def jacobian(self, var):
# not *quite* the jacobian, but nearly.
if var is self.x:
# each x_i: exp(x_i) / sum(exp(x)).
x = value(self.x)
return transpose(exp(x)) / sum(exp(x))
elif var is self.t:
return -eye(rows(self.t))
else:
raise OptimizationError("illegal jacobian")
def jacobian(self, var):
# not *quite* the jacobian, but nearly.
if var is self.x:
# each x_i: exp(x_i) / sum(exp(x)).
x = value(self.x)
return transpose(exp(x)) / sum(exp(x))
elif var is self.t:
return -eye(rows(self.t))
else:
raise OptimizationError('illegal jacobian')
def hessianz(self, firstvar, secondvar, z):
if firstvar is secondvar is self.x:
# Want diag(e^x)/sum(e^x) - e^x/sum(e^x)*transpose(e^x/sum(e^x)).
x = value(self.x)
a = sum(exp(x))
return z * (diag(exp(x)) / a - exp(x) / a * transpose(exp(x)) / a)
elif firstvar is secondvar is self.t:
return zeros(rows(self.t))
elif firstvar is self.x and secondvar is self.t:
return zeros(rows(self.x), rows(self.t))
elif firstvar is self.t and secondvar is self.x:
return zeros(rows(self.t), rows(self.x))
else:
raise OptimizationError('illegal hessian')
def hessianz(self, firstvar, secondvar, z):
if firstvar is secondvar is self.x:
# Want diag(e^x)/sum(e^x) - e^x/sum(e^x)*transpose(e^x/sum(e^x)).
x = value(self.x)
a = sum(exp(x))
return z * (diag(exp(x)) / a - exp(x) / a * transpose(exp(x)) / a)
elif firstvar is secondvar is self.t:
return zeros(rows(self.t))
elif firstvar is self.x and secondvar is self.t:
return zeros(rows(self.x), rows(self.t))
elif firstvar is self.t and secondvar is self.x:
return zeros(rows(self.t), rows(self.x))
else:
raise OptimizationError("illegal hessian")
def classifier2(Y, soft=False):
M = Y.size[0]
# K = Y*X' / sigma
K = matrix(0.0, (width, M))
blas.gemm(X, Y, K, transB='T', alpha=1.0 / sigma, m=width)
# c[i] = ||Yi||^2 / sigma
ones = matrix(1.0, (max(width, n, M), 1))
c = Y**2 * ones[:n]
blas.scal(1.0 / sigma, c)
# Kij := Kij - 0.5 * (ci + aj)
# = || yi - xj ||^2 / (2*sigma)
blas.ger(ones[:width], c, K, alpha=-0.5)
blas.ger(a[:width], ones[:M], K, alpha=-0.5)
# Kij = exp(Kij)
K = exp(K)
# complete K
lapack.potrs(L11, K)
K = matrix([K, matrix(0., (N - width, M))], (N, M))
chompack.trsm(Lc, K, trans='N')
chompack.trsm(Lc, K, trans='T')
x = matrix(b, (M, 1))
blas.gemv(K, z, x, trans='T', beta=1.0)
if soft: return x
else: return matrix([2 * (xk > 0.0) - 1 for xk in x])
def classifier2(Y, soft=False):
M = Y.size[0]
# K = Y*X' / sigma
K = matrix(theta, (width, M))
blas.gemm(X,
Y,
K,
transB='T',
alpha=1.0 / sigma,
beta=-1.0,
m=width)
K = exp(K)
K = div(K - K**-1, K + K**-1)
# complete K
lapack.potrs(L11, K)
K = matrix([K, matrix(0., (N - width, M))], (N, M))
chompack.trsm(Lc, K, trans='N')
chompack.trsm(Lc, K, trans='T')
x = matrix(b, (M, 1))
blas.gemv(K, z, x, trans='T', beta=1.0)
if soft: return x
else: return matrix([2 * (xk > 0.0) - 1 for xk in x])
def Gycall(self):
system.DAE.y = matrix(system.DAE.y)
U = exp(system.DAE.y[system.Bus.a] * 1j)
V = mul(system.DAE.y[system.Bus.v] + 0j, U)
I = self.Y * V
nb = len(system.Bus.a)
diagU = spmatrix(U, system.Bus.a, system.Bus.a, (nb, nb), 'z')
diagV = spmatrix(V, system.Bus.a, system.Bus.a, (nb, nb), 'z')
diagI = spmatrix(I, system.Bus.a, system.Bus.a, (nb, nb), 'z')
dS = self.Y * diagU
dS = diagV * dS.H.T
dS += diagI.H.T * diagU
dR = diagI
dR = dR - self.Y * diagV
dR = diagV.H.T * dR
# system.DAE.Gy = matrix(0.0, (system.DAE.ny, system.DAE.ny))
#
# system.DAE._list2matrix()
# system.DAE.Gy = spmatrix(dR.imag().V, dR.imag().I, dR.imag().J, (system.DAE.ny, system.DAE.ny)) \
# + spmatrix(dR.real().V, dR.real().I, dR.real().J+system.Bus.n, (system.DAE.ny, system.DAE.ny)) \
# + spmatrix(dS.real().V, dS.real().I+system.Bus.n, dS.real().J, (system.DAE.ny, system.DAE.ny)) \
# + spmatrix(dS.imag().V, dS.imag().I+system.Bus.n, dS.imag().J+system.Bus.n, (system.DAE.ny, system.DAE.ny))
Gy = sparse([[dR.imag(), dR.real()], [dS.real(), dS.imag()]])
# system.DAE.Gy = zeros([system.DAE.ny,system.DAE.ny])
system.DAE.Gy = spmatrix(Gy.V, Gy.I, Gy.J,
(system.DAE.ny, system.DAE.ny))
system.DAE.Gy = matrix(system.DAE.Gy)
def classifier(Y, soft=False):
M = Y.size[0]
# K = Y*X' / sigma - theta
K = matrix(theta, (M, Nr))
blas.gemm(Y, Xr, K, transB='T', alpha=1.0 / sigma, beta=-1.0)
K = exp(K)
x = div(K - K**-1, K + K**-1) * zr + b
if soft: return x
else: return matrix([2 * (xk > 0.0) - 1 for xk in x])
def setx0(self):
if self.n == 0:
return
vg = system.DAE.y[self.bv]
vf = mul(self.u, system.Syn6.vf0[self.a])
vrmax = mul(self.u, self.vrmax)
vrmin = mul(self.u, self.vrmin)
# 检查参数
for i in range(self.n):
if self.Te[i] <= 0:
self.Te[i] = 1
print('<%i> Te不能小于等于0，设置Te = 1 [s]' % i)
if self.Tr[i] <= 0:
self.Tr[i] = 0.001
print('<%i> Tr不能小于等于0，设置Te = 0.001 [s]' % i)
if self.K0[i] <= 0:
self.K0[i] = 400
print('<%i> K0不能小于等于0，设置K0 = 400 ' % i)
if self.T1[i] <= 0:
self.T1[i] = 0.1
print('<%i> T1不能小于等于0，设置T1 = 0.1 [s]' % i)
if self.T4[i] <= 0:
self.T4[i] = 0.01
print('<%i> T4不能小于等于0，设置T4 = 0.01 [s]' % i)
#
Ce = -vf - mul(mul(self.Ae, exp(mul(self.Be, vf))), vf)
K1 = mul(self.K0, div(self.T2, self.T1))
K2 = self.K0 - K1
K3 = div(self.T3, self.T4)
K4 = 1 - K3
system.DAE.x[self.vm] = mul(self.u, vg)
self.vref0 = vg - div(Ce, self.K0)
system.DAE.x[self.vr1] = mul(self.u, mul(K2, self.vref0 - vg))
system.DAE.x[self.vr2] = mul(self.u, mul(K4, self.vref0 - vg))
system.DAE.x[self.vf] = vf
system.DAE.y[self.vref] = mul(self.u, self.vref0)
vr = mul(self.u, mul(self.K0, system.DAE.x[self.vr2])) + mul(
K3,
mul(K1, self.vref0 - vg) + system.DAE.x[self.vr1])
for i in range(self.n):
if vr[i] > self.vrmax[i]:
print('Warn: vr1超出最大值vrmax')
if vr[i] < self.vrmin[i]:
print('Warn: vr1小于最小值vrmin')
system.Syn6.vf0[self.a] = 0
def Fxcall(self):
if self.n == 0:
return
vg = system.DAE.y[self.bv]
vrmax = mul(self.u, self.vrmax)
vrmin = mul(self.u, self.vrmin)
system.DAE.Gx = system.DAE.Gx + spmatrix(
self.u, self.vfd, self.vf, (system.DAE.ny, system.DAE.nx))
system.DAE.Fx = system.DAE.Fx - spmatrix(
div(matrix(1.0, (self.n, 1)), self.Tr), self.vm, self.vm,
(system.DAE.nx, system.DAE.nx))
system.DAE.Fy = system.DAE.Fy + spmatrix(div(
self.u, self.Tr), self.vm, self.bv, (system.DAE.nx, system.DAE.ny))
vm = system.DAE.x[self.vm]
vr1 = system.DAE.x[self.vr1]
vr2 = system.DAE.x[self.vr2]
vf = system.DAE.x[self.vf]
vref = system.DAE.y[self.vref]
K1 = div(mul(self.K0, self.T2), self.T1)
K2 = self.K0 - K1
K3 = div(self.T4, self.T3)
K4 = matrix(1, (self.n, 1)) - K3
vr = mul(self.K0, vr2) + mul(K3, mul(K1, vref - vm) + vr1)
Se = mul(self.Ae, exp(mul(self.Be, abs(vf))))
Se = Se + mul(mul(Se, self.Ae), vf)
z = matrix(0, (self.n, 1))
for i in range(self.n):
if vr[i] < vrmax[i] and vr[i] > vrmin[i]:
z[i] = 1
system.DAE.Fx = system.DAE.Fx \
- spmatrix(div(K2, self.T1), self.vr1, self.vm, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(matrix(1.0, (self.n, 1)), self.T1), self.vr1, self.vr1, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(mul(K4, K1), mul(self.K0, self.T3)), self.vr2, self.vm, (system.DAE.nx, system.DAE.nx)) \
+ spmatrix(div(K4, mul(self.T3, self.K0)), self.vr2, self.vr1, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(matrix(1.0, (self.n, 1)), self.T3), self.vr2, self.vr2, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(1+Se, self.Te), self.vf, self.vf, (system.DAE.nx, system.DAE.nx)) \
+ spmatrix(div(mul(z, K3), self.Te), self.vf, self.vr1, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(mul(mul(z, K3), K1), self.Te), self.vf, self.vm, (system.DAE.nx, system.DAE.nx)) \
+ spmatrix(div(mul(mul(z, self.u), self.K0), self.Te), self.vf, self.vr2, (system.DAE.nx, system.DAE.nx))
system.DAE.Fy = system.DAE.Fy \
+ spmatrix(div(K2, self.T1), self.vr1, self.vref, (system.DAE.nx, system.DAE.ny)) \
+ spmatrix(div(mul(K4, K1), mul(self.K0, self.T3)), self.vr2, self.vref, (system.DAE.nx, system.DAE.ny)) \
+ spmatrix(div(mul(mul(z, K3), K1), self.Te), self.vf, self.vref, (system.DAE.nx, system.DAE.ny))
def Fgp(x = None, z = None):
if x is None: return mnl, matrix(0.0, (n,1))
f = matrix(0.0, (mnl+1,1))
Df = matrix(0.0, (mnl+1,n))
# y = F*x+g
blas.copy(g, y)
base.gemv(F, x, y, beta=1.0)
if z is not None: H = matrix(0.0, (n,n))
for i, start, stop in ind:
# yi := exp(yi) = exp(Fi*x+gi)
ymax = max(y[start:stop])
y[start:stop] = base.exp(y[start:stop] - ymax)
# fi = log sum yi = log sum exp(Fi*x+gi)
ysum = blas.asum(y, n=stop-start, offset=start)
f[i] = ymax + math.log(ysum)
# yi := yi / sum(yi) = exp(Fi*x+gi) / sum(exp(Fi*x+gi))
blas.scal(1.0/ysum, y, n=stop-start, offset=start)
# gradfi := Fi' * yi
# = Fi' * exp(Fi*x+gi) / sum(exp(Fi*x+gi))
base.gemv(F, y, Df, trans='T', m=stop-start, incy=mnl+1,
offsetA=start, offsetx=start, offsety=i)
if z is not None:
# Hi = Fi' * (diag(yi) - yi*yi') * Fi
# = Fisc' * Fisc
# where
# Fisc = diag(yi)^1/2 * (I - 1*yi') * Fi
# = diag(yi)^1/2 * (Fi - 1*gradfi')
Fsc[:K[i], :] = F[start:stop, :]
for k in range(start,stop):
blas.axpy(Df, Fsc, n=n, alpha=-1.0, incx=mnl+1,
incy=Fsc.size[0], offsetx=i, offsety=k-start)
blas.scal(math.sqrt(y[k]), Fsc, inc=Fsc.size[0],
offset=k-start)
# H += z[i]*Hi = z[i] * Fisc' * Fisc
blas.syrk(Fsc, H, trans='T', k=stop-start, alpha=z[i],
beta=1.0)
if z is None:
return f, Df
return f, Df, H
def flow(self, y):
if y is not None:
system.DAE.y = matrix(y)
if self.n == 0:
return
chrg = mul(matrix(self.u), 0.5 * matrix(self.b))
y = div(matrix(self.u) + 0j, matrix(matrix(self.r) + 1j * matrix(self.x)))
ts = exp(matrix(self.theta) * math.pi / 180 * 1j)
tps = mul(matrix(self.tap_ratio), ts)
tpj = tps.H.T
ts2 = mul(tps, tpj)
Vf = mul(system.DAE.y[self.vf], exp(system.DAE.y[self.af]*1j))
Vt = mul(system.DAE.y[self.vt], exp(system.DAE.y[self.at] * 1j))
I1 = div(mul(Vf, y+1j*chrg),ts2)-div(mul(Vt, y), tpj)
I2 = mul(Vt, y + 1j * chrg) - div(mul(Vf, y), tps)
MWs = mul(Vf, I1.H.T)
MWr = mul(Vt, I2.H.T)
return [MWs, MWr]
def setx0(self):
vg = system.DAE.y[self.bv]
vf = mul(self.u, system.Syn6.vf0[self.a])
vrmax = mul(self.u, self.vrmax)
vrmin = mul(self.u, self.vrmin)
# 检查参数
for i in range(self.n):
if self.Te[i] == 0:
self.Te[i] = 1
print('<%i> Te不能小于等于0，设置Te = 1 [s]' % i)
if self.Tr[i] <= 0:
self.Tr[i] = 0.001
print('<%i> Tr不能小于等于0，设置Te = 0.001 [s]' % i)
if self.Ke[i] <= 0:
self.Ke[i] = 1
print('<%i> Ke不能小于等于0，设置Ke = 1 ' % i)
if self.Tf[i] <= 0:
self.Tf[i] = 0.1
print('<%i> T1不能小于等于0，设置T1 = 0.1 [s]' % i)
if self.Ta[i] <= 0:
self.Ta[i] = 0.1
print('<%i> T4不能小于等于0，设置T4 = 0.1 [s]' % i)
#
Ce = mul(self.Ke, vf) + mul(mul(self.Ae, exp(mul(self.Be, abs(vf)))),
vf)
system.DAE.x[self.vm] = mul(self.u, vg)
self.vref0 = div(Ce, self.Ka) + vg
system.DAE.x[self.vr1] = Ce
system.DAE.x[self.vr2] = div(mul(-self.Kf, vf), self.Tf)
system.DAE.x[self.vf] = vf
system.DAE.y[self.vref] = mul(self.u, self.vref0)
for i in range(self.n):
if Ce[i] > self.vrmax[i]:
print('Warn: vr1超出最大值vrmax')
if Ce[i] < self.vrmin[i]:
print('Warn: vr1小于最小值vrmin')
for i in range(self.n):
if self.u[i] == 1:
system.Syn6.vf0[self.a[i]] = 0
def gcall(self):
system.DAE.y = matrix(system.DAE.y)
zeros = [0.0] * system.DAE.ny
system.DAE.g = zeros
system.DAE.g = matrix(system.DAE.g)
Vn = exp(system.DAE.y[system.Bus.a] * 1j)
Vc = mul(system.DAE.y[system.Bus.v] + 0j, Vn)
Ic = self.Y * Vc
S = mul(Vc, Ic.H.T)
self.p = S.real()
self.q = S.imag()
for i in range(system.Bus.n):
system.DAE.g[i] = self.p[i]
system.DAE.g[i+system.Bus.n] = self.q[i]
def classifier(Y, soft=False):
M = Y.size[0]
# K = Y*X' / sigma
K = matrix(0.0, (M, Nr))
blas.gemm(Y, Xr, K, transB='T', alpha=1.0 / sigma)
# c[i] = ||Yi||^2 / sigma
ones = matrix(1.0, (max([M, Nr, n]), 1))
c = Y**2 * ones[:n]
blas.scal(1.0 / sigma, c)
# Kij := Kij - 0.5 * (ci + aj)
# = || yi - xj ||^2 / (2*sigma)
blas.ger(c, ones, K, alpha=-0.5)
blas.ger(ones, a[sv], K, alpha=-0.5)
x = exp(K) * zr + b
if soft: return x
else: return matrix([2 * (xk > 0.0) - 1 for xk in x])
def fcall(self):
if self.n == 0:
return
vg = system.DAE.y[self.bv]
vrmax = mul(self.u, self.vrmax)
vrmin = mul(self.u, self.vrmin)
vm = system.DAE.x[self.vm]
vr1 = system.DAE.x[self.vr1]
vr2 = system.DAE.x[self.vr2]
vf = system.DAE.x[self.vf]
vref = system.DAE.y[self.vref]
system.DAE.f[self.vm] = div(mul(self.u, vg - system.DAE.x[self.vm]),
self.Tr)
K1 = div(mul(self.K0, self.T2), self.T1)
K2 = self.K0 - K1
K3 = div(self.T4, self.T3)
K4 = matrix(1, (self.n, 1)) - K3
vr = mul(self.K0, vr2) + mul(K3, mul(K1, vref - vm) + vr1)
system.DAE.f[self.vr1] = div(mul(self.u,
mul(K2, vref - vm) - vr1), self.T1)
system.DAE.f[self.vr2] = div(
mul(self.u,
mul(K4, vr1 + mul(K1, vref - vm)) - mul(self.K0, vr2)),
mul(self.T3, self.K0))
# hard limit
for i in range(self.n):
vr[i] = min(vr[i], vrmax[i])
vr[i] = max(vr[i], vrmin[i])
Se = mul(self.Ae, exp(mul(self.Be, abs(vf))))
system.DAE.f[self.vf] = div(mul(self.u, -vf + vr - mul(Se, vf)),
self.Te)
def Fxcall(self):
vg = system.DAE.y[self.bv]
vrmax = mul(self.u, self.vrmax)
vrmin = mul(self.u, self.vrmin)
system.DAE.Gx = system.DAE.Gx + spmatrix(
self.u, self.vfd, self.vf, (system.DAE.ny, system.DAE.nx))
system.DAE.Fx = system.DAE.Fx - spmatrix(
div(matrix(1.0, (self.n, 1)), self.Tr), self.vm, self.vm,
(system.DAE.nx, system.DAE.nx))
system.DAE.Fy = system.DAE.Fy + spmatrix(div(
self.u, self.Tr), self.vm, self.bv, (system.DAE.nx, system.DAE.ny))
vr1 = system.DAE.x[self.vr1]
vf = system.DAE.x[self.vf]
Ka = mul(self.u, self.Ka)
Kf = mul(self.u, self.Kf)
K5 = div(Kf, self.Tf)
Se = mul(self.Ae, exp(mul(self.Be, abs(vf))))
Se = Se + mul(mul(Se, self.Be), vf)
z = matrix(0, (self.n, 1))
for i in range(self.n):
if vr1[i] < vrmax[i] and vr1[i] > vrmin[i]:
z[i] = 1
system.DAE.Fx = system.DAE.Fx \
- spmatrix(div(matrix(1.0, (self.n, 1)), self.Tf), self.vr2, self.vr2, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(K5, self.Tf), self.vr2, self.vf, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(self.Ke+Se, self.Te), self.vf, self.vf, (system.DAE.nx, system.DAE.nx)) \
+ spmatrix(div(z, self.Te), self.vf, self.vr1, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(mul(z, Ka), self.Ta), self.vr1, self.vm, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(matrix(1.0, (self.n, 1)), self.Ta), self.vr1, self.vr1, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(mul(z, Ka), self.Ta), self.vr1, self.vr2, (system.DAE.nx, system.DAE.nx)) \
- spmatrix(div(mul(mul(z, K5), Ka), self.Ta), self.vr1, self.vf, (system.DAE.nx, system.DAE.nx))
system.DAE.Fy = system.DAE.Fy \
+ spmatrix(div(mul(z, Ka), self.Ta), self.vr1, self.vref, (system.DAE.nx, system.DAE.ny))
def fcall(self):
vg = system.DAE.y[self.bv]
vrmax = mul(self.u, self.vrmax)
vrmin = mul(self.u, self.vrmin)
vm = system.DAE.x[self.vm]
vr1 = system.DAE.x[self.vr1]
vr2 = system.DAE.x[self.vr2]
vf = system.DAE.x[self.vf]
vref = system.DAE.y[self.vref]
system.DAE.f[self.vm] = div(mul(self.u, vg - system.DAE.x[self.vm]),
self.Tr) #
K5 = div(self.Kf, self.Tf)
system.DAE.f[self.vr1] = div(
mul(self.u,
mul(self.Ka, vref - vm - vr2 - mul(K5, vf)) - vr1), self.Ta)
system.DAE.f[self.vr2] = div(mul(-self.u, mul(K5, vf) + vr2), self.Tf)
# non-windup limit
for i in range(self.n):
if vr1[i] >= vrmax[i] and system.DAE.f[self.vr1[i]] > 0:
system.DAE.f[self.vr1[i]] = 0
if vr1[i] <= vrmin[i] and system.DAE.f[self.vr1[i]] < 0:
system.DAE.f[self.vr1[i]] = 0
for i in range(self.n):
vr1[i] = min(vr1[i], vrmax[i])
vr1[i] = max(vr1[i], vrmin[i])
system.DAE.x[self.vr1] = mul(self.u, vr1)
Se = mul(self.Ae, exp(mul(self.Be, abs(vf))))
system.DAE.f[self.vf] = div(
mul(self.u, vr1 - mul(self.Ke, vf) - mul(Se, vf)), self.Te)
def gcall(self):
zeros = [0] * system.Bus.n
Vn = zeros[:]
Vc = zeros[:]
for item1, item2 in zip(system.Bus.a, system.Bus.v):
Vn[item1] = exp(system.DAE.y[item1] * 1j)
Vc[item1] = (system.DAE.y[item2] + 0j) * Vn[item1]
# system.DAE.y = matrix(system.DAE.y)
# Vn = exp(system.DAE.y[system.Bus.a] * 1j)
# Vc = mul(system.DAE.y[system.Bus.v] + 0j, Vn)
Vc = matrix(Vc)
Ic = self.Y * Vc
S = mul(Vc, Ic.H.T)
self.p = S.real()
self.q = S.imag()
for i in range(system.Bus.n):
system.DAE.g[i] = self.p[i]
system.DAE.g[i + system.Bus.n] = self.q[i]
def Fgp(x=None, z=None):
if x is None: return mnl, matrix(0.0, (n, 1))
f = matrix(0.0, (mnl + 1, 1))
Df = matrix(0.0, (mnl + 1, n))
# y = F*x+g
blas.copy(g, y)
base.gemv(F, x, y, beta=1.0)
if z is not None: H = matrix(0.0, (n, n))
for i, start, stop in ind:
# yi := exp(yi) = exp(Fi*x+gi)
ymax = max(y[start:stop])
y[start:stop] = base.exp(y[start:stop] - ymax)
# fi = log sum yi = log sum exp(Fi*x+gi)
ysum = blas.asum(y, n=stop - start, offset=start)
f[i] = ymax + math.log(ysum)
# yi := yi / sum(yi) = exp(Fi*x+gi) / sum(exp(Fi*x+gi))
blas.scal(1.0 / ysum, y, n=stop - start, offset=start)
# gradfi := Fi' * yi
# = Fi' * exp(Fi*x+gi) / sum(exp(Fi*x+gi))
base.gemv(F,
y,
Df,
trans='T',
m=stop - start,
incy=mnl + 1,
offsetA=start,
offsetx=start,
offsety=i)
if z is not None:
# Hi = Fi' * (diag(yi) - yi*yi') * Fi
# = Fisc' * Fisc
# where
# Fisc = diag(yi)^1/2 * (I - 1*yi') * Fi
# = diag(yi)^1/2 * (Fi - 1*gradfi')
Fsc[:K[i], :] = F[start:stop, :]
for k in range(start, stop):
blas.axpy(Df,
Fsc,
n=n,
alpha=-1.0,
incx=mnl + 1,
incy=Fsc.size[0],
offsetx=i,
offsety=k - start)
blas.scal(math.sqrt(y[k]),
Fsc,
inc=Fsc.size[0],
offset=k - start)
# H += z[i]*Hi = z[i] * Fisc' * Fisc
blas.syrk(Fsc,
H,
trans='T',
k=stop - start,
alpha=z[i],
beta=1.0)
if z is None:
return f, Df
return f, Df, H
def build_y(self):
if self.n == 0:
return
for i in range(len(self.tap_ratio)):
if self.tap_ratio[i] == 0:
self.tap_ratio[i] = 1
nb = system.Bus.n
# 处理传输线数据和生成导纳矩阵
chrg = mul(matrix(self.u), 0.5 * matrix(self.b))
y = div(matrix(self.u) + 0j, matrix(matrix(self.r) + 1j * matrix(self.x)))
ts = exp(matrix(self.theta) * math.pi / 180 * 1j)
ts = mul(matrix(self.tap_ratio), ts)
ts2 = mul(ts, ts.H.T)
# ts2real = ts2.real()
# ts2imag = ts2.imag()
# for i in range(len(ts2)):
# ts2real[i] = round(ts2real[i], 15)
# ts2imag[i] = round(ts2imag[i], 15)
# ts2 = ts2real + 1j*ts2imag
yft = div(-y, ts.H.T)
# yftreal = yft.real()
# yftimag = yft.imag()
ytf = div(-y, ts)
# ytfreal = ytf.real()
# ytfimag = ytf.imag()
yff = div(y, ts2) + 1j*chrg
# yffreal = yff.real()
# yffimag = yff.imag()
ytt = y + 1j*chrg
# yttreal = ytt.real()
# yttimag = ytt.imag()
# for i in range(len(ytt)):
# yftreal[i] = round(yftreal[i], 15)
# yftimag[i] = round(yftimag[i], 15)
#
# ytfreal[i] = round(ytfreal[i], 15)
# ytfimag[i] = round(ytfimag[i], 15)
#
# yffreal[i] = round(yffreal[i], 15)
# yffimag[i] = round(yffimag[i], 15)
#
# yttreal[i] = round(yttreal[i], 15)
# yttimag[i] = round(yttimag[i], 15)
#
# yft = yftreal + 1j * yftimag
# ytt = yttreal + 1j * yttimag
# yff = yffreal + 1j * yffimag
# ytf = ytfreal + 1j * ytfimag
self.Y = spmatrix(yft, self.af, self.at, (nb, nb)) +\
spmatrix(ytf, self.at, self.af, (nb, nb)) +\
spmatrix(yff, self.af, self.af, (nb, nb)) +\
spmatrix(ytt, self.at, self.at, (nb, nb))
for i in range(nb):
if self.Y[i, i] == 0:
self.Y[i, i] == -1j*1e-6
system.DAE.Y = self.Y
system.DAE.Y_G = self.Y.real()
system.DAE.Y_B = self.Y.imag()
def eval(obj):
return cvxopt.base.log(sum(exp(obj)))
def setx0(self):
# 常数
self.c1 = [0] * self.n
self.c2 = [0] * self.n
self.c3 = [0] * self.n
# 检查参数
for i in range(self.n):
# 检查惯性 M 和 x'd
if self.M[i] <= 0:
self.M[i] = 10
print('%i 惯性M不能小于等于0，设置M = 10 [kWs/kVa]' % i)
if self.xd1[i] <= 0:
self.xd1[i] = 0.302
print("%i x'd不能小于等于0，设置x'd = 0.302 [p.u.]" % i)
# 检查 xd, T'd0
if self.xd[i] <= 0:
self.xd[i] = 1.9
print("%i xd不能小于等于0，设置xd = 1.9 [p.u.]" % i)
if self.Td01[i] <= 0:
self.Td01[i] = 8
print("%i T'd0不能小于等于0，设置T'd0 = 8 [s]" % i)
# 检查 T''d0, x''d 和 x''q
if self.Td02[i] <= 0:
self.Td02[i] = 0.04
print("%i T''d0不能小于等于0，设置T''d0 = 0.04 [s]" % i)
if self.xd2[i] <= 0:
self.xd2[i] = 0.204
print("%i xd2不能小于等于0，设置xd2= 0.204 [p.u.]" % i)
if self.xq2[i] <= 0:
self.xq2[i] = 0.30
print("%i xq2不能小于等于0，设置xq2= 0.30 [p.u.]" % i)
# 检查 T'q0
if self.Tq01[i] <= 0:
self.Tq01[i] = 0.80
print("%i T'q0不能小于等于0，设置T'q0 = 0.80 [s]" % i)
# 检查 T''q0
if self.Tq02[i] <= 0:
self.Tq02[i] = 0.02
print("%i T''q0不能小于等于0，设置T''q0 = 0.02 [s]" % i)
# 检查 xq x'q
if self.xq[i] <= 0:
self.xq[i] = 1.70
print("%i xq不能小于等于0，设置xq = 1.70 [p.u.]" % i)
if self.xq1[i] <= 0:
self.xq1[i] = 0.5
print("%i xq1不能小于等于0，设置xq1 = 0.5 [p.u.]" % i)
# 检查Taa和饱和因子
# 转子速度
system.DAE._list2matrix()
system.DAE.x[self.omega] = self.u
# 检查有功、无功比例
# idx = []
# for i in self.a:
# for index, j in enumerate(self.a):
# if j == i:
# idx.append(i)
# if len(idx) == 1:
# for i in range(self.n):
# if self.ganmaP[i] != 1:
# self.
# 功率和转子角速度
# print(mul(matrix(self.u), matrix(system.Bus.Pg[self.a])))
system.DAE.y[self.p] = mul(mul(self.u, matrix(system.Bus.Pg[self.a])),
self.ganmaP)
system.DAE.y[self.q] = mul(mul(self.u, matrix(system.Bus.Qg[self.a])),
self.ganmaQ)
self.Pg0 = system.DAE.y[self.p]
Vg = matrix(system.DAE.y[self.v] + 0j)
ag = matrix(exp(system.DAE.y[self.a] * 1j))
V = mul(Vg, ag)
S = system.DAE.y[self.p] - system.DAE.y[self.q] * 1j
I = div(S, V.H.T)
delta = np.angle(V + mul((self.ra + self.xq * 1j), I))
# print(mul(matrix(self.u), matrix(delta)))
# a = mul(matrix(self.u), matrix(delta))
# print(type(system.DAE.x[0]))
system.DAE.x[self.delta] = mul(self.u, matrix(delta))
# d、q轴电压和电流
jpi2 = math.pi / 2 * 1j
# jpi2 = 1.5707963267948966j
Vdq = mul(self.u + 0j, mul(V, exp(matrix(jpi2 - delta * 1j))))
idq = mul(self.u + 0j, mul(I, exp(matrix(jpi2 - delta * 1j))))
Vd = Vdq.real()
Vq = Vdq.imag()
Id = idq.real()
Iq = idq.imag()
# 机械转矩/功率
self.pm0 = mul(Vq + mul(self.ra, Iq), Iq) + \
mul(Vd + mul(self.ra, Id), Id)
self.suijipm0.append(self.pm0)
system.DAE.y[self.pm] = self.pm0
# 剩余状态变量和场电压
K = div(1, (self.ra**2 + mul(self.xq2, self.xd2)))
self.c1 = mul(self.ra, K)
self.c2 = mul(self.xd2, K)
self.c3 = mul(self.xq2, K)
system.DAE.x[self.e2q] = Vq + mul(self.ra, Iq) + mul(self.xd2, Id)
system.DAE.x[self.e2d] = Vd + mul(self.ra, Id) - mul(self.xq2, Iq)
system.DAE.x[self.e1d] = mul(
self.xq - self.xq1 -
div(mul(mul(self.Tq02, self.xq2), self.xq - self.xq1),
mul(self.Tq01, self.xq1)), Iq)
K1 = self.xd - self.xd1 - div(
(mul(mul(self.Td02, self.xd2),
(self.xd - self.xd1))), mul(self.Td01, self.xd1))
K2 = self.xd1 - self.xd2 + div(
mul(mul(self.Td02, self.xd2), self.xd - self.xd1),
mul(self.Td01, self.xd1))
system.DAE.x[self.e1q] = system.DAE.x[self.e2q] + mul(K2, Id) - div(
mul(self.Taa,
mul(K1 + K2, Id) + system.DAE.x[self.e2q]), self.Td01)
# print(type(system.Syn6.synsat()))
# print(system.Syn6.synsat())
self.vf0 = div(
mul(K1, Id) + system.Syn6.synsat(), 1 - div(self.Taa, self.Td01))
system.DAE.y[self.vf] = self.vf0
# !!! 移除静态发电机节点
system.SW.remove(idx='SW_1')
for i in range(system.PV.n):
idx = 'PV_' + str(i + 1)
system.PV.remove(idx)
def eval(obj):
return cvxopt.base.log(sum(exp(obj)))
def kernel_matrix(X,
kernel,
sigma=1.0,
theta=1.0,
degree=1,
V=None,
width=None):
"""
Computes the kernel matrix or a partial kernel matrix.
Input arguments.
X is an N x n matrix.
kernel is a string with values 'linear', 'rfb', 'poly', or 'tanh'.
'linear': k(u,v) = u'*v/sigma.
'rbf': k(u,v) = exp(-||u - v||^2 / (2*sigma)).
'poly': k(u,v) = (u'*v/sigma)**degree.
'tanh': k(u,v) = tanh(u'*v/sigma - theta). kernel is a
sigma and theta are positive numbers.
degree is a positive integer.
V is an N x N sparse matrix (default is None).
width is a positive integer (default is None).
Output.
Q, an N x N matrix or sparse matrix.
If V is a sparse matrix, a partial kernel matrix with the sparsity
pattern V is returned.
If width is specified and V = 'band', a partial kernel matrix
with band sparsity is returned (width is the half-bandwidth).
a, an N x 1 matrix with the products <xi,xi>/sigma.
"""
N, n = X.size
#### dense (full) kernel matrix
if V is None:
if verbose: print("building kernel matrix ..")
# Qij = xi'*xj / sigma
Q = matrix(0.0, (N, N))
blas.syrk(X, Q, alpha=1.0 / sigma)
a = Q[::N + 1] # ai = ||xi||**2 / sigma
if kernel == 'linear':
pass
elif kernel == 'rbf':
# Qij := Qij - 0.5 * ( ai + aj )
# = -||xi - xj||^2 / (2*sigma)
ones = matrix(1.0, (N, 1))
blas.syr2(a, ones, Q, alpha=-0.5)
Q = exp(Q)
elif kernel == 'tanh':
Q = exp(Q - theta)
Q = div(Q - Q**-1, Q + Q**-1)
elif kernel == 'poly':
Q = Q**degree
else:
raise ValueError('invalid kernel type')
#### general sparse partial kernel matrix
elif type(V) is cvxopt.base.spmatrix:
if verbose: print("building projected kernel matrix ...")
Q = +V
base.syrk(X, Q, partial=True, alpha=1.0 / sigma)
# ai = ||xi||**2 / sigma
a = matrix(Q[::N + 1], (N, 1))
if kernel == 'linear':
pass
elif kernel == 'rbf':
ones = matrix(1.0, (N, 1))
# Qij := Qij - 0.5 * ( ai + aj )
# = -||xi - xj||^2 / (2*sigma)
p = chompack.maxcardsearch(V)
symb = chompack.symbolic(Q, p)
Qc = chompack.cspmatrix(symb) + Q
chompack.syr2(Qc, a, ones, alpha=-0.5)
Q = Qc.spmatrix(reordered=False)
Q.V = exp(Q.V)
elif kernel == 'tanh':
v = +Q.V
v = exp(v - theta)
v = div(v - v**-1, v + v**-1)
Q.V = v
elif kernel == 'poly':
Q.V = Q.V**degree
else:
raise ValueError('invalid kernel type')
#### banded partial kernel matrix
elif V == 'band' and width is not None:
# Lower triangular part of band matrix with bandwidth 2*w+1.
if verbose: print("building projected kernel matrix ...")
I = [i for k in range(N) for i in range(k, min(width + k + 1, N))]
J = [k for k in range(N) for i in range(min(width + 1, N - k))]
V = matrix(0.0, (len(I), 1))
oy = 0
for k in range(N): # V[:,k] = Xtrain[k:k+w, :] * Xtrain[k,:].T
m = min(width + 1, N - k)
blas.gemv(X,
X,
V,
m=m,
ldA=N,
incx=N,
offsetA=k,
offsetx=k,
offsety=oy)
oy += m
blas.scal(1.0 / sigma, V)
# ai = ||xi||**2 / sigma
a = matrix(V[[i for i in range(len(I)) if I[i] == J[i]]], (N, 1))
if kernel == 'linear':
Q = spmatrix(V, I, J, (N, N))
elif kernel == 'rbf':
Q = spmatrix(V, I, J, (N, N))
ones = matrix(1.0, (N, 1))
# Qij := Qij - 0.5 * ( ai + aj )
# = -||xi - xj||^2 / (2*sigma)
symb = chompack.symbolic(Q)
Qc = chompack.cspmatrix(symb) + Q
chompack.syr2(Qc, a, ones, alpha=-0.5)
Q = Qc.spmatrix(reordered=False)
Q.V = exp(Q.V)
elif kernel == 'tanh':
V = exp(V - theta)
V = div(V - V**-1, V + V**-1)
Q = spmatrix(V, I, J, (N, N))
elif kernel == 'poly':
Q = spmatrix(V**degree, I, J, (N, N))
else:
raise ValueError('invalid kernel type')
else:
raise TypeError('invalid type V')
return Q, a
