Abstract:
A method includes generating samples of a grid parameter at a point of common coupling, fitting a waveform to the samples, and detecting an islanding condition in response to a parameter of the waveform. The waveform may be fit to the samples using a nonlinear algorithm. A controller includes a waveform fitting circuit to fit a waveform to samples of a grid parameter, an inverter controller to generate one or more switching signals to control an inverter in response to an error signal, and an error generator arranged to generate the error signal in response to a parameter of the waveform.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority from U.S. Provisional Patent Application Ser. No. 61/291,622 titled Phase Recovery in Power Systems filed Dec. 31, 2009. 
    
    
     COPYRIGHT 
     A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent disclosure, as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all copyright rights whatsoever. 
     BACKGROUND 
     Electric utility grids have traditionally been arranged so that power flows radially outward from a centrally located power plant to multiple points of usage. The increasing use of renewable power sources, however, has introduced distributed generation (DG) capacity to power grids. DG power sources may be located anywhere on the grid, typically close to a local power load. Examples of DG power sources include photovoltaic (PV) panels and wind turbines which are scattered at customer locations throughout the grid. At certain times, all of the power from these sources may be consumed by local building loads, while at other times, excess power is fed back into the grid. Thus, utility grids have become complex, interconnected structures with power flowing in multiple directions depending on the availability of power from multiple sources and demand from multiple loads at any specific time. 
     Distributed power sources must include synchronization functionality to enable power from the distributed source to be injected into the grid in phase with the power already flowing in the grid. Most commonly, this functionality is implemented with a phase-locked loop (PLL) which generates a local sine wave reference having the same phase and frequency as the power grid. This reference is then used to inject current in phase with the grid. 
     “Islanding” is a condition in which a portion of the utility grid containing power generation capacity and load becomes isolated from the remainder of the grid, but continues to operate independently because the PLL or other synchronization functionality continues to provide a reference for the power flowing in the isolated portion of the grid. Islanding is problematic, however, because it typically degrades the quality of power flowing in the isolated portion of the grid, creates unsafe conditions for utility workers, causes mismatches when the isolated portion of the grid is eventually reconnected to the main grid, and may cause numerous other problems including mismatches between power generation capacity and demand. Thus, if an islanding condition is detected, the local power generation capacity should be disconnected. This is referred to as anti-islanding (AI) protection, and the detection of islanding conditions is an ongoing challenge. 
     Numerous islanding detection techniques have been developed. Some of the most effective techniques involve the use of positive feedback in the distributed generation control system. A common method is to place a narrow-band low-pass filter and amplification in the grid voltage measurement and current injection feedback loop, with sufficient gain to provide a low frequency (&lt;grid frequency) instability and oscillation that builds up when the grid is disconnected, and dampens down when the grid is connected. Noise seeds the oscillation growth. 
       FIG. 1  illustrates a prior art distributed generation control system having a positive feedback anti-islanding feature. An inverter bridge  10  converts DC power from a DC power source  12  to AC power which is delivered to a local load  14  and utility grid  16  at a point of common coupling (PCC)  18 . A disconnect switch  20  or utility circuit breaker/recloser may isolate the local load  14  from the utility grid  16  in response to one or more fault conditions. 
     The normal negative feedback loop includes a phase-locked loop  22  which generates frequency (ω) and phase (θ) reference signals in response to the output voltage v a  from the inverter at the point of common coupling. An error generator  24  generates a feedback signal ERROR in response to a sample of the output current i a  and a current reference signal i REF . A pulse width modulation (PWM) circuit  26  generates switching signals to control the inverter bridge in response to the signals from the error generator and PLL. 
     The positive feedback portion of the control system includes a low-pass or band-pass filter  28 , an amplifier  30  that determines the loop gain, and a summing circuit  32 . In the absence of the positive feedback loop, the PLL and negative feedback loop through error generator  24  would cause the inverter to continue operating long after the inverter and local load are isolated from the utility grid (islanded). The phase and/or frequency of the PLL, however, would slowly drift until a problematic condition develops. 
     The positive portion of the feedback loop introduces a small amount of positive feedback through summing circuit  32 . When the inverter and local load are connected to the utility grid, the low impedance of the grid overcomes the effect of the positive feedback, and the output of the inverter remains stable. When the inverter and local load are disconnected from the utility grid, however, the positive feedback loop causes one or more parameters of the inverter output to grow, decay or oscillate until it trips a protection feature such as over/under voltage protection (OVP/UVP), over/under current protection (OCP/UCP), or over/under frequency protection (OFP/UFP) which is included in the control system, but not shown in  FIG. 1 . 
     Although prior art positive feedback anti-islanding techniques such as the one illustrated in  FIG. 1  may provide adequate performance in some situations, they suffer from some drawbacks. For example, the presence of the filter in the positive feedback loop causes a significant amount of loop delay which slows down the response to an islanding condition. The positive feedback loop typically provides a 20 Hz oscillation in response to an islanding condition which results in a time constant that may be too long to trigger a shutdown during the time periods mandated by utility grid interconnect standards and regulations. The system of  FIG. 1  may also have difficulty re-synchronizing when grid power is restored. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a prior art distributed generation control system having a positive feedback anti-islanding feature. 
         FIG. 2  illustrates an embodiment of a control system according to some inventive principles of this patent disclosure. 
         FIG. 3  illustrates an embodiment of a waveform fitting system according to some inventive principles of this patent disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 2  illustrates an embodiment of a control technique according to some inventive principles of this patent disclosure. The system of  FIG. 2  includes an inverter bridge  34 , a DC power source  36 , a local load  38 , a grid  40 , a point of common coupling  42  and a disconnect switch  44  or utility circuit breaker/recloser. 
     Rather than a phase-locked loop, however, the controller  46  in the system of  FIG. 2  includes waveform fitting functionality  48  that generates one or more parameters P 1 , P 2  . . . PN by fitting samples of one or more inputs, such as the inverter output voltage v a  or current i a , to a waveform such as a sinewave or other suitable waveform. An error generator  50  generates an error signal Er in response to one or more of the waveform parameters P 1 , P 2  . . . PN. The error signal Er is used by inverter control  52  to generate one or more switching signals Sw to control the inverter bridge  34 , which converts DC power from DC power source  36  to AC power as in the circuit of  FIG. 1 . 
       FIG. 3  illustrates an embodiment of a waveform fitting system according to some inventive principles of this patent disclosure. The embodiment of  FIG. 3  will be described in the context of some example implementation details, and it may be used, for example, to implement the waveform fitting functionality  48  of  FIG. 2 , but the inventive principles are not limited to these specific details or applications. 
     The system of  FIG. 3  may be used to generate any or all of the following four unknown parameters for a sinusoidal waveform
 
 f ( t )= A *sin(ω t +θ)+ B   Eq. 1
 
where:
 
A=the amplitude of the sine wave;
 
ω=2πf (radians/sec) is the angular frequency of the sine wave;
 
θ=the phase in radians; and
 
B is the DC offset.
 
     The angular frequency co and the phase θ are sometimes indicated as w and p, respectively, for convenience such as in computer source code. 
     An analog-to-digital converter  54  samples one or more inputs at a relatively high sample rate such as 100 KHz. A decimation filter  56  implements a low-pass filter by decimating the samples by 2^7*3=384 to generate filtered samples at a lower sample rate of about 260 Hz. Selecting a lower sample rate which nevertheless exceeds 3 times the grid frequency (&gt;=3*f grid =180 Hz for a 60 Hz grid) avoids Nyquist aliasing issues. 
     A first-in-first-out (FIFO) buffer  58  stores five lower rate samples for processing by the waveform fitting algorithm. An offset function  60  selects a quad of 4 out of the 5 samples stored in the FIFO to avoid ill-behaved results from a denominator that may be close or equal to zero as described below. 
     A frequency estimator  62  uses the quad of samples f(0) through f(3) to calculate the frequency ω of the input signal as follows: 
                   ω   =     arccos   ⁡     (           f   ⁡     (   3   )       -     f   ⁡     (   0   )             f   ⁡     (   2   )       -     f   ⁡     (   1   )           /   2     )               Eq   .           ⁢   2               
The denominator in Eq. 2 may be zero or close to zero resulting in a degenerate, or at least ill-behaved result. Thus, the offset function  60  selects a quad of 4 out of the 5 samples that provide the largest denominator.
 
     A rectangular coordinate calculator  64  uses the estimated frequency co and samples f(0) through f(2) to calculate the following two functions of A and θ on a rectangular grid: 
     
       
         
           
             
               
                 
                   
                     
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     A rectangular-to-polar converter  66  converts the rectangular results to polar form to obtain A and θ as follows:
 
 A =√{square root over (( a _sin_ p ) 2 +( a _cos_ p ) 2 )}  Eq. 5
 
θ=arctan( a _sin_ p/a _cos_ p )  Eq. 6
 
where Eq. 6 is derived from tan(θ)=(a_sin_p)/(a_cos_p).
 
     DC offset calculator  68  calculates the DC offset as follows:
 
 B=f (0)− a _sin_ p   Eq. 7
 
     Finally, bounding functionality  70  may implement over/under voltage, current, frequency, etc., checks to turn off the inverter bridge (disconnecting the inverter from the grid) if any of the calculated parameters exceeds any predetermined values. 
     Any of the functionality illustrated in  FIG. 3  may be implemented in hardware, software, firmware or any combination thereof. For example, in an inverter system having control functionality implemented with digital signal processor (DSP), the functionality illustrated in  FIG. 3  may all be implemented as software as described in Appendix A with no additional hardware required. 
     The low-pass decimating filter may be made nominally flat to the grid frequency with significant attenuation (which may be set for example to 70 db) at the harmonics of 60 Hz (i.e. &gt;=120 Hz). For a 50 Hz/60 Hz system, the filter cutoff could be at 100 Hz instead. The sinewave parameters may then be used to reconstruct a “locked” sine reference, similar to that generated by a PLL. However, because there is not a PLL that is trying to build a frequency and phase reference, there may be several potential advantages. 
     A first potential advantage of the inventive principles is a fast “lock-up” time. The delay is almost entirely due to low-pass filtering of harmonics of the grid frequency prior to input to the algorithm. Once five filtered points are available for the algorithm to generate a sine fit, “lock-up” is effectively instantaneous. There may be no need for additional filtering in a feedback loop which could cause additional delay. 
     A second potential advantage of the inventive principles is that the non-linear nature of the recovery algorithm makes the control loop inherently unstable. Without an active power grid, the behavior may become more and more chaotic, and with time, can be easily characterized as out of legal amplitude, frequency, or DC offset bounds. This then triggers disconnection (anti-islanding) from the grid. Under these conditions, the disconnect time, due to the noisy nature of the process, increases only slightly with an increasing number of inverters in parallel. For example, a disconnect in about 0.2 seconds may be achieved, which is about 10 times quicker than the upper time limit of 2 seconds specified by typical standards for a single unit under test. 
     During operation, the algorithm may be arranged to check for out-of-range values of A and ω, and switch off driving the grid if one or the other becomes out of bounds (anti-islanding). Whether driving the grid or not, the system may continue monitoring the grid, so that when grid power is resumed, good values of A and ω may be obtained again, and if within bounds for, e.g., 300 seconds, the system may resume injecting power back into the grid, as required by typical standards. 
     Appendix A illustrates an example of code that may be used to generate and return of new parameters by implementing the algorithm described above in the context of  FIG. 3 . 
     The inventive principles of this patent disclosure have been described above with reference to some specific example embodiments, but these embodiments can be modified in arrangement and detail without departing from the inventive concepts. Such changes and modifications are considered to fall within the scope of the following claims.