def gas_emissivity_mul2_eqn(b, t):
X1 = (b.side_2.properties_in[t].temperature + b.side_2.properties_out[t].temperature)/2
X2 = b.mbl_mul2
X3 = b.side_2.properties_in[t].pressure
X4 = b.side_2.properties_in[t].mole_frac_comp['CO2']
X5 = b.side_2.properties_in[t].mole_frac_comp['H2O']
X6 = b.side_2.properties_in[t].mole_frac_comp['O2']
return b.gas_emissivity_mul2[t] == \
-0.000116906 * X1 \
+1.02113 * X2 \
+4.81687e-07 * X3 \
+0.922679 * X4 \
-0.0708822 * X5 \
-0.0368321 * X6 \
+0.121843 * log(X1) \
+0.0353343 * log(X2) \
+0.0346181 * log(X3) \
+0.0180859 * log(X5) \
-0.256274 * exp(X2) \
-0.674791 * exp(X4) \
-0.724802 * sin(X2) \
-0.0206726 * cos(X2) \
-9.01012e-05 * cos(X3) \
-3.09283e-05 * X1*X2 \
-5.44339e-10 * X1*X3 \
-0.000196134 * X1*X5 \
+4.54838e-05 * X1*X6 \
+7.57411e-07 * X2*X3 \
+0.0395456 * X2*X4 \
+0.726625 * X2*X5 \
-0.034842 * X2*X6 \
+4.00056e-06 * X3*X5 \
+5.71519e-09 * (X1*X2)**2 \
-1.27853 * (X2*X5)**2
def power_flow_through_branch(Vi,
Vj,
delta,
branch,
bus_type="from_bus",
power_type="Reactive"):
if not (power_type == "Active" or power_type == "Reactive"):
raise ValueError(
'Power type must be "Active" (for p) or "Reactive" (for q)')
if not (bus_type == "from_bus" or bus_type == "to_bus"):
raise ValueError(
'Bus type must be "from_bus" (for f) or "to_bus" (for t)')
g = tx_calc.calculate_conductance(branch)
b = tx_calc.calculate_susceptance(branch)
if power_type == "Active":
if bus_type == "from_bus":
return Vi**2 * g - Vi * Vj * g * pe.cos(
delta) - Vi * Vj * b * pe.sin(delta)
else:
return Vj**2 * g - Vi * Vj * g * pe.cos(
delta) - Vi * Vj * b * pe.sin(delta)
else:
if bus_type == "from_bus":
return -Vi**2 * b + Vi * Vj * b * pe.cos(
delta) - Vi * Vj * g * pe.sin(delta)
else:
return -Vj**2 * b + Vi * Vj * b * pe.cos(
delta) - Vi * Vj * g * pe.sin(delta)
def test_expr_hash_unary_expr(model):
model.cons1 = aml.Constraint(model.I,
rule=lambda m, i: aml.cos(m.x[i]) <= 0.5)
hash_cons1 = expr_hash(model.cons1[2].expr)
ex1 = aml.cos(model.x[2]) <= 0.5
assert hash_cons1 == expr_hash(ex1)
def test_expr_equal(model):
assert not expr_equal(1.2, 2.3)
assert expr_equal(model.x[1], model.x[1])
assert expr_equal(model.x[1] + 1.23, model.x[1] + 1.23)
assert not expr_equal(model.x[1], model.y[1, 0])
assert not expr_equal(model.x[1], 2)
sum1 = sum(model.x[i] for i in model.I)
sum2 = sum(model.x[i] for i in model.I)
sum3 = sum((i + 1) * model.x[i] for i in model.I)
sum4 = sum(i * model.x[i] for i in model.I)
sum5 = sum((i + 1) * model.x[i] for i in model.I)
sum6 = sum(model.y[i, 0] for i in model.I)
assert expr_equal(sum1, sum2)
assert not expr_equal(sum1, sum3)
assert not expr_equal(sum1, sum4)
assert expr_equal(sum3, sum5)
assert not expr_equal(sum1, sum6)
fun1 = aml.cos(sum1)
fun2 = aml.cos(sum2)
fun3 = aml.sin(sum1)
assert expr_equal(fun1, fun2)
assert not expr_equal(fun1, fun3)
assert expr_equal(fun1 * fun3, fun2 * fun3)
assert expr_equal(fun1 / fun3, fun2 / fun3)
def _relax_leaf_to_root_cos(node, values, aux_var_map, degree_map, parent_block, relaxation_side_map, counter):
arg = values[0]
degree = degree_map[arg]
if degree == 0:
res = pe.cos(arg)
degree_map[res] = 0
return res
elif (id(arg), 'cos') in aux_var_map:
_aux_var, relaxation = aux_var_map[id(arg), 'cos']
relaxation_side = relaxation_side_map[node]
if relaxation_side != relaxation.relaxation_side:
relaxation.relaxation_side = RelaxationSide.BOTH
degree_map[_aux_var] = 1
return _aux_var
else:
_aux_var = _get_aux_var(parent_block, pe.cos(arg))
arg = replace_sub_expression_with_aux_var(arg, parent_block)
relaxation_side = relaxation_side_map[node]
degree_map[_aux_var] = 1
relaxation = PWCosRelaxation()
relaxation.set_input(x=arg, aux_var=_aux_var, relaxation_side=relaxation_side)
aux_var_map[id(arg), 'cos'] = (_aux_var, relaxation)
setattr(parent_block.relaxations, 'rel'+str(counter), relaxation)
counter.increment()
return _aux_var
def perimeter_if(b):
if self.config.single_side_only:
return (const.pi - 2 * b.alpha_tube) * b.radius_out + b.pitch \
- 2 * b.radius_out * cos(b.alpha_tube)
else:
return 2 * ((const.pi - 2 * b.alpha_tube) * b.radius_out +
b.pitch - 2 * b.radius_out * cos(b.alpha_tube))
def get_pyomo_model():
m = aml.ConcreteModel()
m.x = aml.Var(initialize=10.0)
m.z = aml.Var(initialize=-10.0)
m.c0 = aml.Constraint(expr=aml.cos(m.x) >= 0)
m.c1 = aml.Constraint(expr=aml.cos(m.z) >= 0)
m.o = aml.Objective(expr=aml.cos(m.x))
return m
def perimeter_ss(b, t):
if self.config.single_side_only:
return (const.pi - 2 * b.alpha_slag[t]) \
* (b.radius_out + b.slag_thickness[t]) + \
b.pitch - 2 * (b.radius_out + b.slag_thickness[t]) \
* cos(b.alpha_slag[t])
else:
return 2 * (
(const.pi - 2 * b.alpha_slag[t]) *
(b.radius_out + b.slag_thickness[t]) + b.pitch - 2 *
(b.radius_out + b.slag_thickness[t]) *
cos(b.alpha_slag[t]))
def test_trig_fuctions(self):
m = ConcreteModel()
m.x = Var()
e = differentiate(sin(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s(cos(m.x)))
e = differentiate(cos(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s(-1.0*sin(m.x)))
e = differentiate(tan(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s(1.+tan(m.x)**2.))
e = differentiate(sinh(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s(cosh(m.x)))
e = differentiate(cosh(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s(sinh(m.x)))
e = differentiate(tanh(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s(1.0-tanh(m.x)**2.0))
e = differentiate(asin(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s((1.0 + (-1.0)*m.x**2.)**-0.5))
e = differentiate(acos(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s(-1.*(1.+ (-1.0)*m.x**2.)**-0.5))
e = differentiate(atan(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s((1.+m.x**2.)**-1.))
e = differentiate(asinh(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s((1.+m.x**2)**-.5))
e = differentiate(acosh(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s((-1.+m.x**2.)**-.5))
e = differentiate(atanh(m.x), wrt=m.x)
self.assertTrue(e.is_expression_type())
self.assertEqual(s(e), s((1.+(-1.0)*m.x**2.)**-1.))
def test_cos(self):
m = pe.Block(concrete=True)
m.x = pe.Var(bounds=(0, math.pi))
m.c = pe.Constraint(expr=pe.inequality(body=pe.cos(m.x), lower=-0.5, upper=0.5))
fbbt(m)
self.assertAlmostEqual(pe.value(m.x.lb), math.acos(0.5))
self.assertAlmostEqual(pe.value(m.x.ub), math.acos(-0.5))
m = pe.Block(concrete=True)
m.x = pe.Var()
m.c = pe.Constraint(expr=pe.inequality(body=pe.cos(m.x), lower=-0.5, upper=0.5))
fbbt(m)
self.assertEqual(m.x.lb, None)
self.assertEqual(m.x.ub, None)
def test_pow(self):
m = aml.ConcreteModel()
m.I = range(10)
m.x = aml.Var(m.I)
m.c0 = aml.Constraint(expr=aml.cos(m.x[0])**2.0 >= 1)
m.c1 = aml.Constraint(expr=2**aml.sin(m.x[1]) >= 1)
dag = problem_from_pyomo_model(m)
c0 = dag.constraint('c0')
root_c0 = c0.root_expr
assert isinstance(root_c0, core.PowExpression)
assert root_c0.num_children == 2
assert isinstance(root_c0.children[0], core.CosExpression)
assert isinstance(root_c0.children[1], core.Constant)
assert root_c0.children[1].value == 2.0
c1 = dag.constraint('c1')
root_c1 = c1.root_expr
assert isinstance(root_c1, core.PowExpression)
assert root_c1.num_children == 2
assert isinstance(root_c1.children[0], core.Constant)
assert isinstance(root_c1.children[1], core.SinExpression)
self._check_depth(root_c0)
self._check_depth(root_c1)
def test_convert(self):
u = units
m = ConcreteModel()
m.dx = Var(units=u.m, initialize=0.10188943773836046)
m.dy = Var(units=u.m, initialize=0.0)
m.vx = Var(units=u.m/u.s, initialize=0.7071067769802851)
m.vy = Var(units=u.m/u.s, initialize=0.7071067769802851)
m.t = Var(units=u.min, bounds=(1e-5,10.0), initialize=0.0024015570927624456)
m.theta = Var(bounds=(0, 0.49*3.14), initialize=0.7853981693583533, units=u.radians)
m.a = Param(initialize=-32.2, units=u.ft/u.s**2)
m.obj = Objective(expr = m.dx, sense=maximize)
m.vx_con = Constraint(expr = m.vx == 1.0*u.m/u.s*cos(m.theta))
m.vy_con = Constraint(expr = m.vy == 1.0*u.m/u.s*sin(m.theta))
m.dx_con = Constraint(expr = m.dx == m.vx*u.convert(m.t, to_units=u.s))
m.dy_con = Constraint(expr = m.dy == m.vy*u.convert(m.t, to_units=u.s)
+ 0.5*(u.convert(m.a, to_units=u.m/u.s**2))*(u.convert(m.t, to_units=u.s))**2)
m.ground = Constraint(expr = m.dy == 0)
with self.assertRaises(UnitsError):
u.convert(m.a, to_units=u.kg)
self.assertAlmostEqual(value(m.obj), 0.10188943773836046, places=5)
self.assertAlmostEqual(value(m.vx_con.body), 0.0, places=5)
self.assertAlmostEqual(value(m.vy_con.body), 0.0, places=5)
self.assertAlmostEqual(value(m.dx_con.body), 0.0, places=5)
self.assertAlmostEqual(value(m.dy_con.body), 0.0, places=5)
self.assertAlmostEqual(value(m.ground.body), 0.0, places=5)
def test_updateSurrogateModel(self):
# Set up necessary data objects and Params
self.interface.replaceExternalFunctionsWithVariables()
self.interface.createConstraints()
# Set starter values on the model
self.interface.model.x[0] = 2.0
self.interface.model.z.set_values({0: 5.0, 1: 2.5, 2: -1.0})
self.interface.data.basis_model_output[:] = 0
self.interface.data.grad_basis_model_output[...] = 0
self.interface.data.truth_model_output[:] = 0
self.interface.data.grad_truth_model_output[...] = 0
self.interface.data.value_of_ef_inputs[...] = 0
self.interface.updateSurrogateModel()
# The basis model here is 0, so all basis values should be 0
for key, val in self.interface.data.basis_model_output.items():
self.assertEqual(value(val), 0)
for key, val in self.interface.data.grad_basis_model_output.items():
self.assertEqual(value(val), 0)
for key, val in self.interface.data.truth_model_output.items():
self.assertEqual(value(val), 0.8414709848078965)
# The truth gradients should equal the output of [cos(2-1), -cos(2-1)]
truth_grads = []
for key, val in self.interface.data.grad_truth_model_output.items():
truth_grads.append(value(val))
self.assertEqual(truth_grads, [cos(1), -cos(1)])
# The inputs should be the values of x[0] and x[1]
for key, val in self.interface.data.value_of_ef_inputs.items():
self.assertEqual(value(self.interface.model.x[key[1]]), value(val))
# Change the model values to something else and try again
self.interface.model.x.set_values({0: 0, 1: 0})
self.interface.updateSurrogateModel()
# The basis values should still all be 0
for key, val in self.interface.data.basis_model_output.items():
self.assertEqual(value(val), 0)
for key, val in self.interface.data.grad_basis_model_output.items():
self.assertEqual(value(val), 0)
# We still have not updated this value, so the value should be 0
for key, val in self.interface.data.truth_model_output.items():
self.assertEqual(value(val), 0)
# The truth gradients should equal the output of [cos(0-0), -cos(0-0)]
truth_grads = []
for key, val in self.interface.data.grad_truth_model_output.items():
truth_grads.append(value(val))
self.assertEqual(truth_grads, [cos(0), -cos(0)])
# The inputs should be the values of x[0] and x[1]
for key, val in self.interface.data.value_of_ef_inputs.items():
self.assertEqual(value(self.interface.model.x[key[1]]), value(val))
def test_cos(self):
m = pyo.ConcreteModel()
m.x = pyo.Var(initialize=2.0)
e = pyo.cos(m.x)
derivs = reverse_ad(e)
symbolic = reverse_sd(e)
self.assertAlmostEqual(derivs[m.x], pyo.value(symbolic[m.x]), tol + 3)
self.assertAlmostEqual(derivs[m.x], approx_deriv(e, m.x), tol)
def create_problem():
m = aml.ConcreteModel()
m.I = range(10)
m.x = aml.Var(m.I, bounds=(-1, 2))
m.obj = aml.Objective(expr=sum(m.x[i] for i in m.I))
m.cons = aml.Constraint(
m.I[1:], rule=lambda m, i: aml.cos(m.x[0]) * aml.sin(m.x[i]) >= 0)
return problem_from_pyomo_model(m)
def test_cos(self):
m = pe.ConcreteModel()
m.x = pe.Var(initialize=2.0)
e = pe.cos(m.x)
derivs = reverse_ad(e)
symbolic = reverse_sd(e)
self.assertAlmostEqual(derivs[m.x], pe.value(symbolic[m.x]), tol+3)
self.assertAlmostEqual(derivs[m.x], approx_deriv(e, m.x), tol)
def _eval(node):
name = _tag_name(node)
cs = list(node)
if name == 'negate':
assert len(cs) == 1
return -_eval(cs[0])
elif name == 'number':
return float(node.attrib['value'])
elif name == 'variable':
c = float(node.attrib.get('coef', 1))
return c * self._v(int(node.attrib['idx']))
elif name == 'power':
assert len(cs) == 2
b = _eval(cs[0])
e = _eval(cs[1])
return b**e
elif name == 'square':
assert len(cs) == 1
return _eval(cs[0])**2
elif name == 'sqrt':
assert len(cs) == 1
return aml.sqrt(_eval(cs[0]))
elif name == 'product':
return reduce(op.mul, [_eval(c) for c in cs])
elif name == 'divide':
assert len(cs) == 2
return _eval(cs[0]) / _eval(cs[1])
elif name == 'times':
assert len(cs) == 2
return _eval(cs[0]) * _eval(cs[1])
elif name == 'plus':
assert len(cs) == 2
return _eval(cs[0]) + _eval(cs[1])
elif name == 'sum':
return sum([_eval(c) for c in cs])
elif name == 'minus':
assert len(cs) == 2
return _eval(cs[0]) - _eval(cs[1])
elif name == 'abs':
assert len(cs) == 1
return abs(_eval(cs[0]))
elif name == 'exp':
assert len(cs) == 1
return aml.exp(_eval(cs[0]))
elif name == 'ln':
assert len(cs) == 1
return aml.log(_eval(cs[0]))
elif name == 'sin':
assert len(cs) == 1
return aml.sin(_eval(cs[0]))
elif name == 'cos':
assert len(cs) == 1
return aml.cos(_eval(cs[0]))
elif name == 'log10':
assert len(cs) == 1
return aml.log10(_eval(cs[0]))
raise RuntimeError('unhandled tag {}'.format(name))
def test_problem(self):
problem = self.get_problem(
lambda m: aml.cos(m.x) * aml.sin(m.y) - m.x / (m.y * m.y + 1))
h = IntervalHessianEvaluator(problem)
h.eval_at_x(np.array([I(-1, 2), I(-1, 1)]))
print(h.jacobian[0])
print(h.hessian[0])
assert False
def test_assert_units_consistent_equivalent(self):
u = units
m = ConcreteModel()
m.dx = Var(units=u.m, initialize=0.10188943773836046)
m.dy = Var(units=u.m, initialize=0.0)
m.vx = Var(units=u.m / u.s, initialize=0.7071067769802851)
m.vy = Var(units=u.m / u.s, initialize=0.7071067769802851)
m.t = Var(units=u.min,
bounds=(1e-5, 10.0),
initialize=0.0024015570927624456)
m.theta = Var(bounds=(0, 0.49 * 3.14),
initialize=0.7853981693583533,
units=u.radians)
m.a = Param(initialize=-32.2, units=u.ft / u.s**2)
m.x_unitless = Var()
m.obj = Objective(expr=m.dx, sense=maximize)
m.vx_con = Constraint(expr=m.vx == 1.0 * u.m / u.s * cos(m.theta))
m.vy_con = Constraint(expr=m.vy == 1.0 * u.m / u.s * sin(m.theta))
m.dx_con = Constraint(expr=m.dx == m.vx * u.convert(m.t, to_units=u.s))
m.dy_con = Constraint(
expr=m.dy == m.vy * u.convert(m.t, to_units=u.s) + 0.5 *
(u.convert(m.a, to_units=u.m / u.s**2)) *
(u.convert(m.t, to_units=u.s))**2)
m.ground = Constraint(expr=m.dy == 0)
m.unitless_con = Constraint(expr=m.x_unitless == 5.0)
assert_units_consistent(m) # check model
assert_units_consistent(m.dx) # check var - this should never fail
assert_units_consistent(
m.x_unitless) # check unitless var - this should never fail
assert_units_consistent(m.vx_con) # check constraint
assert_units_consistent(m.unitless_con) # check unitless constraint
assert_units_equivalent(m.dx, m.dy) # check var
assert_units_equivalent(m.x_unitless,
u.dimensionless) # check unitless var
assert_units_equivalent(m.x_unitless, None) # check unitless var
assert_units_equivalent(m.vx_con.body, u.m / u.s) # check constraint
assert_units_equivalent(m.unitless_con.body,
u.dimensionless) # check unitless constraint
assert_units_equivalent(m.dx, m.dy) # check var
assert_units_equivalent(m.x_unitless,
u.dimensionless) # check unitless var
assert_units_equivalent(m.x_unitless, None) # check unitless var
assert_units_equivalent(m.vx_con.body, u.m / u.s) # check constraint
m.broken = Constraint(expr=m.dy == 42.0 * u.kg)
with self.assertRaises(UnitsError):
assert_units_consistent(m)
assert_units_consistent(m.dx)
assert_units_consistent(m.vx_con)
with self.assertRaises(UnitsError):
assert_units_consistent(m.broken)
self.assertTrue(check_units_equivalent(m.dx, m.dy))
self.assertFalse(check_units_equivalent(m.dx, m.vx))
def _result_with_mono_bounds(self, visitor, g, mono_g, bounds_g):
mono = ComponentMap()
mono[g] = mono_g
bounds = ComponentMap()
bounds[g] = bounds_g
expr = pe.cos(g)
matched, result = visitor.visit_expression(expr, mono, bounds)
assert matched
return result
def create_rsv_acopf_model(model_data,
include_feasibility_slack=False,
pw_cost_model='delta'):
model, md = _create_base_power_ac_model(
model_data,
include_feasibility_slack=include_feasibility_slack,
pw_cost_model=pw_cost_model)
bus_attrs = md.attributes(element_type='bus')
branch_attrs = md.attributes(element_type='branch')
bus_pairs = zip_items(branch_attrs['from_bus'], branch_attrs['to_bus'])
unique_bus_pairs = list(
OrderedDict((val, None) for idx, val in bus_pairs.items()).keys())
# declare the rectangular voltages
neg_v_max = map_items(op.neg, bus_attrs['v_max'])
vr_init = {
k: bus_attrs['vm'][k] * pe.cos(radians(bus_attrs['va'][k]))
for k in bus_attrs['vm']
}
libbus.declare_var_vr(model,
bus_attrs['names'],
initialize=vr_init,
bounds=zip_items(neg_v_max, bus_attrs['v_max']))
vj_init = {
k: bus_attrs['vm'][k] * pe.sin(radians(bus_attrs['va'][k]))
for k in bus_attrs['vm']
}
libbus.declare_var_vj(model,
bus_attrs['names'],
initialize=vj_init,
bounds=zip_items(neg_v_max, bus_attrs['v_max']))
# fix the reference bus
ref_bus = md.data['system']['reference_bus']
ref_angle = md.data['system']['reference_bus_angle']
if ref_angle != 0.0:
libbus.declare_eq_ref_bus_nonzero(model, ref_angle, ref_bus)
else:
model.vj[ref_bus].fix(0.0)
model.vr[ref_bus].setlb(bus_attrs['v_min'][ref_bus])
# relate c, s, and vmsq to vm and va
libbus.declare_eq_vmsq(model=model,
index_set=bus_attrs['names'],
coordinate_type=CoordinateType.RECTANGULAR)
libbranch.declare_eq_c(model=model,
index_set=unique_bus_pairs,
coordinate_type=CoordinateType.RECTANGULAR)
libbranch.declare_eq_s(model=model,
index_set=unique_bus_pairs,
coordinate_type=CoordinateType.RECTANGULAR)
return model, md
def setUpClass(cls):
model = pe.ConcreteModel()
cls.model = model
model.x = pe.Var(bounds=(-2, 1))
model.y = pe.Var(bounds=(-1, 1))
model.w = pe.Var()
model.f_x = pe.cos(model.x)*pe.sin(model.y) - model.x/(model.y**2 + 1)
model.obj = pe.Objective(expr=model.w)
model.abb = AlphaBBRelaxation()
model.abb.build(aux_var=model.w, f_x_expr=model.f_x)
def NLP1(z0=[]):
m = pyo.ConcreteModel()
m.z1 = pyo.Var(initialize=z0[0])
m.z2 = pyo.Var(initialize=z0[1])
m.obj = pyo.Objective(expr=3 * pyo.sin(-2 * np.pi * m.z1) + 2 * m.z1 + 4 +
pyo.cos(2 * np.pi * m.z2) + m.z2)
m.cons1 = pyo.Constraint(expr=(-1, m.z1, 1))
m.cons2 = pyo.Constraint(expr=(-1, m.z2, 1))
res = pyo.SolverFactory('ipopt').solve(m)
return [m.z1(), m.z2(), m.obj()]
def test_negation(self):
m = aml.ConcreteModel()
m.I = range(10)
m.x = aml.Var(m.I)
m.c = aml.Constraint(expr=-aml.cos(m.x[0]) >= 0)
dag = problem_from_pyomo_model(m)
constraint = dag.constraint('c')
root = constraint.root_expr
assert isinstance(root, core.NegationExpression)
self._check_depth(root)
def problem():
m = aml.ConcreteModel(name='test_relaxation')
m.I = range(5)
m.x = aml.Var(m.I, domain=aml.NonNegativeIntegers)
m.obj = aml.Objective(expr=m.x[0])
m.cons0 = aml.Constraint(expr=sum(m.x[i] for i in m.I) >= 0)
m.cons1 = aml.Constraint(
expr=-2.0 * aml.sin(m.x[0]) + aml.cos(m.x[1]) >= 0)
m.cons2 = aml.Constraint(expr=m.x[1] * m.x[2] >= 0)
return dag_from_pyomo_model(m)
def pwl_cosine_rule(model, i, branch_name):
branch = branches[branch_name]
from_bus = branch['from_bus']
to_bus = branch['to_bus']
if i == 0:
return model.cos_hat[branch_name] - (
(pe.cos(upper_bound) - pe.cos(lower_bound)) /
(upper_bound - lower_bound) *
((model.va[from_bus] - model.va[to_bus]) - lower_bound) +
pe.cos(lower_bound)) >= 0
else:
if mode == "uniform":
a = lower_bound + i * increment
return 0 <= (-pe.sin(a) *
(model.va[from_bus] - model.va[to_bus] - a) +
pe.cos(a)) - model.cos_hat[branch_name]
elif mode == "curvature":
a = breakpoints[i]
return 0 <= (-pe.sin(a) *
(model.va[from_bus] - model.va[to_bus] - a) +
pe.cos(a)) - model.cos_hat[branch_name]
else:
raise ValueError('Mode must be "uniform" or "curvature" ')
def declare_expr_c(model, index_set, coordinate_type=CoordinateType.POLAR):
"""
Create expression for the nonlinear, nonconvex term based on cosine
of the phase angle difference (polar) or bilinear voltages (rectangular)
"""
m = model
expr_set = decl.declare_set('_expr_c', model, index_set)
m.c = pe.Expression(expr_set)
if coordinate_type == CoordinateType.RECTANGULAR:
for from_bus, to_bus in expr_set:
m.c[(from_bus,to_bus)] = m.vr[from_bus]*m.vr[to_bus] + m.vj[from_bus]*m.vj[to_bus]
elif coordinate_type == CoordinateType.POLAR:
for from_bus, to_bus in expr_set:
m.c[(from_bus,to_bus)] = m.vm[from_bus]*m.vm[to_bus]*pe.cos(m.va[from_bus]-m.va[to_bus])
def test_unary_expressions(self):
m = ConcreteModel()
m.x = Var()
m.y = Var()
m.z = Var()
m.a = Var()
m.b = Var()
m.c = Var()
m.d = Var()
m.c1 = Constraint(expr=0 <= sin(m.x))
m.c2 = Constraint(expr=0 <= cos(m.y))
m.c3 = Constraint(expr=0 <= tan(m.z))
m.c4 = Constraint(expr=0 <= asin(m.a))
m.c5 = Constraint(expr=0 <= acos(m.b))
m.c6 = Constraint(expr=0 <= atan(m.c))
m.c7 = Constraint(expr=0 <= sqrt(m.d))
m.o = Objective(expr=m.x)
self.assertTrue(satisfiable(m) is not False)
def test_unary_expressions(self):
m = ConcreteModel()
m.x = Var()
m.y = Var()
m.z = Var()
m.a = Var()
m.b = Var()
m.c = Var()
m.d = Var()
m.c1 = Constraint(expr=0 <= sin(m.x))
m.c2 = Constraint(expr=0 <= cos(m.y))
m.c3 = Constraint(expr=0 <= tan(m.z))
m.c4 = Constraint(expr=0 <= asin(m.a))
m.c5 = Constraint(expr=0 <= acos(m.b))
m.c6 = Constraint(expr=0 <= atan(m.c))
m.c7 = Constraint(expr=0 <= sqrt(m.d))
m.o = Objective(expr=m.x)
self.assertTrue(satisfiable(m) is not False)
def test_product(self):
m = aml.ConcreteModel()
m.I = range(10)
m.x = aml.Var(m.I)
m.c = aml.Constraint(
range(9),
rule=lambda m, i: aml.sin(m.x[i]) * aml.cos(m.x[i + 1]) >= 0)
dag = problem_from_pyomo_model(m)
assert len(dag.constraints) == 9
for constraint in dag.constraints:
root = constraint.root_expr
assert isinstance(root, core.ProductExpression)
assert root.num_children == 2
child1, child2 = root.children
assert isinstance(child1, core.SinExpression)
assert isinstance(child2, core.CosExpression)
self._check_depth(root)
def declare_eq_c(model, index_set, coordinate_type=CoordinateType.POLAR):
"""
Create a constraint relating c to the voltages
"""
m = model
con_set = decl.declare_set('_con_eq_c', model, index_set)
m.eq_c = pe.Constraint(con_set)
if coordinate_type == CoordinateType.POLAR:
for from_bus, to_bus in con_set:
m.eq_c[(from_bus,
to_bus)] = (m.c[(from_bus, to_bus)] == m.vm[from_bus] *
m.vm[to_bus] *
pe.cos(m.va[from_bus] - m.va[to_bus]))
elif coordinate_type == CoordinateType.RECTANGULAR:
for from_bus, to_bus in con_set:
m.eq_c[(from_bus, to_bus)] = (m.c[(
from_bus, to_bus)] == m.vr[from_bus] * m.m.vr[to_bus] +
m.vj[from_bus] * m.vj[to_bus])
else:
raise ValueError('unexpected coordinate_type: {0}'.format(
str(coordinate_type)))
def create_btheta_losses_dcopf_model(model_data, relaxation_type=RelaxationType.SOC, include_angle_diff_limits=False, include_feasibility_slack=False):
md = model_data.clone_in_service()
tx_utils.scale_ModelData_to_pu(md, inplace = True)
gens = dict(md.elements(element_type='generator'))
buses = dict(md.elements(element_type='bus'))
branches = dict(md.elements(element_type='branch'))
loads = dict(md.elements(element_type='load'))
shunts = dict(md.elements(element_type='shunt'))
gen_attrs = md.attributes(element_type='generator')
bus_attrs = md.attributes(element_type='bus')
branch_attrs = md.attributes(element_type='branch')
load_attrs = md.attributes(element_type='load')
shunt_attrs = md.attributes(element_type='shunt')
inlet_branches_by_bus, outlet_branches_by_bus = \
tx_utils.inlet_outlet_branches_by_bus(branches, buses)
gens_by_bus = tx_utils.gens_by_bus(buses, gens)
model = pe.ConcreteModel()
### declare (and fix) the loads at the buses
bus_p_loads, _ = tx_utils.dict_of_bus_loads(buses, loads)
libbus.declare_var_pl(model, bus_attrs['names'], initialize=bus_p_loads)
model.pl.fix()
### declare the fixed shunts at the buses
_, bus_gs_fixed_shunts = tx_utils.dict_of_bus_fixed_shunts(buses, shunts)
### declare the polar voltages
va_bounds = {k: (-pi, pi) for k in bus_attrs['va']}
libbus.declare_var_va(model, bus_attrs['names'], initialize=bus_attrs['va'],
bounds=va_bounds
)
dva_initialize = {k: 0.0 for k in branch_attrs['names']}
libbranch.declare_var_dva(model, branch_attrs['names'],
initialize=dva_initialize
)
### include the feasibility slack for the bus balances
p_rhs_kwargs = {}
penalty_expr = None
if include_feasibility_slack:
p_rhs_kwargs, penalty_expr = _include_feasibility_slack(model, bus_attrs, gen_attrs, bus_p_loads)
### fix the reference bus
ref_bus = md.data['system']['reference_bus']
ref_angle = md.data['system']['reference_bus_angle']
model.va[ref_bus].fix(radians(ref_angle))
### declare the generator real power
pg_init = {k: (gen_attrs['p_min'][k] + gen_attrs['p_max'][k]) / 2.0 for k in gen_attrs['pg']}
libgen.declare_var_pg(model, gen_attrs['names'], initialize=pg_init,
bounds=zip_items(gen_attrs['p_min'], gen_attrs['p_max'])
)
### declare the current flows in the branches
vr_init = {k: bus_attrs['vm'][k] * pe.cos(bus_attrs['va'][k]) for k in bus_attrs['vm']}
vj_init = {k: bus_attrs['vm'][k] * pe.sin(bus_attrs['va'][k]) for k in bus_attrs['vm']}
p_max = {k: branches[k]['rating_long_term'] for k in branches.keys()}
pf_bounds = {k: (-p_max[k],p_max[k]) for k in branches.keys()}
pf_init = dict()
for branch_name, branch in branches.items():
from_bus = branch['from_bus']
to_bus = branch['to_bus']
y_matrix = tx_calc.calculate_y_matrix_from_branch(branch)
ifr_init = tx_calc.calculate_ifr(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus],
vj_init[to_bus], y_matrix)
ifj_init = tx_calc.calculate_ifj(vr_init[from_bus], vj_init[from_bus], vr_init[to_bus],
vj_init[to_bus], y_matrix)
pf_init[branch_name] = tx_calc.calculate_p(ifr_init, ifj_init, vr_init[from_bus], vj_init[from_bus])
pfl_bounds = {k: (0,p_max[k]**2) for k in branches.keys()}
pfl_init = {k: 0 for k in branches.keys()}
libbranch.declare_var_pf(model=model,
index_set=branch_attrs['names'],
initialize=pf_init,
bounds=pf_bounds
)
libbranch.declare_var_pfl(model=model,
index_set=branch_attrs['names'],
initialize=pfl_init,
bounds=pfl_bounds
)
### declare the angle difference constraint
libbranch.declare_eq_branch_dva(model=model,
index_set=branch_attrs['names'],
branches=branches
)
### declare the branch power flow approximation constraints
libbranch.declare_eq_branch_power_btheta_approx(model=model,
index_set=branch_attrs['names'],
branches=branches,
approximation_type=ApproximationType.BTHETA_LOSSES
)
### declare the branch power loss approximation constraints
libbranch.declare_eq_branch_loss_btheta_approx(model=model,
index_set=branch_attrs['names'],
branches=branches,
relaxation_type=relaxation_type
)
### declare the p balance
libbus.declare_eq_p_balance_dc_approx(model=model,
index_set=bus_attrs['names'],
bus_p_loads=bus_p_loads,
gens_by_bus=gens_by_bus,
bus_gs_fixed_shunts=bus_gs_fixed_shunts,
inlet_branches_by_bus=inlet_branches_by_bus,
outlet_branches_by_bus=outlet_branches_by_bus,
approximation_type=ApproximationType.BTHETA_LOSSES,
**p_rhs_kwargs
)
### declare the real power flow limits
libbranch.declare_ineq_p_branch_thermal_lbub(model=model,
index_set=branch_attrs['names'],
branches=branches,
p_thermal_limits=p_max,
approximation_type=ApproximationType.BTHETA
)
### declare angle difference limits on interconnected buses
if include_angle_diff_limits:
libbranch.declare_ineq_angle_diff_branch_lbub(model=model,
index_set=branch_attrs['names'],
branches=branches,
coordinate_type=CoordinateType.POLAR
)
### declare the generator cost objective
libgen.declare_expression_pgqg_operating_cost(model=model,
index_set=gen_attrs['names'],
p_costs=gen_attrs['p_cost']
)
obj_expr = sum(model.pg_operating_cost[gen_name] for gen_name in model.pg_operating_cost)
if include_feasibility_slack:
obj_expr += penalty_expr
model.obj = pe.Objective(expr=obj_expr)
return model, md