code: from math import pi, sin, cos
  import numpy as np
  
  from dvoc_model.reference_frames import SinCos, Abc, Dq0, AlphaBeta
  from dvoc_model.constants import *
  from dvoc_model.simulate import simulate, shift_controller_angle_half
  from dvoc_model.elements import Node, RefFrames
  from dvoc_model.calculations import calculate_power
  
  
  class Droop(Node):
      def __init__(self,
                   p_ref: float,
                   q_ref: float,
                   m_p: float = 2.6e-3,
                   m_q: float = 5.0e-3,
                   v_nom: float = 120.,
                   hz_nom: float = 60,
                   varphi: float = pi / 2,
                   omega_c: float = 2 * pi * 30,
                   ref: RefFrames = RefFrames.POLAR,
                   dt: float = 1.0 / 10e3,
                   start_eq: bool = True,
                   ):
  
          # set droop controller parameters
          self.v_nom = v_nom
          self.omega_nom = 2 * pi * hz_nom
          self.omega_c = omega_c
          self.m_p = m_p
          self.m_q = m_q
          self.sin_phi = sin(varphi)
          self.cos_phi = cos(varphi)
  
          self.p_ref = p_ref
          self.q_ref = q_ref
          self.dt = dt
          self.line = None
  
          # set low-pass filter initial values
          p_filt = 0
          q_filt = 0
          self.p = 0
          self.q = 0
  
          # initialize state variables
          if ref is RefFrames.POLAR:
              super().__init__((self.v_nom, 0, p_filt, q_filt), ref)
          else:
              v = AlphaBeta.from_polar(self.v_nom, 0)
              super().__init__((v.alpha, v.beta, p_filt, q_filt), ref)
  
          if start_eq:
              shift_controller_angle_half(self, self.ref, self.omega_nom, self.dt)
  
          if ref is RefFrames.POLAR:
              self.state_names = ["v", "theta", "p,filt", "q,filt"]
          else:
              self.state_names = ["v,alpha", "v,beta", "p,filt", "q,filt"]
  
      def low_pass_dynamics(self, x, y_filt):  # TODO: Search how to derive discretization of low pass
          return self.omega_c * (x - y_filt)
  
      def update_states(self):
          self.v = self.states[0]
          self.theta = self.states[1]
          self.p_filt = self.states[2]
          self.q_filt = self.states[3]
  
      def alpha_beta_dynamics(self, x=None, t=None, u=None):
          # Power Calculation
          v = AlphaBeta.from_polar(self.v, self.theta)
          i = self.line.i
          p_calc = 1.5 * (v.alpha * i.alpha + v.beta * i.beta)
          q_calc = 1.5 * (v.beta * i.alpha - v.alpha * i.beta)
  
          self.p = p_calc
          self.q = q_calc
  
          # Low-Pass Filter
          p_filt_dt = self.low_pass_dynamics(p_calc, self.p_filt)
          q_filt_dt = self.low_pass_dynamics(q_calc, self.q_filt)
  
          p_err = self.p_filt - self.p_ref
          q_err = self.q_filt - self.q_ref
  
          # Droop Control
          dadt = None
          dbdt = None
  
          dvdt = dbdt  # TODO: Implement this?
          omega = dadt  # Todo: Implement this?
          return np.array([dvdt, omega, p_filt_dt, q_filt_dt])
  
      def polar_dynamics(self, x=None, t=None, u=None):
          # Power Calculation
          if x is None:
              x = self.states[:, 0]
          v_ab = AlphaBeta.from_polar(x[0], x[1])
          v = x[0]
          theta = x[1]
          p_filt = x[2]
          q_filt = x[3]
  
          i = self.line.i_alpha_beta()
          p, q = calculate_power(v_ab, i)
  
          # Low-Pass Filter
          p_filt_dt = self.low_pass_dynamics(p, p_filt)
          q_filt_dt = self.low_pass_dynamics(q, q_filt)
  
          p_err = p_filt - self.p_ref
          q_err = q_filt - self.q_ref
  
          # Droop Control
          dvdt = (self.v_nom - self.m_q * q) - v
          omega = self.omega_nom - self.m_p * p_err
          return np.array([dvdt, omega, p_filt_dt, q_filt_dt])
  
  
  if __name__ == "__main__":
      import numpy as np
      from matplotlib import pyplot as plt
  
      v_nom = 120
      omega_c = 2*pi*30  # Changing this value changes how quickly P & Q filt reach the average cycle values
      q_ = 0
  
      # grid parameters
      grid = Dq0(SQRT_2*v_nom, 0, 0)
      grid_omega = TWO_PI * 60
  
      # simulation time parameters
      dt = 1 / 10e3
      t = 1000e-3
      ts = np.arange(0, t, dt)
      steps = len(ts)
  
      # create a step function for dispatch (3A to 6A)
      q_ref = q_ * np.ones(steps)
  
      p_ref = 0 * np.ones(steps)
  
      p_ref[len(ts)//8:] = 250  # Add a step in the Active Power reference
      p_ref[len(ts)//4:] = 500  # Add a step in the Active Power reference
      p_ref[len(ts)//2:] = 750  # Add a step in the Active Power reference
  
      controller = Droop(0., 0.)
      data = simulate(controller, p_ref, q_ref, dt, t, Rf=0.8)#, id0=1.93, iq0=-1.23)
  
      plt.show()
  
apis: numpy.arange numpy.ones matplotlib.pyplot.show numpy.array