Abstract:
A power limiting control system includes at least one power generator configured to provide power to a plurality of tools on a drilling rig; and a power limiting controller configured to control the provision of power from the power generator to the plurality of tools. The power limiting controller is adapted to perform a method including determining an individual power consumption for each of the plurality of tools; calculating a total power consumption from each respective individual power consumption of the plurality of tools; comparing the total power consumption of the plurality of tools to a total available power; ranking each respective individual power consumption by load size; and reducing power consumption of at least one of the plurality of tools based on rank when the total power consumption exceeds the total available power.

Description:
BACKGROUND 
       [0001]    1. Field of the Disclosure 
         [0002]    Embodiments disclosed herein relate generally to drilling rigs. More particularly, embodiments disclosed herein relate to power limiting control systems on a drilling rig. 
         [0003]    2. Background Art 
         [0004]    A drilling rig is used to drill a wellbore in a formation. Drilling rigs may be large structures that house equipment used to drill water wells, oil wells, or natural gas extraction wells. Drilling rigs sample sub-surface mineral deposits, test rock, soil and groundwater physical properties, and may also be used to install sub-surface fabrications, such as underground utilities, instrumentation, tunnels or wells. Drilling rigs may be mobile equipment mounted on trucks, tracks, or trailers, or more permanent land or marine-based structures (such as oil platforms). The term “rig,” therefore, generally refers to a complex of equipment that is used to penetrate the surface of the earth&#39;s crust. 
         [0005]    Referring to  FIG. 1 , a conventional drilling rig  30  is shown. Drilling rig  30  includes a derrick  14 , which provides a support structure for a majority of the equipment used to raise and lower a drillstring  25  into and out of a wellbore. The drillstring  25  may be an assembled collection of drillpipe, drill collars, or any other assortment of tools, connected together and run into the wellbore to facilitate the drilling of a well (drillpipe  16  is shown in joints prior to being connected together). 
         [0006]    The drillstring  25  may be raised and lowered into and out of the wellbore by the draw-works  7 , which includes a spool powered by a motor or other power source  5 . A drill line  12 , which may be a thick, stranded metal cable, is run from the draw-works  7  over a crown block  13  and down through a travelling block  11 . Typically, the crown block  13  remains stationary while the travelling block  11  moves vertically with the drillstring  25 . The combination of the crown block  13  and the travelling block  11  provides a significant mechanical advantage for lifting the drillstring  25 . Further, a swivel  18  may be attached to the travelling block  11  to allow rotation of the drillstring  25  without twisting the travelling block  11 . 
         [0007]    The drilling rig  30  further includes a rotary table  20  mounted in a rig floor  21 , which is used to rotate the drillstring  25  along with a kelly drive  19 . Kelly drive  19 , attached at an upper end to the swivel  18  and at a lower end to the drillstring  25 , is inserted through the rotary table  20  to rotate the drillstring  25  (drillstring rotation shown by arrow “R”). Kelly drive  19  may be square, hexagonal, or any other polygonal-shaped tubing and is able to move freely vertically while the rotary table  20  rotates it. Alternatively, drilling rig  30  may include a top drive (not shown) in place of kelly drive  19  and rotary table  20 . Additionally, blowout preventers (“BOPs”) may be located below the rig floor  21  and installed atop a wellhead  27  to prevent fluids and gases from escaping from the wellbore. An annular BOP  23  and one or more ram BOPs  24  are shown and are commonly understood in the art. 
         [0008]    During drilling operations, drilling fluid may be circulated through the system to carry cuttings away from the bottom of the wellbore as drilling progresses. Drilling fluid may be stored in mud tanks  1  before being drawn through suction line  3  by mud pumps  4 . Drilling fluid (drilling fluid route is indicated by arrows “F”) is then pumped from mud pumps  4  through a hose  6 , up a stand pipe  8 , through a flexible hose  9 , and down into the wellbore. Drilling fluid returning from the wellbore is routed through a flow line  28  to shakers  2 , which are used to separate drill cuttings from the drilling fluid before it is pumped back down the wellbore. 
         [0009]    A powering system, which in most modern rigs includes diesel generators (not shown), provides power for all of the machinery on the drilling rig. The powering system may typically include from one to six (or more) diesel generator units depending on the power requirements of the machinery on the drilling rig. The hoisting system (draw works  7 ), the circulating system (mud pumps  4 ), and the rotating system (top-drive or rotary table  20 ) are the major power consumers on the drilling rig, and these systems may subsequently be collectively referred to as the “tools.” Those skilled in the art will understand additional power consuming machinery may be on the drilling rig as well. 
         [0010]    During operation of the drilling rig, there may be situations when the power requirement of the tools exceeds the power generation capacity of the generators (also referred to as an “overload condition”), which may lead to power shutdowns or blackouts on the drilling rig. Alternatively, power generation capacity of the generators may also suddenly decrease if a generator shuts down (or goes offline), which also may lead to an overload condition. 
       SUMMARY OF THE DISCLOSURE 
       [0011]    In general, in one aspect, embodiments disclosed herein relate to a control system and methods of regulating and/or limiting the power available to multiple tools on the drilling rig. 
         [0012]    In general, in one aspect, embodiments disclosed herein relate to a power consumption limiting method for a plurality of tools on a drilling rig, the method comprising: determining an individual power consumption for each of the plurality of tools; calculating a total power consumption from each respective individual power consumption of the plurality of tools; comparing the total power consumption of the plurality of tools to a total available power; ranking each respective individual power consumption by load size; and reducing power available to at least one of the plurality of tools based on rank when the total power consumption exceeds the total available power. 
         [0013]    In general, in one aspect, embodiments disclosed herein relate to a power limiting control system comprising: at least one power generator configured to provide power to a plurality of tools on a drilling rig; a power limiting controller configured to control the provision of power from the power generator to the plurality of tools; wherein the power limiting controller is adapted to perform a method comprising: determining an individual power consumption for each of the plurality of tools; calculating a total power consumption from each respective individual power consumption of the plurality of tools; comparing the total power consumption of the plurality of tools to a total available power; ranking each respective individual power consumption by load size; and reducing power consumption of at least one of the plurality of tools based on rank when the total power consumption exceeds the total available power. 
         [0014]    Other aspects and advantages of the invention will be apparent from the following description and the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0015]      FIG. 1  shows a conventional drilling rig. 
           [0016]      FIG. 2  shows a schematic diagram illustrating a power limiting control system in accordance with one or more embodiments. 
           [0017]      FIG. 3  shows a flow chart diagram illustrating power limiting methods in accordance with one or more embodiments. 
           [0018]      FIG. 4  shows a bar graph illustrating the power limiting controller in State 0 in accordance with one or more embodiments. 
           [0019]      FIG. 5  shows a bar graph illustrating the power limiting controller in State 1 in accordance with one or more embodiments. 
           [0020]      FIG. 6  shows a bar graph illustrating the power limiting controller in State 2 in accordance with one or more embodiments. 
           [0021]      FIG. 7  shows a bar graph illustrating the power limiting controller in State 3 in accordance with one or more embodiments. 
           [0022]      FIG. 8  shows a bar graph illustrating the power limiting controller in State 4 in accordance with one or more embodiments. 
           [0023]      FIG. 9  shows a bar graph illustrating the power limiting controller in State 5 in accordance with one or more embodiments. 
           [0024]      FIG. 10  shows an example schematic diagram illustrating a power limiting control system in accordance with one or more embodiments. 
           [0025]      FIG. 11  shows a block diagram for calculating a torque limit in accordance with one or more embodiments. 
           [0026]      FIG. 12  shows a line graph illustrating showing the allowable rate of change of generator power and the normalized generator power in accordance with one or more embodiments. 
           [0027]      FIG. 13  shows a block diagram for calculating the torque limit and acceleration limit for the drawworks in accordance with one or more embodiments. 
       
    
    
     DETAILED DESCRIPTION 
       [0028]    Embodiments of the present invention will be described below with reference to the figures. In one aspect, embodiments disclosed herein relate to power consumption limiting methods and apparatuses for regulating and/or limiting the power available to multiple tools on a drilling rig. It may be necessary to regulate and/or limit the power consumed by the tools on a drilling rig based on the amount of available power in order to avoid power shutdowns or blackouts due to overload conditions. 
         [0029]    The power limiting methods of embodiments disclosed herein may be capable of managing power provided from multiple generator units, each of which may have different power ratings. While exemplary methods of power management for up to five tools are discussed below, those skilled in the art in possession of the present disclosure will appreciate that embodiments may be capable of handling an unlimited number of tools using the methods of power management described below. 
         [0030]    Referring to  FIG. 2 , a simplified schematic diagram illustrating a power limiting control system  100  for a multiple generator and multiple tool system in accordance with embodiments of the present disclosure is shown. The power limiting control system includes multiple generators  102 , multiple power consuming tools  104 , and a power limiting controller  106 . As shown, the multiple tools  104  controlled by the power limiting controller  106  may be, for example, the draw works, three mud pumps (mud pumps one, two, and three), and the rotary table or top drive. 
         [0031]    In one or more embodiments, the power provided to the multiple tools is controlled by the power limiting controller in accordance with the method shown in  FIG. 3 . As shown, an individual load on each of the power generators is calculated  152  and compared  153  so that the loads from each of the multiple tools can be ranked by a load size (e.g., the tools may be ranked from highest power consumer to lowest power consumer). Based on the respective loads of the multiple tools, a net power available in the system is calculated  154 . Next, the state of the net power is checked  155 . If the net power available in the system is positive  156 , the system may be characterized as in an “under load” condition, and no power limiting is required. However, if the net power available in the system is negative  157 , the system may be characterized as in an “overload” condition, and a reduction of power to the multiple tools is commenced  159  in an order based on load size (e.g., highest to lowest). 
         [0032]    A specific example of the manner in which the power to the multiple tools can be reduced in one or more embodiments is set forth below. Referring to  FIG. 4 , a bar graph illustrating the power limiting controller in State 0, or when the power limiting controller is inactive, in accordance with one or more embodiments is shown. Initially, a normalized individual load on each generator may be calculated by taking a ratio of the generator power and a corresponding rated generator power. These individual loads are then compared and the largest load is selected as a system load. 
         [0033]    Next, a net power available  310  in the system is calculated by subtracting the system load from a threshold value (set at unity) and multiplying this value with the maximum available generator power. The maximum available generator power is the sum of all the individual rated powers of the generators. 
         [0034]    If the net available power  310  is positive, then the system is in an “underload” condition with additional power available for the tools. The total power available to each tool is calculated by adding a percentage of the net available power to their respective tool power consumption values given as feedback. For example, for five tools T 1 , T 2 , T 3 , T 4 , and T 5  with present power consumption values of P(T 1 ), P(T 2 ), P(T 3 ), P(T 4 ), and P(T 5 ), respectively, if the net available power P avl  is positive, then, the total power available (P A ) for each tool is given by the following expressions. 
         [0000]        P   A ( T   1 )= P ( T   1 )+ kP   avl    (1)
 
         [0000]        P   A ( T   2 )= P ( T   2 )+ kP   avl    (2)
 
         [0000]        P   A ( T   3 )= P ( T   3 )+ kP   avl    (3)
 
         [0000]        P   A ( T   4 )= P ( T   4 )+ kP   avl    (4)
 
         [0000]        P   A ( T   5 )= P ( T   5 )+ kP   avl    (5)
 
         [0035]    The constant k is a percentage (range=0 to 1). 
         [0036]    On the contrary, if the net available power is negative, then the system is in an “overload” condition and the power limiting controller is activated. The negative net available power is the amount by which the total tool power consumption must be reduced to bring the system out of the overload condition. 
         [0037]    Initially, the total power available to the top consumer may be reduced until reaching the level of the second highest consumer. Then, both the top consumer and the second highest consumer powers are brought down until reaching the level of the third highest consumer. Once that level is reached for the top two consumers, the available power to the top three consumers is reduced to a level of the fourth highest consumer, and so on. Thus, there are five manners in which the total available power is brought down based on the amount of power reduction required and the individual power consumption of the tools. In one or more embodiments, these five different manners are referred to as machine states and each state is discussed in detail below with respect to  FIGS. 5-9 . 
         [0038]      FIG. 5  is a bar graph that illustrates the power limiting controller in State 1 in accordance with one or more embodiments. In certain embodiments, T 1  to T 5  have a descending order of power consumption with tool T 1  being the highest consumer and T 5  being the lowest. Differences in power consumption between the top consumer and the remaining tools to be δ 1 , δ 2 , δ 3 , and δ 4 . Note, δ 1  is the difference in power between the top consumer and the second highest consumer, δ 2  is the difference between the top consumer and third highest consumer, and so on. The power reduction required is the absolute vale of the negative net available power and is given by P rdn . 
         [0039]    If the power reduction required (P rdn ) is less than the difference in power consumption between top consumer and the second highest consumer (δ 1 ), then the system is said to be in State 1 and the total available power to the highest consumer is reduced. In other words, the highest consumer must retain its status as the top consumer even after the power reduction. The condition for State 1 may be mathematically written as: 
         [0000]      P rdn &lt;δ 1 →State 1
 
         [0040]    The expression for the total available power for the top consumer may be written as: 
         [0000]        P   A ( T   1 )= P ( T   1 )− P   rdn    (6)
 
         [0041]    The power available to the rest of the tools are frozen, that is: 
         [0000]        P   A ( T   2 )= P ( T   2 )   (7)
 
         [0000]        P   A ( T   3 )= P ( T   3 )   (8)
 
         [0000]        P   A ( T   4 )= P ( T   4 )   (9)
 
         [0000]        P   A ( T   5 )= P ( T   5 )   (10)
 
         [0042]    Referring now to  FIG. 6 , a bar graph illustrating the power limiting controller in State 2 in accordance with one or more embodiments is shown. The power limiting control is said to be in the State 2, if the power reduction require (P rdn ) is greater than δ 1  and the total power available to the top two consumers are reduced. This state is illustrated in  FIG. 5 . After the power reduction, the available powers to the top two consumers are the same as shown in  FIG. 5 . If x and (x−δ 1 ) are set as the amount by which the top two consumers are reduced, then, the power reduction required (P rdn ) may be written as: 
         [0000]        P   rdn   =x+ ( x−δ   1 )   (11)
 
         [0043]    Solving the above equation for x gives: 
         [0000]    
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       ( 
                       
                         
                           P 
                           rdn 
                         
                         + 
                         
                           δ 
                           1 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0044]    Using the x value given in Eq. (12), the total available power to the top two consumers may be written as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       A 
                     
                      
                     
                       ( 
                       
                         T 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       P 
                        
                       
                         ( 
                         
                           T 
                           1 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         ( 
                         
                           
                             P 
                             rdn 
                           
                           + 
                           
                             δ 
                             1 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               2 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 2 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               ( 
                               
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                 
                                 
                                   2 
                                   - 
                                   
                                     δ 
                                     1 
                                   
                                 
                               
                               ) 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 2 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   P 
                                   rdn 
                                 
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0045]    The total powers available to the rest of the tools are kept frozen at their current power consumption values. 
         [0046]    Referring now to  FIG. 7 , a bar graph illustrating the power limiting controller in State 3 in accordance with one or more embodiments is shown. The power limiting controller is said to be in State 3, if the following condition is true: 
         [0000]    
       
         
           
             
               
                 
                   ( 
                   
                     
                       P 
                       rdn 
                     
                     + 
                     
                       δ 
                       1 
                     
                   
                   ) 
                 
                 2 
               
               &gt; 
               
                 δ 
                 2 
               
             
             -&gt; 
             
               State 
                
               
                   
               
                
               3 
             
           
         
       
     
         [0047]    In State 3, the available powers to the top three consumers may be reduced and brought to the same level as shown in  FIG. 6 . If x, (x−δ 1 ) and (x−δ 2 ) are set as the amount by which the top three consumers are reduced, then, the power reduction required (P rdn ) may be written as: 
         [0000]        P   rdn   =x +( x−δ   1 )+( x−δ   2 )   (15)
 
         [0048]    Solving the above equation for x gives: 
         [0000]    
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       ( 
                       
                         
                           P 
                           rdn 
                         
                         + 
                         
                           δ 
                           1 
                         
                         + 
                         
                           δ 
                           2 
                         
                       
                       ) 
                     
                     3 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0049]    Using the x value given in Eq. (16), the total available power to the top three consumers may be written as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       A 
                     
                      
                     
                       ( 
                       
                         T 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       P 
                        
                       
                         ( 
                         
                           T 
                           1 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         ( 
                         
                           
                             P 
                             rdn 
                           
                           + 
                           
                             δ 
                             1 
                           
                           + 
                           
                             δ 
                             2 
                           
                         
                         ) 
                       
                       3 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               2 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 2 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 
                                   P 
                                   rdn 
                                 
                                 + 
                                 
                                   δ 
                                   1 
                                 
                                 + 
                                 
                                   δ 
                                   2 
                                 
                               
                               
                                 3 
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 2 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 
                                   P 
                                   rdn 
                                 
                                 - 
                                 
                                   2 
                                    
                                   
                                     δ 
                                     1 
                                   
                                 
                                 + 
                                 
                                   δ 
                                   2 
                                 
                               
                               3 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               3 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 3 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 
                                   P 
                                   rdn 
                                 
                                 + 
                                 
                                   δ 
                                   1 
                                 
                                 + 
                                 
                                   δ 
                                   2 
                                 
                               
                               
                                 3 
                                 - 
                                 
                                   δ 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 3 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 
                                   P 
                                   rdn 
                                 
                                 + 
                                 
                                   δ 
                                   1 
                                 
                                 - 
                                 
                                   2 
                                    
                                   
                                     δ 
                                     2 
                                   
                                 
                               
                               3 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
         [0050]    The total power available to the rest of the tools is kept frozen at their current power consumption values. 
         [0051]    Now referring to  FIG. 8 , a bar graph illustrating the power limiting controller in State 4 in accordance with one or more embodiments is shown. The power limiting controller is said to be in State 4, if: 
         [0000]    
       
         
           
             
               
                 ( 
                 
                   
                     
                       P 
                       rdn 
                     
                     + 
                     
                       δ 
                       1 
                     
                     + 
                     
                       δ 
                       2 
                     
                   
                   3 
                 
                 ) 
               
               &gt; 
               
                 δ 
                 3 
               
             
             -&gt; 
             
               State 
                
               
                   
               
                
               4 
             
           
         
       
     
         [0052]    In State 4, the available power to the top four consumers is reduced and brought to the same level as shown in  FIG. 7 . If x, (x−δ 1 ), (x−δ 2 ), and (x−δ 3 ) are set as the amount by which the top four consumers are reduced, then, the power reduction required (P rdn ) may be written as: 
         [0000]        P   rdn   =x+ ( x−δ   1 )+( x−δ   2 )+( x−δ   3 )   (20)
 
         [0053]    Solving the above equation for x gives: 
         [0000]    
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       ( 
                       
                         
                           P 
                           rdn 
                         
                         + 
                         
                           δ 
                           1 
                         
                         + 
                         
                           δ 
                           2 
                         
                         + 
                         
                           δ 
                           3 
                         
                       
                       ) 
                     
                     4 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
         [0054]    Using the x value given in Eq. (21), the total available power to the top four consumers may be written as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       A 
                     
                      
                     
                       ( 
                       
                         T 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       P 
                        
                       
                         ( 
                         
                           T 
                           1 
                         
                         ) 
                       
                     
                     - 
                     
                       ( 
                       
                         
                           ( 
                           
                             
                               P 
                               rdn 
                             
                             + 
                             
                               δ 
                               1 
                             
                             + 
                             
                               δ 
                               2 
                             
                             + 
                             
                               δ 
                               3 
                             
                           
                           ) 
                         
                         4 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               2 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 2 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                 
                                 ) 
                               
                               
                                 4 
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 2 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   - 
                                   
                                     3 
                                      
                                     
                                       δ 
                                       1 
                                     
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                 
                                 ) 
                               
                               4 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               3 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 3 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                 
                                 ) 
                               
                               
                                 4 
                                 - 
                                 
                                   δ 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 3 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   - 
                                   
                                     3 
                                      
                                     
                                       δ 
                                       2 
                                     
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                 
                                 ) 
                               
                               4 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               4 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 4 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                 
                                 ) 
                               
                               
                                 4 
                                 - 
                                 
                                   δ 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 4 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   - 
                                   
                                     3 
                                      
                                     
                                       δ 
                                       3 
                                     
                                   
                                 
                                 ) 
                               
                               4 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
         [0055]    The total power available to the fifth tool is kept frozen at its current power consumption value. 
         [0056]    Referring now to  FIG. 9 , a bar graph illustrating the power limiting controller in State 5 in accordance with one or more embodiments is shown. In State 5 of the power limiting controller, the available powers to all the tools are reduced and brought to the same level. The condition for entering State 5 is given below: 
         [0000]    
       
         
           
             
               
                 
                   ( 
                   
                     
                       P 
                       rdn 
                     
                     + 
                     
                       δ 
                       1 
                     
                     + 
                     
                       δ 
                       2 
                     
                     + 
                     
                       δ 
                       3 
                     
                   
                   ) 
                 
                 3 
               
               &gt; 
               
                 δ 
                 4 
               
             
             -&gt; 
             
               State 
                
               
                   
               
                
               5 
             
           
         
       
     
         [0057]    If x, (x−δ 1 ), (x−δ 2 ), (x−δ 3 ), and (x−δ 4 ) are set as the amount by which the top five consumers are reduced, then, the power reduction required (P rdn ) may be written as: 
         [0000]        P   rdn   =x+ ( x−δ   1 )+( x−δ   2 )+( x−δ   3 )+( x−δ   4 )   (26)
 
         [0058]    Solving the above equation for x gives: 
         [0000]    
       
         
           
             
               
                 
                   x 
                   = 
                   
                     
                       ( 
                       
                         
                           P 
                           rdn 
                         
                         + 
                         
                           δ 
                           1 
                         
                         + 
                         
                           δ 
                           2 
                         
                         + 
                         
                           δ 
                           3 
                         
                         + 
                         
                           δ 
                           4 
                         
                       
                       ) 
                     
                     5 
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
         [0059]    Using the x value given in Eq. (27), the total available power to the top five consumers may be written as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       A 
                     
                      
                     
                       ( 
                       
                         T 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       P 
                        
                       
                         ( 
                         
                           T 
                           1 
                         
                         ) 
                       
                     
                     - 
                     
                       ( 
                       
                         
                           ( 
                           
                             
                               P 
                               rdn 
                             
                             + 
                             
                               δ 
                               1 
                             
                             + 
                             
                               δ 
                               2 
                             
                             + 
                             
                               δ 
                               3 
                             
                             + 
                             
                               δ 
                               4 
                             
                           
                           ) 
                         
                         5 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               2 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 2 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                   + 
                                   
                                     δ 
                                     4 
                                   
                                 
                                 ) 
                               
                               
                                 5 
                                 - 
                                 
                                   δ 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 2 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   - 
                                   
                                     4 
                                      
                                     
                                       δ 
                                       1 
                                     
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                   + 
                                   
                                     δ 
                                     4 
                                   
                                 
                                 ) 
                               
                               5 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               3 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 3 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                   + 
                                   
                                     δ 
                                     4 
                                   
                                 
                                 ) 
                               
                               
                                 5 
                                 - 
                                 
                                   δ 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 3 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   - 
                                   
                                     4 
                                      
                                     
                                       δ 
                                       2 
                                     
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                   + 
                                   
                                     δ 
                                     4 
                                   
                                 
                                 ) 
                               
                               5 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               4 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 4 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                   + 
                                   
                                     δ 
                                     4 
                                   
                                 
                                 ) 
                               
                               
                                 5 
                                 - 
                                 
                                   δ 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 4 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   - 
                                   
                                     4 
                                      
                                     
                                       δ 
                                       3 
                                     
                                   
                                   + 
                                   
                                     δ 
                                     4 
                                   
                                 
                                 ) 
                               
                               5 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             A 
                           
                            
                           
                             ( 
                             
                               T 
                               5 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 5 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                   + 
                                   
                                     δ 
                                     4 
                                   
                                 
                                 ) 
                               
                               
                                 5 
                                 - 
                                 
                                   δ 
                                   4 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             P 
                              
                             
                               ( 
                               
                                 T 
                                 5 
                               
                               ) 
                             
                           
                           - 
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     P 
                                     rdn 
                                   
                                   + 
                                   
                                     δ 
                                     1 
                                   
                                   + 
                                   
                                     δ 
                                     2 
                                   
                                   + 
                                   
                                     δ 
                                     3 
                                   
                                   - 
                                   
                                     4 
                                      
                                     
                                       δ 
                                       4 
                                     
                                   
                                 
                                 ) 
                               
                               5 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
         [0060]    As an illustrative example of a power limiting control system,  FIG. 10  shows a detailed schematic diagram of a power limiting control system  100  for a multiple generator and multiple tool system in accordance with one or more embodiments. As previously described, the power limiting control system  100  includes multiple generators  102 , multiple tools  104 , and a power limiting controller  106 . In addition, the power limiting control system may further include a torque limiter  108  and multiple tool variable frequency drives (“VFD”)  110 . As shown, in this example, the multiple tools  104  controlled by the power limiting controller  106  are, for example, the draw works, three mud-pumps (mud pumps one, two, and three), and the rotary table or top-drive. As shown, additional power consuming equipment on the drilling rig may include lighting and other accessories as understood by those skilled in the art. 
         [0061]    Individualized loads on each generator may be determined  150  and a resulting system load  152  is determined by taking a ratio of the tool power consumption (power provided to the multiple tools  151  is known) and a rated generator power. Based on the net power available  154 , a decision is made (decision block  108  of power limiting controller  106 ) on whether to activate the power limiting controller  106 . 
         [0062]    For a positive net power available  155  (i.e., net power available&gt;0), the power limiting controller  106  is bypassed and the power is supplied to the multiple tools as is. However, for a negative power available  157  (i.e., net power available&lt;0), the power limiting controller  106  is activated to implement a required power reduction  159 . The power limiting controller  106  reduces power using methods described above, namely reducing power to the multiple tools from a highest power consuming tool to a lowest. In particular, to implement the power reduction for each tool, the power limiting controller  106  sets the torque limit for the motors driving the tools through their respective VFD&#39;s  110 . The torque limit caps the amount of torque produced by the motors, and, thus, power consumed, which is directly proportional to the torque, is regulated. A torque limiting method is described in detail later in the application. Continuous feedback  156  on the power consumption of the tools provides real time feedback to the power limiting controller  106 , which allows for real time adjustments to the power consumption of multiple tools, as required. 
         [0063]    Next, an example of a specific drilling rig tool power consumption and power generation is provided to facilitate understanding of the power limiting controller concepts employed in one or more embodiments. 
         [0064]    In this example, the drilling rig includes three generator units online with a rated capacity of 1000 horsepower (“HP”) each. Thus, maximum available generator power: 1000+1000+1000=3000 HP. There are four tools with the following respective present power consumption: Mud pump one (MP 1 )=710 HP, Mud pump two (MP 2 )=695 HP, Mud pump three (MP 3 )=705 HP, and draw works (DW)=390 HP. Thus, total tool power consumption: 710+695+705+390=2500 HP. Assuming, for purposes of this example, that only these four tools are connected to the generators and there is not other loss, the system load is given by: Load=2500/3000=0.83. Next, the net available power is calculated as: 
         [0000]    
       
         
           
             
               
                 
                   
                     Net 
                     . 
                     available 
                     . 
                     power 
                   
                   = 
                     
                    
                   
                     
                       ( 
                       
                         Threshold 
                         - 
                         Load 
                       
                       ) 
                     
                     * 
                     
                       Max 
                       . 
                       available 
                       . 
                       gen 
                       . 
                       power 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           0.83 
                         
                         ) 
                       
                       * 
                       3000 
                     
                     = 
                     
                       500 
                        
                       
                           
                       
                        
                       HP 
                     
                   
                 
               
             
           
         
       
     
         [0065]    Thus, the net available power is positive and system is in State 0, i.e., power limiting control is not active. The system is in normal operating condition with 83.33% generator load. 
         [0066]    If one of the generator units fails, then, the maximum available generator power will drop, i.e., maximum available generator power=1000+1000=2000 HP. However, the total tool power consumption remains the same, i.e., total tool power consumption=710+695+705+390=2500 HP. Thus, the system load is given by: Load=2500/2000=1.25. Accordingly, the system is in overload condition and the net available power is calculated to be: 
         [0000]    
       
         
           
             
               
                 
                   
                     Net 
                     . 
                     available 
                     . 
                     power 
                   
                   = 
                     
                    
                   
                     
                       ( 
                       
                         Threshold 
                         - 
                         Load 
                       
                       ) 
                     
                     * 
                     
                       Max 
                       . 
                       available 
                       . 
                       gen 
                       . 
                       power 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           1 
                           - 
                           1.25 
                         
                         ) 
                       
                       * 
                       2000 
                     
                     = 
                     
                       
                         - 
                         500 
                       
                        
                       
                           
                       
                        
                       HP 
                     
                   
                 
               
             
           
         
       
     
         [0067]    The net available power is negative and the system enters the power limiting mode. In the power limiting mode, a reduced value of the threshold is used. So, the net available power is recalculated as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     Net 
                     . 
                     available 
                     . 
                     power 
                   
                   = 
                     
                    
                   
                     
                       ( 
                       
                         
                           reduced 
                           . 
                           threshold 
                         
                         - 
                         load 
                       
                       ) 
                     
                     * 
                     
                       Max 
                       . 
                       available 
                       . 
                       gen 
                       . 
                       power 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     
                       
                         ( 
                         
                           0.9 
                           - 
                           1.25 
                         
                         ) 
                       
                       * 
                       2000 
                     
                     = 
                     
                       
                         - 
                         700 
                       
                        
                       
                           
                       
                        
                       HP 
                     
                   
                 
               
             
           
         
       
     
         [0068]    Thus, the total power reduction required is: 
         [0000]      P rdn =700 HP 
         [0069]    Rearranging the tools in the descending order of power consumption results in: 
         [0000]        T   1 =MP1 →P ( T   1 )=710 HP 
         [0000]        T   2 =MP2 →P ( T   2 )=705 HP 
         [0000]        T   3 =MP3 →P ( T   3 )=695 HP 
         [0000]        T   4 =MP4 →P ( T   4 )=390 HP 
         [0070]    The difference in power consumption between the top consumer and the rest of the tools is given by: 
         [0000]      δ 1   =P ( T   1 )− P ( T   2 )=5
 
         [0000]      δ 2   =P ( T   1 )− P ( T   3 )=15
 
         [0000]      δ 3   =P ( T   1 )− P ( T   4 )=320
 
         [0071]    The system satisfies the following conditions: 
         [0000]    
       
         
           
             
               
                 
                   P 
                   rdn 
                 
                 + 
                 
                   δ 
                   1 
                 
               
               2 
             
             = 
             
               
                 352.5 
                 &gt; 
                 15 
               
               = 
               
                 δ 
                 2 
               
             
           
         
       
       
         
           
             
               
                 
                   P 
                   rdn 
                 
                 + 
                 
                   δ 
                   1 
                 
                 + 
                 
                   δ 
                   2 
                 
               
               3 
             
             = 
             
               
                 240 
                 &lt; 
                 320 
               
               = 
               
                 δ 
                 3 
               
             
           
         
       
     
         [0072]    Hence, the system is in State 3 and the available power to the top three consumers is reduced. The power to the top consumer is reduced by the value x, which is calculated to be: 
         [0000]    
       
         
           
             x 
             = 
             
               
                 
                   ( 
                   
                     
                       P 
                       rdn 
                     
                     + 
                     
                       δ 
                       1 
                     
                     + 
                     
                       δ 
                       2 
                     
                   
                   ) 
                 
                 3 
               
               = 
               240 
             
           
         
       
     
         [0073]    Therefore, the total available power to the top three consumers is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       A 
                     
                      
                     
                       ( 
                       
                         T 
                         1 
                       
                       ) 
                     
                   
                   = 
                     
                    
                   
                     
                       P 
                        
                       
                         ( 
                         
                           T 
                           1 
                         
                         ) 
                       
                     
                     - 
                     x 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     710 
                     - 
                     240 
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     470 
                      
                     
                         
                     
                      
                     HP 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     
                       P 
                       A 
                     
                      
                     
                       ( 
                       
                         T 
                         2 
                       
                       ) 
                     
                   
                   = 
                     
                    
                   
                     
                       P 
                        
                       
                         ( 
                         
                           T 
                           2 
                         
                         ) 
                       
                     
                     - 
                     
                       ( 
                       
                         x 
                         - 
                         
                           δ 
                           1 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     705 
                     - 
                     
                       ( 
                       
                         240 
                         - 
                         5 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     470 
                      
                     
                         
                     
                      
                     HP 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     
                       P 
                       A 
                     
                      
                     
                       ( 
                       
                         T 
                         3 
                       
                       ) 
                     
                   
                   = 
                     
                    
                   
                     
                       P 
                        
                       
                         ( 
                         
                           T 
                           3 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         ( 
                         
                           x 
                           - 
                           
                             δ 
                             2 
                           
                         
                         ) 
                       
                        
                       695 
                     
                     - 
                     
                       ( 
                       
                         240 
                         - 
                         15 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     470 
                      
                     
                         
                     
                      
                     HP 
                   
                 
               
             
           
         
       
     
         [0074]    The total available power to the fourth tool is kept frozen at is current power consumption value and is given by: 
         [0000]        P   A ( T   4 )= P ( T   4 )=390 HP 
         [0075]    Methods used to limit the amount of torque available to each of the power consumers are now described in more detail. Based on the available power to each tool (P A ) and the corresponding motor velocity (ω), a torque limit (τ lim ) for each tool may be calculated as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       τ 
                       lim 
                     
                      
                     
                       ( 
                       
                         T 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         P 
                         A 
                       
                        
                       
                         ( 
                         
                           T 
                           1 
                         
                         ) 
                       
                     
                     
                       ω 
                        
                       
                         ( 
                         
                           T 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
         [0076]    Where τ lim (T 1 ) is the torque limit, P A (T 1 ) is the available power, and ω(T 1 ) is the motor velocity for tool  1 . The torque limits for the other tools may be calculated in a similar manner.  FIG. 11  illustrates a representative block diagram for calculating the torque limit. For the drawworks, in addition to the torque limit, a limit is placed on the acceleration of the motor (α max ). The limit may be derived as follows. The mechanical power (P m ) produced by the draw works is given by: 
         [0000]        P   m =τω  (34)
 
         [0077]    Where, τ is the torque produced by the drawworks and ω is its angular velocity. The expression for torque τ is given by: 
         [0000]      τ=τ L   +J   D α  (35)
 
         [0078]    Where, τ L  is the constant load torque acting on the drawworks, J D  is the moment of inertia of the drawworks and α is the angular acceleration of the drawworks. The torque due to friction is assumed to be negligible compared to the load torque, and thus, is neglected. Substituting the torque given in Equation 35 into the mechanical power equation give in Equation 34 yields: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           P 
                           m 
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               
                                 τ 
                                 L 
                               
                               + 
                               
                                 
                                   J 
                                   D 
                                 
                                  
                                 α 
                               
                             
                             ) 
                           
                            
                           ω 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               τ 
                               L 
                             
                              
                             ω 
                           
                           + 
                           
                             
                               J 
                               D 
                             
                              
                             α 
                              
                             
                                 
                             
                              
                             ω 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
         [0079]    In Equation 36, the first term, τ L ω, represents the steady state power and the second term, J D αω, represents the additional power due to the rate of change in the internal kinetic energy of the system. Further, P represents the electrical power supplied by the generator to the drawworks. The relationship between electric power (P) and mechanical power (P m ) is shown as: 
         [0000]        P=P   m +conversion.losses   (37)
 
         [0080]    Conversion losses are assumed to be constant. Differentiating the equation given in Equation 37 with respect to time, t, gives: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                              
                             P 
                           
                           
                              
                             t 
                           
                         
                         = 
                           
                          
                         
                           
                              
                             
                               P 
                               m 
                             
                           
                           
                              
                             t 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             τ 
                              
                             
                                 
                             
                              
                             L 
                              
                             
                               
                                  
                                 ω 
                               
                               
                                  
                                 t 
                               
                             
                           
                           + 
                           
                             
                               J 
                               D 
                             
                              
                             α 
                              
                             
                               
                                  
                                 ω 
                               
                               
                                  
                                 t 
                               
                             
                           
                           + 
                           
                             
                               J 
                               D 
                             
                              
                             
                               
                                  
                                 α 
                               
                               
                                  
                                 t 
                               
                             
                              
                             ω 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               τ 
                               L 
                             
                              
                             α 
                           
                           + 
                           
                             
                               J 
                               D 
                             
                              
                             
                               α 
                               2 
                             
                           
                           + 
                           
                             
                               J 
                               D 
                             
                              
                             ω 
                              
                             
                               
                                  
                                 α 
                               
                               
                                  
                                 t 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
         [0081]    The allowable rate of change of the electric power (dP/dt) of the generator is determined by the power limit controller and is a constant at any given instant of time. In the power limit controller, the allowable rate of change of power (dP/dt) is set based on the normalized power or load. A typical graph between the allowable rate of change of generator power and the normalized generator power (or power normalized with respect to rated power of generator (P r ), i.e., load) is shown in  FIG. 12 . 
         [0082]    As shown in the figure, the allowable rate of change of generator power is reduced to zero beyond the rated power. That is, no additional power is available after the rated power of the generator has been reached. If the generator power is within the threshold value (0.8) then the allowable rate of change of power has a constant value. When the generator power is between the threshold value and the rated power, the allowable rate of change of power is reduced to zero. 
         [0083]    The goal is to find the maximum allowable angular acceleration (α max ) based on the current allowable rate of change of generator power determined by the power limit controller. The maximum allowable angular acceleration (α max ) is calculated at every time step. Considering the equation for rate of change in power given in Equation 38 and assuming the angular acceleration (α) is a constant, the term involving the jerk (dα/dt) will be there momentarily while the angular acceleration goes from zero to a constant value, and thereafter will be zero. Thus, this term (J D ω(dα/dt)) may be neglected and the rate of change in power equation given in Equation 38 can be rewritten as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                        
                       P 
                     
                     
                        
                       t 
                     
                   
                   = 
                   
                     
                       
                         τ 
                         L 
                       
                        
                       α 
                     
                     + 
                     
                       
                         J 
                         D 
                       
                        
                       
                         α 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
           
         
       
     
         [0084]    For a constant dP/dt, Equation 39 reduces to a quadratic equation in α. This equation can be solved to set the maximum allowable angular acceleration (α max ) as: 
         [0000]    
       
         
           
             
               
                 
                   
                     α 
                     max 
                   
                   = 
                   
                     
                       
                         - 
                         
                           τ 
                           L 
                         
                       
                       ± 
                       
                         
                           
                             τ 
                             L 
                             2 
                           
                           + 
                           
                             4 
                              
                             
                               J 
                               D 
                             
                              
                             
                               
                                  
                                 P 
                               
                               
                                  
                                 t 
                               
                             
                           
                         
                       
                     
                     
                       2 
                        
                       
                         J 
                         D 
                       
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
         [0085]      FIG. 13  illustrates a block diagram for calculating the torque limit and acceleration limit for the drawworks. As shown, a maximum allowable angular acceleration limit  202  may be set inputting a rate of change of generator power (dP/dt)  204 , drawworks moment of inertia (J D )  206 , and a load torque on the drawworks (τ L )  208 . 
         [0086]    One or more embodiments of the present invention may provide one or more of the following advantages. Power limiting controllers, in accordance with one or more embodiments, provide methods of avoiding overload conditions (blackouts) by managing power demands from major power consumers (tools) on the drilling rig. In particular, overload conditions may cause damage to the tools or generators causing costly rig downtime and maintenance or equipment replacement costs. In addition, rig downtime causes drilling operations to cease, which is costly. Thus, the power limiting methods disclosed herein may increase drilling efficiency and longevity by avoiding overload conditions. 
         [0087]    While the present disclosure has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments may be devised which do not depart from the scope of the disclosure as described herein. Accordingly, the scope of the disclosure should be limited only by the attached claims.