adding LODF and GLODF code

andes/routines/__init__.py

@@ -10,6 +10,7 @@
 all_routines = OrderedDict([('pflow', ['PFlow']),
                             ('tds', ['TDS']),
                             ('eig', ['EIG']),
+                            ('glodf', ['GLODF']),
                             ])
 
 class_names = list_flatten(list(all_routines.values()))

andes/routines/glodf.py

@@ -0,0 +1,242 @@
+"""
+Generalized Line Outage Distribution Factors (GLODF)
+
+The GLODFs are useful for analyzing the impact of the failure of multiple
+transmission lines on the power flow of the entire system. The GLODFs are a set
+of coefficients that quantify the proportional change in power flows on all
+other lines due to a change in power flow on a specific line. They are 
+computed using the power transfer distribution factors (PTDFs), which describe 
+the impact of a change in power flow on a specific generator or load on the 
+power flows of all other generators or loads.
+"""
+
+import andes
+import pandas as pd
+import numpy as np
+
+class GLODF:
+    """
+    Computes the Global Line Outage Distribution Factors (GLODF) for a power system.
+
+    Parameters
+    system : The power system model.
+    """
+    def __init__(self, system):
+        self.system = system
+        self.Bs = self.get_branch_susceptance()
+        self.Ar = self.get_reduced_incidence()
+        self.Bn = self.get_reduced_nodal_susceptance()
+
+    def get_branch_susceptance(self):
+        """
+        Returns the branch susceptance matrix.
+
+        Returns
+        -------
+        numpy.ndarray : Bs
+            The L x L diagonal matrix of branch susceptances.
+        """
+        return np.diag(1/self.system.Line.x.v)
+
+    def get_reduced_incidence(self):
+        """
+        Returns the reduced incidence matrix.
+
+        Returns
+        -------
+        numpy.ndarray : Ar
+            The L x (N-s) reduced incidence matrix where 's' is the number of 
+            slack buses.
+        """
+        num_line = self.system.Line.n
+        num_bus = self.system.Bus.n
+
+        A = np.zeros((num_line, num_bus))
+
+        for l in range(num_line):
+            A[l,self.system.Line.bus1.v[l]-1] = -1
+            A[l,self.system.Line.bus2.v[l]-1] =  1
+
+        # delete all slack rows as required
+        Ar = np.delete(A, np.asarray(self.system.Bus.idx2uid(self.system.Slack.bus.v)), axis=1)
+        return Ar
+
+    def get_reduced_nodal_susceptance(self):
+        """
+        Returns the reduced nodal susceptance matrix.
+
+        Returns
+        -------
+        numpy.ndarray : Bn
+            The (N-s) x (N-s) reduced nodal susceptance matrix where 's' is the
+            number of slack buses.
+        """
+        return -1.0 * np.dot(np.dot(self.Ar.T, self.Bs), self.Ar)
+
+    def get_isf(self):
+        """
+        Returns the injection shift factor (ISF) matrix.
+
+        Returns
+        -------
+        numpy.ndarray : isf
+            The L x (N-s) injection shift factor matrix.
+        """
+        psi = np.dot(np.dot(self.Bs, self.Ar), np.linalg.inv(self.Bn))
+
+        return psi
+
+    def get_ptdf(self, change_lines):
+        """
+        Returns the power transfer distribution factors for the given lines.
+
+        Parameters
+        ----------
+        change_lines : line indeces
+            List of line indices for which the GLODFs are to be computed.
+
+        Returns
+        -------
+        numpy.ndarray : ptdf
+            The L x (lines) matrix.
+        """        
+        change_lines = np.atleast_1d(change_lines)
+        psi = self.get_isf()
+
+        slack = np.array(self.system.Bus.idx2uid(self.system.Slack.bus.v))
+        non_slack = np.delete(np.arange(self.system.Line.n), slack)
+
+        bfrom = self.system.Bus.idx2uid(self.system.Line.get('bus1', change_lines))
+        bto   = self.system.Bus.idx2uid(self.system.Line.get('bus2', change_lines))
+
+        bfrom_idx = np.zeros_like(bfrom)
+        bto_idx   = np.zeros_like(bto)
+
+        for i in range(np.size(change_lines)):
+            if (bfrom[i] in slack):
+                bfrom_idx[i] = -1
+            else:
+                bfrom_idx[i] = np.argwhere(non_slack == bfrom[i])
+
+            if (bto[i] in slack):
+                bto_idx[i] = -1
+            else:
+                bto_idx[i]   = np.argwhere(non_slack == bto[i])
+
+        # zeros row is needed because power injection at slack bus should yield psi = 0
+        zeros_row = np.zeros((psi.shape[0], 1))
+        psi_zero = np.hstack((psi, zeros_row))
+        phi = psi_zero[:,bfrom_idx] - psi_zero[:,bto_idx]
+        return phi
+
+    def lodf(self, change_line):
+        """
+        Returns the line outage distribution factors (LODFs) matrix for single
+        line outage
+
+        Parameters
+        ----------
+        change_line : line index
+            line indix for which the LODFs are to be computed.
+
+        Returns
+        -------
+        numpy.ndarray : glodf
+            The 1 x L injection shift factor matrix, where 'o' is the number of 
+            outages.
+        """
+        phi = self.get_ptdf(change_line)
+
+        uid_lines = self.system.Line.idx2uid(change_line)
+
+        sigma = phi / (1 - phi[uid_lines])
+        sigma[uid_lines] = 0
+
+        return sigma #[np.arange(sigma.size) != change_line - 1]
+
+    def flow_after_lodf(self, change_line):
+        """
+        Returns the line flows after the line outage
+
+        Parameters
+        ----------
+        change_line : line index
+            line indix for which the LODFs are to be computed.
+
+        Returns
+        -------
+        numpy.ndarray : flow_after
+            The length L vector of line flows after the outage
+        """
+        sigma = np.squeeze(self.lodf(change_line))
+
+        uid_lines = self.system.Line.idx2uid(change_line)
+
+        flow_before = self.system.Line.a1.e
+
+        flow_after = flow_before + flow_before[uid_lines] * sigma
+        flow_after[uid_lines] = 0
+
+        return flow_after
+
+    def glodf(self, change_lines):
+        """
+        Returns the generalized line outage distribution factors (GLODFs) 
+        matrix for the line outages in the change_lines list.
+
+        Parameters
+        ----------
+        change_lines : line indices
+            List of line indices for which the GLODFs are to be computed.
+
+        Returns
+        -------
+        numpy.ndarray : glodf
+            The o x L injection shift factor matrix, where 'o' is the number of 
+            outages.
+        """
+        uid_lines = np.atleast_1d(self.system.Line.idx2uid(change_lines))
+
+        phi = self.get_ptdf(change_lines)
+
+        # right side of equation is all lines
+        right_side = phi.T
+
+        # left side is identity - Phi of change lines
+        Phi = right_side[:,uid_lines]
+        left_side = (np.eye(np.shape(Phi)[0]) - Phi)
+
+        xi = np.linalg.solve(left_side, right_side)
+
+        return xi
+
+    def flow_after_glodf(self, change_lines):
+        """
+        Returns the line flows after the line outages given in change_lines
+
+        Parameters
+        ----------
+        change_lines : line indices
+            List of line indices for which the GLODFs are to be computed.
+
+        Returns
+        -------
+        numpy.ndarray : flow_after
+            The length L vector of line flows after the outages
+        """
+        xi = self.glodf(change_lines)
+
+        uid_lines = np.atleast_1d(self.system.Line.idx2uid(change_lines))
+
+        flow_before = self.system.Line.a1.e
+
+
+        #GLODFs times flow before
+        delta_flow = xi.T @ flow_before[uid_lines]
+        flow_after = flow_before + delta_flow
+
+        # ensure lines that are out have no flow
+        flow_after[uid_lines] = 0
+
+        return flow_after
+

tests/test_glodf.py

@@ -0,0 +1,60 @@
+"""
+GLODF Test Code
+
+Test to ensure IEEE 14 bus system has less than 5% error with the following
+line outages:
+    ['Line_1', 'Line_3', 'Line_5', 'Line_7', 'Line_9',]
+"""
+
+from andes.routines.glodf import GLODF
+import andes
+import numpy as np
+import pandas as pd
+
+def test_flow_after_glodf():
+    """
+    Example code to test the GLODF class
+    """
+    print("GLODF Test")
+    # load system
+    ss = andes.load(andes.get_case("ieee14/ieee14_linetrip.xlsx"))
+
+    # solve system
+    ss.PFlow.run()
+
+    # create GLODF object
+    g = GLODF(ss)
+
+    # lines to be taken out
+    change_lines = ['Line_1', 'Line_3', 'Line_5', 'Line_7', 'Line_9',]
+
+    lines_before = np.copy(ss.Line.a1.e)
+    lines_after = g.flow_after_glodf(change_lines)
+
+    np.set_printoptions(precision=5)
+
+    uid_lines = np.atleast_1d(ss.Line.idx2uid(change_lines))
+    # turn off lines and resolve1
+    for i in range(np.size(change_lines)):
+        ss.Line.u.v[uid_lines] = 0
+    ss.PFlow.run()
+
+    lineflows = {"bus1": ss.Line.bus1.v,
+                 "bus2": ss.Line.bus2.v,
+                 "P1 before": lines_before,
+                 "P1 GLODF": lines_after,
+                 "P1 re-solved": ss.Line.a1.e,
+                 "error": np.abs(lines_after - ss.Line.a1.e) }
+
+    df_lineflow = pd.DataFrame(lineflows, index=ss.Line.idx.v)
+
+    print(df_lineflow)
+
+    percent_error = np.mean(np.abs((ss.Line.a1.e - lines_after))) / np.mean(np.abs(ss.Line.a1.e)) * 100
+    print("normalized absolute percent error: {:.3f}%".format(percent_error))
+
+    # Check if lines_after is close to ss.Line.a1.e
+    assert np.allclose(percent_error, 0, atol=5) # error should be less than 5%
+
+if __name__ == "__main__":
+    test_flow_after_glodf()