Source code for andes.core.discrete

#  [ANDES] (C)2015-2021 Hantao Cui
#  This program is free software; you can redistribute it and/or modify
#  it under the terms of the GNU General Public License as published by
#  the Free Software Foundation; either version 3 of the License, or
#  (at your option) any later version.
#  File name:
#  Last modified: 11/15/20, 3:29 PM

import logging
import numpy as np

from typing import Union, Tuple, List

from andes.core.common import dummify
from import Tab
from andes.utils.func import interp_n2

logger = logging.getLogger(__name__)

[docs]class Discrete: """ Base discrete class. Discrete classes export flag arrays (usually boolean) . """ def __init__(self, name=None, tex_name=None, info=None, no_warn=False, min_iter=2, err_tol=1e-2, ): = name self.tex_name = tex_name = info self.owner = None if not hasattr(self, 'export_flags'): self.export_flags = [] if not hasattr(self, 'export_flags_tex'): self.export_flags_tex = [] self.x_set = list() self.y_set = list() # NOT being used self.warn_flags = [] # warn if flags in `warn_flags` not initialized to zero self.no_warn = no_warn # default minimum iteration number and error tolerance to allow checking # To enable `min_iter` and `err_tol`, a `Discrete` subclass needs to call # `check_iter_err()` manually in `check_var()` and/or `check_eq()`. self.min_iter = min_iter self.err_tol = 1e-2 self.has_check_var = False # if subclass implements `check_var()` self.has_check_eq = False # if subclass implements `check_eq()`
[docs] def check_var(self, *args, **kwargs): """ This function is called in ``l_update_var`` before evaluating equations. It should update internal flags only. """ pass
[docs] def check_eq(self): """ This function is called in ``l_check_eq`` after updating equations. It updates internal flags, set differential equations, and record pegged variables. """ pass
[docs] def get_names(self): """ Available symbols from this class Returns ------- """ return [f'{}_{flag}' for flag in self.export_flags]
[docs] def get_tex_names(self): """ Return tex_names of exported flags. TODO: Fix the bug described in the warning below. Warnings -------- If underscore `_` appears in both flag tex_name and `self.tex_name` (for example, when this discrete is within a block), the exported tex_name will become invalid for SymPy. Variable name substitution will fail. Returns ------- list A list of tex_names for all exported flags. """ return [rf'{flag_tex}^{self.tex_name}' for flag_tex in self.export_flags_tex]
[docs] def get_values(self): return [self.__dict__[flag] for flag in self.export_flags]
@property def class_name(self): return self.__class__.__name__
[docs] def list2array(self, n): for flag in self.export_flags: self.__dict__[flag] = self.__dict__[flag] * np.ones(n, dtype=float)
[docs] def warn_init_limit(self): """ Warn if initialized at limits. """ if self.no_warn: return for f, limit in self.warn_flags: if f not in self.export_flags: logger.error(f'warn_flags contain unknown flag {f}') continue pos = np.argwhere(np.not_equal(self.__dict__[f], 0)).ravel() if not len(pos): continue err_msg = f'{self.owner.class_name}.{} at limits <{self.__dict__[limit].name}>' if isinstance(self.__dict__[limit].v, np.ndarray): lim_value = self.__dict__[limit].v[pos] else: lim_value = self.__dict__[limit].v err_data = {'idx': [self.owner.idx.v[i] for i in pos], 'Flag': [f] * len(pos), 'Input Value': self.u.v[pos], 'Limit': lim_value * np.ones_like(pos), } tab = Tab(title=err_msg, header=err_data.keys(), data=list(map(list, zip(*err_data.values())))) logger.warning(tab.draw())
[docs] def check_iter_err(self, niter=None, err=None): """ Check if the minimum iteration or maximum error is reached so that this discrete block should be enabled. Only when both `niter` and `err` are given, (niter < min_iter) , and (err > err_tol) it will return False. This logic will start checking the discrete states if called from an external solver that does not feed `niter` or `err` at each step. Returns ------- bool True if it should be enabled, False otherwise """ if (niter is not None) and (niter < self.min_iter) and \ (err is not None) and (err > self.err_tol): return False return True
def __repr__(self): return f'{self.__class__.__name__}: {self.owner.__class__.__name__}.{}'
[docs]class LessThan(Discrete): """ Less than (<) comparison function. Exports two flags: z1 and z0. For elements satisfying the less-than condition, the corresponding z1 = 1. z0 is the element-wise negation of z1. Notes ----- The default z0 and z1, if not enabled, can be set through the constructor. """ def __init__(self, u, bound, equal=False, enable=True, name=None, tex_name=None, info=None, cache=False, z0=0, z1=1): super().__init__(name=name, tex_name=tex_name, info=info) self.u = u self.bound = dummify(bound) self.equal: bool = equal self.enable: bool = enable self.cache: bool = cache self._eval: bool = False # if has been eval'ed and cached self.z0 = np.array([z0]) # negation of `self.z1` self.z1 = np.array([z1]) # if the less-than condition (u < bound) is True self.export_flags = ['z0', 'z1'] self.export_flags_tex = ['z_0', 'z_1'] self.has_check_var = True
[docs] def check_var(self, *args, **kwargs): """ If enabled, set flags based on inputs. Use cached values if enabled. """ if not self.enable: return if self.cache and self._eval: return if not self.equal: self.z1[:] = np.less(self.u.v, self.bound.v) else: self.z1[:] = np.less_equal(self.u.v, self.bound.v) self.z0[:] = np.logical_not(self.z1) self._eval = True
[docs]class Limiter(Discrete): """ Base limiter class. This class compares values and sets limit values. Exported flags are `zi`, `zl` and `zu`. Notes ----- If not enabled, the default flags are ``zu = zl = 0``, ``zi = 1``. Parameters ---------- u : BaseVar Input Variable instance lower : BaseParam Parameter instance for the lower limit upper : BaseParam Parameter instance for the upper limit no_lower : bool True to only use the upper limit no_upper : bool True to only use the lower limit sign_lower: 1 or -1 Sign to be multiplied to the lower limit sign_upper: bool Sign to be multiplied to the upper limit equal : bool True to include equal signs in comparison (>= or <=). no_warn : bool Disable initial limit warnings zu : 0 or 1 Default value for `zu` if not enabled zl : 0 or 1 Default value for `zl` if not enabled zi : 0 or 1 Default value for `zi` if not enabled Attributes ---------- zl : array-like Flags of elements violating the lower limit; A array of zeros and/or ones. zi : array-like Flags for within the limits zu : array-like Flags for violating the upper limit """ def __init__(self, u, lower, upper, enable=True, name=None, tex_name=None, info=None, min_iter: int = 2, err_tol: float = 0.01, no_lower=False, no_upper=False, sign_lower=1, sign_upper=1, equal=True, no_warn=False, zu=0.0, zl=0.0, zi=1.0): Discrete.__init__(self, name=name, tex_name=tex_name, info=info, min_iter=min_iter, err_tol=err_tol) self.u = u self.lower = dummify(lower) self.upper = dummify(upper) self.enable = enable self.no_lower = no_lower self.no_upper = no_upper if sign_lower not in (1, -1): raise ValueError("sign_lower must be 1 or -1, got %s" % sign_lower) if sign_upper not in (1, -1): raise ValueError("sign_upper must be 1 or -1, got %s" % sign_upper) self.sign_lower = dummify(sign_lower) self.sign_upper = dummify(sign_upper) self.equal = equal self.no_warn = no_warn self.zu = np.array([zu]) self.zl = np.array([zl]) self.zi = np.array([zi]) self.has_check_var = True self.export_flags.append('zi') self.export_flags_tex.append('z_i') if not self.no_lower: self.export_flags.append('zl') self.export_flags_tex.append('z_l') self.warn_flags.append(('zl', 'lower')) if not self.no_upper: self.export_flags.append('zu') self.export_flags_tex.append('z_u') self.warn_flags.append(('zu', 'upper'))
[docs] def check_var(self, *args, **kwargs): """ Evaluate the flags. """ if not self.enable: return if not self.no_upper: upper_v = -self.upper.v if self.sign_upper.v == -1 else self.upper.v if self.equal: self.zu[:] = np.greater_equal(self.u.v, upper_v) else: self.zu[:] = np.greater(self.u.v, upper_v) if not self.no_lower: lower_v = -self.lower.v if self.sign_lower.v == -1 else self.lower.v if self.equal: self.zl[:] = np.less_equal(self.u.v, lower_v) else: self.zl[:] = np.less(self.u.v, lower_v) self.zi[:] = np.logical_not(np.logical_or(self.zu, self.zl))
[docs]class SortedLimiter(Limiter): """ A limiter that sorts inputs based on the absolute or relative amount of limit violations. Parameters ---------- n_select : int the number of violations to be flagged, for each of over-limit and under-limit cases. If `n_select` == 1, at most one over-limit and one under-limit inputs will be flagged. If `n_select` is zero, heuristics will be used. abs_violation : bool True to use the absolute violation. False if the relative violation abs(violation/limit) is used for sorting. Since most variables are in per unit, absolute violation is recommended. """ def __init__(self, u, lower, upper, n_select: int = 5, name=None, tex_name=None, enable=True, abs_violation=True, min_iter: int = 2, err_tol: float = 0.01, zu=0.0, zl=0.0, zi=1.0, ql=0.0, qu=0.0, ): super().__init__(u, lower, upper, enable=enable, name=name, tex_name=tex_name, min_iter=min_iter, err_tol=err_tol, zu=zu, zl=zl, zi=zi, ) self.n_select = int(n_select) = True if self.n_select == 0 else False self.abs_violation = abs_violation self.ql = np.array([ql]) self.qu = np.array([qu]) # count of ones in `ql` and `qu` self.nql = 0 self.nqu = 0 # smallest and largest `n_select` self.min_sel = 2 self.max_sel = 50 # store the lower and upper limit values with zeros converted to a small number self.lower_denom = None self.upper_denom = None self.export_flags.extend(['ql', 'qu']) self.export_flags_tex.extend(['q_l', 'q_u'])
[docs] def list2array(self, n): """ Initialize maximum and minimum `n_select` based on input size. """ super().list2array(n) if self.min_sel = max(2, int(n / 10)) self.max_sel = max(2, int(n / 2))
[docs] def check_var(self, *args, niter=None, err=None, **kwargs): """ Check for the largest and smallest `n_select` elements. """ if not self.enable: return if not self.check_iter_err(niter=niter, err=err): return super().check_var() # first run - calculate the denominators if using relative violation if not self.abs_violation: if self.lower_denom is None: self.lower_denom = np.array(self.lower.v) self.lower_denom[self.lower_denom == 0] = 1e-6 if self.upper_denom is None: self.upper_denom = np.array(self.upper.v) self.upper_denom[self.upper_denom == 0] = 1e-6 # calculate violations - abs or relative if self.abs_violation: lower_vio = self.u.v - self.lower.v upper_vio = self.upper.v - self.u.v else: lower_vio = np.abs((self.u.v - self.lower.v) / self.lower_denom) upper_vio = np.abs((self.upper.v - self.u.v) / self.upper_denom) # count the number of inputs flagged if self.calc_select() # sort in both ascending and descending orders asc = np.argsort(lower_vio) desc = np.argsort(upper_vio) top_n = asc[:self.n_select] bottom_n = desc[:self.n_select] # `reset_out` is used to flag the reset_out = np.zeros_like(self.u.v) reset_out[top_n] = 1 reset_out[bottom_n] = 1 # set new flags self.zl[:] = np.logical_or(np.logical_and(reset_out, self.zl), self.ql) self.zu[:] = np.logical_or(np.logical_and(reset_out, self.zu), self.qu) self.zi[:] = 1 - np.logical_or(self.zl, self.zu) self.ql[:] = self.zl self.qu[:] = self.zu # compute the number of updated flags ql1 = np.count_nonzero(self.ql) qu1 = np.count_nonzero(self.qu) dqu = qu1 - self.nqu dql = ql1 - self.nql if dqu > 0 or dql > 0: logger.debug("SortedLimiter: flagged %s upper and %s lower limit violations", dqu, dql) self.nqu = qu1 self.nql = ql1
[docs] def calc_select(self): """ Set `n_select` automatically. """ ret = int((np.count_nonzero(self.zl) + np.count_nonzero(self.zu)) / 2) + 1 if ret > self.max_sel: ret = self.max_sel elif ret < self.min_sel: ret = self.min_sel self.n_select = ret
[docs]class HardLimiter(Limiter): """ Hard limiter for algebraic or differential variable. This class is an alias of `Limiter`. """ pass
[docs]class AntiWindup(Limiter): """ Anti-windup limiter. Anti-windup limiter prevents the wind-up effect of a differential variable. The derivative of the differential variable is reset if it continues to increase in the same direction after exceeding the limits. During the derivative return, the limiter will be inactive :: if x > xmax and x dot > 0: x = xmax and x dot = 0 if x < xmin and x dot < 0: x = xmin and x dot = 0 This class takes one more optional parameter for specifying the equation. Parameters ---------- state : State, ExtState A State (or ExtState) whose equation value will be checked and, when condition satisfies, will be reset by the anti-windup-limiter. """ def __init__(self, u, lower, upper, enable=True, no_warn=False, no_lower=False, no_upper=False, sign_lower=1, sign_upper=1, name=None, tex_name=None, info=None, state=None): super().__init__(u, lower, upper, enable=enable, no_warn=no_warn, no_lower=no_lower, no_upper=no_upper, sign_lower=sign_lower, sign_upper=sign_upper, name=name, tex_name=tex_name, info=info) self.state = state if state else u self.has_check_var = False self.has_check_eq = True self.no_warn = no_warn
[docs] def check_var(self, *args, **kwargs): """ This function is empty. Defers `check_var` to `check_eq`. """ pass
[docs] def check_eq(self): """ Check the variables and equations and set the limiter flags. Reset differential equation values based on limiter flags. Notes ----- The current implementation reallocates memory for `self.x_set` in each call. Consider improving for speed. (TODO) """ if not self.no_upper: upper_v = -self.upper.v if self.sign_upper.v == -1 else self.upper.v self.zu[:] = np.logical_and(np.greater_equal(self.u.v, upper_v), np.greater_equal(self.state.e, 0)) if not self.no_lower: lower_v = -self.lower.v if self.sign_lower.v == -1 else self.lower.v self.zl[:] = np.logical_and(np.less_equal(self.u.v, lower_v), np.less_equal(self.state.e, 0)) self.zi[:] = np.logical_not(np.logical_or(self.zu, self.zl)) # must flush the `x_set` list at the beginning self.x_set = list() if not np.all(self.zi): idx = np.where(self.zi == 0) self.state.e[:] = self.state.e * self.zi self.state.v[:] = self.state.v * self.zi if not self.no_upper: self.state.v[:] += upper_v * self.zu if not self.no_lower: self.state.v[:] += lower_v * self.zl self.x_set.append((self.state.a[idx], self.state.v[idx], 0)) # (address, var. values, eqn. values)
# logger.debug(f'AntiWindup for states {self.state.a[idx]}') # Very important note: # `System.fg_to_dae` is called after `System.l_update_eq`, which calls this function. # Equation values set in `self.state.e` is collected by `System._e_to_dae`, while # variable values are collected by the separate loop in `System.fg_to_dae`. # Also, equation values are processed in `TDS` for resetting the `q`.
[docs]class RateLimiter(Discrete): """ Rate limiter for a differential variable. RateLimiter does not export any variable. It directly modifies the differential equation value. Notes ----- RateLimiter inherits from Discrete to avoid internal naming conflicts with `Limiter`. Warnings -------- RateLimiter cannot be applied to a state variable that already undergoes an AntiWindup limiter. Use `AntiWindupRate` for a rate-limited anti-windup limiter. """ def __init__(self, u, lower, upper, enable=True, no_lower=False, no_upper=False, lower_cond=None, upper_cond=None, name=None, tex_name=None, info=None): Discrete.__init__(self, name=name, tex_name=tex_name, info=info) self.u = u self.rate_lower = dummify(lower) self.rate_upper = dummify(upper) # `lower_cond` and `upper_cond` are arrays of 0/1 indicating whether # the corresponding rate limit should be *enabled*. # 0 - disabled, 1 - enabled. # If is `None`, all rate limiters will be enabled. self.rate_lower_cond = dummify(lower_cond) self.rate_upper_cond = dummify(upper_cond) self.rate_no_lower = no_lower self.rate_no_upper = no_upper self.enable = enable self.zur = np.array([0]) self.zlr = np.array([0]) self.has_check_eq = True # Note: save ops by not calculating `zir` # self.zir = np.array([1]) # self.export_flags = ['zir'] # self.export_flags_tex = ['z_{ir}'] if not self.rate_no_lower: self.export_flags.append('zlr') self.export_flags_tex.append('z_{lr}') self.warn_flags.append(('zlr', 'lower')) if not self.rate_no_upper: self.export_flags.append('zur') self.export_flags_tex.append('z_{ur}') self.warn_flags.append(('zur', 'upper'))
[docs] def check_eq(self): if not self.enable: return if not self.rate_no_lower: self.zlr[:] = np.less(self.u.e, self.rate_lower.v) # 1 if at the lower rate limit if self.rate_lower_cond is not None: self.zlr[:] = self.zlr * self.rate_lower_cond.v # 1 if both at the lower rate limit and enabled # for where `zlr == 1`, set the equation value to the lower limit self.u.e[np.where(self.zlr)] = self.rate_lower.v[np.where(self.zlr)] if not self.rate_no_upper: self.zur[:] = np.greater(self.u.e, self.rate_upper.v) if self.rate_upper_cond is not None: self.zur[:] = self.zur * self.rate_upper_cond.v self.u.e[np.where(self.zur)] = self.rate_upper.v[np.where(self.zur)]
[docs]class AntiWindupRate(AntiWindup, RateLimiter): """ Anti-windup limiter with rate limits """ def __init__(self, u, lower, upper, rate_lower, rate_upper, no_lower=False, no_upper=False, rate_no_lower=False, rate_no_upper=False, rate_lower_cond=None, rate_upper_cond=None, enable=True, name=None, tex_name=None, info=None): RateLimiter.__init__(self, u, lower=rate_lower, upper=rate_upper, enable=enable, no_lower=rate_no_lower, no_upper=rate_no_upper, lower_cond=rate_lower_cond, upper_cond=rate_upper_cond, ) AntiWindup.__init__(self, u, lower=lower, upper=upper, enable=enable, no_lower=no_lower, no_upper=no_upper, name=name, tex_name=tex_name, info=info, )
[docs] def check_eq(self): RateLimiter.check_eq(self) AntiWindup.check_eq(self)
[docs]class Selector(Discrete): """ Selection between two variables using the provided reduce function. The reduce function should take the given number of arguments. An example function is `np.maximum.reduce` which can be used to select the maximum. Names are in `s0`, `s1`. Warnings -------- A potential bug when more than two inputs are provided, and values in different inputs are equal. Only two inputs are allowed. Examples -------- Example 1: select the largest value between `v0` and `v1` and put it into vmax. After the definitions of `v0` and `v1`, define the algebraic variable `vmax` for the largest value, and a selector `vs` :: self.vmax = Algeb(v_str='maximum(v0, v1)', tex_name='v_{max}', e_str='vs_s0 * v0 + vs_s1 * v1 - vmax') self.vs = Selector(self.v0, self.v1, fun=np.maximum.reduce) The initial value of `vmax` is calculated by ``maximum(v0, v1)``, which is the element-wise maximum in SymPy and will be generated into ``np.maximum(v0, v1)``. The equation of `vmax` is to select the values based on `vs_s0` and `vs_s1`. Notes ----- A common pitfall is the 0-based indexing in the Selector flags. Note that exported flags start from 0. Namely, `s0` corresponds to the first variable provided for the Selector constructor. See Also -------- numpy.ufunc.reduce : NumPy reduce function andes.core.block.HVGate andes.core.block.LVGate """ def __init__(self, *args, fun, tex_name=None, info=None): super().__init__(tex_name=tex_name, info=info) # TODO: only allow two inputs self.input_vars = args = fun self.n = len(args) self._inputs = None self._outputs = None # TODO: allow custom initial value for i in range(len(self.input_vars)): self.__dict__[f's{i}'] = np.array([0]) self.export_flags = [f's{i}' for i in range(len(self.input_vars))] self.export_flags_tex = [f's_{i}' for i in range(len(self.input_vars))] self.has_check_var = True
[docs] def check_var(self, *args, **kwargs): """ Set the i-th variable's flags to 1 if the return of the reduce function equals the i-th input. """ if self._inputs is None: # input is only evaluated at the first time due to memory stability self._inputs = [self.input_vars[i].v for i in range(self.n)] if self._outputs is None: self._outputs = else: self._outputs[:] = for i in range(self.n): self.__dict__[f's{i}'][:] = np.equal(self._inputs[i], self._outputs)
[docs]class Switcher(Discrete): """ Switcher based on an input parameter. The switch class takes one v-provider, compares the input with each value in the option list, and exports one flag array for each option. The flags are 0-indexed. Exported flags are named with `_s0`, `_s1`, ..., with a total number of `len(options)`. See the examples section. Notes ----- Switches needs to be distinguished from Selector. Switcher is for generating flags indicating option selection based on an input parameter. Selector is for generating flags at run time based on variable values and a selection function. Examples -------- The IEEEST model takes an input for selecting the signal. Options are 1 through 6. One can construct :: self.IC = NumParam(info='input code 1-6') # input code self.SW = Switcher(u=self.IC, options=[0, 1, 2, 3, 4, 5, 6]) If the IC values from the data file ends up being :: self.IC.v = np.array([1, 2, 2, 4, 6]) Then, the exported flag arrays will be :: {'IC_s0': np.array([0, 0, 0, 0, 0]), 'IC_s1': np.array([1, 0, 0, 0, 0]), 'IC_s2': np.array([0, 1, 1, 0, 0]), 'IC_s3': np.array([0, 0, 0, 0, 0]), 'IC_s4': np.array([0, 0, 0, 1, 0]), 'IC_s5': np.array([0, 0, 0, 0, 0]), 'IC_s6': np.array([0, 0, 0, 0, 1]) } where `IC_s0` is used for padding so that following flags align with the options. """ def __init__(self, u, options: Union[list, Tuple], info: str = None, name: str = None, tex_name: str = None, cache=True): super().__init__(name=name, tex_name=tex_name, info=info) self.u = u self.options: Union[List, Tuple] = options self.cache: bool = cache self._eval: bool = False # if the flags has been evaluated for i in range(len(options)): self.__dict__[f's{i}'] = 0 self.export_flags = [f's{i}' for i in range(len(options))] self.export_flags_tex = [f's_{i}' for i in range(len(options))] self.has_check_var = True
[docs] def check_var(self, *args, **kwargs): """ Set the switcher flags based on inputs. Uses cached flags if cache is set to True. """ if self.cache and self._eval: return for v in self.u.v: if v not in self.options and not np.isnan(v): raise ValueError(f'option {v} is invalid for {self.owner.class_name}.{}. ' f'Options are {self.options}.') if len(self.u.v) > 0: for i in range(len(self.options)): self.__dict__[f's{i}'][:] = np.equal(self.u.v, self.options[i]) self._eval = True
[docs] def list2array(self, n): """ This forces to evaluate Switcher upon System setup """ super().list2array(n) self.check_var()
[docs]class DeadBand(Limiter): r""" The basic deadband type. Parameters ---------- u : NumParam The pre-deadband input variable center : NumParam Neutral value of the output lower : NumParam Lower bound upper : NumParam Upper bound enable : bool Enabled if True; Disabled and works as a pass-through if False. Notes ----- Input changes within a deadband will incur no output changes. This component computes and exports three flags. Three flags computed from the current input: - zl: True if the input is below the lower threshold - zi: True if the input is within the deadband - zu: True if is above the lower threshold Initial condition: All three flags are initialized to zero. All flags are updated during `check_var` when enabled. If the deadband component is not enabled, all of them will remain zero. Examples -------- Exported deadband flags need to be used in the algebraic equation corresponding to the post-deadband variable. Assume the pre-deadband input variable is `var_in` and the post-deadband variable is `var_out`. First, define a deadband instance `db` in the model using :: self.db = DeadBand(u=self.var_in, center=self.dbc, lower=self.dbl, upper=self.dbu) To implement a no-memory deadband whose output returns to center when the input is within the band, the equation for `var` can be written as :: var_out.e_str = 'var_in * (1 - db_zi) + \ (dbc * db_zi) - var_out' """ def __init__(self, u, center, lower, upper, enable=True, equal=False, zu=0.0, zl=0.0, zi=0.0, name=None, tex_name=None, info=None): Limiter.__init__(self, u, lower, upper, enable=enable, equal=equal, zi=zi, zl=zl, zu=zu, name=name, tex_name=tex_name, info=info) = dummify(center) # CURRENTLY NOT IN USE
[docs] def check_var(self, *args, **kwargs): """ Notes ----- Updates three flags: zi, zu, zl based on the following rules: zu: 1 if u > upper; 0 otherwise. zl: 1 if u < lower; 0 otherwise. zi: not(zu or zl); """ Limiter.check_var(self, *args, **kwargs)
[docs]class DeadBandRT(DeadBand): r""" Deadband with flags for directions of return. Parameters ---------- u : NumParam The pre-deadband input variable center : NumParam Neutral value of the output lower : NumParam Lower bound upper : NumParam Upper bound enable : bool Enabled if True; Disabled and works as a pass-through if False. Notes ----- Input changes within a deadband will incur no output changes. This component computes and exports five flags. The additional two flags on top of `DeadBand` indicate the direction of return: - zur: True if the input is/has been within the deadband and was returned from the upper threshold - zlr: True if the input is/has been within the deadband and was returned from the lower threshold Initial condition: All five flags are initialized to zero. All flags are updated during `check_var` when enabled. If the deadband component is not enabled, all of them will remain zero. Examples -------- To implement a deadband whose output is pegged at the nearest deadband bounds, the equation for `var` can be provided as :: var_out.e_str = 'var_in * (1 - db_zi) + \ dbl * db_zlr + \ dbu * db_zur - var_out' """ def __init__(self, u, center, lower, upper, enable=True): """ """ DeadBand.__init__(self, u, center=center, lower=lower, upper=upper, enable=enable) # default state if not enabled self.zur = np.array([0.]) self.zlr = np.array([0.]) self.export_flags.extend(['zur', 'zlr']) self.export_flags_tex.extend(['z_ur', 'z_lr']) self.has_check_var = True
[docs] def check_var(self, *args, **kwargs): """ Notes ----- Updates five flags: zi, zu, zl; zur, and zlr based on the following rules: zu: 1 if u > upper; 0 otherwise. zl: 1 if u < lower; 0 otherwise. zi: not(zu or zl); zur: - set to 1 when (previous zu + present zi == 2) - hold when (previous zi == zi) - clear otherwise zlr: - set to 1 when (previous zl + present zi == 2) - hold when (previous zi == zi) - clear otherwise """ DeadBand.check_var(self, *args, **kwargs) if not self.enable: return # square return dead band self.zur[:] = np.equal(self.zu + self.zi, 2) + self.zur * np.equal(self.zi, self.zi) self.zlr[:] = np.equal(self.zl + self.zi, 2) + self.zlr * np.equal(self.zi, self.zi)
[docs]class Delay(Discrete): """ Delay class to memorize past variable values. Delay allows to impose a predefined "delay" (in either steps or seconds) for an input variable. The amount of delay is a scalar and has to be fixed at model definition in the current implementation. """ def __init__(self, u, mode='step', delay=0, name=None, tex_name=None, info=None): Discrete.__init__(self, name=name, tex_name=tex_name, info=info) if mode not in ('step', 'time'): raise ValueError(f'mode {mode} is invalid. Must be in "step" or "time"') self.u = u self.mode = mode self.delay = delay self.export_flags = ['v'] self.export_flags_tex = ['v'] self.has_check_var = True self.t = np.array([0]) self.v = np.array([0]) self._v_mem = np.zeros((0, 1)) self.rewind = False
[docs] def list2array(self, n): """ Allocate memory for storage arrays. """ super().list2array(n) if self.mode == 'step': self._v_mem = np.zeros((n, self.delay + 1)) self.t = np.zeros(self.delay + 1) else: self._v_mem = np.zeros((n, 1))
[docs] 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 __repr__(self): out = '' out += f'v:\n {self.v}\n' out += f't:\n {self.t}\n' out += f'_v_men: \n {self._v_mem}\n' return out
[docs]class Average(Delay): """ Compute the average of a BaseVar over a period of time or a number of samples. """
[docs] def check_var(self, dae_t, *args, **kwargs): Delay.check_var(self, dae_t, *args, **kwargs) if dae_t == 0: self.v[:] = self._v_mem[:, -1] self._v_mem[:, :-1] = 0 return else: nt = len(self.t) self.v[:] = 0.5 * np.sum((self._v_mem[:, 1-nt:] + self._v_mem[:, -nt:-1]) * (self.t[1:] - self.t[:-1]), axis=1) / (self.t[-1] - self.t[0])
[docs]class Derivative(Delay): """ Compute the derivative of an algebraic variable using numerical differentiation. """ def __init__(self, u, name=None, tex_name=None, info=None): Delay.__init__(self, u=u, mode='step', delay=1, name=name, tex_name=tex_name, info=info)
[docs] def check_var(self, dae_t, *args, **kwargs): Delay.check_var(self, dae_t, *args, **kwargs) # Note: # Very small derivatives (< 1e-8) could cause numerical problems (chattering). # Need to reset the output to zero following a rewind. if (dae_t == 0) or (self.rewind is True): self.v[:] = 0 else: self.v[:] = (self._v_mem[:, 1] - self._v_mem[:, 0]) / (self.t[1] - self.t[0]) self.v[np.where(self.v < 1e-8)] = 0
[docs]class Sampling(Discrete): """ Sample an input variable repeatedly at a given time interval. """ def __init__(self, u, interval=1.0, offset=0.0, name=None, tex_name=None, info=None): Discrete.__init__(self, name=name, tex_name=tex_name, info=info) self.u = u self.interval = interval self.offset = offset self.export_flags = ['v'] self.export_flags_tex = ['v'] self.has_check_var = True self.v = np.array([0]) self._last_t = np.array([0]) self._last_v = np.array([0]) self.indices = np.array([0]) self.rewind = False
[docs] def list2array(self, n): super().list2array(n) self._last_v = np.zeros(n)
[docs] def check_var(self, dae_t, *args, **kwargs): """ Check and update the output. Notes ----- Present output stored in `v`. Output of the last step is stored in `_last_v`. Time for the last output is stored in `_last_t`. Initially, store `v` and `_last_v`. If time progresses and `dae_t` is a multiple of `period`, update `_last_v` and then `v`. Record `_last_t`. If time does not progress, update `v`. If time rewinds, restore `_last_v` to `v`. """ self.rewind = False if dae_t == 0: # initial step self._last_v[:] = self.u.v[:] self.v[:] = self.u.v[:] elif dae_t > self._last_t: do_sample = (dae_t - self.offset - self._last_t) > self.interval if do_sample: self._last_v[:] = self.v self.v[:] = self.u.v self._last_t[0] = dae_t elif dae_t == self._last_t: if len(self.indices) > 0: self.v[:] = self.u.v else: # if dae_t < self._last_t self.rewind = True if self._last_t[0] > dae_t: self.v[:] = self._last_v self._last_t[0] = dae_t
[docs]class ShuntAdjust(Discrete): """ Class for adjusting switchable shunts. Parameters ---------- v : BaseVar Voltage measurement lower : BaseParam Lower voltage bound upper : BaseParam Upper voltage bound bsw : SwBlock SwBlock instance for susceptance gsw : SwBlock SwBlock instance for conductance dt : NumParam Delay time u : NumParam Connection status min_iter : int Minimum iteration number to enable shunt switching err_tol : float Minimum iteration tolerance to enable switching """ def __init__(self, *, v, lower, upper, bsw, gsw, dt, u, enable=True, min_iter=2, err_tol=1e-2, name=None, tex_name=None, info=None, no_warn=False): Discrete.__init__(self, name=name, tex_name=tex_name, info=info, no_warn=no_warn) self.v = v self.lower = lower self.upper = upper self.bsw = bsw self.gsw = gsw self.dt = dt self.u = u self.enable = enable self.min_iter = min_iter self.err_tol = err_tol self.has_check_var = True self.t_last = None self.t_enable = None self.direction = None
[docs] def check_var(self, dae_t, *args, niter=None, err=None, **kwargs): """ Check voltage and perform shunt switching. Parameters ---------- niter : int or None Current iteration step """ if not self.enable: return if self.t_last is None: self.t_last = np.zeros_like(self.v.v) self.t_enable = np.ones_like(self.v.v, dtype=int) self.direction = np.zeros_like(self.v.v, dtype=int) if not self.check_iter_err(niter=niter, err=err): return # determine the shunt +/- direction self.direction[:] = 0 self.direction[np.logical_and(self.v.v < self.lower.v, self.bsw.sel < self.bsw.maxsel)] = 1 self.direction[np.logical_and(self.v.v > self.upper.v, self.bsw.sel > 0)] = -1 self.direction *= self.u.v.astype(int) # consider online statuses if not np.any(self.direction): return # allow unlimited switching in power flow if dae_t == 0.0: self.t_enable[:] = 1.0 # consider delay for time-domain simulation else: self.t_enable[:] = (dae_t - self.t_last - self.dt.v) >= 0 self.direction[:] *= self.t_enable if not np.any(self.direction): return logger.debug("--- Shunt Switch at t=%.6g, niter=%d ---", dae_t, niter) logger.debug("Delay enable flags=%s, adjusted levels=%s.", self.t_enable, self.direction) logger.debug("Bus voltage=%s", self.v.v) logger.debug("Before: b=%s, g=%s", self.bsw.v, self.gsw.v) self.bsw.adjust(self.direction) self.gsw.adjust(self.direction) self.t_last[self.direction != 0] = dae_t logger.debug("After: b=%s, g=%s", self.bsw.v, self.gsw.v)