Patent Publication Number: US-9906033-B2

Title: Consensus-based power control apparatus

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to power control apparatuses, and more particularly, to a consensus-based power control apparatus applicable to a grid system having at least two power generating apparatuses. 
     2. Description of Related Art 
     In a grid system constituted by a plurality of power generating apparatuses such as synchronous generators, wind power generators and water power generators, since the power generating apparatuses usually generate significantly different real power input signals (representing actual real power outputs of the apparatuses) or reactive power input signals (representing actual reactive power outputs of the apparatuses) and the grid system lacks an ability to distribute the real power input signals and the reactive power input signals of the power generating apparatuses, the real power input signals and the reactive power input signals of the power generating apparatuses cannot become (or tend to become) uniform or have predetermined ratios, thus adversely affecting the overall energy stability of the grid system. 
       FIG. 1  is a schematic block diagram of a conventional synchronous generator  1 . Referring to  FIG. 1 , the synchronous generator  1  has a first subtraction unit  11 , a second subtraction unit  12 , an inertia unit  13 , a first integral unit  14 , a friction unit  15  and a second integral unit  16 . 
     The first subtraction unit  11  subtracts a real power input signal P e  from a real power command signal P M  to generate a real power difference signal A 1 . The second subtraction unit  12  subtracts a feedback frequency signal A 2  from the real power difference signal A 1  to generate a real power output signal A 3 . The inertia unit  13  multiplies the real power output signal A 3  by an inertia constant to generate a frequency differential signal {dot over (ω)}. The first integral unit  14  integrates the frequency differential signal {dot over (ω)} to generate a frequency signal ω. The friction unit  15  multiplies the frequency signal ω by a friction constant to generate the feedback frequency signal A 2 . The second integral unit  16  integrates the frequency signal ω to generate an electric angle signal θ. 
     However, when a plurality of synchronous generators  1  are applied in a grid system, since the grid system lacks the ability to distribute real power input signals P e  and reactive power input signals (not shown) of the synchronous generators  1 , the real power input signals Pe and the reactive power input signals of the synchronous generators  1  cannot become (or tend to become) uniform or have predetermined ratios. Consequently, the overall energy of the grid system lacks stability. 
     Therefore, there is a need to provide a consensus-based power control apparatus so as to overcome the above-described drawbacks. 
     SUMMARY OF THE INVENTION 
     The present invention provides a consensus-based power control apparatus that can control real power and reactive power input signals of a power generating apparatus in a grid system. 
     The consensus-based power control apparatus of the present invention is applicable to a grid system having a first power generating apparatus and at least a second power generating apparatus. The power control apparatus comprises a real power control module providing a real power command signal and receiving a real power input signal of the first power generating apparatus. The real power control module comprises: a real power consensus unit for providing a real power consensus signal between the first power generating apparatus and the second power generating apparatus; and a frequency restoration unit for generating a frequency restoration signal according to the real power consensus signal, thereby allowing the real power control module to generate a first real power output signal of the first power generating apparatus according to the real power command signal, the real power input signal and the frequency restoration signal. The power control apparatus further comprises a reactive power control module providing a reactive power command signal and receiving a reactive power input signal of the first power generating apparatus. The reactive power control module comprises: a reactive power consensus unit for providing a reactive power consensus signal between the first power generating apparatus and the second power generating apparatus; and a voltage restoration unit for generating a voltage differential restoration signal according to the reactive power consensus signal, thereby allowing the reactive power control module to generate a reactive power output signal of the first power generating apparatus according to the reactive power command signal, the reactive power input signal and the voltage differential restoration signal. 
     The real power control module can further comprise: a first subtraction unit for subtracting the real power input signal from the real power command signal to generate a real power difference signal; and a second subtraction unit for subtracting the frequency restoration signal from the real power difference signal to generate the first real power output signal. 
     The real power control module can further comprise a first addition unit and the frequency restoration unit can further comprise a first integral sub-unit. The first addition unit adds the first real power output signal and the real power consensus signal, the first integral sub-unit integrates the output of the first addition unit, and the frequency restoration unit multiplies the output of the first integral sub-unit by a frequency restoration constant to generate the frequency restoration signal. 
     The real power control module can further comprise a third subtraction unit for subtracting a first electric angle differential signal from the first real power output signal to generate a second real power output signal of the first power generating apparatus. 
     The real power control module can further comprise: a virtual inertia unit for multiplying the second real power output signal by an inertia constant to generate a frequency differential signal; and a second integral unit for integrating the frequency differential signal to generate a second electric angle differential signal, thereby allowing the real power control module to multiply the second electric angle differential signal by a real power droop constant to generate the first electric angle differential signal. 
     The real power control module can further comprise: a second addition unit for adding the second electric angle differential signal and a frequency constant; and a third integral unit for integrating the output of the second addition unit to generate an electric angle signal. 
     The reactive power control module can further comprise: a fourth subtraction unit for subtracting the reactive power input signal from the reactive power command signal to generate a reactive power difference signal; and a fifth subtraction unit for subtracting the voltage differential restoration signal from the reactive power difference signal to generate the reactive power output signal. 
     The reactive power control module can further comprise a third addition unit and the voltage restoration unit can further comprise a fourth integral sub-unit. The third addition unit adds the reactive power output signal and the reactive power consensus signal, the fourth integral sub-unit integrates the output of the third addition unit, and the voltage restoration unit multiplies the output of the fourth integral sub-unit by a voltage restoration constant to generate the voltage differential restoration signal. 
     The reactive power control module can further comprise a fifth integral unit. The reactive power control module multiplies the reactive power output signal by a reactive power droop constant to generate a voltage differential signal and the fifth integral unit integrates the voltage differential signal to generate a voltage difference signal. 
     The reactive power control module can further comprise: a fourth addition unit for adding the voltage difference signal and a voltage constant to generate a voltage command signal; and a sixth subtraction unit for subtracting a voltage feedback signal from the voltage command signal to generate a voltage error signal. 
     The power control apparatus can further comprise a modulation module having a proportional integral (PI) control unit for changing a voltage error signal of the reactive power control module into a current command signal and a predictive current control unit for generating a current output signal according to the current command signal and a current feedback signal. 
     The modulation module can further have: a transformation frame unit for generating a control force signal according to the current output signal and an electric angle signal of the real power control module; and a PWM (Pulse Width Modulation) unit for changing the control force signal into a PWM signal. 
     Therefore, the consensus-based power control apparatus of the present invention can be applied in a grid system having a first power generating apparatus and at least a second power generating apparatus connected or adjacent to the first power generating apparatus. The real power control module of the power control apparatus has a real power consensus unit for providing a real power consensus signal between the first power generating apparatus and the second power generating apparatus, and the reactive power control module of the power control apparatus has a reactive power consensus unit for providing a reactive power consensus signal between the first power generating apparatus and the second power generating apparatus. As such, the present invention can control real power and reactive power input signals of the first power generating apparatus through the real power and reactive power consensus signals. 
     Further, when a plurality of power control apparatuses of the present invention are applied in a grid system having a plurality of power generating apparatuses, the power control apparatuses are capable of distributing real power and reactive power input signals of the power generating apparatuses so as to cause the real power and reactive power input signals of the power generating apparatuses to become (or tend to become) uniform or have predetermined ratios and cause the overall energy of the grid system to achieve stability. 
     Furthermore, the power control apparatus of the present invention has a virtual inertia unit for providing a suitable inertia for the first power generating apparatus so as to cause frequency signals of the first power generating apparatus to have smaller jitter and greater stability. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic block diagram of a conventional synchronous generator; 
         FIG. 2  is a schematic block diagram of a consensus-based power control apparatus of the present invention; 
         FIG. 3  is a schematic block diagram showing application of a plurality of power control apparatuses of the present invention in a plurality of power generating apparatuses of a grid system; 
         FIGS. 4A and 4B  are schematic waveform diagrams of real power input signals of the power generating apparatuses of the grid system in cases when each of the power control apparatuses has a real power consensus unit and when it does not; 
         FIGS. 5A and 5B  are schematic waveform diagrams of frequency signals of the power generating apparatuses of the grid system in cases when each of the power control apparatuses has a real power consensus unit and when it does not; 
         FIGS. 6A and 6B  are schematic waveform diagrams of reactive power input signals of the power generating apparatuses of the grid system in cases when each of the power control apparatuses has a reactive power consensus unit and when it does not; 
         FIGS. 7A and 7B  are schematic waveform diagrams of voltage output signals of the power generating apparatuses of the grid system in cases when each of the power control apparatuses has a reactive power consensus unit and when it does not; and 
         FIG. 8  is a schematic waveform diagram showing a comparison of different frequency signals of one of the power generating apparatuses of the grid system in cases when the corresponding power control apparatus has a virtual inertia unit and when it does not. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The following illustrative embodiments are provided to illustrate the disclosure of the present invention, these and other advantages and effects can be apparent to those in the art after reading this specification. 
       FIG. 2  is a schematic block diagram of a consensus-based power control apparatus C of the present invention, and  FIG. 3  is a schematic block diagram showing application or mounting of a plurality of power control apparatuses C (for example, six power control apparatuses C 3 , C 4 , C 5 , C 7 , C 10  and C 13 ) of the present invention in a plurality of power generating apparatuses G (for example, six power generating apparatuses G 3 , G 4 , G 5 , G 7 , G 10  and G 13 ) of a grid system  5 , respectively. 
     In the present embodiment, the grid system  5  of  FIG. 3  has a plurality of buses B (for example, fourteen buses B 1  to B 14 ) and a plurality of transmission lines l for electrically connecting the power generating apparatuses G, the power control apparatuses C and a plurality of loads S (for example, four loads S 6 , S 8 , S 11  and S 14 ). 
     Referring to  FIG. 3 , the load S 6  when light consumes a real power of 0.044 kW and a reactive power of 0.036 kvar and when heavy consumes a real power of 0.13 kW and a reactive power of 0.11 kvar. The load S 8  and the load S 11  when light consume a real power of 0.43 kW and a reactive power of 0.31 kvar and when heavy consume a real power of 1.30 kW and a reactive power of 0.93 kvar. The load S 14  when light consumes a real power of 1.32 kW and a reactive power of 0.94 kvar and when heavy consumes a real power of 3.95 kW and a reactive power of 2.82 kvar. 
     Referring to  FIGS. 2 and 3 , the power control apparatuses C can be power control circuits, synchronverters or distributed interface converters (DICs). The grid system  5  can be an isolated micro-grid system. The power generating apparatuses G can be synchronous generators, wind power generators, water power generators, thermal power generators or nuclear power generators. 
     In an embodiment, the grid system  5  of  FIG. 3  only has a first power generating apparatus and at least a second power generating apparatus. For example, the first power generating apparatus is any one of the power generating apparatuses G (for example, G 3 , G 4 , G 5 , G 7 , G 10  and G 13 ), and the second power generating apparatus is at least one of the power generating apparatuses G that is adjacent to the first power generating apparatus. Further, the first power generating apparatus is electrically or signally connected to the second power generating apparatus through at least one transmission line  1 . For example, if the first power generating apparatus of  FIG. 3  is G 3 , the second power generating apparatuses are G 4 , G 7  and G 10 . In another example, if the first power generating apparatus of  FIG. 3  is G 13 , the second power generating apparatus is G 4 . 
     Referring to  FIG. 2 , the power control apparatus C mainly has a real power control module  2  and a reactive power control module  3 . For purposes of simplification, the power generating apparatus G 13  of  FIG. 3  is exemplified as a first power generating apparatus, the power generating apparatus G 4  is a second power generating apparatus, and the power control apparatus C 13  serves as the power control apparatus C of  FIG. 2 . 
     Referring to  FIGS. 2 and 3 , the power control apparatus C 13  (C) is electrically connected to the power generating apparatus G 13  or mounted inside the power generating apparatus G 13 . The power control apparatus C 13  (C) and the power generating apparatus G 13  are adjacent to the power generating apparatus G 4  and electrically or signally connected to the power generating apparatus G 4  through the transmission line  1 . 
     The real power control module  2  of the power control apparatus C 13  (C) provides a real power command signal P i * and receives a real power input signal P i  of the power generating apparatus G 13 . Further, the real power control module  2  has a real power consensus unit  202  for providing a real power consensus signal D 2  between the power generating apparatus G 13  and the power generating apparatus G 4 , and a frequency restoration unit  203  for generating a frequency restoration signal D 3  according to the real power consensus signal D 2 . According to the real power command signal P i *, the real power input signal P i  and the frequency restoration signal D 3 , the real power control module  2  generates a first real power output signal D 4  of the power generating apparatus G 13 . 
     In particular, the real power control module  2  further has a first subtraction unit  201  for subtracting the real power input signal P i  from the real power command signal P i * to generate a real power difference signal D 1 . The first subtraction unit  201  can be a hardware subtractor or a software subtraction program. 
     The real power control module  2  further has a second subtraction unit  206 . The second subtraction unit  206  is electrically or signally connected to the first subtraction unit  201  for subtracting the frequency restoration signal D 3  from the real power difference signal D 1  and thereby generating the first real power output signal D 4 . The second subtraction unit  206  can be a hardware subtractor or a software subtraction program. 
     The real power control module  2  further has a first addition unit  207 . The first addition unit  207  is electrically or signally connected to the second subtraction unit  206  and the real power consensus unit  202  for adding the first real power output signal D 4  and the real power consensus signal D 2 . The first addition unit  207  can be a hardware adder or a software addition program. The second subtraction unit  206 , the first addition unit  207  and the frequency restoration unit  203  constitute a first closed loop. 
     The frequency restoration unit  203  has a first integral sub-unit  204 . The first integral sub-unit  204  is electrically or signally connected to the first addition unit  207 , for integrating the output of the first addition unit  207 . The first integral sub-unit  204  can be a hardware integrator or a software integral program. Further, the frequency restoration unit  203  multiplies the output of the first integral sub-unit  204  by a frequency restoration constant  205  to generate the frequency restoration signal D 3 . The frequency restoration signal D 3  is used to restore the frequency of the first real power output signal D 4 . 
     The real power control module  2  further has a third subtraction unit  208 . The third subtraction unit  208  is electrically or signally connected to the second subtraction unit  206  for subtracting a first electric angle differential signal D 5  from the first real power output signal D 4  and thereby generating a second real power output signal D 6  of the power generating apparatus G 13 . The third subtraction unit  208  can be a hardware subtractor or a software subtraction program. 
     The real power control module  2  further has a virtual inertia unit  209 . The virtual inertia unit  209  is electrically or signally connected to the third subtraction unit  208  for multiplying the second real power output signal D 6  by an inertia constant  210  and thereby generating a frequency differential signal {umlaut over (θ)} i . As such, a suitable rotational inertia J is added to the second real power output signal D 6  of the power generating apparatus G 13 . The rotational inertia J is not equal to zero. That is, J≠0. 
     The real power control module  2  further has a second integral unit  211 . The second integral unit  211  is electrically or signally connected to the virtual inertia unit  209  for integrating the frequency differential signal {umlaut over (θ)} i  and thereby generating a second electric angle differential signal {dot over (θ)} i . Further, the real power control module  2  multiplies the second electric angle differential signal {dot over (θ)} i  by a real power droop constant  212  to generate the first electric angle differential signal D 5 . The second integral unit  211  can be a hardware integrator or a software integral program. The third subtraction unit  208 , the virtual inertia unit  209  and the second integral unit  211  form a second closed loop. 
     The real power control module  2  further has a second addition unit  213 . The second addition unit  213  is electrically or signally connected to the second integral unit  211  for adding the second electric angle differential signal {dot over (θ)} i  and a frequency constant ω b . The second addition unit  213  can be a hardware adder or a software addition program. 
     The real power control module  2  further has a third integral unit  214 . The third integral unit  214  is electrically or signally connected to the second addition unit  213  for integrating the output of the second addition unit  213  and thereby generating an electric angle signal θ i . The third integral unit  214  can be a hardware integrator or a software integral program. 
     Further, the reactive power control module  3  of the power control apparatus C 13  (C) provides a reactive power command signal Q i * and receives a reactive power input signal Q i  of the power generating apparatus G 13 . Further, the reactive power control module  3  has a reactive power consensus unit  302  for providing a reactive power consensus signal E 2  between the power generating apparatus G 13  and the power generating apparatus G 4 , and a voltage restoration unit  303  for generating a voltage differential restoration signal E 3  according to the reactive power consensus signal E 2 . According to the reactive power command signal Q i *, the reactive power input signal Q i  and the voltage differential restoration signal E 3 , the reactive power control module  3  generates a reactive power output signal E 4  of the power generating apparatus G 13 . 
     In particular, the reactive power control module  3  further has a fourth subtraction unit  301  for subtracting the reactive power input signal Q i  from the reactive power command signal Q i * to generate a reactive power difference signal E 1 . The fourth subtraction unit  301  can be a hardware subtractor or a software subtraction program. 
     The reactive power control module  3  further has a fifth subtraction unit  306 . The fifth subtraction unit  306  is electrically or signally connected to the fourth subtraction unit  301  for subtracting the voltage differential restoration signal E 3  from the reactive power difference signal E 1  and thereby generating the reactive power output signal E 4 . The fifth subtraction unit  306  can be a hardware subtractor or a software subtraction program. 
     The reactive power control module  3  further has a third addition unit  307 . The third addition unit  307  is electrically or signally connected to the fifth subtraction unit  306  and the reactive power consensus unit  302  for adding the reactive power output signal E 4  and the reactive power consensus signal E 2 . The third addition unit  307  can be a hardware adder or a software addition program. The fifth subtraction unit  306 , the third addition unit  307  and the voltage restoration unit  303  constitute a third closed loop. 
     The voltage restoration unit  303  has a fourth integral sub-unit  304 . The fourth integral sub-unit  304  is electrically or signally connected to the third addition unit  307  for integrating the output of the third addition unit  307 . The fourth integral sub-unit  304  can be a hardware integrator or a software integral program. Further, the voltage restoration unit  303  multiplies the output of the fourth integral sub-unit  304  by a voltage restoration constant  305  to generate the voltage differential restoration signal E 3 . The voltage differential restoration signal E 3  is used to restore the voltage of the reactive power output signal E 4 . 
     The reactive power control module  3  further has a fifth integral unit  309 . The fifth subtraction unit  309  is electrically or signally connected to the fifth subtraction unit  306 . The reactive power control module  3  multiplies the reactive power output signal E 4  by a reactive power droop constant  308  to generate a voltage differential signal {dot over (V)} i   • , and the fifth integral unit  309  integrates the voltage differential signal {dot over (V)} i   •  to generate a voltage difference signal ΔV i . The fifth integral unit  309  can be a hardware integrator or a software integral program. 
     The reactive power control module  3  further has a fourth addition unit  310 . The fourth addition unit  310  is electrically or signally connected to the fifth integral unit  309  for adding the voltage difference signal ΔV i  and a voltage constant V i,0  and thereby generating a voltage command signal V i *. The fourth addition unit  310  can be a hardware adder or a software addition program. 
     The reactive power control module  3  further has a sixth subtraction unit  311 . The sixth subtraction unit  311  is electrically or signally connected to the fourth addition unit  310  for subtracting a voltage feedback signal V i,dq  from the voltage command signal V i * and thereby generating a voltage error signal E 5 . The sixth subtraction unit  311  can be a hardware subtractor or a software subtraction program. 
     The power control apparatus C 13  (C) further has a modulation module  4  electrically or signally connected to the real power control module  2  and the reactive power control module  3 . The modulation module  4  can be a hardware modulator or a software modulation program. 
     The modulation module  4  has a proportional integral (PI) control unit  401 . The PI control unit  401  is electrically or signally connected to the sixth subtraction unit  311  of the reactive power control module  3  for changing the voltage error signal E 5  into a current command signal F 1 . 
     The modulation module  4  further has a predictive current control unit  402 . The predicative current control unit  402  is electrically or signally connected to the PI control unit  401  for generating a current output signal F 2  according to the current command signal F 1  and a current feedback signal i i,dq . 
     The modulation module  4  further has a transformation frame unit  403 . The transformation frame unit  403  is electrically or signally connected to the third integral unit  214  of the real power control module  2  and the predicative current control unit  402  for generating a control force signal F 3  according to the current output signal F 2  and the electric angle signal θ i  of the real power control module  2 . 
     The modulation module  4  further has a PWM (Pulse Width Modulation) unit  404 . The PWM unit  404  is electrically or signally connected to the transformation frame unit  403  for changing the control force signal F 3  into a PWM signal m. 
     In the power control apparatuses C (for example, C 3 , C 4 , C 5 , C 7 , C 10  and C 13 ) and the power generating apparatuses G (for example, G 3 , G 4 , G 5 , G 7 , G 10  and G 13 ) of  FIGS. 2 and 3 , ideally, the power control apparatuses C adjust the ratios of the real power input signals P i  (for example, P 1 , P 2 , . . . P m ) to the real power control signals P i * (for example, P 1 *, P 2 *, . . . P m *) to be equal and adjust the ratios of the reactive power input signals Q i  (for example, Q 1 , Q 2 , . . . Q m ) to the reactive power control signals Q i * (for example, Q 1 *, Q 2 *, . . . Q m *) to be equal, thereby causing the real power input signals and the reactive power input signals of the power generating apparatuses G to become (or tend to become) uniform or have predetermined ratios. For example, a real power ratio equation (1) and a reactive power ratio equation (2) are shown as follows.
 
 P   1   /P*   1   = . . . P   m   /P*   m   (1)
 
 Q   1   /Q*   1   = . . . Q   m   /Q*   m   (2)
 
     In equations (1) and (2), m represents the number of the power generating apparatuses G, P 1  to P m  represent real power input signals of the power generating apparatuses G, P 1  * to P m * represent real power command signals of the power generating apparatuses G, Q 1  to Q m  represent reactive power input signals of the power generating apparatuses G, and Q 1 * to Q m * represent reactive power command signals of the power generating apparatuses G. 
     Referring to  FIGS. 2 and 3 , the power control apparatuses C can generate second electric angle differential signals {dot over (θ)} i , real power command signals P i *, real power consensus signals D 2  etc. according to a following real power equation (3), and generate reactive power command signals Q i *, reactive power consensus signals E 2  etc. according to a following reactive power equation (4). 
     
       
         
           
             
               
                 
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     In the above-described equations (3) and (4), i represents a denoted number (for example,  13 ) of the first power control apparatus C (for example, C 13 ) or the first power generating apparatus G (for example, G 13 ), j represents a denoted number (for example, 4) of the second power control apparatus C (for example, C 4 ) or the second power generating apparatus G (for example, G 4 ), D p,i  represents a real power droop constant of the first power control apparatus C, D p,j  represents a real power droop constant of the second power control apparatus C, D q,i  represents a reactive power droop constant of the first power control apparatus C, D q,j  represents a reactive power droop constant of the second power control apparatus C, J i  represents a rotational inertia constant of the first power control apparatus C, k p,i  represents a frequency restoration constant of the first power control apparatus C, k q,i  represents a voltage differential restoration constant of the first power control apparatus C, l ij  represents the first power control apparatus C is connected to the second power control apparatus C through a transmission line  1 , P i  represents a real power input signal of the first power generating apparatus G, P i * represents a real power command signal of the first power control apparatus C, p i  and ω i  represent frequency signals of the first power control apparatus C, {dot over (p)} i  and {dot over (ω)} i  represent frequency differential signals of the first power control apparatus C, p j  represents a frequency signal of the second power control apparatus C, Q i  represents a reactive power input signal of the first power generating apparatus G, Q i * represents a reactive power command signal of the first power control apparatus C, q i  and V i  represent voltage signals of the first power control apparatus C, {dot over (q)} i  and {dot over (v)} i  represent voltage differential signals of the first power control apparatus C, ω b  represent a frequency constant of the first power control apparatus C, and {dot over (θ)} i  represents a second electric angle differential signal of the first power control apparatus C. 
     The overall energy of the grid system  5  of  FIG. 3  is calculated according to following energy equations (5), (6) and (7) so as to cause the overall energy of the grid system  5  to achieve stability.
 
 U   1 ( x )=KE(ω)+PE( y )  (5)
 
KE(ω)=1/2Σ j=1   m    J   j ω j   2   (6)
 
PE( y )= W   1 ( y )+ W   2 ( y )+ W   3 ( y )+ W   4 ( p,q )  (7)
 
     In the above-described equations (5) to (7), U 1 (x) represents overall energy of the grid system  5 , KE(ω) represents kinetic energy of the grid system  5 , and PE(y) represents potential energy of the grid system  5 . Further, J j  represents a rotational inertia constant of a single power control apparatus C, m represents the number of the power generating apparatuses x and y represent variable vector signals of the grid system  5 , W 1 , W 2 , W 3  and W 4  represent potential energies of the grid system  5 , and ω j  represents a frequency signal of a single power control apparatus C. 
     Furthermore, the calculation is performed according to the equations (5) to (7) in combination with following equations (8) to (10). 
     
       
         
           
             
               
                 
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                   ( 
                   10 
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     In the above-described equations (8) to (10), B ij  represents an admittance of a transmission line  1  of the grid system  5 , K represents a ratio of resistance to inductance of the transmission line  1  of the grid system  5 , m and n represent the number of the power generating apparatuses G, p and ω represent frequency signals of the grid system  5 , p i , p j  and ω i  represent frequency signals of a single power control apparatus C, P j * represents a real power command signal of a single power control apparatus C, P Lj  represents the amount of real power of a single load S, q and v represent voltage signals of the grid system  5 , Q j * represents a reactive power command signal of a single power control apparatus C, Q L,j  represents the amount of reactive power of a single load S, T represents transpose, V i , V j , q i  and q j  represent voltage signals of a single power control apparatus C, v i  represents a natural logarithm of the voltage signal V i , v j  represents a natural logarithm of the voltage signal V j , x i  and y i  represent variable vector signals of a single power control apparatus C, θ and θ ij  represent electric angle signals of the grid system  5 , θ i  and θ j  represent electric angle signals of a single power control apparatus C. 
       FIGS. 4A and 4B  are schematic waveform diagrams of real power input signals of the power generating apparatuses G (for example, G 3 , G 4 , G 5 , G 7 , G 10  and G 13 ) of the grid system  5  in cases when each of the power control apparatuses C (for example, C 3 , C 4 , C 5 , C 7 , C 10  and C 13 ) has the real power consensus unit  202  of  FIG. 2  and when it does not. 
     Referring to  FIG. 4A , when each of the power control apparatuses C does not have the real power consensus unit  202  (the real power consensus signal D 2 ) of  FIG. 2 , the real power input signals of the power generating apparatuses G are significantly different. 
     Referring to  FIG. 4B , when each of the power control apparatuses C of  FIG. 3  has the real power consensus unit  202  (the real power consensus signal D 2 ) of  FIG. 2 , the real power input signals of the power generating apparatuses G become or tend to become uniform. 
       FIGS. 5A and 5B  are schematic waveform diagrams of frequency signals of the power generating apparatuses G (for example, G 3 , G 4 , G 5 , G 7 , G 10  and G 13 ) of the grid system  5  in cases when each of the power control apparatuses C (for example, C 3 , C 4 , C 5 , C 7 , C 10  and C 13 ) has the real power consensus unit  202  of  FIG. 2  and when it does not. 
     Referring to  FIGS. 5A and 5B , the frequency signals of the power generating apparatuses G become or tend to become uniform no matter whether each of the power control apparatuses C has the real power consensus unit  202  (the real power consensus signal D 2 ) of  FIG. 2  or not. 
       FIGS. 6A and 6B  are schematic waveform diagrams of reactive power input signals of the power generating apparatuses G (for example, G 3 , G 4 , G 5 , G 7 , G 10  and G 13 ) of the grid system  5  in cases when each of the power control apparatuses C (for example, C 3 , C 4 , C 5 , C 7 , C 10  and C 13 ) has the reactive power consensus unit  302  of  FIG. 2  and when it does not. 
     Referring to  FIG. 6A , when each of the power control apparatuses C does not have the reactive power consensus unit  302  (the reactive power consensus signal E 2 ) of  FIG. 2 , the reactive power input signals of the power generating apparatuses G are significantly different. 
     Referring to  FIG. 6B , when each of the power control apparatuses C of  FIG. 3  has the reactive power consensus unit  302  (the reactive power consensus signal E 2 ) of  FIG. 2 , the reactive power input signals of the power generating apparatuses G become or tend to become uniform. 
       FIGS. 7A and 7B  are schematic waveform diagrams of voltage output signals of the power generating apparatuses G (for example, G 3 , G 4 , G 5 , G 7 , G 10  and G 13 ) of the grid system  5  in cases when each of the power control apparatuses C (for example, C 3 , C 4 , C 5 , C 7 , C 10  and C 13 ) has the reactive power consensus unit  302  of  FIG. 2  and when it does not. 
     Referring to  FIGS. 7A and 7B , the difference between the voltage output signals of the power generating apparatuses G is not significant no matter whether each of the power control apparatuses C has the reactive power consensus unit  302  (the reactive power consensus signal E 2 ) of  FIG. 2  or not. 
       FIG. 8  is a schematic diagram showing a comparison of different frequency signals of one of the power generating apparatuses G (for example, G 13 ) of the grid system  5  in cases when the corresponding power control apparatus C (for example, C 13 ) has the virtual inertia unit  209  of  FIG. 2  and when it does not. 
     Referring to  FIG. 8 , when the power control apparatus C of  FIG. 3  does not have the rotational inertia constant of the virtual inertia unit  209  of  FIG. 2  (i.e., J=0), the frequency signal of the power generating apparatus G has larger jitter and less stability. But when the power control apparatus C of  FIG. 3  has the rotational inertia constant of the virtual inertia unit  209  of  FIG. 2  (i.e., J≠0), the frequency signal of the power generating apparatus G has smaller jitter and greater stability. 
     Therefore, the consensus-based power control apparatus of the present invention can be applied in a grid system having a first power generating apparatus and at least a second power generating apparatus connected or adjacent to the first power generating apparatus. The real power control module of the power control apparatus has a real power consensus unit for providing a real power consensus signal between the first power generating apparatus and the second power generating apparatus, and the reactive power control module of the power control apparatus has a reactive power consensus unit for providing a reactive power consensus signal between the first power generating apparatus and the second power generating apparatus. As such, the present invention can control real power and reactive power input signals of the first power generating apparatus through the real power and reactive power consensus signals. 
     Further, when a plurality of power control apparatuses of the present invention are applied in a grid system having a plurality of power generating apparatuses, the power control apparatuses are capable of distributing real power and reactive power input signals of the power generating apparatuses so as to cause the real power and reactive power input signals of the power generating apparatuses to become (or tend to become) uniform or have predetermined ratios and cause the overall energy of the grid system to achieve stability. 
     Furthermore, the power control apparatus of the present invention has a virtual inertia unit for providing a suitable inertia for the first power generating apparatus so as to cause frequency signals of the first power generating apparatus to have smaller jitter and greater stability. 
     The above-described descriptions of the detailed embodiments are only to illustrate the preferred implementation according to the present invention, and it is not to limit the scope of the present invention. Accordingly, all modifications and variations completed by those with ordinary skill in the art should fall within the scope of present invention defined by the appended claims.