symbolic dynamic models for highly varying power system loads

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ABSTRACT Representation and modeling of loads in a power system are very important, as a system may have different types of complex loads. The work reported here is aimed at loads which are highly varying in nature, such as electric arc furnaces and steel rolling mills. These loads do not have fully accepted physical models because of the unpredictable nature of load current, but they often have a rich set of operating data over a wide range of operation. The application of Symbolic Dynamics in load modeling, as presented in this thesis, is a novel concept. The scope of this concept is twofold. One aspect is the utilization of time series historical data of voltages and currents to formulate the model. The model might be used in routine power engineering applications such as power flow studies, transient stability studies and short circuit studies. The second aspect is the utilization of historical voltage and current data to predict future load current values. The predictions could then be used for power conditioning. An example of the power conditioning application is active filtering of unwanted components of load current. Symbolic Dynamics is based on the coding of signals as ‘symbols’, which appear in groups known as ‘words’. Thus, bus voltage and load current are descretized to be represented by symbols. The states of these time varying signals can be represented by words. A ‘symbolic dynamic dictionary’ is formed from historical time series data. The words and the symbols themselves are treated much as they might in a natural language. Symbolic dynamic modeling has been applied to both synthetic and alternating current (AC) electric arc furnace data. The tests have been used to compare the symbolic dynamic model response to the actual measurements. Comparisons presented herein
include statistical tests, electric power quality indices, and a new proposed index to compare nonsinusoidal signals.
Page 1: ARIZONA STATE UNIVERSITY POWER SYST
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 and 10: LIST OF FIGURES Figure Page 2.1 Rep
Page 11 and 12: G n H 0 H 1 IM IO I pred IREQ J KS
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
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41 2. Constant number of cells: The
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43 Table 4.2 Test statistics for di
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45 Table 4.5 Results for RT-D03 Ind
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47 was recorded with the same sampl
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49 RT-E02: In this test maximum wor
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51 RT-E04: To implement the propose
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53 4.5 Discussion Load modeling: Fo
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55 Table 4.11 Execution time compar
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57 • Implementing a probabilistic
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59 integration of physical informat
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61 [1] M. S. Chen, “Determining l
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63 [18] R. B. Fancher, A. E. Hulse,
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67 A.1 Dictionary Formation In this
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69 data sets and compares them by c
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71 c=zeros(w,1); c(1:w)=x(s:s+w-1);
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73 kount1(r1)=kount1(r1)+1; kount1(
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75 y1=sin(x1*pi/12.5)+(1/3)*sin(3*x
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77 if (r>=cwf(i))&(r
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79 % A program to forecast a signal
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81 f=f-1; end rr=rr+1; end r=r+1; e
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83 for jj=1:f if(d(jj,2:nw)==0) min
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85 A.5 Forecasting a signal using M
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87 end f=f+1; d(f,1:w)=(c(1:w))'; e
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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
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93 APPENDIX B ILLUSTRATIVE EXAMPLE
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96 Z can be defined as Z(i) = Z(i+1
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98 For a given s, the table entry i
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100
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102 Phase B EAF current 6 4 CT Curr
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104 Table C.1 Sample data sheet for
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symbolic dynamic models for highly varying power system loads

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