def nr_step(self): """ Single step using Newton-Raphson method. Returns ------- float maximum absolute mismatch """ system = self.system # evaluate discrete, differential, algebraic, and Jacobians system.dae.clear_fg() system.l_update_var(self.models, niter=self.niter, err=self.mis[-1]) system.s_update_var(self.models) system.f_update(self.models) system.g_update(self.models) system.l_update_eq(self.models) system.fg_to_dae() if self.config.method == 'NR': system.j_update(models=self.models) elif self.config.method == 'dishonest': if self.niter < self.config.n_factorize: system.j_update(self.models) # prepare and solve linear equations self.inc = -matrix([matrix(system.dae.f), matrix(system.dae.g)]) self.A = sparse([[system.dae.fx, system.dae.gx], [system.dae.fy, system.dae.gy]]) if not self.config.linsolve: self.inc = self.solver.solve(self.A, self.inc) else: self.inc = self.solver.linsolve(self.A, self.inc) system.dae.x += np.ravel(np.array(self.inc[:system.dae.n])) system.dae.y += np.ravel(np.array(self.inc[system.dae.n:])) # find out variables associated with maximum mismatches fmax = 0 if system.dae.n > 0: fmax_idx = np.argmax(np.abs(system.dae.f)) fmax = system.dae.f[fmax_idx] logger.debug("Max. diff mismatch %.10g on %s", fmax, system.dae.x_name[fmax_idx]) gmax_idx = np.argmax(np.abs(system.dae.g)) gmax = system.dae.g[gmax_idx] logger.debug("Max. algeb mismatch %.10g on %s", gmax, system.dae.y_name[gmax_idx]) mis = max(abs(fmax), abs(gmax)) if self.niter == 0: self.mis[0] = mis else: self.mis.append(mis) system.vars_to_models() return mis
def run(self, **kwargs): """ Full Newton-Raphson method. Returns ------- bool convergence status """ system = self.system self.summary() self.init() if system.dae.m == 0: logger.error("Loaded case contains no power flow element.") system.exit_code = 1 return False t0, _ = elapsed() self.niter = 0 while True: mis = self.nr_step() logger.info(f'{self.niter}: |F(x)| = {mis:<10g}') if mis < self.config.tol: self.converged = True break elif self.niter > self.config.max_iter: break elif np.isnan(mis).any(): logger.error('NaN found in solution. Convergence not likely') self.niter = self.config.max_iter + 1 break elif mis > 1e4 * self.mis[0]: logger.error('Mismatch increased too fast. Convergence not likely.') break self.niter += 1 _, s1 = elapsed(t0) if not self.converged: if abs(self.mis[-1] - self.mis[-2]) < self.config.tol: max_idx = np.argmax(np.abs(system.dae.xy)) name = system.dae.xy_name[max_idx] logger.error('Mismatch is not correctable possibly due to large load-generation imbalance.') logger.error(f'Largest mismatch on equation associated with <{name}>') else: logger.error(f'Power flow failed after {self.niter + 1} iterations for {system.files.case}.') else: logger.info(f'Converged in {self.niter+1} iterations in {s1}.') if self.config.init_tds: system.TDS.init() if self.config.report: system.PFlow.report() system.exit_code = 0 if self.converged else 1 return self.converged
def run(self): """ Full Newton-Raphson method Returns ------- """ system = self.system logger.info('-> Power flow calculation with Newton Raphson method:') self._initialize() if system.dae.m == 0: logger.error("Loaded case file contains no element.") return False t0, _ = elapsed() self.niter = 0 while True: mis = self.nr_step() logger.info(f'{self.niter}: |F(x)| = {mis:<10g}') if mis < self.config.tol: self.converged = True break elif self.niter > self.config.max_iter: break elif mis > 1e4 * self.mis[0]: logger.error( 'Mismatch increased too fast. Convergence not likely.') break self.niter += 1 _, s1 = elapsed(t0) if not self.converged: if abs(self.mis[-1] - self.mis[-2]) < self.config.tol: max_idx = np.argmax(np.abs(system.dae.xy)) name = system.dae.xy_name[max_idx] logger.error( 'Mismatch is not correctable possibly due to large load-generation imbalance.' ) logger.error( f'Largest mismatch on equation associated with <{name}>') else: logger.error( f'Power flow failed after {self.niter + 1} iterations for {system.files.case}.' ) else: logger.info(f'Converged in {self.niter+1} iterations in {s1}.') if self.config.report: system.PFlow.write_report() return self.converged
def check_var(self, dae_t, *args, **kwargs): # Storage: # Output values is in the first col. # Latest values are stored in /appended to the last column self.rewind = False if dae_t == 0: self._v_mem[:] = self.u.v[:, None] elif dae_t < self.t[-1]: self.rewind = True self.t[-1] = dae_t self._v_mem[:, -1] = self.u.v elif dae_t == self.t[-1]: self._v_mem[:, -1] = self.u.v elif dae_t > self.t[-1]: if self.mode == 'step': self.t[:-1] = self.t[1:] self.t[-1] = dae_t self._v_mem[:, :-1] = self._v_mem[:, 1:] self._v_mem[:, -1] = self.u.v else: self.t = np.append(self.t, dae_t) self._v_mem = np.hstack((self._v_mem, self.u.v[:, None])) if dae_t - self.t[0] > self.delay: t_interp = dae_t - self.delay idx = np.argmax(self.t >= t_interp) - 1 v_interp = interp_n2(t_interp, self.t[idx:idx + 2], self._v_mem[:, idx:idx + 2]) self.t[idx] = t_interp self._v_mem[:, idx] = v_interp self.t = np.delete(self.t, np.arange(0, idx)) self._v_mem = np.delete(self._v_mem, np.arange(0, idx), axis=1) self.v[:] = self._v_mem[:, 0]
def _itm_step(self): """ Integrate with Implicit Trapezoidal Method (ITM) to the current time. This function has an internal Newton-Raphson loop for algebraized semi-explicit DAE. The function returns the convergence status when done but does NOT progress simulation time. Returns ------- bool Convergence status in ``self.converged``. """ system = self.system dae = self.system.dae self.mis = 1 self.niter = 0 self.converged = False self.x0 = np.array(dae.x) self.y0 = np.array(dae.y) self.f0 = np.array(dae.f) while True: self._fg_update(models=system.exist.pflow_tds) # lazy Jacobian update if dae.t == 0 or \ self.config.honest or \ self.custom_event or \ not self.last_converged or \ self.niter > 4 or \ (dae.t - self._last_switch_t < 0.1): system.j_update(models=system.exist.pflow_tds) # set flag in `solver.worker.factorize`, not `solver.factorize`. self.solver.worker.factorize = True # `Tf` should remain constant throughout the simulation, even if the corresponding diff. var. # is pegged by the anti-windup limiters. # solve implicit trapezoidal method (ITM) integration self.Ac = sparse([[self.Teye - self.h * 0.5 * dae.fx, dae.gx], [-self.h * 0.5 * dae.fy, dae.gy]], 'd') # equation `self.qg[:dae.n] = 0` is the implicit form of differential equations using ITM self.qg[:dae.n] = dae.Tf * (dae.x - self.x0) - self.h * 0.5 * (dae.f + self.f0) # reset the corresponding q elements for pegged anti-windup limiter for item in system.antiwindups: for key, _, eqval in item.x_set: np.put(self.qg, key, eqval) self.qg[dae.n:] = dae.g if not self.config.linsolve: inc = self.solver.solve(self.Ac, matrix(self.qg)) else: inc = self.solver.linsolve(self.Ac, matrix(self.qg)) # check for np.nan first if np.isnan(inc).any(): self.err_msg = 'NaN found in solution. Convergence is not likely' self.niter = self.config.max_iter + 1 self.busted = True break # reset small values to reduce chattering inc[np.where(np.abs(inc) < self.tol_zero)] = 0 # set new values dae.x -= inc[:dae.n].ravel() dae.y -= inc[dae.n: dae.n + dae.m].ravel() # store `inc` to self for debugging self.inc = inc system.vars_to_models() # calculate correction mis = np.max(np.abs(inc)) # store initial maximum mismatch if self.niter == 0: self.mis = mis self.niter += 1 # converged if mis <= self.config.tol: self.converged = True break # non-convergence cases if self.niter > self.config.max_iter: tqdm.write(f'* Max. iter. {self.config.max_iter} reached for t={dae.t:.6f}, ' f'h={self.h:.6f}, mis={mis:.4g} ') # debug helpers g_max = np.argmax(abs(dae.g)) inc_max = np.argmax(abs(inc)) self._debug_g(g_max) self._debug_ac(inc_max) break if mis > 1e6 and (mis > 1e6 * self.mis): self.err_msg = 'Error increased too quickly. Convergence not likely.' self.busted = True break if not self.converged: dae.x[:] = np.array(self.x0) dae.y[:] = np.array(self.y0) dae.f[:] = np.array(self.f0) system.vars_to_models() self.last_converged = self.converged return self.converged
def run(self, **kwargs): """ Full Newton-Raphson method. Returns ------- bool convergence status """ system = self.system if self.config.check_conn == 1: self.system.connectivity() self.summary() self.init() if system.dae.m == 0: logger.error("Loaded case contains no power flow element.") system.exit_code = 1 return False t0, _ = elapsed() self.niter = 0 while True: mis = self.nr_step() logger.info('%d: |F(x)| = %.10g', self.niter, mis) if mis < self.config.tol: self.converged = True break if self.niter > self.config.max_iter: break if np.isnan(mis).any(): logger.error('NaN found in solution. Convergence not likely') self.niter = self.config.max_iter + 1 break if mis > 1e4 * self.mis[0]: logger.error('Mismatch increased too fast. Convergence not likely.') break self.niter += 1 _, s1 = elapsed(t0) if not self.converged: if abs(self.mis[-1] - self.mis[-2]) < self.config.tol: max_idx = np.argmax(np.abs(system.dae.xy)) name = system.dae.xy_name[max_idx] logger.error('Mismatch is not correctable possibly due to large load-generation imbalance.') logger.error('Largest mismatch on equation associated with <%s>', name) else: logger.error('Power flow failed after %d iterations for "%s".', self.niter + 1, system.files.case) else: logger.info('Converged in %d iterations in %s.', self.niter + 1, s1) # make a copy of power flow solutions self.x_sol = system.dae.x.copy() self.y_sol = system.dae.y.copy() if self.config.init_tds: system.TDS.init() if self.config.report: system.PFlow.report() system.exit_code = 0 if self.converged else 1 return self.converged
def _itm_step(self): """ Integrate with Implicit Trapezoidal Method (ITM) to the current time. This function has an internal Newton-Raphson loop for algebraized semi-explicit DAE. The function returns the convergence status when done but does NOT progress simulation time. Returns ------- bool Convergence status in ``self.converged``. """ system = self.system dae = self.system.dae self.mis = 1 self.niter = 0 self.converged = False self.x0 = np.array(dae.x) self.y0 = np.array(dae.y) self.f0 = np.array(dae.f) while True: self._fg_update(models=system.exist.pflow_tds) # lazy Jacobian update if dae.t == 0 or self.niter > 3 or (dae.t - self._last_switch_t < 0.2): system.j_update(models=system.exist.pflow_tds) self.solver.factorize = True # TODO: set the `Tf` corresponding to the pegged anti-windup limiters to zero. # Although this should not affect anything since corr. mismatches in `self.qg` are reset to zero # solve implicit trapezoidal method (ITM) integration self.Ac = sparse([[self.Teye - self.h * 0.5 * dae.fx, dae.gx], [-self.h * 0.5 * dae.fy, dae.gy]], 'd') # equation `self.qg[:dae.n] = 0` is the implicit form of differential equations using ITM self.qg[:dae.n] = dae.Tf * (dae.x - self.x0) - self.h * 0.5 * (dae.f + self.f0) # reset the corresponding q elements for pegged anti-windup limiter for item in system.antiwindups: for key, val in item.x_set: np.put(self.qg, key, 0) self.qg[dae.n:] = dae.g if not self.config.linsolve: inc = self.solver.solve(self.Ac, -matrix(self.qg)) else: inc = self.solver.linsolve(self.Ac, -matrix(self.qg)) # check for np.nan first if np.isnan(inc).any(): self.err_msg = 'NaN found in solution. Convergence not likely' self.niter = self.config.max_iter + 1 self.busted = True break # reset small values to reduce chattering inc[np.where(np.abs(inc) < self.tol_zero)] = 0 # set new values dae.x += inc[:dae.n].ravel() dae.y += inc[dae.n: dae.n + dae.m].ravel() system.vars_to_models() # calculate correction mis = np.max(np.abs(inc)) if self.niter == 0: self.mis = mis self.niter += 1 # converged if mis <= self.config.tol: self.converged = True break # non-convergence cases if self.niter > self.config.max_iter: logger.debug(f'Max. iter. {self.config.max_iter} reached for t={dae.t:.6f}, ' f'h={self.h:.6f}, mis={mis:.4g} ') # debug helpers g_max = np.argmax(abs(dae.g)) inc_max = np.argmax(abs(inc)) self._debug_g(g_max) self._debug_ac(inc_max) break if mis > 1000 and (mis > 1e8 * self.mis): self.err_msg = 'Error increased too quickly. Convergence not likely.' self.busted = True break if not self.converged: dae.x = np.array(self.x0) dae.y = np.array(self.y0) dae.f = np.array(self.f0) system.vars_to_models() return self.converged