symbolic dynamic models for highly varying power system loads

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NOMENCLATURE α c γ CDSM CNLRF CSI CW F D DSAP EAF EPRI f FACTS FFT fix F m f xi GA GABPE Significance level A dictionary for signal χ A dictionary for signal γ Composite dynamic static model Constrained nonlinear recursive filter Common signal index Cumulative fractional occurrence in working dictionary Symbolic dynamical dictionary Distribution system aggregation program Electric arc furnace Electric power research institute Fractional occurrence associated with the dictionary Flexible AC transmission systems Fast Fourier transform Matlab function to round off a number Empirical distribution function for the population having m number of elements Fractional occurrence of i th word in X dictionary Genetic algorithm Genetic algorithm based parameter estimation
G n H 0 H 1 IM IO I pred IREQ J KS test M D M F N NLDM N w PRS PSCAD Q(s) q * α rand RT S/N Empirical distribution function for the population having n number of elements Null hypothesis: F(t)=G(t) for all t Hypothesis: F(t)≠G(t) for at least one t Induction motor Input output Predicted value of current Hydro Quebec Institute of Research Two-sided, two-sample Kolmogorov Smirnov statistics Kolmogorov-Smirnov test Mini dictionary, derived from the symbolic dynamic dictionary D Fractional occurrence associated with mini dictionary Number of cells used to descretize a signal Nonlinear dynamic models Maximum word length in a dictionary Pseudo random sequences Power system computer aided design. Significance function in KS test Parameter in the KS significance function Matlab function for generating a random number Real test, performed on actual EAF data Signal to noise ratio
Page 1 and 2: ARIZONA STATE UNIVERSITY POWER SYST
Page 3 and 4: include statistical tests, electric
Page 5 and 6: CHAPTER Page 2.6 Forecasting a sign
Page 7 and 8: LIST OF TABLES Table Page 3.1 Test
Page 9: LIST OF FIGURES Figure Page 2.1 Rep
Page 13 and 14: 1 CHAPTER 1 1.1 Motivation INTRODUC
Page 15 and 16: 3 Static load model: Most of the lo
Page 17 and 18: 5 the voltage response of the load
Page 19 and 20: 7 In 1999-2000, Dinesh at Arizona S
Page 21 and 22: 9 increasing or decreasing the valu
Page 23 and 24: 11 initial conditions, which genera
Page 25 and 26: 13 equipment. It simply identifies
Page 27 and 28: 15 Fractional occurrence: Fractiona
Page 29 and 30: 17 consecutive symbols at a time, a
Page 31 and 32: 19 CSI = ∑( f χ i * fγi) /( f
Page 33 and 34: 21 To check the accuracy of the abo
Page 35 and 36: CHAPTER 3 SYNTHETIC TESTS AND RESUL
Page 37 and 38: 25 3.4 Analysis tools To analyze th
Page 39 and 40: 27 The KS method involves identifyi
Page 41 and 42: 29 3.5 Test results ST-A01: The aim
Page 43 and 44: 31 ST-B02: Here the Matlab inline f
Page 45 and 46: 33 Table 3.5 Results for tests in c
Page 47 and 48: 35 Table 3.6 Results for category D
Page 49 and 50: 37 Table 3.7 Results for category E
Page 51 and 52: 39 CHAPTER 4 TESTS ON INDUSTRIAL AR
Page 53 and 54: 41 2. Constant number of cells: The
Page 55 and 56: 43 Table 4.2 Test statistics for di
Page 57 and 58: 45 Table 4.5 Results for RT-D03 Ind
Page 59 and 60: 47 was recorded with the same sampl
Page 61 and 62:
49 RT-E02: In this test maximum wor
Page 63 and 64:
51 RT-E04: To implement the propose
Page 65 and 66:
53 4.5 Discussion Load modeling: Fo
Page 67 and 68:
55 Table 4.11 Execution time compar
Page 69 and 70:
57 • Implementing a probabilistic
Page 71 and 72:
59 integration of physical informat
Page 73 and 74:
61 [1] M. S. Chen, “Determining l
Page 75:
63 [18] R. B. Fancher, A. E. Hulse,
Page 79 and 80:
67 A.1 Dictionary Formation In this
Page 81 and 82:
69 data sets and compares them by c
Page 83 and 84:
71 c=zeros(w,1); c(1:w)=x(s:s+w-1);
Page 85 and 86:
73 kount1(r1)=kount1(r1)+1; kount1(
Page 87 and 88:
75 y1=sin(x1*pi/12.5)+(1/3)*sin(3*x
Page 89 and 90:
77 if (r>=cwf(i))&(r
Page 91 and 92:
79 % A program to forecast a signal
Page 93 and 94:
81 f=f-1; end rr=rr+1; end r=r+1; e
Page 95 and 96:
83 for jj=1:f if(d(jj,2:nw)==0) min
Page 97 and 98:
85 A.5 Forecasting a signal using M
Page 99 and 100:
87 end f=f+1; d(f,1:w)=(c(1:w))'; e
Page 101 and 102:
89 if(d(j,i+1)~=0) if(x(nx)==d(j,i)
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91 end end newwd; wdlen; mm=wdlen+1
Page 105:
93 APPENDIX B ILLUSTRATIVE EXAMPLE
Page 108 and 109:
96 Z can be defined as Z(i) = Z(i+1
Page 110 and 111:
98 For a given s, the table entry i
Page 112 and 113:
100
Page 114 and 115:
102 Phase B EAF current 6 4 CT Curr
Page 116:
104 Table C.1 Sample data sheet for
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