FxLMS Algorithm Implementation

In document UNIVERSITA’ DEGLI STUDI DI PARMA (Page 85-91)

Chapter 4: Active Noise Cancellation System Implementation

4.2 MATLAB/Simulink ANC Model Implementation

4.2.2 FxLMS Algorithm Implementation

The energy carrier substitution pattern is frequently presented as linear and simple. The idea is that new energy carriers are introduced because of their superiority and that they replace inferior energy carriers. Environmentalists, who for ideological reasons want traditional energy carriers to be competitive with modern ones, have recently questioned this view. One example is Greenberg who attempts to kill the myth of simple serial transitions, which state that wood was replaced by coal, which was replaced by oil, electricity and gas. She believes that this view has distorted historical investigations because traditional sources of energy have not been included, only “commercial“ ones.13 This proposition is too simplistic. In reality “a far more complex pattern prevailed in which adoption of coal-fuelled technologies supplemented rather than replaced renewable energy sources“ and oil did not replace coal after the introduction of the automobile; its dominance was not established in most Western European countries until the 1960s. 14

Let us examine how the idea of serial transition applies in the case of Sweden. Was there a simple substitution pattern? My quantitative account of energy carriers forms the basis for an answer to this question. Most previous studies of the relative shares of Swedish energy carriers have the deficiency of

13Darmstadter, J. (1971): “Energy in the World economy: A Statistical Review of Trends in Output, Trade and Consumption Since 1925“, Baltimore, for instance totally excluded renewables.

14 Greenberg, D. (1992): “Fuelling the Illusion of Progress: Energy and Industrialisation in the European Experience”, in Byrne, J. & D. Rich (eds) Energy and Environment, The Policy Challenge, Energy Policy Studies, vol 6, London, p 90.

falling CO2 emission factors. Traditional energy carriers like firewood and muscle energy normally emit only as much CO2 as is sequestered from the atmosphere when trees and green plants grow and are therefore regarded as nil emitters of CO2 in this context. In a long-term perspective, however changes in the use of land occur, which may affect the carbon storage of the vegetation and soil. Thenext chapter describes changes in Swedish standing timber volumes and estimates the effects on CO2 emissions. Special attention is given to the role of firewood consumption for these changes.

Because the composition of energy carriers is crucial for CO2 intensity, it is of interest to understand the driving forces behind past transitions in energy systems and naturally there are additional reasons for such an interest. My analysis focuses on the costs involved in energy consumption: purchasing price, costs for handling as well as external costs and the relative shifts in emphasis between these costs as income rises.

The substitution pattern

The energy carrier substitution pattern is frequently presented as linear and simple. The idea is that new energy carriers are introduced because of their superiority and that they replace inferior energy carriers. Environmentalists, who for ideological reasons want traditional energy carriers to be competitive with modern ones, have recently questioned this view. One example is Greenberg who attempts to kill the myth of simple serial transitions, which state that wood was replaced by coal, which was replaced by oil, electricity and gas. She believes that this view has distorted historical investigations because traditional sources of energy have not been included, only “commercial“ ones.13 This proposition is too simplistic. In reality “a far more complex pattern prevailed in which adoption of coal-fuelled technologies supplemented rather than replaced renewable energy sources“ and oil did not replace coal after the introduction of the automobile; its dominance was not established in most Western European countries until the 1960s. 14

Let us examine how the idea of serial transition applies in the case of Sweden. Was there a simple substitution pattern? My quantitative account of energy carriers forms the basis for an answer to this question. Most previous studies of the relative shares of Swedish energy carriers have the deficiency of

13Darmstadter, J. (1971): “Energy in the World economy: A Statistical Review of Trends in Output, Trade and Consumption Since 1925“, Baltimore, for instance totally excluded renewables.

14 Greenberg, D. (1992): “Fuelling the Illusion of Progress: Energy and Industrialisation in the European Experience”, in Byrne, J. & D. Rich (eds) Energy and Environment, The Policy Challenge, Energy Policy Studies, vol 6, London, p 90.

not disclosing their sources, which is especially troublesome when it comes to the firewood estimates. The graph by IVA for the period 1800-1975 leaves out all information of its sources and it has been reprinted in some articles in spite of not incorporating, for example, changes in firewood consumption during the World Wars.15 Kaijser’s figure for the period 1870-1990 is less schematic and it allows for impacts of the World Wars, but it completely lacks information of its sources. His figure is almost identical to a figure provided by Johansson, which does not contain any source information either. 16 Kaijser and Johansson have probably used the available statistics for modern energy carriers, but for most of the period there are no statistics for firewood and it is important that the authors disclose either the basis for their own firewood estimates, or that they provide references for the estimates. Ljungberg estimated the relative shares of firewood, coal, electricity and heating oil in the period 1890-1980, and did include source information, but the accounts were not complete, since petrol and kerosene were omitted and the firewood series ended in the mid 1950s.17

Figure 5.1 Relative shares of the energy carriers 1800-2000

0%

20%

40%

60%

80%

100%

1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

%el(S)

%oil

%spl+peat

%fwood

%muscle

Sources: see figure 3.2. Comment: The energy carriers are: natural gas, peat, spent pulping liquor (spl), electricity (calculated in the Swedish manner), raw oil, coal, firewood and animate energy.

%gas

%coal

15 For instance it was uncritically used in Olsson, S-O.(1993), op. cite, p 229.

16 Kaiser, A.(1994), op. cite, p 158. Johansson, T.B. Nationalencyclopedin, volume 5, 1991, p 496.

The only difference is the relative share of oil after 1970.

17 Ljungberg, J.(1984):”Perspektiv på energipriserna” in Energi och strukturförändring i Sverige, Allmänna energisystemstudier, Energiforskningsnämnden, Efn/AES 1984:1, p 26. Ljungberg uses Arpi as source for his household firewood estimate.

not disclosing their sources, which is especially troublesome when it comes to the firewood estimates. The graph by IVA for the period 1800-1975 leaves out all information of its sources and it has been reprinted in some articles in spite of not incorporating, for example, changes in firewood consumption during the World Wars.15 Kaijser’s figure for the period 1870-1990 is less schematic and it allows for impacts of the World Wars, but it completely lacks information of its sources. His figure is almost identical to a figure provided by Johansson, which does not contain any source information either. 16 Kaijser and Johansson have probably used the available statistics for modern energy carriers, but for most of the period there are no statistics for firewood and it is important that the authors disclose either the basis for their own firewood estimates, or that they provide references for the estimates. Ljungberg estimated the relative shares of firewood, coal, electricity and heating oil in the period 1890-1980, and did include source information, but the accounts were not complete, since petrol and kerosene were omitted and the firewood series ended in the mid 1950s.17

Figure 5.1 Relative shares of the energy carriers 1800-2000

0%

20%

40%

60%

80%

100%

1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

%el(S)

%oil

%spl+peat

%fwood

%muscle

Sources: see figure 3.2. Comment: The energy carriers are: natural gas, peat, spent pulping liquor (spl), electricity (calculated in the Swedish manner), raw oil, coal, firewood and animate energy.

%gas

%coal

15 For instance it was uncritically used in Olsson, S-O.(1993), op. cite, p 229.

16 Kaiser, A.(1994), op. cite, p 158. Johansson, T.B. Nationalencyclopedin, volume 5, 1991, p 496.

The only difference is the relative share of oil after 1970.

17 Ljungberg, J.(1984):”Perspektiv på energipriserna” in Energi och strukturförändring i Sverige, Allmänna energisystemstudier, Energiforskningsnämnden, Efn/AES 1984:1, p 26. Ljungberg uses Arpi as source for his household firewood estimate.

My results of the relative shares of the energy carriers in the period 1800-2000 are depicted in figure 5.1. The most conspicuous feature is that there have been spectacular changes in the energy carriers’ relative shares. Transitions have taken place. A closer look at figure 5.1 does, however, reveal that in most cases they were neither abrupt nor simple. Some of them were gradual and they were also temporarily reversed during the World Wars. The diffusions of coal and electricity occurred at a particularly gradual pace, while oil had a more rapid breakthrough. A gradual diffusion of electricity is hardly surprising, given the systemic properties of electric provision. The reason why coal diffused more slowly than oil may also be linked to the infrastructure of supply. While coal was diffused on the basis of ships and railways and was restricted to urban areas, oil diffusion was related to the establishment of a road structure, which enabled a more far-reaching diffusion of oil into rural areas.

Until after the Second World War there were no rapid transitions at all and the only abrupt changes were substitution effects of the Wars. Coal gradually replaced firewood from the 1820s and at the onset of the First World War it had passed firewood. Firewood did however temporarily regain its leading position when coal imports were restricted during the war. Electricity diffused slowly from the 1890s and the rate accelerated during the First World War. In addition, during the Second World War there was a relative increase in domestic firewood and hydropower at the expense of imported fossil fuels.

After the Second World War more spectacular changes took place. First of all oil increased its share immensely during the 1950s and 1960s. Second, electricity rapidly increased its share in the early 1970s at the expense of oil, due to the introduction of the nuclear program. Third, traditional energy carriers rapidly lost ground after the Second World War until 1975. Firewood continuously lost shares of the energy consumption until 1970 but in the 1980s it regained some of its lost ground. The retrogression of firewood was partly outbalanced by a related expansion of spent pulping liquor, a wood based waste product of the pulp industry, which gained a fairly important position after the Second World War. Muscle energy became completely insignificant in relative terms after the Second World War, as an effect of the diffusion of tractors in agriculture and the subsequent motorization of forestry, which were the two remaining areas, where muscle energy was still used to a significant extent.

Substitution patterns have been gradual and sometimes reversed, which is not in accordance with the notion of a simple serial transition and one might wonder why such an idea has won ground. One obvious reason for the belief in the serial transition idea is its appealing simplicity and the fact that fundamental transitions have occurred. Another reason may be the myth of salvation. Basalla portrays the myths surrounding new energy carriers. He discerns a historically repeated pattern of immense expectations of new energy carriers in the US, until

My results of the relative shares of the energy carriers in the period 1800-2000 are depicted in figure 5.1. The most conspicuous feature is that there have been spectacular changes in the energy carriers’ relative shares. Transitions have taken place. A closer look at figure 5.1 does, however, reveal that in most cases they were neither abrupt nor simple. Some of them were gradual and they were also temporarily reversed during the World Wars. The diffusions of coal and electricity occurred at a particularly gradual pace, while oil had a more rapid breakthrough. A gradual diffusion of electricity is hardly surprising, given the systemic properties of electric provision. The reason why coal diffused more slowly than oil may also be linked to the infrastructure of supply. While coal was diffused on the basis of ships and railways and was restricted to urban areas, oil diffusion was related to the establishment of a road structure, which enabled a more far-reaching diffusion of oil into rural areas.

Until after the Second World War there were no rapid transitions at all and the only abrupt changes were substitution effects of the Wars. Coal gradually replaced firewood from the 1820s and at the onset of the First World War it had passed firewood. Firewood did however temporarily regain its leading position when coal imports were restricted during the war. Electricity diffused slowly from the 1890s and the rate accelerated during the First World War. In addition, during the Second World War there was a relative increase in domestic firewood and hydropower at the expense of imported fossil fuels.

After the Second World War more spectacular changes took place. First of all oil increased its share immensely during the 1950s and 1960s. Second, electricity rapidly increased its share in the early 1970s at the expense of oil, due to the introduction of the nuclear program. Third, traditional energy carriers rapidly lost ground after the Second World War until 1975. Firewood continuously lost shares of the energy consumption until 1970 but in the 1980s it regained some of its lost ground. The retrogression of firewood was partly outbalanced by a related expansion of spent pulping liquor, a wood based waste product of the pulp industry, which gained a fairly important position after the Second World War. Muscle energy became completely insignificant in relative terms after the Second World War, as an effect of the diffusion of tractors in agriculture and the subsequent motorization of forestry, which were the two remaining areas, where muscle energy was still used to a significant extent.

Substitution patterns have been gradual and sometimes reversed, which is not in accordance with the notion of a simple serial transition and one might wonder why such an idea has won ground. One obvious reason for the belief in the serial transition idea is its appealing simplicity and the fact that fundamental transitions have occurred. Another reason may be the myth of salvation. Basalla portrays the myths surrounding new energy carriers. He discerns a historically repeated pattern of immense expectations of new energy carriers in the US, until

their problems, in the form of environmental costs and/or insufficient supply, make the expectations erode at a later stage. These high expectations leave traces in the historical relationships at certain periods, while the less mythical, older energy sources do not leave as many. 18 There is therefore a risk that historians will overestimate the new energy carriers and neglect the old ones. In the Swedish context the importance of fuel-wood has been particularly neglected. Another reason for oversimplified schematic figures, like the one presented by IVA, may be that relative shares of the energy carriers have been based on benchmark data instead of annual figures.

It is not easy to characterize the development in a simple and unambiguous manner. The appropriate choice of method of characterization depends on the goal, but the basis should be consistent and clearly stated. If the organizing principle is the relative consumption of the energy carriers the following characterization may be suggested: (1) 1800-1850: the firewood and muscle period (2) 1850-1900: the firewood, coal and muscle period (3): 1900-1950: the coal, firewood, oil, electricity and muscle period (4): 1950-2000: the oil, electricity, firewood, spent pulping liquor and coal period. This characterization rather indicates a larger variety in supply over time than a serial transition. If the label is based on only the main energy carrier of each period, the following pattern may be suggested: (1) 1800-1900: the firewood period, (2) 1900-1950:

the coal period, (3) 1950-2000: the oil period. If the guiding principle is instead relative progress of energy carriers and only the most expansive energy carrier is to be mentioned the following pattern is appropriate: (1) 1800-1850: the muscle period (2) 1850-1950: the coal period (3) 1950-1970: the oil period (4) 1970-1990: the electricity period. 5) 1990-2000: the bio-energy period.19

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