Controllable risk parameter for device control system
TECHNICAL FIELD 
     This invention relates to a device control system and, in particular, to a consumption control arrangement which monitors the operation of a number of resource consuming devices, predicts their future activity and regulates their operation based on past consumption and predicted future activity. The function of the device control system is to maintain the overall demand (which is defined to be the rate of resource consumption over a specified time interval) for the resource below a predetermined demand threshold. The device control system includes a customer controlled risk parameter which enables the customer to select the amount of future activity prediction used by the device control system in selecting loads to be shed. By limiting the amount of future activity prediction, the customer allows the actual resource consumption level to approach the demand threshold. 
     BACKGROUND ART 
     There have been numerous prior art device control systems, generally in the field of electrical energy consumption. Prior art control systems operate on a crude load shedding basis: they disable (shed) an energy consuming load when the predetermined demand threshold is reached and maintain the energy consuming load in the shed state for an extended period of time. Many of these prior art control systems suffer from a tendency to overreact to peak loads by shedding too many energy consuming loads for too extended a period of time, which reduces the operating efficiency of the customer&#39;s equipment which the system is designed to control. Other prior art control systems underregulate the energy consuming loads, which permits the demand to exceed the demand threshold too frequently. In all of these systems, the customer does not have the ability to control the system&#39;s risk determination parameters, which prevents the customization of the system to each application. 
     DESCRIPTION OF THE INVENTION 
     The subject device control system solves these problems by providing a sophisticated device control arrangement which estimates, to a high degree of precision, the minimum load which must be shed to prevent the demand from exceeding the predetermined demand threshold. To accomplish this, the past performance of the resource consuming loads in the system is monitored and future load activity is estimated on an iterative basis to develop an accurate picture of the past, present and future controlled device activity. In addition, a customer-controlled risk parameter is provided which enables the customer to weigh the device control system activity determination. The resultant information is compared with the predetermined demand threshold. The result of this comparison is used to precisely regulate the resource consuming devices which are under the control of the subject device control system such that the maximum demand is satisfied without exceeding the predetermined demand threshold. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 illustrates, in block diagram form, the overall system aspects of the subject device control system; 
     FIG. 2 depicts the details of the system consumption monitor for the floating window demand interval; 
     FIG. 3 depicts the details of the system consumption monitor for the fixed window demand interval; 
     FIG. 4 represents a timing diagram for the consumption monitor circuit of FIG. 2; and 
     FIG. 5 represents the customer controlled data entry facility. 
    
    
     DETAILED DESCRIPTION OF THE DRAWING 
     FIG. 1 illustrates, in block diagram form, the preferred embodiment of the device control system of my invention. This system controls a plurality of devices or loads (L1-Lk), which devices utilize some resource, the rate of consumption of which is to be controlled. The system of FIG. 1 is a generalized system arrangement which, in a typical application, would be implemented to control the rate of electrical energy consumption on a customer&#39;s premises. Such an implementation of this system can be seen in U.S. Pat. No. 4,266,097 issued to T. B. Cannon et al on May 5, 1981 wherein the device control system uses a stored program business communication system to regulate the operation of various energy consuming devices. 
     The devices or loads (L1-Lk), illustrated in FIG. 1, very likely would be the heating, ventilating and air conditioning (HVAC) equipment which is operational on the customers premises. This HVAC equipment L1-Lk will be assumed to be powered by commercial 60 Hz ac line voltage (identified as &#34;resource source&#34; on FIG. 1) which is supplied by service lines S1-Si to consumption monitors P1-Pi and thence via power feed lines F1-Fk to loads L1-Lk, respectively. Consumption monitors P1 through Pi can be arranged on a one to one basis with an associated load or may monitor the consumption of a plurality of loads, as determined by the needs of the system. In the electrical energy consumption case, consumption monitors P1 through Pi would be power meters which measure the amount of electricity consumed by the associated loads. These power meters output a signal indicative of this electricity consumption to system control 100 on leads M1 through Mi, respectively. Consumption monitors P1-Pi are shown on FIG. 1 as series connected devices, although they could be connected in the bridged mode, dependent upon the meter design and the resource to be monitored. 
     Energy Control Units EC1-ECk 
     The plurality of loads L1-Lk illustrated in FIG. 1 are assumed, for this description, to be controlled by energy control units (EC1-ECk) which are associated on a one to one basis with loads L1-Lk via leads C1-Ck respectively. A plurality of loads can be controlled by a single energy control unit but, for simplicity of description, the one-to-one configuration will be described herein. The energy control units EC1-ECk may also be powered by the commercial 60 Hz ac line voltage. The energy control units EC1-ECk enable their associated HVAC loads L1-Lk to operate under control of their internal thermostats or other regulatory circuitry until selected ones of energy control units EC1-ECk receive appropriate control signals from system control 100 via leads TR1-TRk. This control function is activated when system consumption monitor 101 determines that a load should be disabled and places an appropriate set of signals on bus LB to load interface 102. Load interface 102 is a multiplexer circuit which translates the control signals on bus LB to an appropriate activation signal which is to be applied to the designated one or ones of leads TR1 through TRk to thereby activate the associated energy control unit to disable the load that it controls. When an energy control unit, such as unit EC1, receives the control signal on the associated control lead (TR1), the energy control unit EC1 terminates the operation of the associated load (L1) by overriding the operation of the internal thermostat or control circuitry of HVAC equipment L1 via lead C1. 
     A detailed description of a typical energy control unit can be found in the above-referenced T. B. Cannon et al patent as can a description of load interface 102 which would comprise the line circuits, tone trunk, switching network and power meter interface of the Cannon patent. Thus, the particular control elements described above are well-known in the art, and it is certain elements of the control circuitry of system consumption monitor 101 which comprise this invention and which significantly depart from prior device control systems. System consumption monitor 101 is shown in FIG. 2 and is described in U.S. Pat. No. 4,489,386 issued Dec. 12, 1984, to J. H. Breddan. This arrangement is the preferred embodiment of the basic control circuitry that is used in the device control system of FIG. 1 to provide the desired load control operation. The addition of the controllable risk parameter to this basic control circuitry is the subject of this invention and is described below. 
     System Constraints 
     In the consumption of a resource, there are numerous economic or legal constraints upon the consuming customer which forces bounds upon the resource consuming activity. In the electricity consumption area, a significant factor is the severe economic penalty imposed by the local utility company upon excessive peak loads caused by a customer. Avoiding this economic penalty, which is imposed by the utility company, is a significant motivating force in selecting an implementation of the subject device control system to control electricity consumption, which implementation enables the customer to customize the operation of the device control system for each application. 
     The parameters defining peak demand vary from utility company to utility company but demand is defined to be the average energy consumption rate of a particular customer over a predetermined fixed interval of time, called a demand interval. The highest value which the demand reaches during the billing period is the peak demand, and the customer is generally charged a fixed dollar amount per kilowatt of the peak by the utility company. Thus, the customer sets the demand threshold to the lowest possible level that is still high enough not to interfere seriously with the day-to-day operation of the business in order to minimize the cost of the resource. 
     Demand Interval 
     Each demand interval is comprised of a fixed number n of monitoring intervals. For example, a demand interval may be a 15 minute period which consists of 15 one minute monitoring intervals. Thus, the device control system must monitor the on-going energy consumption of the customer and shed sufficient loads to assure that the electrical energy demand during this demand interval does not exceed the predetermined demand threshold. In calculating the demand, a demand interval called a &#34;fixed window&#34; is sometimes used in which each demand interval begins at a predetermined time, and where the demand intervals do not overlap in time. However, if the customer knows both the duration of this fixed window and the start time of the fixed window, the customer can spread the peak load activity over two fixed windows by activating the devices which cause the peak load just prior to the end of one fixed window and the beginning of the next. 
     In order to avoid such manipulations, which still cause the peak load at the utility, many local utility companies are switching to a &#34;floating window&#34; mode of analysis where the demand for any and every possible demand interval (which in many cases means a demand calculation is made each minute) cannot exceed the predetermined demand threshold. This prevents the customer from attempting to insert a peak load on-line at the boundary of a window which is fixed in time. Thus, the subject device control system must operate under the assumption that the present monitoring interval appears at any and every possible point within a fixed duration demand interval. This enables the subject system to operate asynchronously with respect to the utility company monitoring intervals. The subject system accomplishes this by iteratively analyzing the present consumption, past consumption and predicted future activity. 
     System Consumption Monitor 
     To illustrate the controllable risk parameter of this invention, the basic device control system functions of the aforementioned J. A. Breddan patent are described first. FIG. 2 illustrates this implementation of system consumption monitor 101 wherein these basic device control system functions are accomplished. The system illustrated in FIG. 2 may be implemented in any one of a number of ways: by analog devices, software routines on a digital computer, hard-wired digital logic or many other conceivable implementations. For the sake of economics, system consumption monitor 101 would probably be implemented by a software package run on a microprocessor or a minicomputer and the following discussion will be based on the assumption that the implementation is such. Thus, FIG. 2 can be viewed as a system state diagram which illustrates the functions realized in system consumption monitor 101. Given this level of detail, any competent practitioner of the engineering or computer arts could suitably design a circuit or program the selected processor in straightforward fashion to provide a particular implementation. 
     Fixed Window 
     The system disclosed in FIG. 2 is an implementation used for device control in the above-mentioned floating window demand interval constraint situation. However, the control scheme for the floating window includes an iterative repetition of the fixed window scheme. It is therefore advantageous to first describe a system implementation (shown in FIG. 3) used for device control in a fixed window environment. Thus, for a fixed window, system consumption monitor 101 analyzes past and future system performance for a predetermined demand interval. For the purpose of presenting an example, we will consider the case where n, the number of monitoring intervals in the fixed window demand interval, is equal to 15 and the present time corresponds to the tenth monitoring interval (represented by i=10) of the demand interval. The present monitoring interval is always assumed to have just ended when the calculations discussed below begin. This example characterizes a situation where, for this device control system, there are fifteen monitoring intervals in a demand interval and the device control system is presently ending the tenth monitoring interval during the fixed window or demand interval. System consumption monitor 101 therefore has five remaining monitoring intervals during which the energy consuming loads can be disabled or reactivated so that the maximum number of energy consuming loads are active without exceeding the predetermined demand threshold. 
     State 200 in FIG. 3 illustrates the first step of operation of system consumption monitor 101 and consists of the determination of the present electrical energy consumption during the present monitoring interval. This is accomplished by load interface 102 summing the output of consumption monitors P1-Pi and transmitting the resultant sum to system consumption monitor 101 via bus LB. When this sum is received, system consumption monitor 101 advances to state 201 which is the computation of the &#34;present load&#34; which is the sum of the present active energy consuming load and the load that would have been presented by the devices that are presently disabled by the subject device control system. This operation represents a conversion of the raw data obtained from consumption monitors P1-Pi and the shed device data stored in system consumption monitor 101 to a set of consumption figures indicative of the presently active and presently disabled loads. The result of this computation is stored in the memory of system consumption monitor 101 as illustrated by state 202 wherein this information is read into two history files or memories (not shown) of system consumption monitor 101. This information is generated once every monitoring interval and the history files of system consumption monitor 101 contain a listing of the loads shed and the actual consumption for each monitoring interval of the entire previous demand interval. 
     History Files 
     Before proceeding with the description of the states depicted in FIG. 3, a slight digression is in order. At this point the system has progressed through state 202 and the result has been the compilation of history files for two types of quantities. One file is set up for a history of the actual consumption figures for each of the previous n monitoring intervals (often this amounts to a minute by minute history). The second file is used to record a history of what the consumption figures (for each of those same n monitoring intervals) would have been had there been no loads shed during those monitoring intervals. 
     The use of these two separate history files is one of the key elements of the subject system and is discussed here in some detail. The basic approach in the fixed window scheme (detailed below) is to attempt to predict what the demand would be at the end of the window if no control action is taken (i.e., if no loads are shed) between the present moment and the end of the window. This quantity will be compared with the allowed demand, and control actions will be taken if the prediction is higher than allowed. Again the details of how this is done are presented below, but the point here is that the two separate history files are needed to come up with the best possible prediction of what the demand would be at the end of the window if no control actions are taken from the present moment forward. 
     The demand prediction is considered as consisting of two separate parts. One is the consumption which has taken place thus far in the window. This can be determined precisely by summing the figures from the first history file (actual consumption) for the monitoring intervals which occurred in the present window. The second part of the demand prediction consists of predictions for what will be consumed in each of the monitoring intervals remaining in the window if no loads are shed. These predictions are done on the basis of (possibly among other things) the entries in the second history file (once again, details will follow). 
     The reason for the separate history file being kept for the case where no loads are shed is to provide a common denominator from which to base predictions. Prior art control schemes explicitly or implicitly attempt to base predictions on actual consumption data points which are kept in the first history file in this system. Since different loads may have been shed in each of the previous monitoring intervals, these data points can essentially be on different footings, and basing predictions on them therefore increases the probable error factor. 
     The terminology used in the detailed description below has the potential for being a bit confusing, but the following points should help clarify any potential misunderstanding. The term &#34;load&#34; is used in two different ways. The term is often used to refer to a resource consuming device (i.e., a control action results in loads being shed). The term is also used to describe the total system request for the resource. In this context, the second history file keeps track of the load that the system experienced in each of the previous n monitoring intervals. The difference between the two uses of the word &#34;load&#34; is usually made clear by the context. The word &#34;consumption&#34; usually refers to actual consumption, as kept in the history file. Perhaps the biggest potential for confusion arises from the fact that at some point in the control scheme, we must add together a consumption figure (to represent what has been consumed thus far) and a load figure (to predict what will happen in the monitoring intervals remaining in the window), in order to come up with the demand prediction. For the purposes of this discussion (and the state diagrams) this total will be called a &#34;consumption&#34; figure in spite of the fact that it includes components of what we are calling &#34;load&#34;. 
     Prediction 
     Proceeding with the description of system states, the system consumption monitor 101 next advances to state 203 wherein system consumption monitor 101 estimates the load for each monitoring interval remaining in the present window and stores these results in a future file (not shown) of system consumption monitor 101. This prediction operation typically would be a function of the actual consumption taken over the entire previous demand interval and extrapolated over the entire subsequent demand interval. Thus, the future load would be the estimated consumption of all presently active loads plus the estimated consumption of all the loads presently in the shed state. Once this consumption prediction has been completed, an analysis is activated by advancing to state 206. 
     Function 206 obtains from the history file, the values of actual consumption for all of the monitoring intervals in the present window which have elapsed (a total of ten monitoring intervals in the example). Upon completion of this task, system consumption monitor 101 activates function 207 which obtains the values of predicted load for the monitoring intervals remaining in the fixed window (which, in the example, is five monitoring intervals) from the future file. As a result of these two memory read operations, function 208 is enabled to compute a prediction of how much of the resource will be consumed during the entire window if no loads are shed between the present moment and the end of the fixed window. System consumption monitor 101 activates function 209 which generates a figure indicative of the allowed consumption for the remainder of the window. The allowed consumption is the maximum consumption which will not cause the predetermined demand threshold to be exceeded. Function 210 is enabled by this result to compute the difference between allowed consumption and the present consumption rate for the active energy consuming loads during the remainder of the window. This difference represents the amount of consumption which must be avoided via load shedding by the end of the window if the predetermined demand threshold is not to be exceeded. System consumption monitor 101 then activates function 214 which computes the load to be shed based upon the above-determined difference value. The load to be shed is a function of the total excess consumption divided by the number of monitoring intervals remaining in the window. Thus, function 214 outputs a number which indicates the load per monitoring interval that must be shed to avoid exceeding the predetermined demand threshold. This number which is outputted by function 214 activates function 215 which compares this output with an indication of the loads presently shed and determines whether function 216 or 217 should be activated to respectively shed additional loads or restore already shed loads to the active state. Thus, system consumption monitor 101 performs an analysis of the demand based not only on past consumption but also on predicted future load activity, taking into account the loads presently disabled. 
     Floating Window 
     The same basic system structure is used for the floating window case as can be seen by the system structure illustrated in FIG. 2. The approach for the floating window is a conceptual extension of the fixed window case. If there are n monitoring intervals in the demand interval, then the present monitoring interval can be thought of as being contained in n different possible fixed windows. Each window results in a demand calculation which is considered by the device control system in determining the peak demand. This approach is illustrated in FIG. 4 wherein the horizontal axis across the figure indicates time (divided into monitoring intervals) with both the present monitoring interval and the present time indicated. Above this axis, the time span of window 1 is indicated, which includes the present monitoring interval plus the past n-1 monitoring intervals. Window 2, as shown on FIG. 4, is time-shifted one monitoring interval from window 1 so that the demand calculation includes the past n-2 monitoring intervals, the present monitoring interval and the next future monitoring interval. It is obvious from FIG. 4 that all subsequent windows are similarly time-shifted so that all possible window configurations which include the present monitoring interval are considered. Thus, in this situation, i (in states 204 through 208, and 211 through 213 in FIG. 2) would be a variable and an iterative analysis, of the type described above, would be activated n times or once for every possible demand interval configuration that would include the present monitoring interval. 
     Thus, system consumption monitor 101 enables function 204 which sets the window width to n monitoring intervals and sets the variable i=1 so that the analysis (states 205-213) is performed n times. The purpose of this iterative analysis is to develop a profile of every possible demand interval that includes the present monitoring interval. In this fashion, the system operation can be controlled so that the peak demand does not exceed the demand threshold for any and every possible demand interval. The combined prediction and recording activity in this analysis is what renders the resultant load shed determination so accurate. 
     Thus, the first possible demand interval that includes the present monitoring interval is the one wherein i=1. In this case, the next to the last monitoring interval in the demand interval has just ended and there are 14 past monitoring intervals in the window. System consumption monitor 101 branches at state 205 to a computation function 206 which reads the value of variable i and then computes the present and past consumption for window i. The first time through the loop, i=1 and the relevant data includes a listing of the activity for the present and past 14 monitoring intervals as listed in the history file of system consumption monitor 101. These past consumption entries are combined by function 207 with the predicted future load in this window, where the future load is the total of the predicted loads for the next monitoring interval, as estimated during the prediction step of function 203. These entries are all summed by system consumption monitor 101 enabling function 208 to obtain a number indicative of consumption for all n monitoring intervals of the demand interval which comprises the first window. 
     System consumption monitor 101 then advances to state 209 where it computes the permitted consumption based on the predetermined demand threshold which applies to this device control system. A comparator function is performed at step 210 to compare the total demand for this first window as computed by system consumption monitor during step 208 with the allowed demand as determined by system consumption monitor 101 during step 209. The difference between these two factors is calculated and the resultant figure is an indication of the excess consumption for the first window. This excess consumption figure is divided in step 211 by the number of monitoring intervals remaining in this window to come up with a figure indicative of the load to be shed for each monitoring interval remaining in this window in order that the demand threshold is not exceeded. In this case, since this is the first window, there remain one monitoring interval during which a correction can be effected in order not to exceed the demand threshold. Thus, any excess demand computed during step 210 must be compensated for within the remaining monitoring interval, and so step 211 divides the result of step 210 by one. 
     Since there is an indeterminate starting time for the window monitored by the utility company, the set of computations in steps 205-212 must be reiterated n times so that the worse case condition can be identified and then appropriate corrections made. A comparison is made in step 212 wherein the variable i is compared with the variable m to determine whether all possible window configurations have been realized. In this example, n window configurations are studied so m=n. In the case just described, only the first window has been studied and i=1. So system consumption monitor 101 branches to state 213 where i is incremented by 1. System consumption monitor 101 again branches at state 205 to step 206 which reflects the process wherein the computation of past, present and future activities in this new window is determined. The case where i=2 considers actual consumption figures for the last past n-2 monitoring intervals, and predicted load values for two monitoring intervals. Any excess consumption computed in state 210 is divided by two in state 211. The same logic applies for i=,4, . . . n. The program which runs on the processor in system consumption monitor 101 repeats steps 206-213 n times so that each possible window configuration is analyzed and the shed values for each window are stored in a shed table (not shown) of system consumption monitor 101. 
     When the table entries have all been generated, system consumption monitor 101 branches to state 214 where these table entries are analyzed to determine the total desired load to be shed in the system. This analysis typically would be a simple determination of the maximum shed value listed in the table to guarantee that the predetermined threshold is not exceeded. This maximum shed value is then passed to a comparator operation in step 215 where it is compared with the actual load presently shed by the system to determine whether more loads need to be shed or whether too many loads have been shed and some can be switched back on line. 
     If too many loads have been shed, the system consumption monitor 101 would branch to state 217 wherein loads would be switched back to the active state. This function is performed in well-known fashion to enable the selected loads to resume normal operation. If insufficient loads have presently been shed, system consumption monitor 101 would branch to state 216 wherein additional loads would be shed by system consumption monitor 101 placing the appropriate control signals on bus LB. There control signals will be translated by load interface 102 to an activation signal or signals which are transmitted to the designated ones of load control EC1 to ECk thereby disabling the associated loads to reduce system consumption. 
     Controllable Risk Parameter 
     The shed value determination is made in the floating window case just described based upon a worstcase analysis of the n calculated window configurations. It is apparent that this is a conservative approach to load control wherein the customer receives a high probability of not exceeding the predetermined demand threshold. However, the load control system in doing so may reduce the operating efficiency of the customer&#39;s controlled loads by shedding more loads than necessary in many situations. This conservative load shedding approach is based on the assumption that the economic cost of exceeding the predetermined demand threshold is far greater than the economic cost of unnecessary load shedding. However, the relative costs of these two situations vary with different customer applications. Since each customer application is different, it is desirable for the customer to have the capability of customizing the operation of the load control system. Therefore, the subject device control system includes a controllable risk parameter which enables the customer to establish the level of risk taken by the device control system in calculating the loads to be shed. 
     There are numerous ways of providing a controllable risk parameter. FIG. 1 illustrates a CRT display device (104) which is used by the customer to input data into the subject device control system. This CRT display device (104) can be directly wired to the subject device control system (100) or connectable via a dial-up port. In either case, the CRT display device (104) provides a customer (in well-known fashion) with direct access to the risk parameter register (103) which stores the controllable risk parameter. FIG. 5 illustrates a typical screen display on CRT 104. In addition to the standard parameters illustrated on CRT 104, the controllable risk parameter is provided in the form of a variable shown as the &#34;reaction minute&#34;. The cursor (502) on FIG. 5 is shown placed next to the data entry line wherein the customer inputs the reaction minute controllable risk parameter. 
     The controllable risk parameter is an indication to the subject device control system of how conservatively the customer wants the load shedding operation to be. To implement this feature requires some data input from the customer to the device control system. The subject arrangement provides for data to be input to steps 208 or 212. These steps are where the actual consumption for past intervals is combined with predicted consumption for future intervals for each of the n window configuration and where the number of window configurations analyzed (m) is determined, respectively. The customer can input prediction weighting data into a table in risk parameter register 103 in step 208 (or step 211) to weight the calculated sums computed for each of the n window configurations. These weight factors are then used to reduce the value of the calculated sum for the corresponding window configuration and the new value indicates the exact sum to be used for the load control calculation. 
     However, it is difficult to ascribe a particular weight value to each of the n window configurations and an alternate possibility is the use of a binary weighting system wherein each of the n window configurations is multiplied by a weighting factor of either 0 or 1. The reaction minute risk parameter illustrated in line 502 of FIG. 5 is exactly this embodiment. The reaction minute value input by the customer indicates where the iterative calculation of the new sums is truncated after a certain fixed number of window calculations. The reaction minute provides a value for the variable m in step 212 of FIG. 2. The system consumption monitor 101 reads the value of the reaction minute (m) out of the risk parameter register 103 at step 212. The reaction minute (m) indicates the number of window configurations out of the n possible window configurations that are used by the device control system in computing the load to be shed. This truncation eliminates the window configurations which are more heavily populated with predicted values of consumption as opposed to past measured actual consumption. Thus, the customer can determine, by inputting a value for the reaction minute variable (m) on line 502 of FIG. 5, the amount of weight to be given by the device control system to predicted values of consumption as opposed to past history, measured values of consumption. In this fashion, the customer can determine the level of risk taken by the device control system in regulating the operation of the control device. 
     By eliminating the more predictive window configurations, the customer is assuming that future activity will not significantly vary from past actual performance. Thus, in the case of a sudden flurry of load activity, the more predictive window configurations (which look only at the most recent past) predict continued heavy consumption while the less predictive window configurations average this sudden activity over a number of intervals of past actual consumption to deemphasize the effect of the sudden activity. The customer can therefore tailor the response of the device control system by eliminating some number of the more predictive window configurations and taking the risk that the sudden load activity will continue and the demand threshold will be exceeded. 
     While a specific embodiment of the invention has been disclosed, variations in structural detail, within the scope of the appended claims, are possible and are contemplated. There is no intention of limitation to what is contained in the abstract or the exact disclosure as herein presented. The above-described arrangements are only illustrative of the application of the principles of the invention. Normally, other arrangements may be devised by those skilled in the art without departing from the spirit and the scope of the invention.