La EIA y el Patrimonio de Áreas Naturales del Estado 158

The literature discussed in Section 2.3 is on the load forecasting in LV network applications and how choosing the forecast model variables can affect the prediction model performance.

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The literature shows that there are no studies which specifically forecast RTG cranes and there is only one study that analyses the daily diesel RTG crane demand over only eight days period [19]. However, the study in [19] does not investigate the peak demand, the volatility nature of the demand or the correlation between the demand and external variables, so a significant part of this thesis is on the study of the RTG crane electrical demand and forecast. This section introduces an overview of the electrified RTG crane demand in order to investigate the non- smooth and stochastic demand behaviour of the crane. In order to show the behaviour of the RTG crane demand over a long period of time, the half hourly demand has been plotted in Figure 3-1 for the 3-month data set. This plot for a long period of time aims to highlight any possible seasonal trends. A line has been plotted in Figure 3-1 to examine the linear long-term trend in the data, as described in Equation (3-1).

D̂L (n) = a + b n, (3-1) where D̂L ∈ ℝNis the RTG crane demand, N is the total length of analysed data and n is a half hour time step over the data set period and a, b ∈ ℝ (a = 21.1 and b= −0.0003). In this study, the R-squared (R2_{) statistics have been used to measure the goodness of the data fit with the} regression line, as described in Equation (3-2).

R2= 1 −er eb

(3-2)

where e_r is the sum of squared errors of the proposed regression line trend and e_b is the sum of squared errors of the baseline model, as described in Equations (3-3) and (3-4), respectively.

er= ∑ ( DL (n) − D̂L (n)) 2 , N n=1 (3-3) eb = ∑( DL (n) − μ)2, N n=1 (3-4)

where the RTG crane demand, D_L , data set has N values can be specified as

DL = ( DL (1), DL (2) , . . , DL (N)) T

, D̂L (n) the predicted demand value based on the regression line trend at n and μ is the mean of the crane demand data, as described in Equation (3-5).

62 μ =1 N ∑ DL (n) N n=1 . (3-5)

The plotted trend line in Figure 3-1 show that the average demand (21.1 kWh) exhibits verily little linear trend and is quite flat from the start to the end of the data. The linear fit gives an R2 value of 0.017. In other words, the linear model only explains 1.7% of the load variability and is an insufficient for explaining the majority of the demand behaviour. As seen in Figure 3-1, the distribution of the base or average demand and peak demand values show volatile behaviour and there is no strong seasonalites or patterns from month-to-month or week to week without a clear sign of patterns. This irregular behaviour is likely due to the effect of operator behaviour decisions. The work activity inside ports will also depend on the occurrence or the movement of shipments which may have annual seasonalites but they are not obvious on our time scale considered. For example, a port may have many ships berthed at the same time and this requires increased crane activity.

Jan Feb March

Time K w h 0 10 20 30 40 50 60 70 80

Figure 3-1:The half hourly RTG crane demand (blue line) with linear model fit to the data (dotted).

Analysis of the RTG crane demand data is shown in Table 3-1 to present various statistics of D_L including the average values and variability at half hourly and daily resolutions. The equations of average demand, μ, and standard deviation, σ, used in this section are presented in (3-5) and (3-6). In addition, to show the extent of variability between standard deviation and mean, the coefficient of variation, CV, also known as the relative standard deviation is

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expressed in Equation (3-7). Furthermore, the total daily crane demand is also presented in Table 3-1. σ = √∑ ( DL (n) − μ) 2 N n=1 N − 1 (3-6) CV = 100 σ μ (3-7)

Table 3-1:Summary of the electrified RTG crane demand.

The RTG crane demand resolutions 𝛍 𝛔 CV Maximum demand (kWh) Minimum demand (kWh) Half hourly 21.10 14.85 70.38% 72.3 0.0 Daily 516.65 294.02 56.90% 865.6 120.9

Table 3-1 shows the standard deviation, σ, for the half hourly demand profile is 14.85 kWh and 294.02 kWh for the daily crane demand. This shows a significant sign that the crane demand data is volatile and varies significantly around the mean value with 70.38% and 56.90% coefficients of variation for half hourly and daily demand, respectively. In general, the high standard deviation and coefficient of variation values are due to the diversity in the container weight (5 to 40 tonnes per container) and number of crane moves, as will be shown later. Furthermore, the histogram of the half hourly crane demand is plotted and fitted with a normal distribution line and lognormal fit in Figure 3-2 to present the relation between the D_L , μ and σ. However, the data is clearly not normally distributed which complicates analysis. The half hourly RTG crane demand values are distributed between 0 kWh and 73 kWh, which gives a wide range of possible crane demand values and illustrate the uncertainty in the crane demand. It is observed that a high number of instances are clustered between 0 kWh to 15 kWh and not around the μ value, leading to further emphasise that the normal distribution is not able to accurately describe the distribution of the crane data. Furthermore, the lognormal gives a better fit compared to the normal distribution but still does not completely explain the data. The histogram distribution has a long tail compared to that expressed by a normal distribution better describing the large values of demand which are more likely to occur. The high number of occurrences for the low demand, as presented Figure 3-2, is mainly related to the large

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amount of low activity at the port including maintenance periods. In the literature, Papaioannou et al. [19] analysed and studied the energy usage by the various RTG crane motors. On average an RTG crane is in idle mode (waiting mode without lifting activity) about 30% of the day time [19], which explains the high number of instances for the low demand values.

In addition, Figure 3-3 shows an alternative visualisation of the distribution of crane demand for the demand data at Port of Felixstowe. Based on the average half hourly crane demand, in Table 3-1, the RTG crane demand is divided into four main categories: low demand (0-10 kWh), normal demand (10-30 kWh), high demand (30-50 kWh) and high peak demand (above 50 kWh). As seen in Figure 3-3, the low demand values occur about 27% of the time while about 21% and 5% of the time the electrical crane demand is high or has high peak demand, respectively. The remaining 47% of the time crane remains consumed around the average demand value. 0 10 20 30 40 50 60 70 RTG Crane demand (Kwh) 200 400 600 800 1000 1200 F re que nc y Lognormal fit

Figure 3-2: Illustration of RTG crane demand data in a histogram along with a normal distribution fit and lognormal.

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Figure 3-3: Distribution of half hourly RTG crane demand.

In the literature, Papaioannou et al. [19] analysed the energy usage for diesel RTG crane over eight days only with average daily demand equal to 518.75 kWh. In [19], the analysis showed that the RTG crane works about 50% and 12.5 % of the testing days with high demand above 700 and 800 kWh, respectively. In this thesis, to investigate the distribution of peak demand on a daily level over 3 months, Table 3-2 presents the percentage of time that the daily crane demand is over the average value. On average an RTG crane is working 9.8% of the time at a high demand level (above 800 kWh) and 31.6% of the time above 700 kWh. Furthermore, an important aim of the research is to reduce the percentage of time that that crane demand exceeded the average demand, as shown in Figure 3-3 and Table 3-2. This will be tested using an optimal ESS controller based on the future knowledge of the demand. In the following sections, the analysis of the RTG crane demand time series patterns, demand characteristics and demand correlation with external variables are presented.

Table 3-2:Percentage of time that the crane daily demand is over the average value.

Percentage of time Daily average demand

Over 700 kWh 31.6%

516.6 kWh Over 800 kWh 9.8%