**2. Case report**

P.A., a 6-year-old girl, was referred to our institution in May 2005 with a diagnosis of appendicitis. The girl had been complaining of right lower abdominal pain for 6 months. More recently, the pain was exacerbated by walking and coughing. Abdominal ultrasound showed a slight effusion of the pelvic fossa. Her postnatal history showed some period of constipation spaced by regular daily evacuations. Blood examinations showed neutrophil leucocytosis. The patient underwent laparoscopic appendectomy using the three-trocar technique, three endo-loops and the Liga-Sure for the hemostasis. During the laparoscopic exploration no hyperplastic mesenteric lymphnode was found. The appendix appeared moderately hyperemic with a slight enlargement of two-thirds of its distal portion (Fig. 1).

The postoperative course was uneventful and the girl was discharged on day 1, without any complications. The appendix underwent a routine histological examination. The morphological appearance showed thickened lamina propria and submucosa, which were occupied by pseudonodules of immunocompetent cells (Fig. 2), characterized by lymphocytes with small nuclei with a narrow cytoplasmic rim and plasma cell (Fig. 3). Immunohistochemical studies revealed positivity for CD20 (CD20, pan B cell), and

<sup>\*</sup> Corresponding Author

Appendiceal MALT Lymphoma in Childhood – Presentation and Evolution 421

Fig. 3. Hematoxylin–eosin staining. Hyperdense lymphocytic population with small nuclei and narrow cytoplasmic rim and some plasmacytoid and monocytoid elements with great

negativity for CD5 (CD5, Pan T cell, and B cell subsets) and CD10 using monoclonal antibodies, and positivity for anti-k (immunoglobulin light chain) using polyclonal antibodies, in addition to a low positivity to Ki-67 (proliferation-associated marker). Extensive further examination revealed that the lymphoma was restricted to the distal

Abdominal MRI, OGDS, and capsule endoscopy of the ileum were all negative; the search for *H. pylori* was also negative. No chemotherapy was performed. After a 15-months followup, the patient was doing well (Marte et al., 2008). Calprotectin and clinical evaluation were repeated yearly showing no problem and the patient was asymptomatic. 3 year after, the yearly follow-up showed a slight increase of fecal calprotectin values (40µg/g) with recurrent abdominal pain and occasional episodes of diarrhea. The girl underwent a new clinical evaluation, small bowel radiological contrast study, videocapsule, OGDS, and colonoscopic examination. No fever or weight loss was present; erythrocyte sedimentation rate, C-reactive protein level were slightly higher. Perinuclear antineutrophil cytoplasmatic antibodies (pANCA) and Anti-Saccharomyces cerevisiae (ASCA) antibodies are not

The small bowel x-ray contrast, OGDS and videocapsule study demonstrated no abnormalities. Colon biopsies revealed a mild nonspecific IBD extending till 90 cm from the

portion of the appendix (stage IA) and was not associated with any specific infection.

and hyperchromatic nuclei.

increased too.

anal verge. (Fig.4,5,6,7)

Fig. 1.

Fig. 2. Hematoxylin–eosin staining. The wall of appendix is thickened, and occupied by a compact nodular formation. The serous and muscular tunic appear thin.

Fig. 2. Hematoxylin–eosin staining. The wall of appendix is thickened, and occupied by a

compact nodular formation. The serous and muscular tunic appear thin.

Fig. 1.

Fig. 3. Hematoxylin–eosin staining. Hyperdense lymphocytic population with small nuclei and narrow cytoplasmic rim and some plasmacytoid and monocytoid elements with great and hyperchromatic nuclei.

negativity for CD5 (CD5, Pan T cell, and B cell subsets) and CD10 using monoclonal antibodies, and positivity for anti-k (immunoglobulin light chain) using polyclonal antibodies, in addition to a low positivity to Ki-67 (proliferation-associated marker). Extensive further examination revealed that the lymphoma was restricted to the distal portion of the appendix (stage IA) and was not associated with any specific infection.

Abdominal MRI, OGDS, and capsule endoscopy of the ileum were all negative; the search for *H. pylori* was also negative. No chemotherapy was performed. After a 15-months followup, the patient was doing well (Marte et al., 2008). Calprotectin and clinical evaluation were repeated yearly showing no problem and the patient was asymptomatic. 3 year after, the yearly follow-up showed a slight increase of fecal calprotectin values (40µg/g) with recurrent abdominal pain and occasional episodes of diarrhea. The girl underwent a new clinical evaluation, small bowel radiological contrast study, videocapsule, OGDS, and colonoscopic examination. No fever or weight loss was present; erythrocyte sedimentation rate, C-reactive protein level were slightly higher. Perinuclear antineutrophil cytoplasmatic antibodies (pANCA) and Anti-Saccharomyces cerevisiae (ASCA) antibodies are not increased too.

The small bowel x-ray contrast, OGDS and videocapsule study demonstrated no abnormalities.  (Fig.4,5,6,7)

Appendiceal MALT Lymphoma in Childhood – Presentation and Evolution 423

Fig. 6. Absent mucosal surface epithelium with focal reduction of the glands. The lamina

propria is edematous, site of microbleeds and is infiltrated by elements of immunocompetent and heaps of eosinophils. (20 X). 90 cm from the anal verge.

Fig. 4. Colonoscopy. Rectum and sigmoid colon: mucosal redness, nonspecific inflammatory pattern.

Fig. 5. Colonoscopy. Rectum and sigmoid colon: mucosal redness, nonspecific inflammatory pattern.

Fig. 4. Colonoscopy. Rectum and sigmoid colon: mucosal redness, nonspecific inflammatory

Fig. 5. Colonoscopy. Rectum and sigmoid colon: mucosal redness, nonspecific inflammatory

pattern.

pattern.

Fig. 6. Absent mucosal surface epithelium with focal reduction of the glands. The lamina propria is edematous, site of microbleeds and is infiltrated by elements of immunocompetent and heaps of eosinophils. (20 X). 90 cm from the anal verge.

Appendiceal MALT Lymphoma in Childhood – Presentation and Evolution 425

Fig. 8. Recto-sigmoid junction (10X). Mucosal home-based micro-inflammatory polyps. The glandular portion is moderately reduced. The lamina propria is edematous and infiltrated

by immunocompetent elements.

Fig. 7. Rectum (20X): 2 small erosions of the mucosa, glandular patrimony preserved, but low in mucus cells. The lamina propria is diffusely infiltrated by immunocompetent cells (lymphocytes and plasma cells).

Fig. 7. Rectum (20X): 2 small erosions of the mucosa, glandular patrimony preserved, but low in mucus cells. The lamina propria is diffusely infiltrated by immunocompetent cells

(lymphocytes and plasma cells).

Fig. 8. Recto-sigmoid junction (10X). Mucosal home-based micro-inflammatory polyps. The glandular portion is moderately reduced. The lamina propria is edematous and infiltrated by immunocompetent elements.

Appendiceal MALT Lymphoma in Childhood – Presentation and Evolution 427

rectum (Matsudo et al., 1997) following *H. pylori* eradication. Other risk factors for MALT lymphoma include autoimmune diseases like Hashimoto thyroiditis or Sjogren syndrome, and Borrelia burgdorferi for skin lymphoma. A further prerequisite for the development of MALT lymphoma in children may be the presence of HIV infection (Teruya-Feldestein et al., 1995; Mo et al., 2004). In some patients no risk factors can be identified. The most common sites are the stomach and salivary glands. Others sites are: ocular adnexa, the lungs, thyroid and the skin (Zucca et al., 2000). Some retrospective analyses of histopathological results of appendectomy specimens performed for acute appendicitis in a large sample of patients, including children, report a prevalence of appendiceal malignant tumors ranging from 0.4 (Tchana et al., 2006) to 1.5% (Ravi et al., 2006). Among the malignant tumors, carcinoids have the highest incidence (Tchana et al., 2006; Ravi et al., 2006) and 70–90% of these tumors are discovered incidentally because they are usually restricted to the distal appendix (Akerstrom, 1989; Aranha & Greenle, 1980). From a review of the literature we found only one case of appendix lymphoma in paediatric age presenting with intussusception symptoms (Karabulut et al., 2005). Our report probably represents the first case of MALT lymphoma of the appendix found accidentally in a child during an appendectomy. MALT lymphomas manifest with aspecific symptoms. In our case, the clinical presentation was characterized by recurrent abdominal pain, and the only element of suspicion was the enlargement of the distal portion of the appendix. The subsequent evolution to a mild form of IBD could be considered as an evolution of the appendiceal malt-limphoma for which the phenomenon should be considered a prodromal presentation of a more extensive bowel disease which require a close follow-up and specific therapy (Aomatsu et al., 2011). Otherwise we can't exclude that the subsequent IBD could be an autonomous, subsequent disease considered that, also in this case, there are no data in the Literature. Furthermore, given the previous appendiceal malt-lymphoma, the efficacy of mesalazine alone, without the use of immunosuppressive drugs, can be considered a very favorable factor in our case. In conclusion, even if the occurrence of malignant appendiceal pathology in children is rare (Setty & Termuhlen, 2010), the probability that it is asymptomatic is very high. According to our experience, our case suggests that histological examination should always be performed following appendectomy in children and that if a MALT lymphoma were discovered, a close follow-up is strongly recommended, not only for the MALT lymphoma recurrence but

also for its possible evolution towards an inflammatory bowel disease.

lymphoma after treatment for *H. pylori*, *Lancet* 348:268–269.

inflammatory bowel disease, *Dig Dis Sci*. Aug;56(8):2372-7.

classification project, *Blood* 89:3909–3918.

gastrointestinal tract, *Am Surg* 46(8):429–435.

Akerstrom G (1989). Surgical treatment of patients with the carcinoid syndrome, *Acta Oncol*

Alkan S, Karcher DS, Newman MA, Cohen P (1996). Regression of salivary gland MALT

Anonymous (1997). A clinical evaluation of the international lymphoma study group

Aomatsu T, Yoden A, Matsumoto K, Kimura E, Inoue K, Andoh A, Tamai H (2011). Fecal

Aranha GV, Greenle HB (1980). Surgical management of carcinoid tumors of the

classification of non Hodgkin's lymphoma. The non Hodgkin's lymphoma

calprotectin is a useful marker for disease activity in pediatric patients with

**4. References**

28(3):409–414.

Fig. 9. Mucosal lymphocytes nodule. Glands, well structured, present a reduction of mucus cells. The lamina propria is infiltrated by immunocompetent elements. (20x). 15 cm from the anal verge.

A 6 weeks cycle of Mesalazine (5ASA), 2gr/day was administered to the patient obtaining the induction of remission and then repeated every 2 months for the prevention of recurrences. At present the patient is doing well and a strict clinical serologic follow-up with calprotectin, P-Anca and ASCA is scheduled every 6 months and, yearly, colonoscopy.


3. VS30 and fundamental period

constructions at the Port/Coastal Area, and/or a high degree of consolidation due to the constant presence of heavy weight (containers) that are located at these sites for shipping purposes. Note that the DFA predicted very well the H/V ratios in such circumstances as well, for both, the fundamental period and the overall shape of the transfer function. It is noted that this consolidated layer at the top of the Port Area behaves as a low pass filter and does not have an influence in the fundamental period of motion of the whole soil system; such feature was corroborated

performing the DFA without the stiff top layer at Mucurapo Secondary School (see Figure 10b). Sea Lots site at the South East of POS (see Figure 1 at site 6X) is characterized by the lowest VS of 50 m/s for all array sites that correspond to a swamp area overlaid by stiff deposits. Such low values of VS have been observed in

Figure 11 depicts the comparison between the 1-D SH wave amplification employing the Vs profiles obtained by the GAs and the H/V observed spectral ratios. We also adopted for the surface sediments above the bedrock a low-quality

Comparison of H/V spectral ratios and 1-D SH wave transfer function; case (1) only up wave amplification and case (2) up + down amplification with refraction and reflection in bedrock. (a) Queen's Park Savannah array (1X), (b) Port Area (5X), (c) Mucurapo Secondary School (3X), (d) Sea Lots (8X), (e) Nelson Mandela Park (2X), (f) Woodford Square (8X), (g) Federation Park (4X), (h) St. James hospital (9X), and (i) St. Benedict's Children's home (7X). The fundamental period of soil T is indicated by the arrows.

sedimentary stratigraphy of natural intertidal flats [26].

Natural Hazards - Risk, Exposure, Response, and Resilience

Figure 11.

70

2.2 H/V ratios and 1-D theoretical transfer function for SH-waves

An important parameter in the modification of seismic waves propagating toward the surface is the composition of the near-surface soil layers. In different building codes around the world, the average shear wave velocity of the upper 30 m (VS30) has been adopted to characterize the response of seismic waves to the influence of near-surface strata.

In first instance, we compared the VS30 obtained from our microtremors array observation and the ones estimated by the empirical formulas of Matsuoka et al. [27] employing 2000 sites in Japan based on geomorphological units.

We calculated the VS30 from our microtremor results using the following formula:

$$V\_S \mathbf{30} = \frac{\mathbf{30}}{\sum\_{i=1}^{N} \frac{h\_i}{V\_i}} \tag{10}$$

where hi and Vi denote the thickness (in meters) and the shear wave velocity of the ith layer; N is the total number of soil layers respectively.

We classified the sites (1X–5X, 8X) as a Gravelly Terrace, Sea Lots (site 6X) as a Reclaimed Land, and St. Dominic's Children's Home to the East (7X) and St. James Hospital to the West (9X) as Mountain Foot Slope sites (see Figure 1). The empirical formulas to estimate VS30 (m/s) for the Gravelly Terrace (Eq. (11)), the Reclaimed Land (Eq. (12)), and the Mountain Foot Slope (Eq. (13)) yield:

$$\log \text{VSS30} = 2.493 + 0.072 \log Ev + 0.027 \log Sp} - 0.164 \log Dm \pm 0.122(\sigma) \tag{11}$$

$$
\log \text{VS} \mathfrak{B} = 2.37 \mathfrak{B} - 0.124 \log \text{D}m \pm 0.12 \mathfrak{B}(\sigma) \tag{12}
$$

$$\log \text{VSA} = 2.602 \pm 0.092(\sigma) \tag{13}$$

where Ev is the elevation (m), Sp refers to the Tangent of Slope\*1000, Dm yields the distance (km) from mountain or hill, and σ denotes the standard deviation. We took Dm as the shortest distance to the Northern Range or the Laventille Metalimestone foothills (Figure 1). The results are presented in Figure 12. In general the estimated VS30 from the empirical formulas of Matsuoka et al. [27] estimates well the velocities obtained by the GA's from our array measurements in the range of �σ (standard deviation). We also compared the VS30 of our microtremors array profiles with the ones estimated by Allen and Wald [28] using the topographic slope as a proxy of site conditions employing the USGS Web Server (earthquake.usgs.gov/hazards/apps/vs30/). We retrieved the correspondent predicted VS30 at the location of each microtremors array. The most noticeable difference is observed for the mountain foot slope in St. James (site 9X). However, we did not find a good correlation when comparing with soil types proposed by

#### Figure 12.

Comparison of VS30 (m/s) retrieved from our microtremors array and the empirical formulas of Matsuoka [27] and the method of Allen and Wald [28]. The shadowed area represents the classification of Zhao and Xu [29] based on fundamental period of soil and VS30.

Zhao and Xu [29] based on NEHRP classes on VS30 (shadowed areas in Figure 12). This leads to suggest to characterize the soil at POS by the fundamental period rather than the VS30 [30]; Zhao and Xu [29] suggest also that site period is a better parameter for characterizing soil conditions, in very deep or very soft sediments.

#### 4. Preliminary assessment of liquefaction susceptibility

Nakamura [31] proposed a technique to investigate the liquefaction susceptibility based on microtremor measurements, namely, the vulnerability index Kg for the surface ground, as follows:

$$K\_{\rm g} = \frac{{A\_{\rm g}}^2}{F\_{\rm g}} \tag{14}$$

of Saint James in the Coastal area yields a possibility of high liquefaction potential. Evidence of soil subsidence is already present in some structures near the Port Area as the Lighting House Tower (Figure 14). Next to it, the Eric Williams Complex known as the Twin Towers which are one of the tallest buildings in POS (92 m height) has been constructed in the 1980s incorporating piles on their foundations; the eyewitness during the construction process affirmed that some piles sank totally during their driving process due to extremely soft soil conditions found at that time in the coastal area. Several new high-rise buildings including hotels, a water front, high-income class dwellings, amenity centers, and the Port itself are located in this high liquefaction susceptibility area. Ironically, Sea Lots located to the West is characterized by a very low-income social class; it is also a prone area of high potential of liquefaction. It is noted that the study of Kraft [32] employing the methodology of Holzer et al. [33] yielded similar conclusions for POS and another

Preliminary liquefaction hazard map for Port of Spain City, employing Nakamura index Kg, (see Eq. (14)).

Estimation of Shear Wave Velocity Profiles Employing Genetic Algorithms and the Diffuse Field…

DOI: http://dx.doi.org/10.5772/intechopen.85129

cities of Trinidad employing regional geological map conditions.

Zones yielding a Kg above 20 are suggested to a high liquefaction susceptibility.

Shear wave velocity VS profiles were determined by performing nine

microtremors array surveys in Port of Spain (POS), Trinidad, employing the spatial autocorrelation SPAC method and genetic algorithms (GAs); the results yielded VS between 50 and 2000 m/s at POS. The ellipticity pattern for the first mode of Rayleigh waves explains the resulting predominant peak in the H/V Nakamura ratios for all array sites. We validated the soil profiles retrieved by the SPAC and GAs'schemes comparing the synthetics' horizontal-to-vertical spectral (H/V) ratios

5. Conclusions

73

Figure 13.

where Ag is the amplification factor referenced to the engineering bedrock and Fg is the predominant frequency of vibration of the soil profile (the inverse of the period); both values can be taken from the horizontal-to-vertical spectral ratio (H/V) of microtremors; Ag is considered to be the H/V ratio at the predominant frequency. Values of Kg greater than 20 are considered likely to liquefy. The authors computed the liquefaction potential using Eq. (14) at each point and develop an iso-liquefaction potential map interpolating the Kg value of the 1181 single mobile microtremors data employed in Salazar et al. [1] (Figure 13). The results are very concerning regarding this hazard because the water table in POS can be found just at the surface, the soil conditions then are saturated sands and gravels, and sometimes poorly consolidated reclaimed land has been placed specially in the coastal areas. The areas with a high liquefaction susceptibility are The Port, Sea Lots, some parts of Woodbrook, a small spot in Cocorite (where in fact reclaimed land exists), and some small areas in the Queen's Park Savannah and Federation Park. Also South Estimation of Shear Wave Velocity Profiles Employing Genetic Algorithms and the Diffuse Field… DOI: http://dx.doi.org/10.5772/intechopen.85129

Figure 13.

Zhao and Xu [29] based on NEHRP classes on VS30 (shadowed areas in Figure 12). This leads to suggest to characterize the soil at POS by the fundamental period rather than the VS30 [30]; Zhao and Xu [29] suggest also that site period is a better parameter for characterizing soil conditions, in very deep or very soft sediments.

Comparison of VS30 (m/s) retrieved from our microtremors array and the empirical formulas of Matsuoka [27] and the method of Allen and Wald [28]. The shadowed area represents the classification of Zhao and Xu

Nakamura [31] proposed a technique to investigate the liquefaction susceptibility based on microtremor measurements, namely, the vulnerability index Kg for the

> 2 Fg

(14)

Kg ¼ Ag

where Ag is the amplification factor referenced to the engineering bedrock and Fg is the predominant frequency of vibration of the soil profile (the inverse of the period); both values can be taken from the horizontal-to-vertical spectral ratio (H/V) of microtremors; Ag is considered to be the H/V ratio at the predominant frequency. Values of Kg greater than 20 are considered likely to liquefy. The authors computed the liquefaction potential using Eq. (14) at each point and develop an iso-liquefaction potential map interpolating the Kg value of the 1181 single mobile microtremors data employed in Salazar et al. [1] (Figure 13). The results are very concerning regarding this hazard because the water table in POS can be found just at the surface, the soil conditions then are saturated sands and gravels, and sometimes poorly consolidated reclaimed land has been placed specially in the coastal areas. The areas with a high liquefaction susceptibility are The Port, Sea Lots, some parts of Woodbrook, a small spot in Cocorite (where in fact reclaimed land exists), and some small areas in the Queen's Park Savannah and Federation Park. Also South

4. Preliminary assessment of liquefaction susceptibility

surface ground, as follows:

[29] based on fundamental period of soil and VS30.

Natural Hazards - Risk, Exposure, Response, and Resilience

Figure 12.

72

Preliminary liquefaction hazard map for Port of Spain City, employing Nakamura index Kg, (see Eq. (14)). Zones yielding a Kg above 20 are suggested to a high liquefaction susceptibility.

of Saint James in the Coastal area yields a possibility of high liquefaction potential. Evidence of soil subsidence is already present in some structures near the Port Area as the Lighting House Tower (Figure 14). Next to it, the Eric Williams Complex known as the Twin Towers which are one of the tallest buildings in POS (92 m height) has been constructed in the 1980s incorporating piles on their foundations; the eyewitness during the construction process affirmed that some piles sank totally during their driving process due to extremely soft soil conditions found at that time in the coastal area. Several new high-rise buildings including hotels, a water front, high-income class dwellings, amenity centers, and the Port itself are located in this high liquefaction susceptibility area. Ironically, Sea Lots located to the West is characterized by a very low-income social class; it is also a prone area of high potential of liquefaction. It is noted that the study of Kraft [32] employing the methodology of Holzer et al. [33] yielded similar conclusions for POS and another cities of Trinidad employing regional geological map conditions.


**4.3. The revenue loss estimates of base erosion and profit shifting (BEPS)**

In the aftermath of the global financial crisis, and the fiscal problems that followed in many countries, the public and policy makers paid greater attention to the tax avoidance of multinational companies. Similarly, researchers devoted greater efforts to estimating the scale and nature of the associated tax losses.

Corporate tax is an important source of government revenue in all regions of the world. As shown in **Figure 6**, though there is an annual fluctuation, on average in the OECD governments raise around 10% of their total tax revenue from CIT, which is approximately 3% of GDP [44]. CIT accounts for a larger share of total tax revenues on average in lower-income countries than in high-income countries [6].

Making estimates of the global losses due to base erosion and profit shifting requires complex and rigorous research. Currently, the most comprehensive studies available are from the International Monetary Fund (IMF) researchers Crivelli et al. and Cobham and Janský whose study has been recently published by the United Nations University World Institute for Development Economics Research (UNU-WIDER) in Helsinki [6, 9, 45].

Using panel data for 173 countries over 33 years, Crivelli et al. examine the magnitude and features of international fiscal externalities. In particular, they focus on the spillovers from tax policy decisions in individual jurisdictions onto others. They develop and use an innovative method allowing a distinction between spillover effects through real investment decisions

**Figure 6.** Taxes on corporate income as percentage of total taxation, OECD average. Source: OECD, 2017.

and through avoidance techniques and quantify the revenue losses through the latter. In total, they estimate global revenue losses at around US\$650 billion annually, of which around onethird relate to developing countries. The concentration as a share of gross domestic product (GDP) is somewhat higher in developing countries compared to OECD economies [45].

Cobham and Gibson combine this finding with data on the relatively greater reliance on corporate tax revenue in developing countries to show that the estimated losses are around 2–3% of total tax revenue in OECD countries, but 6–13% in developing countries [46].

Applying a methodology developed by researchers at the International Monetary Fund to an improved dataset Cobhan and Jansky estimate revenue losses of around US\$500 billion per year globally [6]. Though the largest losses are suffered by rich economies such as the United States, relative losses are more intensive in lower-income countries. While any estimates of this intentionally hidden phenomenon are necessarily uncertain, the size of magnitude suggests that the economic development of countries may in some cases be substantially damaged by the activities of multinational companies.

In country-specific research, Clausing using Bureau of Economic Analysis survey data on US multinational corporations during 1983–2012 finds that profit shifting is likely costing the US government between \$77 billion and \$111 billion in corporate tax revenue by 2012, and these revenue losses have increased substantially in recent years [7]. Those findings are corroborated by other researchers who estimate that the US tax losses from profit shifting of multinational firms may approach or even exceed \$100 billion per year [8].

However, accumulated losses are staggering. Recent estimates show that Fortune 500 corporations are avoiding up to \$767 billion in US federal income taxes by holding more than \$2.6 trillion of "permanently reinvested" profits offshore. In their latest annual financial reports, 29 of these corporations reveal that they have paid an income tax rate of 10% or less in countries where these profits are officially held, indicating that most of these profits are likely in offshore tax havens [47].

This might be viewed as evidence that lowering corporate tax rates is an effective tool against avoidance. Narrower studies, however, such as the studies by Cobham and Janský (2017) and Clausing [7] provide evidence that profit shifting has grown strongly even as effective tax rates have fallen. Cobham and Janský (2017) document effective tax rates for US-headquartered multinationals of 0–5% in the major misalignment jurisdictions to which most profit is shifted, compared to 15–20% in the USA and other economies on average [6].


**5. The electric field in the surrounding of a 400 kV PUAC 2150/490/65 power line**

We deal with electric field in the surroundings of electrically charged bodies, for example in the vicinity of electric energy transmission lines, transmission antennas of telecommunications equipment. Electric fields are everywhere, where electric charge is present. Every electric conductor under voltage creates an electric field around itself. The field exists even when no current is flowing through the conductor, so even when the power line is not laden with users. The higher the voltage is the greater the electric field. Electric fields have the highest intensity close to the source and decrease very rapidly with distance. Metal shields them very well, but other material weaken it as well. The intensity of electric fields of power lines is greatly reduced by walls, buildings and trees. The electric fields of underground cables are also reduced by the soil.

We have determined that with the use of insulation made from polyurethane we can reduce the electric field intensity on the surface of covered conductors and that it is possible to operate at 400 kV. Due to the increased voltage it is necessary to examine the impact of such above ground power lines on the environment in accordance with our regulations.

#### **5.1. Electromagnetic radiation**

392 Polyurethane

**4. The mechanics of the PUAC 2150/490/65 power line**

impact of power lines by means of non-ionizing radiation.

**Figure 10.** Cross section of the proposed covered conductor

**Figure 11.** The calculated sag of the power line PUAC 2150/490/65

Mechanical calculations showed that the proposed cable (figure 10) meets the requirements. With the calculation of the formed catenary we get the height at which the conductor needs to be over the ground (figure 11) and thus the input data to determine the environmental

> Exposure to electromagnetic radiations is not something new. It accompanies us from the very beginning of human existence. Here we think of natural sources of radiation. Another story is artificially generated sources, which are much stronger in intensity and more recently also increased in number. Man is now, unlike in the past, at home and at work, exposed to a complex mix of electric and magnetic fields.

> The main sources of electric and magnetic fields of low frequencies 50 Hz are artificial sources of electromagnetic radiations, namely those caused by man, which are devices for transmitting and distributing electricity, electrical substations, and all devices that use electricity for their operation. The intensity of electromagnetic radiations emitted by artificial sources, in comparison with natural resources (the Earth's static magnetic field, electric field caused by the discharge in the atmosphere - lightning) is much higher. When an electrical device is plugged in, an electric field is generated in its surroundings. The higher the voltage, the stronger the electric field at a certain distance from the device. The electric field is present even when the device is not working because there is no need for the electric current to flow to create voltage. The magnetic field on the other hand requires a flow of electrons, so it occurs only when the device is plugged in and the current is flowing. Under these conditions both fields exist in the room. The greater the power consumption and thus the electric current, the stronger the magnetic field is.

#### **5.2. Evaluation of electromagnetic fields in the Slovenian legislation**

The Slovenian government adopted a regulation on electromagnetic radiations in the natural and living environment, which specifies the maximum allowed threshold of radiations. The regulation protects the most sensitive areas (EMR protection zone I, which

includes living environment, schools, kindergartens, hospitals) with an additional preventive factor.

These areas demand increased protection against radiation therefore they are subject to ten times more severe limitations than in the European Union. For EMR protection zone II (areas with no residential building), the restrictions for magnetic fields are the same as in the European Union but for the intensity of the electric field two times higher values are allowed.

The maximum levels of radiation for networks with a frequency of 50 Hz are 500 V/m and 10 µT for EMR protection zones I and 10000 V/m and 100 µT for EMR protection zones II. Radiation with frequencies of 50 Hz includes electromagnetic fields from distribution substations, over ground and underground power lines, high voltage transformers and others. This is described under the Slovenian Regulation (2nd paragraph of article 2). At this frequency we distinguish two fields:

When calculating the effects of electromagnetic radiation we have to consider the most unfavorable impact on nature that can occur in normal operations.

#### **5.3. Electric field intensity in the vicinity of an overhead power line**

For the straight infinitely long conductor we assume that the electric charge is evenly distributed over the whole surface (uniform linear charge density). The charge on such a conductor can be described with an infinite line charge, which in any given point of T (x, y) (Fig. 12) leads to the following vector of electric field intensity:

$$
\bar{E} = \bar{1}\_{\text{r}} \cdot \frac{q\_{+}}{2 \cdot \pi \cdot \varepsilon\_{0}} \cdot \frac{1}{\left| \overline{r\_{+}} \right|} \tag{23}
$$

Polyurethane as an Isolation for Covered Conductors 395

where:

[ ] *q* is the columnar vector of positive charge, *V* is the columnar vector of conductor potentials,

*C* is the square matrix of the capacitance.

**Figure 12.** Electric field of a line charge

To determine the electric field intensity we have to determine the charge on the phase conductors. These are obtained from the current values of the voltage taking into account the capacitance. In Figure 13 current value of tension on the 400 kV overhead line are shown.

**Figure 13.** Current values of voltage in each phase of a three-phase conductor

*5.3.1. Voltage on conductors*

Where:

To calculate the electric field intensity of a conductor above a conductive surface we use the method of equivalent charges. Its main idea is the exchange of the surface charge near a conductive surface (in our case soil) with a charge opposite in sign but equal in quantity that is projected over a conductive surface.

$$
\begin{bmatrix} q\_+ \end{bmatrix} = \begin{bmatrix} \mathbf{C} \end{bmatrix} \cdot \begin{bmatrix} V \end{bmatrix}\_{\prime\prime}
$$

**Figure 12.** Electric field of a line charge

#### *5.3.1. Voltage on conductors*

394 Polyurethane

Where: 1r

*r*

0

preventive factor.

frequency we distinguish two fields:

is the unit vector of distance,

is the vacuum permittivity.

is projected over a conductive surface.

point of observation and

*q* is the positive value of the line charge,

includes living environment, schools, kindergartens, hospitals) with an additional

These areas demand increased protection against radiation therefore they are subject to ten times more severe limitations than in the European Union. For EMR protection zone II (areas with no residential building), the restrictions for magnetic fields are the same as in the European Union but for the intensity of the electric field two times higher values are allowed. The maximum levels of radiation for networks with a frequency of 50 Hz are 500 V/m and 10 µT for EMR protection zones I and 10000 V/m and 100 µT for EMR protection zones II. Radiation with frequencies of 50 Hz includes electromagnetic fields from distribution substations, over ground and underground power lines, high voltage transformers and others. This is described under the Slovenian Regulation (2nd paragraph of article 2). At this

 The electric field, which is described with the effective value of the electric field intensity *E* [V/m] and depends on the voltage of the radiation source or the element The magnetic field, which is described with the Magnetic flux density *B* [T] which depends on the electric current passing through the source of radiation or the element.

When calculating the effects of electromagnetic radiation we have to consider the most

For the straight infinitely long conductor we assume that the electric charge is evenly distributed over the whole surface (uniform linear charge density). The charge on such a conductor can be described with an infinite line charge, which in any given point of T (x, y)

> 0 1 1 2 *q E*

(23)

 *r*

is the absolute value of the distance vector between the electric charge and the

To calculate the electric field intensity of a conductor above a conductive surface we use the method of equivalent charges. Its main idea is the exchange of the surface charge near a conductive surface (in our case soil) with a charge opposite in sign but equal in quantity that

*q CV* ,

unfavorable impact on nature that can occur in normal operations.

(Fig. 12) leads to the following vector of electric field intensity:

**5.3. Electric field intensity in the vicinity of an overhead power line**

r

To determine the electric field intensity we have to determine the charge on the phase conductors. These are obtained from the current values of the voltage taking into account the capacitance. In Figure 13 current value of tension on the 400 kV overhead line are shown.

**Figure 13.** Current values of voltage in each phase of a three-phase conductor

#### *5.3.2. Charge on conductors*

We get the matrix of capacitance *C* by first determining the elements of the potential coefficients of the conductor *p* (Tičar I., Zorič T., 2003):

$$p\_{\rm ii} = 18 \cdot 10^9 \cdot \ln \frac{H\_{\rm ii}}{r} \qquad \left[\frac{\rm m}{\rm F}\right] \tag{24}$$

Polyurethane as an Isolation for Covered Conductors 397

L1

*H*L1L1'

**Figure 14.** Mirror projections over the conductive surface plane

**Figure 15.** Current values of electric charge on the conductor

*d*L1L2

*d*L2L3

*H*L1L3'

*y*

*H*L2L1'

*H*L1L2'

L1' L3'

L2

L3

*H*L3L3'

*x*

*d*L1L2

*H*L2L2'

*H*L3L2'

*H*L2L3' *H*L3L1'

L2'

$$p\_{\rm ii} = 18 \cdot 10^9 \cdot \ln \frac{H\_{\rm ii}}{d\_{\rm ii}} \qquad \left[ \frac{\rm m}{\rm F} \right] \text{.} \tag{25}$$

where:

Distances established like that apply to bare conductors (line charge) in the air with a constant relative permittivity ε0. In our case, where we are dealing with insulation around the conductors, the electric charge gathers on the edge of the insulation and we have to consider that the distance between conductors is reduced by the thickness of the insulation. So when we consider these reductions in distance and the designations on figure 14 we get the new:

»Individual« potential coefficient:

$$p\_{ii} = \frac{\frac{1}{\mathcal{E}\_{r2}} \cdot \ln \frac{r\_2}{r\_1} + \ln \frac{H\_{ii}}{r\_2}}{2 \cdot \pi \cdot \varepsilon\_0} \tag{26}$$

»Mutual« potential coefficient

$$p\_{ij} = \frac{\frac{1}{\mathcal{E}\_{r2}} \cdot \ln \frac{r\_2}{r\_1} + \ln \frac{H\_{ij}}{d}}{2 \cdot \pi \cdot \varepsilon\_0} \tag{27}$$

We deal with three potential of conductors, four line charges and nine potential coefficients, which we can combine into a matrix.

$$
\begin{bmatrix} V\_{\rm L1} \\ V\_{\rm L2} \\ V\_{\rm L3} \end{bmatrix} = \begin{bmatrix} p\_{\rm L11,1} & p\_{\rm L11,2} & p\_{\rm L11,3} \\ p\_{\rm L21,1} & p\_{\rm L21,2} & p\_{\rm L21,3} \\ p\_{\rm L31,1} & p\_{\rm L31,2} & p\_{\rm L31,3} \end{bmatrix} \cdot \begin{bmatrix} q\_{\rm L1} \\ q\_{\rm L2} \\ q\_{\rm L3} \end{bmatrix} \tag{28}
$$

**Figure 14.** Mirror projections over the conductive surface plane

where:

*5.3.2. Charge on conductors*

coefficients of the conductor *p* (Tičar I., Zorič T., 2003):

*p*ii is the individual potential coefficient, *p*ij is the mutual potential coefficient,

*d*ij is the distance between multi-phase conductors,

*ε*0 is the vacuum permittivity,

other multi-phase conductors.

»Individual« potential coefficient:

»Mutual« potential coefficient

which we can combine into a matrix.

ii

ij

*p*

We get the matrix of capacitance *C* by first determining the elements of the potential

9 ii

9 ij

*H*ii is the distance between the multi-phase conductors ant there mirror projections, *H*ij is the distance between the multi-phase conductors and the mirror projections of

Distances established like that apply to bare conductors (line charge) in the air with a constant relative permittivity ε0. In our case, where we are dealing with insulation around the conductors, the electric charge gathers on the edge of the insulation and we have to consider that the distance between conductors is reduced by the thickness of the insulation. So when we

> 2 r2 1 2 0

2 2 1

>

1 ln ln

2

We deal with three potential of conductors, four line charges and nine potential coefficients,

L1 L1L1 L1L2 L1L3 L1 L2 L2L1 L2L2 L2L3 L2 L3 L3L1 L3L2 L3L3 L3

*V ppp q V ppp q V ppp q*

*r*

0

*r H r d*

*r H r r*

*ii*

*ij*

(26)

(27)

(28)

1 ln ln

2

*ii*

*ij*

*p*

*p*

consider these reductions in distance and the designations on figure 14 we get the new:

*p d*

m 18 10 ln

*H*

*r*

ij m 18 10 ln , F *H*

F

(25)

(24)

**Figure 15.** Current values of electric charge on the conductor

From the equation 1 *C p* and by considering the geometry on figure 15 we get the current value of the electric charge on the conductors:

$$
\begin{bmatrix} q \ \end{bmatrix} = \begin{bmatrix} p \ \end{bmatrix}^{-1} \cdot \begin{bmatrix} \mathcal{U} \ \end{bmatrix} \tag{29}
$$

Polyurethane as an Isolation for Covered Conductors 399

**Figure 17.** The electric field intensity on the edge of the insulation of the conductor L2

**Figure 18.** The electric field intensity on the edge of the insulation of the conductor L3

#### *5.3.3. Electric field intensity*

With the current values of electric charge on the conductor we calculated the components of the electric field intensity that exists because of the charge on all three phases.

We get the greatest electrical field intensity in the substance 2 at a radius *r*2 (figure 4):

$$E\_{2\max} = \frac{q}{2 \cdot \pi \cdot \varepsilon\_0 \cdot \varepsilon\_{t2}} \cdot \frac{1}{r\_2} = \frac{U \cdot \frac{1}{r\_2}}{\varepsilon\_{t2} \cdot \left(\frac{1}{\varepsilon\_{t1}} \cdot \ln\frac{r\_2}{r\_1} + \frac{1}{\varepsilon\_{t2}} \cdot \ln\frac{r\_3}{r\_2}\right)} \tag{30}$$

We calculated the electric field intensity in several points of the space around the conductor. The points were selected at the edge of the insulation (at the radius *r*2) of the multi-phase conductors. The radius was chosen so that the distance to the neighbouring conductors was as small as possible. As seen in figure 5, the point for the phase L1 is at (4.6785; 27.9785), for the phase L2 at (3.9215; 30.9785) and for the phase L3 at(5.4785; 25.0215). We got the electric field intensity at the edge of the insulation for each individual phase conductor (figure 16, figure 17 and figure 18) with vector addition of the contribution of all the electric charges (equation 23). The geometric sum of the current values (the current value of the electric field intensity) is a periodic quantity, but not a sinus one.

**Figure 16.** Electric field intensity on the edge of the insulation of the conductor L1 in the point (-4.6785; 27.9785)

**Figure 17.** The electric field intensity on the edge of the insulation of the conductor L2

27.9785)

From the equation 1 *C p* and by considering the geometry on figure 15 we get the

With the current values of electric charge on the conductor we calculated the components of

the electric field intensity that exists because of the charge on all three phases.

*q r E*

We get the greatest electrical field intensity in the substance 2 at a radius *r*2 (figure 4):

1 *qp U* (29)

2

1

*U*

*r r r*

r1 1 r2 2

*r r*

(30)

0 r2 2 2 3

1 , 2 1 1 ln ln

r2

We calculated the electric field intensity in several points of the space around the conductor. The points were selected at the edge of the insulation (at the radius *r*2) of the multi-phase conductors. The radius was chosen so that the distance to the neighbouring conductors was as small as possible. As seen in figure 5, the point for the phase L1 is at (4.6785; 27.9785), for the phase L2 at (3.9215; 30.9785) and for the phase L3 at(5.4785; 25.0215). We got the electric field intensity at the edge of the insulation for each individual phase conductor (figure 16, figure 17 and figure 18) with vector addition of the contribution of all the electric charges (equation 23). The geometric sum of the current values (the current value of the electric field

**Figure 16.** Electric field intensity on the edge of the insulation of the conductor L1 in the point (-4.6785;

current value of the electric charge on the conductors:

2 max

intensity) is a periodic quantity, but not a sinus one.

*5.3.3. Electric field intensity*

**Figure 18.** The electric field intensity on the edge of the insulation of the conductor L3

We get the effective value of the electric field intensity by summing over the whole period. By definition, the effective value of the periodic quantity is the one which makes the same effect as the corresponding one-way quantity. In our case the effective value of the electric field intensity is as follows.

$$E\_{\rm ef} = \frac{1}{T} \cdot \int\_0^T E^2(t) \cdot \mathbf{d}t \tag{31}$$

Polyurethane as an Isolation for Covered Conductors 401

**Figure 19.** The electrical field intensity perpendicular to the bisector of the span in the point of the

distance of 30 m away from the bisector of the power line.

The value of the electric field intensity falls under the permitted limit of the regulation at a

**6. The calculation of the electric field intensity with the finite element**

The planned covered conductor does not float in the air by itself, but is mounted in a threephase electric system and hanged on a steel construction. Because of that, an analytical approach is not sufficient and the approximate results have to be checked with the finite

**6.1. Calculation of the electric field intensity at the edge of the insulation of the**

Based on the measurements on figure 5, we calculated the maximum electric field intensity of the phase L1, using the computer program ELEFANT®. For the basic harmonic current this holds true when the voltage of the phase L1 is 326 kV and 163 kV for the phase L2 and L3. The phase to phase voltage from phase L1 to the other two phases is then at an amplitude value of 400 kV – 565.69 kV. From figure 20 you can see that the electric field intensity does not exceed the value of 0.1 MV/m, which is less than what we got from our

greatest sag.

**method**

element method.

analytical calculation (equation 22).

**conductor**

here:

*E*ef is the effective value of the electric field intensity, *T* is the period,

*E* is the vector sum of all the contributing charges.

#### *5.3.4. The electric field intensity on the edge of the insulation*

The highest current value of the electric field intensity in the point (-4.6785; 27.9785) – on the edge of the insulation of the conductor L1 is 24.366e+003 V/m with the effective value of 17.235e+003 V/m.

The highest current value of the electric field intensity in the point (3.9215; 30.9785) – on the edge of the insulation of the conductor L2 is 19.865e+003 V/m with the effective value of 14.287e+003 V/m.

The highest current value of the electric field intensity in the point (5.4785; 25.0215) – on the edge of the insulation of the conductor L3 je 33.813e+003 V/m with the effective value of 24.023e+003 V/m.

From the calculations and figures, we see that the electrical field intensity at the edge of the insulation of any of these three conductors does not exceed the critical dielectric strength of air.


**2. Wind speed variability**

Overall wind variability consists of different fluctuating terms with different periods, depend‐ ing on the sources. For instance, fluctuating term can be caused by day-night effects (e.g., the effects of sea breeze), because there are "quick" fluctuations in some minute periods.

Figure 2 shows a typical power curve of a variable speed wind turbine generator. In general, the operating wind speed is divided into different regions. In Region 1 and Region 2 (low to rated wind speed), a wind turbine is operated in variable speed at a constant pitch angle (typically 0o ). The output power of the generator is low to rated power. The operation is op‐ timum because the turbine is operated at the maximum performance coefficient Cp. When wind speed varies, the output power varies as the cube of wind speed variations. Once wind reaches its rated speed, the rotational speed also reaches the rated speed. This rotational speed must be limited by the pitch control to keep the rotor speed from a runaway condition and to limit the mechanical stresses of the wind turbine structure (tower, blades, and gear‐ box). The output power is limited to its rated value.

Thus, wind power output varies only when wind speeds are below rated value. Below rated wind speed, the rate of change of the output power ( *dP dt* ) is either positive or negative, de‐ pending on the direction of wind speed change. Above rated wind speeds, any fluctuations will be capped at rated by the pitch action, or *dP dt* =0.

**Figure 2.** Power curve of a typical wind turbine generator

Additionally, many wind power plants are co-located in the same region where wind resour‐ ces are excellent; thus, the spatial diversity among wind power plants contributes to a smooth‐ er output power of the region than the output power of an individual wind power plant.

**Figure 1.** Real and reactive power output of a wind power plant; (a) Single turbine representation (b) Sixteen turbines

Figure 1(a) shows the fluctuation in the output power when the wind power plant is repre‐ sented by a single turbine. Figure 1(b) illustrates the real and reactive power output when the wind power plant is represented by sixteen turbines. With greater wind diversity, as shown in Figure 1(b), the power fluctuation is smoother than that with less wind turbine

Overall wind variability consists of different fluctuating terms with different periods, depend‐ ing on the sources. For instance, fluctuating term can be caused by day-night effects (e.g., the

Figure 2 shows a typical power curve of a variable speed wind turbine generator. In general, the operating wind speed is divided into different regions. In Region 1 and Region 2 (low to rated wind speed), a wind turbine is operated in variable speed at a constant pitch angle

timum because the turbine is operated at the maximum performance coefficient Cp. When wind speed varies, the output power varies as the cube of wind speed variations. Once wind reaches its rated speed, the rotational speed also reaches the rated speed. This rotational speed must be limited by the pitch control to keep the rotor speed from a runaway condition and to limit the mechanical stresses of the wind turbine structure (tower, blades, and gear‐

Thus, wind power output varies only when wind speeds are below rated value. Below rated

). The output power of the generator is low to rated power. The operation is op‐

*dt* ) is either positive or negative, de‐

effects of sea breeze), because there are "quick" fluctuations in some minute periods.

representation

286 Advances in Wind Power

(typically 0o

representation, as shown in Figure 1(a) [1].

box). The output power is limited to its rated value.

wind speed, the rate of change of the output power ( *dP*

**2. Wind speed variability**

If the power controller is not properly designed, wind fluctuations may excite the mechani‐ cal resonance of the structure or gearbox, which may lead to mechanical failures of the wind turbine [2]–[3].

Spectral tools are often used to analyze wind speed variability because they make it possible to study different frequency fluctuation terms. The most popular one used for this purpose is the Power Spectral Density (PSD).

The PSD of a function is defined by the Fourier transform of its autocorrelation. PSD is therefore expressed in frequency domain. Its physical meaning is related to fluctuating ki‐ netic energy on a certain frequency.

Van der Hoven [4] analyzed the PSD of horizontal wind speed, based mainly on measure‐ ments done at Brookhaven National Laboratory. Figure 3 shows such spectra, with two main peaks and a spectral gap between them. The first peak occurred at a period of around four days and was caused by migratory pressure systems of a synoptic weather map scale. The second peak occurred at a period of 1 minute because of a mechanical and/or convective type of turbulence. Van der Hoven's observations also showed some relation between the spectral gap shape and surface roughness under some circumstances. Additional analysis shows more complex spectra, especially over the ocean or in smooth terrains [5]–[9]; where there is an important contribution of mesoscale fluctuations combined with various phe‐ nomena such as convective longitudinal rolls [11] or cumulus clouds [12] that may contain considerable spectral density in the frequency range. At some other places, the gap was veri‐ fied by experimental data [4], [13]–[14].

**Figure 3.** Spectrum estimated by Van der Hoven [4]

PSD spectrum is usually calculated by using short segments of data with similar atmospher‐ ic characteristics. The reduction or removal of the spectral gap introduces some difficulties on the analysis because microscale and macroscale are no longer separated. This limits the findings of particular atmospheric regimes lasting long enough to calculate a meaningful spectrum. Thus, some researchers are considering the use of more complex spectral tools based on time and frequency domain. For instance, the Hilbert-Huang transform has been used for analyzing wind fluctuations over the North Sea [8].

Wind speed variability is important with regard to power system management. An example of the significance of these power fluctuations is in Energinet.dk (the Danish Transmission System Operator). According to [15], Energinet.dk has observed that power fluctuations from the 160-MW offshore wind power plant at Horns Rev in West Denmark introduce sev‐ eral challenges to reliable operation of the local power system. The power fluctuations also contribute to deviations from the planned power exchange with the Central European Pow‐ er System. Moreover, it was observed that the timescale of the power fluctuations was from tens of minutes to several hours.

Figure 4 shows the relation between time and geographical scales and the impacts affecting power system operation. Depending on the level of the wind power penetration, power fluc‐ tuations due to wind speed variability may influence the frequency regulation; transmission and distribution efficiency, and load flow; or even efficiency of the thermal and hydro pow‐ er plants connected to the same grid.

**Figure 4.** Time and geographical scales of power system issues [16]

Van der Hoven [4] analyzed the PSD of horizontal wind speed, based mainly on measure‐ ments done at Brookhaven National Laboratory. Figure 3 shows such spectra, with two main peaks and a spectral gap between them. The first peak occurred at a period of around four days and was caused by migratory pressure systems of a synoptic weather map scale. The second peak occurred at a period of 1 minute because of a mechanical and/or convective type of turbulence. Van der Hoven's observations also showed some relation between the spectral gap shape and surface roughness under some circumstances. Additional analysis shows more complex spectra, especially over the ocean or in smooth terrains [5]–[9]; where there is an important contribution of mesoscale fluctuations combined with various phe‐ nomena such as convective longitudinal rolls [11] or cumulus clouds [12] that may contain considerable spectral density in the frequency range. At some other places, the gap was veri‐

PSD spectrum is usually calculated by using short segments of data with similar atmospher‐ ic characteristics. The reduction or removal of the spectral gap introduces some difficulties on the analysis because microscale and macroscale are no longer separated. This limits the findings of particular atmospheric regimes lasting long enough to calculate a meaningful spectrum. Thus, some researchers are considering the use of more complex spectral tools based on time and frequency domain. For instance, the Hilbert-Huang transform has been

Wind speed variability is important with regard to power system management. An example of the significance of these power fluctuations is in Energinet.dk (the Danish Transmission System Operator). According to [15], Energinet.dk has observed that power fluctuations from the 160-MW offshore wind power plant at Horns Rev in West Denmark introduce sev‐ eral challenges to reliable operation of the local power system. The power fluctuations also contribute to deviations from the planned power exchange with the Central European Pow‐ er System. Moreover, it was observed that the timescale of the power fluctuations was from

fied by experimental data [4], [13]–[14].

288 Advances in Wind Power

**Figure 3.** Spectrum estimated by Van der Hoven [4]

tens of minutes to several hours.

used for analyzing wind fluctuations over the North Sea [8].


*Edited by Fethi Derbel*

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Studying a LW-VCSEL-Based Resonant Cavity Enhanced Photodetector and Its Application in Microwave Photonics Circuits

*Mikhail E. Belkin, Leonid I. Zhukov, Dmitriy A. Fofanov, Mikhail G. Vasil'ev and Alexander S. Sigov*