network and it outputs the control parameters which correspond to the position of each of the air intake valves (e.g., four valves) of the turbine.

[0056] Preferably, the neural net is run on a computer while other components are controlled by PLCs. For example, at least one PLC reports all of the input parameters to the computer, and the computer then reports control parameters back to the PLC. The PLC then adjusts those control parameters. Then, the PLC reports a new set of input and process parameters to the computer and the sequence is repeated.

[0057] The system and method resembles a classic proportional-integral-derivative (PID) controller loop, but differs because machine learning (which is predictive) is leveraged.

[0058] Preferably, the neural net is trained and supervised learning is utilized. The target dissolved oxygen concentration (e.g., a continuous value) downstream of the dam is known, so control is needed to achieve that target.

[0059] In one exemplary embodiment, the loop (sequence) is repeated every 30 seconds. In another exemplary embodiment, the loop (sequence) is repeated every 60 seconds. In yet another exemplary embodiment, the loop (sequence) is repeated every 60 minutes.

[0060] Various other types of machine learning algorithms may be used, such as Almeida-Pineda recurrent backpropagation, ALOPEX, backpropagation, bootstrap aggregating, CN2 algorithm, constructing skill trees, Dehaene-Changeux model, diffusion map, dominance-based rough set approach, dynamic time warping, error-driven learning, evolutionary multimodal optimization, expectationmaximization algorithm, FastICA, forwardbackward algorithm, GeneRec, Genetic Algorithm for Rule Set Production, growing self-organizing map, HEXQ, hyper basis function network, IDistance, K-nearest neighbors algorithm, kernel methods for vector output, kernel principal component analysis, Leabra, Linde-Buzo-Gray algorithm, local outlier factor, logic learning machine, LogitBoost, manifold alignment, minimum redundancy feature selection, mixture of experts, multiple kernel learning, non-negative matrix factorization, online machine learning, out-of-bag error, prefrontal cortex basal ganglia working memory, PVLV, Q-learning, quadratic unconstrained binary optimization, query-level feature, Quickprop, radial basis function network, randomized weighted majority algorithm, reinforcement learning, repeated incremental pruning to produce error reduction (RIPPER), Rprop, rule-based machine learning, skill chaining, Sparse PCA, state-action-reward-state-action, stochastic gradient descent, Structured kNN, T-distributed stochastic neighbor embedding, temporal difference learning, wake-sleep algorithm, and weighted majority algorithm (machine learning).

[0061] Machine learning methods that may be used include, but are not limited to, instance-based algorithm (e.g., K-nearest neighbors algorithm (KNN), Learning vector quantization (LVQ), Self-organizing map (SOM)), regression analysis (e.g., logistic regression, Ordinary least squares regression (OLSR), linear regression, stepwise regression, and multivariate adaptive regression splines (MARS)), regularization algorithm (e.g., ridge regression, Least Absolute Shrinkage and Selection Operator (LASSO), elastic net, and Least-angle regression (LARS)), and classifiers (e.g., probabilistic classifier, Naive Bayes classifier, binary classifier, linear classifier, and hierarchical classifier).

[0062] In some alternate embodiments, machine learning is not used. Rather, a PID loop or other control algorithm is used.

[0063] The system and method disclosed herein also may be applied to dams used in agricultural and flood control that don't produce power, or to processing plants.

[0064] Preferably, five core variables are used in the system and method disclosed herein: desired power output of a single plant as well as dissolved oxygen content of water and temperature of water both upstream and downstream. In another embodiment, for example, seven core variables may include: desired power output of each of three unit in a plant as well as dissolved oxygen content of water and temperature of water both upstream and downstream.

[0065] In one embodiment, a neural net is created for operating one unit, i.e. one turbine. However, the plant may have multiple turbines which are not all running at the same power output, because they may not all be on (e.g., sometimes the operator only wants to generate a small amount of power because either that is all that can be sold, there is a maintenance outage, there is a lack of water, the price dictates the decision, or regulatory requirements). In some embodiments, a unit may be substantially always operated. In one example, the outputs of neural nets from a unit 1 and a unit 3 may be used as an input to a unit 2. In another example, if units 1 and 3 are always online and valves are open to provide full aeration, and unit 2 is just being brought online, it may not be necessary to open valves for unit 2 as much or at all because units 1 and 3 are already achieving the desired aeration. However, an optimization may be performed for distributing aeration maximally efficiently across the units.

[0066] Typically, the less aeration the turbine is providing, the more efficient it is.

[0067] In addition, a neural net on unit 2 may be used to predict how open the valves are on units 1 and 3 because units 1 and 3 will perform in some repeatable fashion over time. Thus, another auxiliary parameter that may be used is the power generated (e.g., real power) or power quality on other generating units.

[0068] In one embodiment, a single neural net is provided for each turbine. In another embodiment, a single neural net is provided for multiple turbines (such as units 1, 2, and 3). An advantage based on a single unit is that individual neural nets adapt to the peculiarities of each turbinethe net tunes to that turbine. Sometimes in a plant, the turbines are different types, and/or have different aeration systems, power ratings, and retrofitting or rebuilds.

[0069] Preferably, the valves used for aeration are motorized to permit operator adjustment. In addition, preferably the valves are analog so that they may be continuously controlled with respect to how open or closed the valve may be set. Preferably, the valves provide a linear relationship between flow as a function amount of openness of valve (desired openness).

[0070] The system and method disclosed herein improves upon the practice of most operators to keep the aeration valves 100% open (or some other fixed value), so they are potentially adding more oxygen than necessary to meet desired DO levels and decreasing the efficiency of power generation.

[0071] A schematic showing operation of an exemplary neural net for setting valve position is shown in FIG. 1.

[0072] In an exemplary embodiment, the algorithm is provided with 24 data points. The dissolved oxygen concentration is determined one hour after the algorithm is run, and then the valve openness is adjusted. The algorithm may set the valve openness at 12:00 a.m., and then at 1:00 a.m. account for the then-current dissolved oxygen concentration and adjust the valve openness. This sequence may be repeated every hour, nominally for a day over some range of values that are preselected. The algorithm may sweep the entire range of the valve. The 24 data points may be used at the start, and then backpropagation may be used based on the 24 values, determining a best guess as to each of the weights (multipliers) of each unit in the neural network, and then the algorithm may operate over the next 24 hours without intervention. Then, data may again be collected and the algorithm may be retrained based on 48 data points. The algorithm may be retrained every day for some period of time, or alternatively the most recent period of data (e.g., 10 years) may be retained. In one preferred embodiment, at least 10 data points are retained for each day of the year.

[0073] In alternate embodiments, instead of day of the year, the month of the year is used, or the day and the month of the year are used.

[0074] In one exemplary neural net, two hidden layers are used at the outset.

[0075] The output layer may have 4 units or as many units as there are aeration devices to be controlled.

[0076] An exemplary embodiment has 20 input units and four output units (one for each of four valves). Alternatively, if there are six valves, then there are six output units.

[0077] In one embodiment, all valves are controlled with one output unit. However, in another embodiment, in order to get more granularity (e.g., more efficient outcomes), each valve is controlled with its own output unit.

[0078] In one embodiment, IFM Efector, Inc. model TT1291 (TT-150KFED06-/US/) temperature sensors are used. Also, in one embodiment, In-Situ Inc. Rugged Dissolved Oxygen (RDO) PRO-X optical dissolved oxygen probes are used.

[0079] The embodiments herein optionally may be presented as including individual functional blocks including functional blocks comprising devices, device components, steps or routines in a method embodied in software, or combinations of hardware and software.

[0080] In some embodiments the computer-readable storage devices, mediums, and memories for use in connection with the embodiments herein may include a cable or wireless signal containing a bit stream and the like. However, when mentioned, non-transitory computer-readable storage media expressly exclude media such as energy, carrier signals, electromagnetic waves, and signals per se.

[0081] Methods in accordance with the embodiments herein may be implemented using computer-executable instructions that are stored or otherwise available from computer readable media. Such instructions may comprise, for example, instructions and data which cause or otherwise configure a general purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. Portions of computer resources used can be accessible over a network. The computer executable instructions may be, for example, binaries, intermediate format instructions such as assembly language, firmware, or source code. Examples of computer-readable media that may be used to store instructions, information used, and/or information created during methods in accordance with the embodiments herein include, but are not limited to, magnetic or optical disks, flash memory, USB devices provided with non-volatile memory, and networked storage devices.

[0082] Devices implementing methods in accordance with the embodiments herein may comprise hardware, firmware and/or software, and may take any of a variety of form factors including, but not limited to, laptops, smart phones, small form factor personal computers, personal digital assistants, rackmount devices, and standalone devices. Functionality described herein also can be embodied in peripherals or add-in cards and may be implemented on a circuit board among different chips or different processes executing in a single device, for example.

[0083] The instructions, media for conveying such instructions, computing resources for executing them, and other structures for supporting such computing resources are means for providing the functions described herein.

[0084] While various descriptions of the inventions are described above, it should be understood that the various features can be used singly or in any combination thereof. Therefore, the inventions are not to be limited to only the specifically preferred embodiments depicted or otherwise described herein.

[0085] Further, it should be understood that variations and modifications within the spirit and scope of the inventions may occur to those skilled in the art to which the inventions pertain. Accordingly, all expedient modifications readily attainable by one versed in the art from the disclosure set forth herein that are within the scope and spirit of the inventions are to be included as further embodiments of the inventions. The scope of the inventions is accordingly defined as set forth in the appended claims.