CPF: Change the continuation direction when the operating point moves…

CHANGES.md

@@ -12,6 +12,11 @@ For change history for [MOST][3], see [most/CHANGES.md](most/CHANGES.md).
 Since last release
 ------------------
 
+#### 12/6/17
+  - Fix bug #23 where the continuation power flow could switch
+    directions unexpectedly when the operating point switched from
+    stable to unstable manifold or vice-versa after hitting a limit.
+
 #### 11/29/17
   - Add new option `knitro.maxit` to set maximum number of iterations
     for AC OPF solver using Knitro.

lib/cpf_tangent.m

@@ -1,8 +1,8 @@
 function z = cpf_tangent(V, lam, Ybus, Sbusb, Sbust, pv, pq, ...
-                            zprv, Vprv, lamprv, parameterization)
+                            zprv, Vprv, lamprv, parameterization, direction)
 %CPF_TANGENT  Computes normalized tangent predictor for continuation power flow
 %   Z = CPF_TANGENT(V, LAM, YBUS, SBUSB, SBUST, PV, PQ, ...
-%                                 Z, VPRV, LAMPRV, PARAMETERIZATION)
+%                                 ZPRV, VPRV, LAMPRV, PARAMETERIZATION, DIRECTION)
 %
 %   Computes a normalized tangent predictor for the continuation power flow.
 %
@@ -19,7 +19,9 @@
 %       ZPRV : normalized tangent prediction vector from previous step
 %       VPRV : complex bus voltage vector at previous solution
 %       LAMPRV : scalar lambda value at previous solution
-%       PARAMETERIZATION : Value of cpf.parameterization option.
+%       PARAMETERIZATION : value of cpf.parameterization option.
+%       DIRECTION: continuation direction (+1 for postive lambda
+%                  increase, -1 otherwise)
 %
 %   Outputs:
 %       Z : the normalized tangent prediction vector
@@ -68,6 +70,6 @@
 %% compute normalized tangent predictor
 z = zprv;
 s = zeros(npv+2*npq+1, 1);
-s(end,1) = 1;                       %% increase in the direction of lambda
+s(end,1) = sign(direction);
 z([pv; pq; nb+pq; 2*nb+1]) = J\s;   %% tangent vector
 z = z/norm(z);                      %% normalize tangent predictor

lib/mpver.m

@@ -28,7 +28,7 @@
 v{1} = struct(  'Name',     'MATPOWER', ... 
                 'Version',  '6.1-dev', ...
                 'Release',  '', ...
-                'Date',     '22-Nov-2017' );
+                'Date',     '06-Dec-2017' );
 if nargout > 0
     if nargin > 0
         rv = v{1};

lib/runcpf.m

@@ -376,7 +376,9 @@
 
     %% initialize tangent predictor: z = [dx;dlam]
     z = [zeros(2*nb, 1); 1];
-    z = cpf_tangent(V, lam, Ybus, Sbusb, Sbust, pv, pq, z, V, lam, parm);
+    direction = 1;
+    z = cpf_tangent(V, lam, Ybus, Sbusb, Sbust, pv, pq, ...
+                    z, V, lam, parm, direction);
 
     %% initialize state for current continuation step
     cx = struct(...         %% current state
@@ -456,8 +458,9 @@
         else                %% otherwise
             tx = cx;            %% use cx as the previous state
         end
-        nx.z = cpf_tangent(nx.V, nx.lam, Ybus, cb_data.Sbusb, cb_data.Sbust, cb_data.pv, cb_data.pq, ...
-                                    cx.z, tx.V, tx.lam, nx.parm);
+        nx.z = cpf_tangent(nx.V, nx.lam, Ybus, cb_data.Sbusb, cb_data.Sbust, ...
+                            cb_data.pv, cb_data.pq, ...
+                            cx.z, tx.V, tx.lam, nx.parm, direction);
 
         %% detect events
         for k = 1:nef
@@ -507,6 +510,7 @@
             end
         else
             loc_msg = '';
+            direction = 1;
         end
 
         %% invoke callbacks - "iterations" context
@@ -522,6 +526,18 @@
                 done.msg = 'Too many rollback steps triggered by callbacks!';
             end
         else
+            if ~done.flag && evnts(1).zero
+                mpce = cpf_current_mpc(cb_data.mpc_base, cb_data.mpc_target, Ybus, Yf, Yt, cb_data.ref, cb_data.pv, cb_data.pq, nx.V, nx.lam, mpopt);
+                J = makeJac(mpce);
+                opts.tol = 1e-3;
+                opts.it = 2*nb;
+                %% retain original direction for buses with negative V-Q
+                %% sensitivity, otherwise change direction based on tangent
+                %% direction and manifold (eigenvalue)
+                if isempty(find(nx.z(nb+pq) > 0, 1))
+                    direction = sign(nx.z(end)*min(real(eigs(J,1,'SR',opts))));
+                end
+            end
             rb_cnt_cb = 0;              %% reset rollback counter for callbacks
         end