CAPÍTULO V: RESULTADOS Y DISCUSIÓN 27
5.3 Determinación del efecto de las variables del proceso de acidólisis enzimática
The research accomplished in this thesis has highlighted a number of new research topics that need more investigation. These topics are beyond the scope of this thesis and are summarized as follows:
• The proposed approach can be enhanced by incorporating some partial information of the system topology or the system parameters as constraints in the objective function of the estimation algorithm. Convergence properties of the on- line algorithm can be enhanced by introducing variable step size.
• The model for the measurement system can be enhanced with the addition of harmonic current measurements. Also, the estimation of harmonic sources can be extended for the estimation of harmonic voltage sources.
• The research on BSS of under-determined mixtures has promising results. These techniques can be used to identify the harmonic distortion levels on several branches with a few measurements at the point of common coupling.
• The proposed approach can be tested with unbalanced three-phase harmonic analysis. At the time of the research on this topic, there were not enough real measurement data available. The proposed approach can be tested on a real system.
• The approach used for the location estimation of harmonic sources can be applied for the parameter estimation of the power system at fundamental and harmonic frequencies. The estimate of the reduced system impedance matrix can be obtained through active load profile estimation which can be used to identify the topology changes in the system.
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APPENDIX A: FIGURES
Figure A-1 Load profiles of 7th, 11th, 13th and 17th harmonic current over 1-day period
8 16 24 0.005 0.01 0.015 0.02 5th Harmonic Time (hour) R e a l p a rt (p u ) Bus 9 8 16 24 -0.035 -0.03 -0.025 -0.02 5th Harmonic Time (hour) Im a g in a ry p a rt (p u ) Bus 9 8 16 24 0.01 0.015 0.02 0.025 7th Harmonic Time (hour) R e a l par t ( pu) Bus 9 8 16 24 0 0.005 0.01 0.015 7th Harmonic Time (hour) Im agi na ry par t ( pu) Bus 9 8 16 24 0.005 0.01 0.015 0.02 11th Harmonic Time (hour) R e a l par t ( pu) Bus 9 8 16 24 -10 -5 0 5x 10 -3 11th Harmonic Time (hour) Im agi na ry par t ( pu) Bus 9
Figure A-2 Actual and estimated harmonic components of harmonic current source at Bus 9
8 16 24 -5 0 5 10 15x 10 -3 13th Harmonic Time (hour) R e a l par t ( pu) Bus 9 8 16 24 0 0.005 0.01 0.015 13th Harmonic Time (hour) Im agi na ry par t ( pu) Bus 9 8 16 24 0 0.005 0.01 0.015 17th Harmonic Time (hour) R e a l par t ( pu) Bus 9 8 16 24 0 0.005 0.01 0.015 17 Harmonic Time (hour) Im agi na ry par t ( pu) Bus 9
8 16 24 0 0.005 0.01 0.015 5th Harmonic Time (hour) R e a l par t ( pu) Bus 12 8 16 24 -0.02 -0.015 -0.01 -0.005 5th Harmonic Time (hour) Im agi na ry par t ( pu) Bus 12 8 16 24 -5 0 5 10x 10 -3 7th Harmonic Time (hour) R e a l par t ( pu) Bus 12 8 16 24 -0.015 -0.01 -0.005 0 7th Harmonic Time (hour) Im agi na ry par t ( pu) Bus 12 8 16 24 -10 -5 0 5x 10 -3 11th Harmonic Time (hour) R e a l par t ( pu) Bus 12 8 16 24 -10 -5 0 5x 10 -3 11th Harmonic Time (hour) Im agi na ry par t ( pu) Bus 12
Figure A-3 Actual and estimated harmonic components of harmonic current source at Bus 12
8 16 24 -10 -5 0 5x 10 -3 13th Harmonic Time (hour) R e a l par t ( pu) Bus 12 8 16 24 -10 -5 0 5x 10 -3 13th Harmonic Time (hour) Im agi na ry par t ( pu) Bus 12 8 16 24 -10 -5 0 5x 10 -3 17th Harmonic Time (hour) R e a l par t ( pu) Bus 12 8 16 24 -5 0 5 10x 10 -3 17th Harmonic Time (hour) Im agi na ry par t ( pu) Bus 12
APPENDIX B: TEST SYSTEM PARAMETERS
Table B-1 Parameters of modified IEEE 14-Bus test system
bus type Pd Qd Gs Bs area Vm Va base
KV zone Vmax Vmin
bus = 1 3 0 0 0 0 1 1.06 0 0 1 1.06 0.94 2 2 21.7 12.7 0 0 1 1.045 -4.98 0 1 1.06 0.94 3 2 0 0 0 0 1 1.01 -12.72 0 1 1.06 0.94 4 1 0 0 0 0 1 1.019 -10.33 0 1 1.06 0.94 5 1 0 25 0 0 1 1.02 -8.78 0 1 1.06 0.94 6 2 11.2 7.5 0 0 1 1.07 -14.22 0 1 1.06 0.94 7 1 0 0 0 0 1 1.062 -13.37 0 1 1.06 0.94 8 2 0 0 0 0 1 1.09 -13.36 0 1 1.06 0.94 9 1 30 10 0 0 1 1.056 -14.94 0 1 1.06 0.94 10 1 9 5.8 0 0 1 1.051 -15.1 0 1 1.06 0.94 11 1 3.5 1.8 0 0 1 1.057 -14.79 0 1 1.06 0.94 12 1 15 10 0 0 1 1.055 -15.07 0 1 1.06 0.94 13 1 0 0 0 0 1 1.05 -15.16 0 1 1.06 0.94 14 1 14.9 5 0 0 1 1.036 -16.04 0 1 1.06 0.94
bus Pg Qg Qmax Qmin Vsp base status Pmax Pmin
gen = 1 232.4 -16.9 10 0 1.06 100 1 332.4 0 2 40 42.4 50 -40 1.045 100 1 140 0 3 0 23.4 40 0 1.01 100 1 100 0 6 0 12.2 24 -6 1.07 100 1 100 0 8 0 17.4 24 -6 1.09 100 1 100 0
Table B-1 (continued)
fbus tbus r x b rateA rateB rateC ratio angle status
branch = 1 2 0.01938 0.05917 0.0528 9900 0 0 0 0 1 1 5 0.05403 0.22304 0.0492 9900 0 0 0 0 1 2 3 0.04699 0.19797 0.0438 9900 0 0 0 0 1 2 4 0.05811 0.17632 0.0340 9900 0 0 0 0 1 2 5 0.05695 0.17388 0.0346 9900 0 0 0 0 1 3 4 0.06701 0.17103 0.0128 9900 0 0 0 0 1 4 5 0.01335 0.04211 0 9900 0 0 0 0 1 4 7 0 0.20912 0 9900 0 0 0.978 0 1 4 9 0 0.55618 0 9900 0 0 0.969 0 1 5 6 0 0.25202 0 9900 0 0 0.932 0 1 6 11 0.09498 0.19890 0 9900 0 0 0 0 1 6 12 0.12291 0.25581 0 9900 0 0 0 0 1 6 13 0.06615 0.13027 0 9900 0 0 0 0 1 7 8 0 0.17615 0 9900 0 0 0 0 1 7 9 0 0.11001 0 9900 0 0 0 0 1 9 10 0.03181 0.08450 0 9900 0 0 0 0 1 9 14 0.12711 0.27038 0 9900 0 0 0 0 1 10 11 0.08205 0.19207 0 9900 0 0 0 0 1 12 13 0.22092 0.19988 0 9900 0 0 0 0 1 13 14 0.17093 0.34802 0 9900 0 0 0 0 1
Table B-2 Parameters of modified IEEE 30-Bus test system
bus type Pd Qd Gs Bs area Vm Va Base
KV zone Vmax Vmin
bus = 1 3 0 0 0 0 1 1.06 0 132 1 1.06 0.94 2 2 0 0 0 0 1 1.043 -5.48 132 1 1.06 0.94 3 1 21.7 12.7 0 0 1 1.021 -7.96 132 1 1.06 0.94 4 1 0 0 0 0 1 1.012 -9.62 132 1 1.06 0.94 5 2 0 0 0 0 1 1.01 -14.37 132 1 1.06 0.94 6 1 0 0 0 0 1 1.01 -11.34 132 1 1.06 0.94 7 1 22.5 11 0 0 1 1.002 -13.12 132 1 1.06 0.94 8 2 30 30 0 0 1 1.01 -12.1 132 1 1.06 0.94 9 1 0 0 0 0 1 1.051 -14.38 1 1 1.06 0.94 10 1 0 0 0 0 1 1.045 -15.97 33 1 1.06 0.94 11 2 0 0 0 0 1 1.082 -14.39 11 1 1.06 0.94 12 1 0 0 0 0 1 1.057 -15.24 33 1 1.06 0.94 13 1 0 0 0 0 1 1.071 -15.24 11 1 1.06 0.94 14 1 17 13 0 0 1 1.042 -16.13 33 1 1.06 0.94 15 1 0 0 0 0 1 1.038 -16.22 33 1 1.06 0.94 16 1 0 40 0 0 1 1.045 -15.83 33 1 1.06 0.94 17 1 0 0 0 0 1 1.04 -16.14 33 1 1.06 0.94 18 1 3.2 0.9 0 0 1 1.028 -16.82 33 1 1.06 0.94 19 1 0 0 0 0 1 1.026 -17 33 1 1.06 0.94 20 1 2.2 0.7 0 0 1 1.03 -16.8 33 1 1.06 0.94 21 1 0 0 0 0 1 1.033 -16.42 33 1 1.06 0.94 22 1 0 0 0 0 1 1.033 -16.41 33 1 1.06 0.94 23 1 3.2 1.6 0 0 1 1.027 -16.61 33 1 1.06 0.94 24 1 0 0 0 0 1 1.021 -16.78 33 1 1.06 0.94 25 1 20.6 18.9 0 0 1 1.017 -16.35 33 1 1.06 0.94 26 1 0 0 0 0 1 1 -16.77 33 1 1.06 0.94 27 1 0 0 0 0 1 1.023 -15.82 33 1 1.06 0.94 28 1 0 0 0 0 1 1.007 -11.97 132 1 1.06 0.94 29 2 2.4 0.9 0 0 1 1.003 -17.06 33 1 1.06 0.94 30 1 25 16 0 0 1 0.992 -17.94 33 1 1.06 0.94
bus Pg Qg Qmax Qmin Vsp base status Pmax Pmin
gen = 1 300 -16.1 10 0 1.01 100 1 360.2 0 2 40 50 50 -40 1.01 100 1 140 0 5 0 37 40 -40 1.01 100 1 100 0 8 0 37.3 40 -10 1.01 100 1 100 0 11 0 16.2 24 -6 1.01 100 1 100 0 29 0 10.6 24 -6 1.07 100 1 100 0
Table B-2 (continued)
fbus tbus r x b rateA rateB rateC ratio angle status
branch = 1 2 0.0192 0.0575 0.0528 200 200 200 0 0 1 1 3 0.0452 0.1652 0.0408 200 200 200 0 0 1 2 4 0.0570 0.1737 0.0368 200 200 200 0 0 1 3 4 0.0132 0.0379 0.0084 200 200 200 0 0 1 2 5 0.0472 0.1983 0.0418 200 200 200 0 0 1 2 6 0.0581 0.1763 0.0374 200 200 200 0 0 1 4 6 0.0119 0.0414 0.0090 200 200 200 0 0 1 5 7 0.0460 0.1160 0.0204 200 200 200 0 0 1 6 7 0.0267 0.0820 0.0170 200 200 200 0 0 1 6 8 0.0120 0.0420 0.0090 200 200 200 0 0 1 6 9 0 0.2080 0 200 200 200 0.978 0 1 6 10 0 0.5560 0 200 200 200 0.969 0 1 9 11 0 0.2080 0 200 200 200 0 0 1 9 10 0 0.1100 0 200 200 200 0 0 1 4 12 0 0.2560 0 200 200 200 0.932 0 1 12 13 0 0.1400 0 200 200 200 0 0 1 12 14 0.1231 0.2559 0 200 200 200 0 0 1 12 15 0.0662 0.1304 0 200 200 200 0 0 1 12 16 0.0945 0.1987 0 200 200 200 0 0 1 14 15 0.2210 0.1997 0 200 200 200 0 0 1 16 17 0.0524 0.1923 0 200 200 200 0 0 1 15 18 0.1073 0.2185 0 200 200 200 0 0 1 18 19 0.0639 0.1292 0 200 200 200 0 0 1 19 20 0.0340 0.0680 0 200 200 200 0 0 1 10 20 0.0936 0.2090 0 200 200 200 0 0 1 10 17 0.0324 0.0845 0 200 200 200 0 0 1 10 21 0.0348 0.0749 0 200 200 200 0 0 1 10 22 0.0727 0.1499 0 200 200 200 0 0 1 21 22 0.0116 0.0236 0 200 200 200 0 0 1 15 23 0.1000 0.2020 0 200 200 200 0 0 1 22 24 0.1150 0.1790 0 200 200 200 0 0 1 23 24 0.1320 0.2700 0 200 200 200 0 0 1 24 25 0.1885 0.3292 0 200 200 200 0 0 1 25 26 0.2544 0.3800 0 200 200 200 0 0 1 25 27 0.1093 0.2087 0 200 200 200 0 0 1 28 27 0 0.3960 0 200 200 200 0.968 0 1 27 29 0.2198 0.4153 0 200 200 200 0 0 1 27 30 0.3202 0.6027 0 200 200 200 0 0 1 29 30 0.2399 0.4533 0 200 200 200 0 0 1 8 28 0.0636 0.2000 0.0428 200 200 200 0 0 1 6 28 0.0169 0.0599 0.0130 200 200 200 0 0 1
APPENDIX C: SYMBOLS : field of complex numbers
║·║ : norm (length) of vector
A : mixing matrix
A-1 : inverse of a matrix A
AH : hermitian transpose (complex conjugate, transpose) of a matrix A aij : ij-th element of matrix A
Cxx, Cx : covariance matrix of x
D : skew symmetric matrix e : error vector
E : expectation operator
f : frequency
F(·) : cumulative distribution function (cdf) f(·), g(·), G(·) : scalar valued function
h : harmonic order H : measurement matrix H(·) : marginal entropy
h(·) : set of nonlinear equations relating measurements to states
I : current
I : current vector I : identity matrix I(·) : mutual information i, j, k, p ,q, r, Q, R : discrete index
J : Jacobian
J(·) : cost, objective function K(·) : Kullback-Leibler divergence k, α : scalar constant
K, Λ, T : diagonal matrix L(·) : log-likelihood
M : number of mixtures (measurements) Mij : cumulant matrix n : noise vector n : number of buses N : number of sources N(·) : negentropy P : active power P : permutation matrix
p(·) : probability density function (pdf) Q : reactive power
r : residual error
R : resistance
S : apparent power S : matrix of sources
Ŝ : matrix of separated signals ŝ : vector of separated signals s : vector of source signals si : i-th element of vector s
sT : transpose of a vector s T : number of samples ti : time or sample index
v : eigenvector
V : orthogonal matrix
V : voltage
V : voltage vector
w : rows of separating matrix W, B : separating matrix
X : matrix of observed (measured) discrete-time data X : reactance
x : vector of mixtures (measurements, observations) x, x : state and state vector
Y : admittance
Y : admittance matrix
y : random variable
Z : impedance
Z : impedance matrix
Z : matrix of whitened signals z : measurement vector z : vector of whitened signals
δji : Kronecker delta µ : mean value θ : phase angle κi(·) : i-th cumulant λ : eigenvalue µi(·) : i-th moment σ : standard deviation σ2 : variance τ : time lag
φ(·), ψ(·) : nonlinear activation function Ф : component-wise filter
APPENDIX D: ABBREVIATIONS ASD : adjustable speed drive
BSS : blind source separation DC : direct current
e.m.f : electromotive force
EASI : equivariant adaptive separation via independence ERCOT : Electric Reliability Council of Texas