Abstract:
A method and system to control distributed energy resources in an electric power system includes generation, storage and controllable loads. The system uses time synchronized measurements of voltage phasor and current phasors and their derivative information that may include real and reactive power to regulate and decouple both static and dynamic effects of real and reactive power flow through the local electric power system connected to the area electric power system. The method and system provides precise real and reactive power demand set point pairs; damping of real and reactive power fluctuations in the local electric power system; decoupling between real and reactive power demand response set points by means of a multivariable control system that uses time synchronized measurements of voltage and current phasors and their derivative information.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to electrical power grids and, more specifically, to methods and systems for monitoring and controlling power flow in such electrical power grids. 
       BACKGROUND OF THE INVENTION 
       [0002]    Distributed energy resources (DERs), which include renewable energy power sources, such as solar photovoltaic (PV) arrays and wind turbines, are often connected directly to distribution systems that are part of an area electric power systems (EPS). A large fraction of renewable energy resources will be installed in utility and customer owned distribution systems as individual States try to attain their Renewable Portfolio Standards (RPS). At 50% or greater total renewable generation, it will be difficult to control frequency and voltage to within acceptable standards without active feedback controls. Additionally, some cities such as San Diego are planning on having 100 percent renewable energy within its city limits by 2035. Many of the renewable power sources will come from small residential rooftop solar systems operating in low voltage distribution systems. There will be many independent participants installing renewable DERs without knowledge of the impact on the grid of the distributed resources and without adequate control of local frequency and voltage. The renewable energy resources (Solar PV, fuel cell, battery, wind) have little or no inertia since they are connected to a power electronics device that converts DC power into AC power. Diesel generators, on the other hand, have inertia and will contribute this to the adjacent connected grid load. Controllable loads can also be considered DERs since their power consumption can be regulated thus providing an additional means of control and providing inertia from the load side. These forms of DERs have higher inertia loads than typical renewable generation; however, they both should be used in a coordinated control system to regulate the frequency and voltage of the local EPS. 
         [0003]    Low inertia systems are difficult to control compared to systems with high inertia from rotating energy sources. The IEEE 1547.4 standards clearly point out the sensitivity of DERs to instability and voltage stability issues in the presence of low inertia generation sources. Lack of control of the power characteristics DER power injection can cause large variations in frequency or voltage exceeding standards that can cause the feeder or substation to disconnect from the area EPS. In a typical distribution feeder, one or more DERs may supply up to 10 MW of power. With adequate control and coordination, one or more DERs in combination with multiple feeders can form the basis of a microgrid. 
         [0004]    U.S. Pat. No. 8,457,912 describes a method of creating a smooth angle from the discontinuous angle measured from the PMU. The method includes detecting the change in direction of the angle and compensating for the discontinuous wrap at plus or minus 180°. This method is required in order to compute a smooth angle and a smooth angle difference that are used in the control system. 
         [0005]    U.S. Pat. No. 8,498,752 describes a method of decoupling real and reactive power from changes in voltage and angle. It also teaches that the control system can be reversed so that the voltage and angle can be controlled to a constant value by simultaneously changing the real and reactive power. The controller uses the basic principle that the response to real and reactive power injection causes a simultaneous change to voltage and angle by fundamental physics known as ohms law. 
         [0006]    The controller also assumes that the network impedance is constant and is a known value. The nonlinear systems are linearized around and operating point resulting in a linear set of equations that are used in that the coupled controller. The patent teaches how the system can be linearized around an operating point and then any linear control System Technology can be used to configure the controller. 
         [0007]    U.S. patent application Ser. No. 14/956,684 teaches how multiple decoupled controllers can be configured in cascade mode to form a hierarchical control system. It provides an explicit example of how the Smith predictor controller could be used in the control system design. Additionally, the controller technology recommended is based on commonly used proportional plus interval plus derivative control. The patent also teaches that the controls can be reversed so that the input and output variables at any one level can be reversed to form a set of hierarchical controllers that can be configured in cascade mode to perform a number of control system functions in Electric Power Networks. 
       SUMMARY OF THE INVENTION 
       [0008]    The present invention relates to the use of a hierarchy of 2×2 decoupled controllers for controlling DERs connected to power grids. These DERs can be any combination of very low inertia DERs such as batteries and solar PV arrays or slower responding DERs such as controllable loads in buildings, conventional thermal inertia based generation or any mix of hydro or wind generation with differing dynamic response. This invention is related to prior work by one of the present inventors, namely, two U.S. Pat. Nos. 8,498,752 and 8,457,912 and patent application U.S. Pat. No. 14/956,684, all of which are incorporated herein by reference. These teach how to decouple voltage and frequency and unwrap angle information from phasor measurement units (PMUs). The controls are accomplished by using real time feedback control to regulate voltage and frequency (or angle) by adjusting real and reactive power. 
         [0009]    The teachings of the present invention improves and extends the above prior work in various significant ways. The teachings of the present invention provide a unique and innovative approach to using phasor measurements directly in the control system. It also clearly teaches how the controller can be designed without the explicit knowledge of the impedance between two points in the power grid. This invention also teaches that the phasor controls can also be reversed and used in a cascade mode. It also teaches that both the voltage phasors and current phasors can be used as the primaries measured variables in the control system. In both cases, the control system is linear in the phasor variables. This makes the controller easy to tune and configure using conventional off the shelf control System Technology tools. Other unique features of the invention include the use of a filtered output from the controller, a use of a filtered derivative to compute the derivative action of the controller and the separation of the proportional integral part of the controller. Additionally, a unique method of decoupling is performed outside of the controller function in a separate decoupling matrix. This makes the coupling far easier than in prior work. Additionally, the present invention explicitly outlines the use of setpoint feed forward control, which is important for fast response to the disturbances in the Power Network. Additionally, the controller explicitly includes a method of modelling the process that includes four linear filters that are used to represent the dynamic state of the control system. These filters are extensively used in the controller such that the internal functionality of the controller has a limited number of independent control system objects. This current controller can be configured so that it operates as a controller without using the Smith predictor, a controller that can be used specifically for power control, and a controller that can be configured as two independent single input single output controllers. The present invention also explicitly describes how the controller can be configured control the current and power angle or the voltage and voltage angle. This flexibility is useful in the control of microgrids. 
         [0010]    According to teachings of the present invention, the controller in U.S. Pat. No. 8,498,752 can be re-structured to control voltage magnitude and voltage angle and or the current magnitude and power angle by adjusting real and reactive power setpoint pairs of the DER, and the controls can be reversed and used to control real and reactive power using voltage magnitude and voltage angle or current magnitude and power angle setpoint pairs. The control system uses the unwrapped angle rather than a frequency signal derived from the angle measurement. Using this control system automatically controls frequency since it is defined as the rate of change of voltage angle and, hence, if the angle is constant, by definition, the frequency is constant. According to teachings of the present invention, the controller may be operated at higher speeds compared to conventional Energy Management Systems, and time synchronized data may be used in the control system operations. The present invention provides an enhancement to traditional real and reactive power control that currently uses slow speed and non-synchronized open loop control. 
         [0011]    In one aspect, the invention uses time synchronized real and reactive power measurements in a high-speed feedback control system designed to mitigate disturbances while regulating the system to a specified real and reactive power setpoints. It also includes a control system that controls the state or the power of the system using the same controller structure. It incorporates a separate proportional integral combined with a derivative filter to mitigate power grid disturbances and also an output filter to adjust the output signal according to the response characteristics of the DERs. The invention provides an increase in the performance of the control system by using decoupled time synchronous input and output measurements. It uses either the decoupled pair (voltage magnitude and voltage angle) or the decoupled pair (current magnitude and power angle) as measured variables to precisely control real and reactive power while operating at high rates. This control structure can be reversed to form a decoupled control system regulating the pair (real power and reactive power) to obtain decoupled phasor output setpoints pairs for either (current magnitude and power angle) or (voltage magnitude and voltage angle.) These identically structured controllers can be used in cascade mode to directly control the power demand of the DER. 
         [0012]    According to another aspect, the invention provides a control system including a first 2×2 decoupled controller that controls current magnitude and power angle (difference between the voltage angle and current angle) by adjusting real and reactive power using real time feedback, and a reverse 2×2 decoupled controller that controls real and reactive power by adjusting current magnitude and power angle setpoints using real time feedback. The first 2×2 decoupled controller and second 2×2 decoupled controller can be used independently or where the second the second 2×2 decoupled controller is a supervisory controller of the first 2×2 decoupled controller. 
         [0013]    In some embodiments, the first 2×2 decoupled controller is a unit level controller directly manipulating devices that control the supply and/or demand of a power bus, and the second 2×2 decoupled controller controls real and reactive power of the grid to specified setpoints by adjusting current magnitude and power angle setpoints of one or more unit controllers using real time feedback. In this case, the supervisory controller has specified real and reactive power setpoints. 
         [0014]    In one aspect, the invention provides a method for decoupling control of real and reactive power of a local electrical power system having multiple distributed energy resources at non-co-located points. The multiple distributed energy resources may include a combination of energy generation devices, controllable energy loads, and energy storage devices. The method includes feeding back time-synchronized measurements of voltage phasors and current phasors from multiple phasor measurement units to multivariable linear decoupling controllers; and controlling the distributed energy resources by the multivariable linear decoupling controllers, wherein the controlling comprises sending to the distributed energy resources real and reactive power setpoint pairs derived from the time-synchronized measurements of voltage phasors and current phasors using linear control. 
         [0015]    The feeding back may include feeding back phasor measurements from multiple level 1 controllers to a level 2 controller, such that the multivariable linear decoupling controllers form a hierarchical feedback control system; converting measured real and reactive power values to current and power angle phasors; and/or converting measured real and reactive power values to voltages and voltage angle differences between points of interest and the distributed energy resources. 
         [0016]    Controlling the distributed energy resources by the multivariable linear decoupling controllers may include: using a proportional-integral controller combined with a derivative filter to mitigate power grid disturbances, and an output filter to adjust output setpoint pairs according to a response characteristics of the distributed energy resources; using an internal predictive model to account for system dynamics and transport delay in obtaining phasor feedback; using a feed forward filter for providing a faster phasor control in response to immediate set point changes; and/or computing the real and reactive power setpoint pairs to achieve a predetermined power control at a Point Of Interest. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]      FIG. 1  is a schematic block diagram of a traditional power controlled single Distributed Energy Resource (DER), accepting a real/reactive power reference input for the controlled DER and producing a real/reactive power output at the DER, monitored and controlled using a power controller that produces real/reactive power input at the DER and uses feedback of the produced real/reactive power output at the DER. 
           [0018]      FIG. 2  is a schematic block diagram of a phasor controlled single Distributed Energy Resource (DER), accepting a real/reactive power reference input for the controlled DER and producing a real/reactive power output at the DER, monitored and controlled by a phasor controller that produces real/reactive power input at the DER and uses feedback of the produced real/reactive power output at the DER, according to an embodiment of the present invention. 
           [0019]      FIG. 3  is a schematic block diagram of a Level 1 phasor controlled single Distributed Energy Resource (DER), accepting a real/reactive power reference input for the controlled DER and producing a real/reactive power output at the DER, monitored and controlled by a Level 1 phasor controller that produces real/reactive power input at the DER and uses feedback of the produced phasor output at the DER, according to an embodiment of the present invention. 
           [0020]      FIG. 4  is a schematic block diagram of a Level 2 phasor controlled multiple Distributed Energy Resource (DER), accepting a real/reactive power reference input at a Point Of Interest (POI) and producing a real/reactive power output at the POI, monitored and controlled by a Level 2 phasor controller that distributes and schedules real/reactive power input at the multiple DER and uses feedback of the produced phasor output at the POI, according to an embodiment of the present invention. 
           [0021]      FIG. 5  is a schematic block diagram of a voltage phasor control multiple Distributed Energy Resource (DER), accepting a voltage phasor reference input at a Point Of Interest (POI) and producing a voltage phasor output at the POI, monitored and controlled by a voltage phasor controller that distributes and schedules voltage amplitude input and voltage phase angles at the multiple DER and uses feedback of the produced phasor output at the POI, according to an embodiment of the present invention. 
           [0022]      FIG. 6  is a schematic block diagram of the preferred embodiment of the control algorithms inside the phasor controller used in Level 1 and Level 2 phasor controlled Distributed Energy Resources, according to an embodiment of the present invention. 
           [0023]      FIG. 7  is a schematic block diagram of an alternative embodiment of the control algorithms inside the phasor controller used in Level 1 and Level 2 phasor controlled Distributed Energy Resources, according to an embodiment of the present invention. 
           [0024]      FIG. 8  is a schematic diagram of an area EPS connected to a local EPS having a hierarchical control of DERs, according to an embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
     Nomenclature and Abbreviations 
       [0025]    V—voltage amplitude measured in volt
 
β—unwrapped voltage phase angle, measured in radians
 
v—voltage phasor consisting of (V,β) pair
 
f—power frequency
 
I—current amplitude measured in ampere
 
γ—unwrapped current phase angle measured in radians
 
i—current phasor consisting of (I,γ) pair
 
α—power angle and defined as difference between β and γ
 
I p —current power phasor I p =Ie jα 
 
I c =real part of current power phasor
 
I s —imaginary part of current power phasor
 
       VA—Voltage Ampere 
       [0026]    P—real power, measured in Watt.
 
Q—reactive power, measured in VA
 
S—apparent power (complex number S=P+jQ)
 
Z—complex impedance Z=|Z|e jθ 
 
|Z|—absolute value of complex impedance
 
θ—angle of impedance Z
 
δ—difference between voltage angles β b  at location b and voltage angle β a  at location a in EPS
 
a tan 2( )—four quadrant inverse tangent
 
Area EPS—the main power grid that connects many local EPS
 
Local EPS—a local power grid such as a Micro grid
 
Macro grid—the main power grid to which the microgrid is attached
 
Micro grid—a collection of loads and resources that act as a single point of control to the macro-grid and can disconnect and re-connect to the macro-grid
 
Area EPS is generally the part the network supplying power to the microgrid. Often this is at a higher voltage (69 kV) compared to the local EPS (12 kV). There is a transformer and a breaker between the two. The breaker a remotely operated switch that separates the local EPS from the area EPS. The breaker separating the two grids is called a Point of Common Coupling if the local EPS is a microgrid. It is important that the local EPS can be continually connected to the area EPS, but our controller provides demand regulation services to the local EPS. A local EPS could be a commercial or industrial building with solar PV and a Battery.
 
       POI—Point Of Interest 
       [0027]    PCC—Point of Common Coupling (which may refer to POI)
 
DER—distributed energy resources, examples include Photovoltaic or Battery Inverter based systems, fuel cells, wind power, CHP such as combined cycle gas turbine or micro generator, fuel cells and batteries.
 
PMU—phasor measurement unit
 
Control—the process of adjusting the input to a system to cause the output to achieve a specified setpoint.
 
Setpoint—the specified value of an output variable in a process
 
Controller—the system that compares the controller setpoint with the output variable and makes adjustments to the process input variables. This can be hardware or software. In this description, the controller is software.
 
CDER—a controlled distributed energy resource
 
MDER—multiple distributed energy resources
 
       MIMO—Multi Input, Multi Output 
     PI—Proportional and Integral 
     FD—Filtered Derivative 
     Relation Between Phasors and Real/Reactive Power 
       [0028]    The electric behavior at any Point Of Interest (POI) in a (single phase) Alternating Current (AC) electric power system (EPS) is characterized by a voltage of the format v(t)=V sin(2πft+β) and a current of the format i(t)=I sin(2πft+γ). The AC voltage magnitude V and voltage angle β, collectively called the voltage phasor v=(V,β) and the AC current magnitude I and current angle γ, collectively called the current phasor i=(I,γ) are related through Ohm&#39;s law. In an EPS, the complex impedance plays an important role in Ohm&#39;s law. In case the complex impedance is a linear (dynamic) system, the complex impedance can be represented by a complex number |Z|e jθ  and denoted simply by the complex number Z with an absolute value of the impedance denoted by |Z| and a phase shift of the impedance denoted by θ. With the notion of a complex impedance Z, Ohm&#39;s law for a linear (dynamic) system states that the voltage phasor v and current phasor i are related via v=Zi. This makes the magnitude V related to the current magnitude I via the equation V=|Z|I, whereas the voltage angle β is related to the current angle γ via β=θ+γ due to the complex calculation v=Zi. The impedance Z in an EPS may refer to, but is not limited to, an electrical source producing electrical power, an electrical line transporting electrical power or an electrical load consuming electrical power. 
         [0029]    As outlined in referenced U.S. Pat. No. 8,498,752, the AC voltage magnitude V, voltage angle β, the AC current magnitude I, current angle γ, and the AC frequency f are available from Phasor Measurement Units deployed in an EPS. The AC voltage magnitude V and voltage angle β are collectively called the voltage phasor v and the voltage phasor v can be represented by the pair v=(V,β) or the complex vector v=e jβ , where j is the complex number with j 2 =−1. Similarly, the AC current magnitude I and current angle γ are collectively called the current phasor i and the current phasor i can be represented by the pair i=(I,γ) or the complex vector i=e jγ . The voltage phasor v and current phasor i can be used to obtain derivative information that may include, but is not limited to, the real power P and reactive power Q that characterize the electrical power flow from, through or into an impedance Z located in the EPS. 
         [0030]    In case the impedance Z=|Z|e jθ  between a location a and a location b in an EPS is known and characterized by its amplitude |Z| and its phase angle θ, the real power P and reactive power Q flow through the known impedance from location a to location b can be computed by 
         [0000]    
       
         
           
             P 
             = 
             
               
                 
                   
                     
                       V 
                       a 
                     
                      
                     
                       V 
                       a 
                     
                   
                   
                     2 
                      
                     
                        
                       Z 
                        
                     
                   
                 
                  
                 
                   cos 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               - 
               
                 
                   
                     
                       V 
                       a 
                     
                      
                     
                       V 
                       b 
                     
                   
                   
                     2 
                      
                     
                        
                       Z 
                        
                     
                   
                 
                  
                 
                   cos 
                    
                   
                     ( 
                     
                       θ 
                       - 
                       δ 
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           and 
         
       
       
         
           
             Q 
             = 
             
               
                 
                   
                     
                       V 
                       a 
                     
                      
                     
                       V 
                       a 
                     
                   
                   
                     2 
                      
                     
                        
                       Z 
                        
                     
                   
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               - 
               
                 
                   
                     
                       V 
                       a 
                     
                      
                     
                       V 
                       b 
                     
                   
                   
                     2 
                      
                     
                        
                       Z 
                        
                     
                   
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     
                       θ 
                       - 
                       δ 
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    where V a  and V b  are the voltage amplitudes respectively at location a and location b and where δ=β b −β a , is the difference between voltage phase angle β b  at location b and voltage phase angle β a , at location a. The above formula indicates that real P and reactive Q power flow between two locations in an EPS can be derived from the equivalent impedance Z between the two locations in the power grid and the voltage phasor measurements=(V a ,β a ) and v b =(V b , β b ) respectively at the two locations a and b in the EPS. 
         [0031]    In case the power flow at a particular POI in the EPS needs to be monitored and controlled, both the voltage the voltage phasor (V,β) and the current phasor (I,γ) can be used to compute the real power P and reactive power Q. Particular POI in the EPS may include, but are not limited to, the location of a Distributed Energy Resource (DER) in the EPS or a Point Of Interest (POI) in the EPS that may include the Point Of Interest (POI) where a local EPS connects to the main EPS. The real power P and reactive power Q flow at a POI can be computed by 
         [0000]    
       
         
           
             P 
             = 
             
               
                 VI 
                 2 
               
                
               
                 cos 
                  
                 
                   ( 
                   α 
                   ) 
                 
               
             
           
         
       
       
         
           and 
         
       
       
         
           
             Q 
             = 
             
               
                 VI 
                 2 
               
                
               
                 sin 
                  
                 
                   ( 
                   α 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where V and I are respectively the voltage amplitude V and the current amplitude I at the POI, and the angle α=β−γ is the difference between voltage phase angle β and the current phase angle γ at the POI. The angle α is also referred to as the power angle α, as it directly related to the (normalized) size and direction of the real and reactive power flow with cos(α) and sin(α) always in the range between −1 and 1. Based on the power angle α we also define the notion of a current power phasor I p =Ie jα  that combines the information on the current amplitude I and power angle α. 
         [0032]      FIG. 1  depicts the conceptual arrangement of a standard power-based approach to control a power source producing real/reactive AC power in an EPS via power feedback. As shown in the arrangement of  FIG. 1 , the power source  1  conceptually accepts a real/reactive input pair denoted by in [P,Q] and will produce an actual real/reactive output pair at the DER denoted by DER [P,Q]. To ensure the produced real/reactive output pair DER [P,Q] matches a desired reference real/reactive output pair denoted by ref DER [P,Q] in  FIG. 1 , a power control  3  implements a control algorithm that compares ref DER [P,Q] and DER [P,Q] and produces the real/reactive power input in [P,Q]. It is clear that the power control algorithm is using feedback information of the produced real/reactive power output (DER power feedback) to monitor and control the produced power at the output of the DER. 
         [0033]    Although direct feedback information of power flow as illustrated in  FIG. 1  is a viable approach to monitor and control the power flow produced by a power source, the above formulae indicate that real/reactive power flow at a POI in a power grid can be derived directly from the time synchronized measurements of the voltage phasor v=(V,β) and the current phasor i=(I,γ), collectively called the phasors. Therefore, the size and direction of real and reactive power flow at any POI in a PES can be controlled by changing the voltage phasor v=(V,β) or the current phasor i=(I,γ) and in particular the power angle α=β−γ and the product VI of the voltage amplitude V and current amplitude I. Although there seems to be no distinction between using phasors [v,i] information or real/reactive power [P,Q] information, there are three clear advantages of using phasors [v,i] for (power) control instead of using the real/reactive power pair [P,Q]. 
         [0034]    The first advantage of using phasor [v,i] for feedback is due to the fact that phasors at different locations in an EPS may be linearly (dynamically) related. The linear relation is guaranteed provided the impedance Z between the phasors is a linear dynamic system. However, even if Z is a linear dynamic impedance, the real/reactive power [P,Q] will always be a non-linear relation due to the product of voltage phasor v and current phasor i. For example, the voltage phasor v out  over a load modelled by the impedance Z L  and produced by a voltage source v in  with a line impedance Z in  is given by v out =Zv in  where 
         [0000]    
       
         
           
             Z 
             = 
             
               
                 Z 
                 L 
               
               
                 
                   Z 
                   L 
                 
                 + 
                 
                   Z 
                   
                     i 
                      
                     
                         
                     
                      
                     n 
                   
                 
               
             
           
         
       
     
         [0035]    If indeed Z is a linear dynamic impedance, the voltage phasor v out  depends linearly on the voltage phasor v in . Hence, using using phasors [v,i] for feedback allows the use of linear control algorithms to control phasor and the resulting power flow in an EPS. 
         [0036]    The second advantage of using phasor [v,i] for feedback is due to the fact that the real/reactive power pair [P,Q] is inherently a trigonometric statically coupled pair and related via the apparent power S=P+jQ and the power angle α mentioned above. This means that increasing the size |S| of the apparent power may be done by either increasing the real power P or the reactive power Q, but to maintain the same ratio between P and Q, any changes in P must be coupled to the changes in Q. This always requires the real/reactive power pair [P,Q] to be treated as a coupled pair during power control. Using phasors [v,i] for feedback and in particular using either the current amplitude/power angle pair [I,α] or the Voltage amplitude/power angle pair [V, a] does not require static coupling between a phasor amplitude and power angle pair. 
         [0037]    The third advantage of using phasor [v,i] for feedback is due to the fact that the phasor pair [v,i] contains more information than the real/reactive power pair [P,Q]. As shown below, power flow information represented by the real/reactive pair [P,Q] does not contain full information about the voltage v=(V,β) and current phasor i=(I,γ): only the phase difference α=β−γ (power angle) between the voltage angle β and the current angle γ and the product VI of the voltage amplitude V and current amplitude I can be reconstructed from the real/reactive pair [P,Q]. However, having access to the phasor pair [v,i] allows power(flow) at a particular POI in an EPS to be computed, whereas the individual voltage phasor v=(V,β) and current phasor i=(I,γ) also contain information about the individual voltage amplitude V, current amplitude I and voltage angle β and current angle γ useful for voltage angle or current angle tracking control systems. 
         [0038]      FIG. 2  depicts the conceptual arrangement of a phasor-based control approach to control a power source  12  inside the power source  2  which is a modified version of power source  1  shown earlier in  FIG. 1 . For notational convenience, the formulae for computing the real/reactive power pair [P,Q] on the basis of phasors pair [v,i] is denoted by the function PQ( ) and indicated by the function blocks  6  and  8  in  FIG. 2 . The function operation [P,Q]=PQ(v,i) indicates that the (single phase) real/reactive power pair [P,Q] is computed from information of the voltage phasor v and current phasor i according to P=VI/2−cos (a) and Q=VI/2·sin(α) in which α=β−γ. The computation of real/reactive power can easily be extended to common three phase AC system where three voltage and current phasors for each phase are available. 
         [0039]    Conversely, given a real and reactive power pair (P,Q) at any POI in the EPS, the power angle α=β−γ and the product VI of the voltage amplitude V and current amplitude I and can be computed via 
         [0000]      α= a  tan 2( Q,P )
 
         [0000]      and 
         [0000]        VI= 2·√{square root over ( P   2   +Q   2 )}
 
         [0000]    where a tan 2( ) denotes the four quadrant inverse tangent, creating a power phase angle α in the interval between −π and π radians. The above formulae indicate that information on the real and reactive power pair [P,Q] is not sufficient to reconstruct the full information on the voltage phasor v=(V,β) and/or the current phasor i=(I,γ). Only the difference α=β−γ between the voltage angle β and the current angle γ and the product |S|=VI of the voltage amplitude V and current amplitude I can be reconstructed. However, additional information on either the voltage phasor v=(V,β) or the current phasor i=(I,γ) suffices to reconstruct the phasor pair [v,i] from real and reactive power pair (P,Q). 
         [0040]    For notational convenience, the inverse operation from the real and reactive power pair [P,Q] back to any information on the phasors will be denoted by the function invPQ( ) and marked as function block  10  and  12  in  FIG. 2 . The information on the phasors computed by the function invPQ( ) may use information on the voltage phasor v=(V,β) or the current phasor i=(I,γ) and may also have different embodiments, altering the signals used in the internal phasor control  16  in  FIG. 2 . 
         [0041]    In one embodiment called polar phasor current control, the function operation [I, α]=invPQ(P,Q) may refer to the computation of the polar coordinates (I, α) representing the power angle α=β−γ and the current amplitude I of the complex power current I p =Ie jα  computed from information of the real power P and reactive power Q according to α=a tan 2(Q,P) and I=2/V·√{square root over (P 2 +Q 2 )}. 
         [0042]    In another embodiment function called rectangular current phasor control the operation [I c ,I s ]=invPQ(P,Q) may refer to the computation of the rectangular coordinates [I c ,I s ] representing the real part I c =I cos (α) and the imaginary part I s =I sin (α) of the complex power current I p =Ie jα  computed from information of the real power P and reactive power Q according to I c =2P/V and I s =2Q/V assuming the voltage V≠0. 
         [0043]    It is worth noting that if the function invPQ( ) simply passes through the real and reactive power [P,Q]=invPQ(P,Q), the phasor control  16  in  FIG. 2  has the result that power control  4  reduces back to the power control  3  of  FIG. 1 . Clearly, the use of phasor control  16  allows for different embodiments that exploit the three clear advantages of using phasors [v,i] for (power) control instead of using the real/reactive power pair [P,Q] as mentioned earlier. For notational convenience we use the same notation of phasors [v,i] as the output of the function invPQ( ) marked as function block  12  in  FIG. 2  to refer to the different embodiments that convert information on real and reactive power pair [P,Q] back to any information on the phasors. 
         [0044]    For comparison we now refer to both  FIG. 1  and  FIG. 2 , where in  FIG. 1  the power source  1  and a power control  3  systems are present, while in  FIG. 2  these are modified to become power source  2  and a power control  4  systems. However, in  FIG. 2  the invPQ ( ) function block  12  is placed at the input of the phasor source  14  and PQ ( ) function block  8  is placed at the output of the phasor source  14 . This concept allows the power source  2  to be represented as a series connection of the invPQ ( ) function block  12 , a phasor source  14  and a PQ ( ) function block  8 . Similarly, with the invPQ ( ) function block  10  in place at the input of the phasor control  16  and PQ ( ) function block  6  in place at the output of the phasor control  16 , internally the power control  4  can now be represented as a series connection of the invPQ ( ) function block  10 , a phasor control  16  and a PQ ( ) function block  6 . 
         [0045]    Although the external arrangement of power control using the novel phasor-based approach in  FIG. 2  appears the same as in  FIG. 1 , the internal phasor-based operation is significantly different. The advantage of separating the invPQ ( ) function block  10 , the phasor control  16  and the PQ ( ) function block  6  from the power control  4  allows the phasor control algorithm in the phasor control  16  to be designed on the basis of phasor source  14 . With the linear dynamic relationship between phasors (v,i) in the presence of a linear impedance Z in the EPS, the phasor control algorithm may be linear and will be much easier to design. Furthermore, due to trigonometric static coupling between P and Q in the real/reactive power pair [P,Q], the separation of the invPQ ( ) function block  10  and the PQ ( ) function block  6 , a decoupling based phasor control system is provided in the form of the phasor control  16 . However, the phasor-based approach in  FIG. 2  is still using real/reactive power [P,Q] as feedback information and an additional step is taken to also replace the feedback information on the real/reactive power [P,Q] with feedback information on the actual phasor [v,i] to provide a true decoupling synchrophasor based control system. 
       Level 1 Control of a Controlled Distributed Energy Resource 
       [0046]      FIG. 3  depicts the conceptual arrangement of a decoupling synchrophasor based control system called the Level 1 Controlled Distributed Energy Resource or Level 1 CDER for short. The Level 1 indication is used to distinguish the hierarchical controller structure defined over several levels to define a decoupling synchrophasor based control system for multiple distributed energy resources. The control algorithm in  FIG. 3  uses real-time feedback measurements of the phasors (V,β) and (I,γ) to control real/reactive power pair (P,Q) at a POI in an EPS. As a result, the PQ( ) function block  8  has now been split from power source  14  used earlier in  FIG. 2  and direct DER phasor feedback information is sent back to the Level 1 Controller  18  in  FIG. 3 . The series connection of the invPQ( ) function block  12  and the phasor source  14  has been labelled Level 0 CDER  34  to distinguish this DER at the lower level 0 from the phasor controlled DER at the higher level 1. The combination of the Level 0 CDER along with the DER phasor information feeding back into the Level 1 Controller  18  and producing real/reactive power input DER [P,Q]  30  for the Level 0 CDER  34  is now indicated as a Level 1 CDER  20  in  FIG. 3 . It should be noted that the Level 1 CDER  20  has the same input/output format as the Level 0 CDER  34 , enabling the hierarchical structure of different controller levels. 
         [0047]    The information and power flow of the Level 1 CDER  20  in  FIG. 3  is as follows. Starting from the left side of  FIG. 3 , the real/reactive power reference signal labelled DER ref [P,Q]  22  feeds into the Level 1 CDER  20  and then into the Level 1 Controller  18 . In the Level 1 Controller  18  first the real/reactive power reference signal DER ref [P,Q]  22  is converted into a phasor reference signal DER ref [v,i]  24  via the invPQ( ) function block  10 . The invPQ( ) function block  10  in  FIG. 3  is the same invPQ( ) function block  2  in  FIG. 2 . The invPQ( ) function block  10  requires information on either the voltage phasor v=(V,β) or the current phasor i=(I,γ) indicated by the (dotted) phasor information signal  26 . 
         [0048]    The phasor reference signal DER ref [v,i]  24  produced by the invPQ( ) function block  10  in  FIG. 3  may have different embodiments, altering the signals used in the internal phasor control  16  in  FIG. 3 . In one embodiment called polar phasor current control, the function operation [I, α]=invPQ(P,Q) may refer to the computation of the polar coordinates (I,α) representing the power angle α=β−γ and the current amplitude I of the complex power current I p =Ie jα  computed from information of the real power P and reactive power Q according to α=a tan 2(Q,P) and I=2/V·√{square root over (P 2 +Q 2 )}. In another embodiment function called rectangular current phasor control the operation [I c ,I s ]=invPQ(P,Q) may refer to the computation of the rectangular coordinates [I c ,I s ] representing the real part I c =I cos (α) and the imaginary part I s =I sin (α) of the complex power current I p =Ie jα  computed from information of the real power P and reactive power Q according to I c =2P/V and I s =2Q/V assuming the voltage V≠0. 
         [0049]    Both the DER ref [v,i]  24  phasor reference signal and the DER [v,i]  28  phasor feedback signal enter the phasor control  16  that will compute a phasor control signal. More details on the inner workings of phasor control  16  is included in the discussion of  FIG. 6  below. 
         [0050]    The phasor control signal computed by the algorithm in phasor control  16  is then converted again to an DER power input signal DER [P,Q]  30  via the PQ( ) function block  6 , defined also earlier in  FIG. 2 . The DER power input signal DER [P,Q]  30  is processed by the invPQ( ) function block  12  and the phasor source  14 , both defined earlier in  FIG. 2 , to produce a phasor output DER [v,i]  28 . The phasor output DER [v,i]  28  is now fed back to the Level 1 controller  18  for continuous monitoring of phasor behavior. Although not essential for the (feedback) operation of the phasor controller DER in  FIG. 3 , the phasor output DER [v,i]  28  can be converted back to real/reactive power signal DER [P,Q]  32  via the same PQ( ) function block  8  defined earlier in  FIG. 2 . The PQ( ) function block  8  given in  FIG. 3  can be used to compare the (tracking) performance of real/reactive power signal DER [P,Q]  32  with respect to the real/reactive power reference signal DER ref [P,Q]  22 . 
         [0051]    The Level 1 CDER in  FIG. 3  combines the benefits of the phasor controlled DER of  FIG. 2  with phasor feedback to obtain more information about the individual voltage phasor signal v=(V,β) and current phasor signal i=(I,γ). Although conceptually, the arrangement of power control of the novel phasor-based approach in  FIG. 3  is the same as in  FIG. 2 , the advantage of splitting the PQ ( ) function block  8  from the phasor source  14  and providing direct phasor (v,i) feedback is that more information is brought into the Level 1 controller  18 . Both voltage angle β and current angle γ are now available instead of the power angle α=β−γ only. Furthermore, the separation allows the dynamics of the control algorithm in the phasor control  16  to be designed on the basis of the dynamics of the phasor source  14 . 
         [0052]    As indicated earlier, with the linearity of the phasors (v,i) in the presence of linear impedances Z in the EPS, such a control algorithm will be much easier to design. In essence the feedback algorithm of the Level 1 CDER  20  in  FIG. 3  internally uses phasor information, while from the outside the benefits of the feedback control in terms of power flow control can be observed from the real/reactive power signal DER [P,Q]  32 . The concept of phasor feedback and the use of linear control algorithms feedback can also be extended to the case of multiple DERs. 
       Control of Multiple Distributed Energy Resources for Phasor Tracking 
       [0053]      FIG. 4  summarizes the concept of the preferred embodiment of a decoupling synchrophasor based control system for a Multiple Distributed Energy Resources (MDER) that uses phasor signals for feedback to track real and reactive power reference signals. In the MDER  102 , parallel placed lower level Controlled Distributed Energy Resources (CDERs) are now controlled by a Level 2 Controller  108 . For reason of clarity and brevity,  FIG. 4 , shows an embodiment where the MDER  102  has only two parallel placed CDERs, given by the same generic function of the Level 1 CDER  20  defined earlier in  FIG. 3  and labeled Level 1 CDER #1  132  and Level 1 CDER #2  134  in  FIG. 4 . However, embodiments of the same concept may include single or multiple instances of the Level 1 CDER  20  defined earlier in  FIG. 3  and may also include single or multiple instances of the Level 0 CDER  34  defined earlier in  FIG. 3 . 
         [0054]    As indicated earlier in  FIG. 3 , the Level 1 CDER  20  has the same input/output format as the Level 0 CDER  34  and the input to both a Level 1 CDER  20  and a Level 0 CDER  34  is a real/reactive input (reference) DER [P,Q]  30  signal and the output of both a Level 1 CDER  20  and a Level 0 CDER  34  is a DER [v,i]  28  phasor signal. This conformance and modularity allows a hierarchical control architecture at different levels, where similar phasor control  16  defined earlier in  FIG. 3  can be used. The hierarchical control architecture at different levels is exploited in the Level 2 CDER  106  given in  FIG. 4 . The main difference between the Level 1 CDER  20  in  FIG. 3  and the Level 2 CDER  106  in  FIG. 4  is the fact that feedback information of a phasor signal POI [v,i]  142  at a Point Of Interest (POI) is used. Although a single POI phasor signal POI [v,i]  142  is used for feedback, multiple DERs in the MDER  102  are controlled to a desired POI [v,i]  142  phasor signal at a POI to achieve the desired real/reactive power flow POI ref [P,Q]  144  at a POI. 
         [0055]    The information and power flow of the Level 2 CDER  106  in  FIG. 4  is as follows. Starting from the left side of  FIG. 4 , the real/reactive POI power reference signal labelled POI ref [P,Q]  104  feeds into the Level 2 CDER  106  and then into the Level 2 Controller  108 . In the Level 2 Controller  108  first the real/reactive POI power reference signal POI ref [P,Q]  104  is separated into individual real/reactive power reference signals  112  and  114  for each Level 1 distributed energy resource by the load flow &amp; DER scheduler functional block  110 . 
         [0056]    An embodiment of the load flow &amp; DER scheduler  110  may include an algorithm that decides which DERs participate in the level 2 control and at what percentage they will contribute. More advanced logic or load flow calculations can also be included in the load flow &amp; DER scheduler functional block  110 . The load flow and DER scheduler functions are current state of the art functions and are not included in this invention. This function is shown to indicate that the power allocation to individual DERs need to be determined algorithmically. So any method is suitable to be included. 
         [0057]    The individual real/reactive power reference signals  112  and  114  for each level 1 DER are converted to individual phasor reference signals DER #1 ref [v,i]  116  and DER #2 ref [v,i]  118  by the separate invPQ( ) function blocks  158  and  160  in  FIG. 4 . The invPQ( ) function blocks  158  and  160  in  FIG. 4  have the same generic functionality as the invPQ( ) function block  10  defined earlier in  FIG. 2  and  FIG. 3 , but requires information on voltage phasor v=(V,β) or the current phasor i=(I,γ) of each DER indicated by the (dotted) phasor information signals  120  and  122 . 
         [0058]    The phasor reference signals DER #1 ref [v,i]  116  and DER #2 ref [v,i]  118  produced by the invPQ( ) function blocks  158  and  160  in  FIG. 4  may have different embodiments, altering the phasor reference signals DER #1 ref [v,i]  116  and DER #2 ref [v,i]  118  feeding into in the phasor control  162  and  164  in  FIG. 4 . In one embodiment called polar phasor current control, the function operation [I,α]=invPQ(P,Q) may refer to the computation of the polar coordinates (I,α) representing the power angle α=β−γ and the current amplitude I of the complex power current I p =Ie jα  computed from information of the real power P and reactive power Q according to α=a tan 2(Q,P) and I=2/V·√{square root over (P 2 +Q 2 )}. In another embodiment function called rectangular current phasor control the operation [I c ,I s ]=invPQ(P,Q) may refer to the computation of the rectangular coordinates [I c ,I s ] representing the real part I c =I cos (α) and the imaginary part I s =I sin (α) of the complex power current I p =Ie jα  computed from information of the real power P and reactive power Q according to I c =2P/V and I s =2Q/V assuming the voltage V≠0. 
         [0059]    To use the individual phasor reference signals DER #1 ref [v,i]  116  and DER #2 ref [v,i]  118  for control in the phasor control  162  and  164 , the DER #1 ref [v,i]  116  and DER #2 ref [v,i]  118  reference signals must be compared to individual phasor measurement signals DER #1 [v,i]  124  and DER #2 [v,i]  126  respectively. Since the separation of the individual phasor reference signals DER #1 ref [v,i]  116  and DER #2 ref [v,i]  118  were generated by the load flow &amp; DER scheduler functional block  110 , the individual phasor measurement signals DER #1 [v,i]  124  and DER #2 [v,i]  126  are generated by the same algorithm as used in the load flow &amp; DER scheduler functional block  110  duplicated in  FIG. 4  as block  100 . 
         [0060]    For that purpose, the POI phasor measurement signal POI [v,i]  142  is first sent through the PQ( ) functional block  146  to convert POI [v,i]  142  into a POI real/reactive power that is then subjected to the load flow &amp; DER scheduler  100 . For the conversion back to the individual phasor measurement signals DER #1 [v,i]  124  and DER #2 [v,i]  126 , the invPQ( ) function blocks  152  and  154  are used and require information on either the voltage phasor v=(V,β) or the current phasor i=(I,γ) of each CDER indicated by the phasor information signals  120  and  122 . The same phasor information signals  120  and  122  were used earlier to create the signals DER #1 ref [v,i]  116  and DER #2 ref [v,i]  118  via the invPQ( ) function blocks  158  and  160 . 
         [0061]    The phasor reference signals DER #1 ref [v,i]  116 , DER #2 ref [v,i]  118  and the phasor feedback signals DER #1 ref [v,i]  124  and DER #2 ref [v,i]  126  enter the two individual phasor control  162  and  164  blocks that will compute a phasor control signal. In some embodiments the functional block of the phasor control  162  and  164  may have the same control algorithms as used in  FIG. 3  for the Level 1 CDER  20 , but may have different numerical values for the control algorithm, depending on the dynamics of the level 1 CDER to be controlled at level 2. For example, the Level 1 CDER #1  132  may refer to the fast dynamics on a battery/inverter system, while the Level 1 CDER #2  134  may refer to the slower dynamics on a gas turbine/generator system. Due to the difference between in dynamics between Level 1 CDER #1  132  and Level 1 CDER #2  134 , the phasor control  162  and  164  for each Level 1 CDER may be similar in terms of algorithm, but different in terms of the numerical value used in the algorithm. More details on the inner workings of phasor control  162  and  164  block is included in the discussion of  FIG. 6  below. 
         [0062]    The phasor control signal computed by the algorithms in the individual phasor control  162  and  164  blocks are then converted to DER power reference input signals DER #1 ref [P,Q]  128  and DER #1 ref [P,Q]  130  via the PQ( ) function blocks  148  and  150 . The PQ( ) function blocks  148  and  150  in  FIG. 4  have the same generic functionality as the PQ( ) function block  6  in  FIG. 2  and  FIG. 3 . The DER power reference input signal DER #1 ref [P,Q]  128  is processed by the Level 1 CDER #1  132  to an individual phasor output signal DER #1 [v,i]  136 . Similarly, the DER power reference input signal DER #2 ref [P,Q]  130  is processed by the Level 1 CDER #2  134  to an individual phasor output signal DER #2 [v,i]  138 . The processing by the Level 1 CDER #1  132  or Level 1 CDER #2  134  has the same generic functionality as the Level 1 CDER  20  defined earlier in  FIG. 3 . 
         [0063]    The aggregated effect of the phasor output signals DER #1 [v,i]  136  and DER #2 [v,i]  138  is combined via the functional block representing the line impedances &amp; grid dynamics  140  and results in a measurable phasor signal at the Point Of Interest POI [v,i]  142  in  FIG. 4 . The line impedances &amp; grid dynamics  140  in  FIG. 4  is a lumped functional block that represents the interconnections and electrical parameters of the EPS that would lead to the Point Of Interest phasor signal POI [v,i]  142  due to changes in the phasor output signals DER #1 [v,i]  136  and DER #2 [v,i]  138  produced by the Level 1 CDER #1  132  and Level 1 CDER #2  134 . The phasor signal POI [v,i]  142  is again fed back to the Level 2 controller  108  for continuous monitoring of phasor behavior and control power flow. Although not essential for the (feedback) operation of the Level 2 controller  108  in  FIG. 4 , the phasor signal POI [v,i]  142  can be converted back to a POI real/reactive power signal POI [P,Q]  144  via the PQ( ) function block  146  given in  FIG. 4 . The PQ( ) function block  144  given in  FIG. 4  can be used to compare the (tracking) performance of real/reactive power signal POI [P,Q]  144  with respect to the real/reactive power reference signal POI ref [P,Q]  104 . 
         [0064]    The voltage and current angles can be measured accurately using PMUs; however, as taught in the U.S. Pat. No. 8,457,912, the wrapping angle measurements of the phasors (V,β), (I,γ) are not smooth and therefore cannot be used for feedback control. This invention uses the smooth and unwrapped angle measurements as taught in U.S. Pat. No. 8,457,912 as well as the time synchronized values of the phasors (V,β), (I,γ) and the real/reactive power pair (P,Q) from a PMU or relay. These measurements, reported at high data rates, providing the means for the controllers to execute at much shorter time intervals compared to existing grid and macro-grid control systems. 
         [0065]    The local EPS includes a number of protective relays, in particular across the circuit breaker separating the area EPS from the local EPS. Most modern relays include PMU calculations and provide these measurements at high data rates (60 Hz) to multiple clients. The controller subscribes to these PMU measurement streams to obtain the measurements needed for control. There are certain time delays in receiving the data; hence the need for the Smith Predictor functionality. In other implementations, where electromechanical relays are used, a new PMU measurement device is installed at the required location in the grid. These PMUs send the measurements to the controller using the same message protocols as used by the relays. 
       Control of Multiple Distributed Energy Resources for Voltage Phasor Tracking 
       [0066]      FIG. 5  summarizes the concept of an alternative embodiment of a decoupling synchrophasor based control system for a Multiple Distributed Energy Resources (MDER) that uses phasor signals for feedback to track a voltage phasor reference signal ref [V,beta]  504 . The voltage phasor typically consist of (V,β) pair, where V is the voltage amplitude and β is the voltage angle. Tracking the voltage amplitude V and voltage angle β phasor reference signal ref [V,beta]  504  at a POI of the EPS and especially the Point of Common Coupling (PCC) of the EPS is important in case the EPS is disconnected from the main grid. Tracking the voltage amplitude V and voltage angle β of the main grid as a phasor reference signal ref [V,beta]  504  allows quick connect and disconnect of the EPS for islanding operations. Similar to  FIG. 4 , parallel placed Controlled Distributed Energy Resources (CDERs) in a single MDER  502  are now controlled by the Voltage Phasor Controller  508 . For reason of clarity and brevity,  FIG. 5  shows an embodiment where the MDER  502  has only two parallel placed CDERs and labeled CDER #1  532  and CDER #2  534  in  FIG. 5 . However, embodiments of the same concept may include single or multiple instances of the CDER Controlled Distributed Energy Resources (CDERs). 
         [0067]    It can be observed that the Voltage Phasor Controller  508  has the same generic functionality as the Level 2 CDER  106  in  FIG. 4 , however all of the PQ ( ) and invPQ( ) function blocks are removed. However, the phasor control  562  and  564  in  FIG. 5  have the same the same generic functionality the phasor control  162  and  164  in  FIG. 4  promoting modularity of the control architecture, where similar phasor control  16  defined earlier in  FIG. 3  can be used. 
         [0068]    The information flow of the Voltage Control  506  in  FIG. 5  is as follows. Starting from the left side of  FIG. 5 , the voltage phasor reference signal labelled ref [V,beta]  504  feeds into the Voltage Control  506  and then into the Voltage Phasor Controller  508 . In the Voltage Phasor Controller  508  the voltage phasor reference signal ref [V,beta]  506  is separated into individual voltage phasor reference signals DER #1 ref [V,beta]  516  and DER #2 ref [V,beta] 518 by the Voltage Phasor Scheduler functional block  510 . 
         [0069]    An embodiment of the Voltage Phasor Scheduler  510  may include an algorithm that decides which DERs participate in the voltage phasor control and at what percentage they will contribute. More advanced logic or load flow calculations can also be included in the Voltage Phasor Scheduler functional block  510 . 
         [0070]    To use the individual voltage phasor reference signals DER #1 ref [V,beta]  516  and DER #2 ref [V,beta]  518  for control in the phasor control  562  and  564 , the DER #1 ref [V,beta]  516  and DER #2 ref [V,beta]  518  reference signals must be compared to individual voltage phasor measurement signals DER #1 [V,beta]  524  and DER #2 [V,beta]  526  respectively. Since the separation of the individual phasor voltage reference signals DER #1 ref [V,beta]  516  and DER #2 ref [V,beta]  518  were generated by the Voltage Phasor Scheduler functional block  510 , the individual voltage phasor measurement signals DER #1 [V,beta]  524  and DER #2 [V,beta]  526  are generated by the same algorithm as used in the Voltage Phasor Scheduler functional block  510  duplicated in  FIG. 5  as block  500  with as input the POI voltage phasor feedback measurement signal POI [v,beta]  542 . 
         [0071]    The phasor reference signals DER #1 ref [V,beta]  516 , DER #2 ref [V,beta]  518  and the phasor feedback signals DER #1 ref [V,beta]  524  and DER #2 ref [V,beta]  526  enter the two individual phasor control  562  and  564  blocks that will compute a phasor control signals DER #1 [V,f]  528  and DER #2 [V,f]  530  where the variable f now refers to the frequency of the Voltage phasor. Conversion to frequency is done to accommodate the input to the voltage sources CDER #1  532  and CDER #2  534  that again produce a voltage phasor DER #1 [V,beta]  536  and voltage phasor DER #2 [V,beta]  538 . CDERs such as inverters typically allow independent specification of Voltage amplitude V and frequency f of the AC voltage signal. In some embodiments the functional block of the phasor control  562  and  564  may have the same control algorithms as used in  FIG. 4  phasor control  162  and  164  but may have different numerical values for the control algorithm, depending on the dynamics of the CDER to be controlled. More details on the inner workings of phasor control  562  and  564  block is included in the discussion of  FIG. 6  below. 
         [0072]    The aggregated effect of the voltage phasor DER #1 [V,beta]  536  produced by the voltage source CDER #1  532  and the voltage phasor DER #2 [V,beta]  538  produced by the voltage source CDER #2  534  is combined via the functional block representing the line impedances &amp; grid dynamics  540  and results in a measurable voltage phasor signal POI [V,beta]  542  at the Point Of Interest in  FIG. 5 . The line impedances &amp; grid dynamics  540  in  FIG. 5  is a lumped functional block that represents the interconnections and electrical parameters of the EPS that would lead to the Point Of Interest phasor signal POI [V,beta]  542  due to changes in the phasor output signals DER #1 [V,beta]  536  and DER #2 [V,beta]  538  produced by the voltage sources CDER #1  532  and CDER #2  534 . The voltage phasor signal POI [V,beta]  542  at the POI is again fed back to the Voltage Controller  508  for continuous monitoring of voltage phasor behavior and track voltage amplitude V and voltage angle β. power flow. 
       Phasor Controller 
       [0073]      FIG. 6  summarizes the concept of the preferred embodiment of the phasor control  264  which implements the functionality of the phasor control  16  in  FIG. 2  and  FIG. 3 , the phasor controls  162  and  164  in  FIG. 4  and the phasor controls  562  and  564  in  FIG. 5 . 
         [0074]    The preferred embodiment of phasor control  264  is a two-input, two-output decoupling synchrophasor based control algorithm that computes a phasor control output signal DER [v,i]  256  from a phasor reference signal ref [v,i]  210  and a phasor feedback signal [v,i]  202 . The phasor control  264  also includes a simulation signal  204  and a prediction  206  signal produced by a predictive model  208  to account for transport delay in obtaining the phasor feedback data [v,i]  202 . An alternative embodiment of the phasor control  264  is given in the phasor control  364  in  FIG. 7  where the predictive model  208  has been eliminated. 
         [0075]    The information and power flow of the phasor control  264  in  FIG. 6  is as follows. Starting from the left side of  FIG. 6 , both the phasor reference signal ref [v,i]  210  and the phasor feedback data [v,i]  202  enter the phasor control  264 . In comparison with  FIG. 3 , the phasor reference signal ref [v,i]  210  may represent the phasor reference signal DER ref [v,i]  24  in  FIG. 3 . In comparison with  FIG. 4 , the phasor reference signal ref [v,i]  210  may represent the phasor reference signal DER #1 ref [v,i]  116  or the phasor reference signal DER #2 ref [v,i]  118  in  FIG. 4 . 
         [0076]    In the phasor control  264  of  FIG. 6 , first the difference between the phasor reference signal ref [v,i]  210  and the phasor feedback data [v,i]  202  is computed by the difference junction  214  leading to the phasor error signal  216 . The simulation signal  204  is added to the error signal  216  by the summing junction  218  leading to the simulation error signal  220 . Subsequently, the difference between the simulation error signal  220  and the prediction signal  206  produced by the difference junction  222  leads to the control input signal  224  that is fed into the diagonal PI controller  226 . At the same time, the prediction signal  206  is fed into the diagonal FD controller  228 . 
         [0077]    The role of the predictive model  208  is clear from the above described signal path. If the predictive model  208  provides an accurate simulation that includes the same transport delay  230  and the same dynamics modelled by the dynamic model  232  as seen in the phasor feedback data [v,i]  202 , then the simulation error signal  220  would be zero and only the prediction signal  206  will appear in the control input signal  224 . Since the prediction signal  206  is equivalent to the simulation signal  204 , but without the transportation delay, the effect of transport delay in the phasor feedback data [v,i]  202  is completely compensated for, as only the prediction signal  206  will appear in the control input signal  224  that is fed into the diagonal PI controller  226 . At the same time, the same prediction signal  206  is fed into the diagonal FD controller  228 . As a result, the predictive model  208  also known as a Smith Predictor is an important ingredient of the decoupling synchrophasor based control algorithm used in the phasor control  264 . 
         [0078]    The diagonal PI controller  226  is a Proportional Integral (PI) controller. One embodiment of the diagonal PI controller  226  is the computation of the PI control output signal  234  as the sum of a proportional gain K p  amplified control input signal  224  and an integral gain K i  amplified time integrated control input signal  224 . Other embodiments may include other linear combinations of a gain amplified control input signal  224  and time integrated control input signal  224  implemented in discrete-time filters. 
         [0079]    The diagonal FD controller  228  is a Filtered Derivative (FD) controller. One embodiment of the diagonal FD controller  228  is the computation of the FD control output signal  236  as a derivative gain K d  amplified filtered prediction signal  206 . In the alternative embodiment of the phasor control  264  in  FIG. 6 , the diagonal FD controller  228  may be a derivative gain K d  amplified filtered phasor feedback signal [v,i]  202  implemented in discrete-time filters. Conventionally, the derivative operates on the error signal. In our case, in contrast, it operates on measured or predicted signal. The derivative contribution is not affected by setpoint changes that cause large output changes. Our controller responds to process disturbances rather than setpoint changes. We also have setpoint feedforward term for handing setpoint changes. 
         [0080]    Worth noting is the fact that both the control input signal  224 , the prediction signal  206  and the phasor feedback signal [v,i]  202  are (at least) two dimensional input signals. As indicated earlier, in one embodiment called polar phasor current control, the phasor feedback signal [v,i]  202  may refer to the to the polar coordinates (I,α) representing the power angle α=β−γ and the current amplitude I of the complex power current I p =Ie jα . In another embodiment called rectangular current phasor control the phasor feedback signal [v,i]  202  may refer to the rectangular coordinates [I c ,I s ] representing the real part I c =I cos (α) and the imaginary part I s =I sin (α) of the complex power current I p =Ie jα . 
         [0081]    Given the fact that the control input signal  224  is at least a two dimensional signal, the diagonal PI controller  226  is a Proportional Integral (PI) controller that operates on each of the two signals included in the two dimensional control input signal  224  independently. The independent operation maintains decoupling between each of the two signals included in the two dimensional control input signal  224 . Similarly, the diagonal FD controller  228  is a Filtered Derivative (FD) controller that operates on each of the two signals included in the two dimensional prediction signal  206  or the phasor feedback signal [v,i]  202  independently. The independent operation maintains decoupling between each of the two signals included in the two dimensional control input signal  224 . 
         [0082]    Further decoupling is accomplished in the phasor control  264  of  FIG. 6  by sending a linear combination of the PI control output signal  234  and the FD control output signal  236  produced by the difference or summing junction  238  as a control signal  240  to a multi-input, multi-output decoupling filter  242 . The preferred embodiment of the decoupling filter  242  includes an output filter that can adjust the output signal according to the characteristics of the DER and is a multivariable dynamic system that aims to decouple the phasor feedback signal [v,i] either at the DER at Level 1 or at the POI at Level 2 control. The decoupling and output filters are combined into one filter for each of the elements in the decoupling matrix. This takes into account the dynamic decoupling and the output filters. The output filter is used to remove signals that the DER would not be able to respond to. For example, a rotating generator would not be able to respond to a 60 Hz varying signal, so this high frequency information is filtered out for this device. On the other hand, an inverter can respond to high frequency commands, and thus its output filter would be a high pass filter. That is, it filters out the low frequency content of the output signal. Thus, fast control signals go to inverters and slow control signals go to generators. This is not commonly done in control systems in industry and provides distinct advantages. An alternative embodiment of the decoupling filter  242  is to configured it as two single input and single output (SISO) controllers. 
         [0083]    The output signal  244  of the decoupling filter  242  is combined by the summing junction  246  with the feedforward control signal  248  of the feedforward filter  250 . The feedforward filter  250  directly takes the phasor reference signal rev [v,i]  210  to generate the feedforward control signal  248 . The feedforward filter  250  in the phasor control  264  allows the control signals to directly respond to any changes in the phasor reference signal rev [v,i]  210  without first having to go through the diagonal PI controller  226  and may allow for a faster phasor control in response to set point changes in the phasor reference signal rev [v,i]  210  signal. The preferred embodiment of the feedforward filter  250  has the same generic functionality as the decoupling filter  242 : a multivariable dynamic system that also aims to decouple the real and reactive output signal [P,Q] either at the DER at Level 1 or at the POI at Level 2 control. An alternative embodiment of the feedforward filter  250  is a fixed matrix gain to maintain or promote statically decoupled phasor feedback signal [v,i] either at the DER at Level 1 or at the POI at Level 2. 
         [0084]    The final stage of the phasor control  264  of the preferred embodiment of  FIG. 6  is to send the summation signal  252  obtained by summing junction  246  to a phasor saturation  254  to limit the phasor control output signal DER [v,i]  256 . The phasor saturation may have different embodiments and can limit the range or rate of change of the power angle α, the maximum current amplitude I, and/or the maximum and minimum rectangular coordinates [I c ,I s ] representing the real part I c =I cos (α) and the imaginary part I s =I sin (α) of the complex power current I p =Ie jα  or any variations of these signals and/or their rate of change. In  FIG. 6  the phasor control output signal DER [v,i]  256  is in turn used to produce the simulation  204  and prediction  206  signals to compensate for actual transport delay  230  using a dynamic model  232  that models the dynamics in the phasor feedback signal [v,i]  202 . 
         [0085]      FIG. 7  summarizes the concept of the alternative embodiment of the phasor control  364  which implements the functionality of the phasor control  16  in  FIG. 2  and  FIG. 3  and the phasor controls  162  and  164  in  FIG. 4 . The alternative embodiment of phasor control  364  is also a two-input, two-output decoupling synchrophasor based control algorithm that computes a phasor control output signal DER [v,i]  356  from a phasor reference signal ref [v,i]  310  and a phasor feedback signal [v,i]  302 . In the alternative embodiment of the phasor control  364  is given in  FIG. 7  the predictive model  208  of the preferred embodiment of  FIG. 6  has been eliminated. 
         [0086]    The information and power flow of the phasor control  364  in  FIG. 7  is as follows. Starting from the left side of  FIG. 7 , both the phasor reference signal ref [v,i]  310  and the phasor feedback data [v,i]  302  enter the phasor control  364 . In comparison with  FIG. 3 , the phasor reference signal ref [v,i]  310  may represent the phasor reference signal DER ref [v,i]  24  in  FIG. 3 . In comparison with  FIG. 4 , the phasor reference signal ref [v,i]  310  may represent the phasor reference signal DER #1 ref [v,i]  116  or the phasor reference signal DER #2 ref [v,i]  118  in  FIG. 4 . 
         [0087]    In the phasor control  364  of  FIG. 7 , first the difference between the phasor reference signal ref [v,i]  310  and the phasor feedback data [v,i]  302  is computed by the difference junction  314  leading to the phasor error signal  324 . This signal is fed into the diagonal PI controller  326 . 
         [0088]    The diagonal PI controller  326  is a Proportional Integral (PI) controller. One embodiment of the diagonal PI controller  326  is the computation of the PI control output signal  334  as the sum of a proportional gain K p  amplified control input signal  324  and an integral gain K i  amplified time integrated control input signal  324 . Other embodiments may include other linear combinations of a gain amplified control input signal  324  and time integrated control input signal  324  implemented in discrete-time filters. 
         [0089]    The diagonal FD controller  328  is a Filtered Derivative (FD) controller. One embodiment of the diagonal FD controller  328  is the computation of the FD control output signal  336  as a derivative gain K d  amplified high pass filtered prediction signal  306 . In the alternative embodiment of the phasor control  364  in  FIG. 7 , the diagonal FD controller  328  may be a derivative gain K d  amplified high pass filtered phasor feedback signal [v,i]  302  implemented in discrete-time filters. 
         [0090]    Worth noting is the fact that both the control input signal  324 , the prediction signal  306  and the phasor feedback signal [v,i]  302  are (at least) two dimensional input signals. As indicated earlier, in one embodiment called polar phasor current control, the phasor feedback signal [v,i]  302  may refer to the to the polar coordinates (I,α) representing the power angle α=β−γ and the current amplitude I of the complex power current I p =Ie jα . In another embodiment called rectangular current phasor control the phasor feedback signal [v,i]  302  may refer to the rectangular coordinates [I c ,I s ] representing the real part I c =I cos (α) and the imaginary part I s =I sin (α) of the complex power current I p =Ie jα . 
         [0091]    Given the fact that the control input signal  324  is at least a two dimensional signal, the diagonal PI controller  326  is a Proportional Integral (PI) controller that operates on each of the two signals included in the two dimensional control input signal  324  independently. The independent operation maintains decoupling between each of the two signals included in the two dimensional control input signal  324 . Similarly, the diagonal FD controller  328  is a Filtered Derivative (FD) controller that operates on each of the two signals included in the two dimensional prediction signal  306  or the phasor feedback signal [v,i]  302  independently. The independent operation maintains decoupling between each of the two signals included in the two dimensional control input signal  324 . 
         [0092]    Further decoupling is accomplished in the phasor control  364  of  FIG. 7  by sending the difference (or sum) of the PI control output signal  334  and the FD control output signal  236  produced by the difference or summing junction  338  as a control signal  340  to a multi-input, multi-output decoupling filter  342 . The preferred embodiment of the decoupling filter  342  includes an output filter that can adjust the output signal according to the characteristics of the DER and is a multivariable dynamic system that aims to decouple the real and reactive output signal [P,Q] either at the DER at Level 1 or at the POI at Level 2 control. An alternative embodiment of the decoupling filter  342  is a fixed matrix gain to statically decouple the phasor feedback signal [v,i] either at the DER at Level 1 or at the POI at Level 2. 
         [0093]    The output signal  344  of the decoupling filter  342  is combined by the summing junction  246  with the feedforward control signal  348  of the feedforward filter  350 . The feedforward filter  350  directly takes the phasor reference signal rev [v,i] to generate the feedforward control signal  348 . The feedforward filter  350  in the phasor control  364  allows the control signals to directly react to any changes in the phasor reference signal rev [v,i]  310  without first having to go through the diagonal PI controller  326  and may allow for a faster phasor control in response to set point changes in the phasor feedback signal [v,i]. The preferred embodiment of the feedforward filter  350  is similar to the decoupling filter  342 : a multivariable dynamic system that also aims to decouple the phasor feedback signal [v,i] either at the DER at Level 1 or at the POI at Level 2 control. An alternative embodiment of the feedforward filter  350  is a fixed matrix gain to maintain or promote statically decoupled the phasor feedback signal [v,i] either at the DER at Level 1 or at the POI at Level 2. 
         [0094]    The final stage of the phasor control  364  of the alternative embodiment of  FIG. 7  is to send the summation signal  352  obtained by summing junction  346  to a phasor saturation  354  to limit the phasor control output signal DER [v,i]  356 . The phasor saturation may have different embodiments and can limit the range or rate of change of the power angle α, the maximum current amplitude I, and/or the maximum and minimum rectangular coordinates [I c ,I s ] representing the real part I c =I cos (α) and the imaginary part I s =I sin (α) of the complex power current I p =Ie jα  or any variations of these signals and/or their rate of change. 
         [0095]    The functional blocks described herein can best be implemented in commercial computing platforms such as advanced Programmable Logic Controllers (PLCs) or in industrial grade PCs such as the SEL 3355 that runs multiple tasks, one of which is the controller. The controller processing functionality can be written in any computer language, but one implementation is using C++ running on Windows or Linux operating systems. The output commands from then controller may use standard control protocols such as IEC 61850 Goose or Modbus over Ethernet. In order to maintain high security, fiber optic connections are generally used between the controller platform and the inverter device that is used to control the real and reactive power flow to the local EPS. For example, the PQ( ) and invPQ( ) functions are preferably implemented using the standard trigonometry and square root functions provided in the computer language used to implement the controller. 
         [0096]      FIG. 8  shows the relationship between the area Electric Power System (EPS)  800  and a local EPS  802 . Two local EPS systems  802  and  804  are shown connected to the area EPS  800 . An electrical disconnect switch  806  is shown between the area EPS  800  and the local EPS  802 . This is called the Point of Common Coupling. When this switch is opened, the local EPS  802  must maintain its own supply and demand balance. The energy demand has to match the energy supply. In this figure, two level one controlled distributed energy resources (CDER) DER 1  808  and DER 2  810  are shown being controlled by a Level 2 Power/Voltage controller  812 . This controller supervises the two CDERs  808  and  810  to maintain an energy balance while disconnected and provide control of the total demand of the grid while the local EPS  802  is connected to the area EPS  800 . 
         [0097]    The demand setpoint is determined in two ways: if connected, the demand from the area EPS is determined such that the maximum value to the local EPS  802  is achieved; if disconnected, the supply and demand is determined by the available energy in the CDERs  808  and  810  and the production of power from uncontrolled DERs  814 ,  816 , or loads  818 . 
         [0098]    PMUs are used for control of the CDERs  808  and  810  at high data rates, typically 60 Hz. The setpoints for the CDERs are determined by the level 2 Power/Voltage controller  812 . Note that the level 2 controller  812  sends both real and reactive power commands to the CDERS  808  and  810  as well as frequency and voltage setpoint commands. The real and reactive power commands ensure an energy balance in the local EPS and the frequency and voltage setpoints ensure that the voltage and voltage angle of the local EPS tracks the voltage and voltage angle of the area EPS. This allows the local EPS  802  to disconnect and reconnect to the area EPS  800  on command. This is an important feature of any microgrid controller.