Optimal Allocation of Curtailment Levels of PV Power Output in Different Regions in Consideration of Reduction of Aggregated Fluctuations

Due to the high penetration of photovoltaic power generation system (PV) anticipated in the future, the curtailment of PV power output becomes crucial, not only to maintain supply-demand balance but also to preserve an adequate capacity for the frequency control. When the curtailment level (CL) of the aggregated PV power output is determined in a day-ahead unit commitment (UC) scheduling, different CL should be applied to different regions with distinctive weather modes in the power system area so that the fluctuations of aggregated PV power output are minimized. The objective of this study is to optimally allocate the CL to each region based on the short-term forecasting of the weather modes so that the hourly maximum fluctuation of the aggregated PV power output (MFagg) is minimized as long as the aggregated average power output (Avgagg) becomes the same as the scheduled value in UC. Based on the past observations of PV power output, the proposed method employs relations between the regions’ MF and CL (MF-CL patterns), and relations between the regions’ Avg and CL (Avg-CL patterns) for several typical weather modes. Thus, a specific MF-CL pattern and Avg-CL pattern are determined for each region based on the short-term forecasting of the weather mode, and the CL optimization is proceeded by using these patterns. The proposed methods are tested by using the time-series of PV power output at 61 observation points in the central region of Japan for one year. As a result, it is demonstrated that merely acknowledging the weather mode of each region enabled the proposed methods to reduce MFagg significantly and these results are practically similar to the method where perfect short-term forecasting of PV power output was utilized in the entire year

Positive Correlations between Short-Term and Average Long-Term Fluctuations in Wind Power Output

Wind power has been increasingly deployed in the last decade to decarbonize the electricity sector. Wind power output changes intermittently depending on weather conditions. In electrical power systems with high shares of variable renewable energy sources, such as wind power, system operators aim to respond flexibly to fluctuations in output. Here, we investigated very short-term fluctuations, short-term fluctuations (STFs), and long-term fluctuations (LTFs) in wind power output by analyzing historical output data for two northern and one southern balancing areas in Japan. We found a relationship between STFs and the average LTFs. The percentiles of the STFs in each month are approximated by linear functions of the monthly average LTFs. Furthermore, the absolute value of the slope of this function decreases with wind power capacity in the balancing area. The LTFs reflect the trend in wind power output. The results indicate that the flexibility required for power systems can be estimated based on wind power predictions. This finding could facilitate the design of the balancing market in Japan

Parameter Scaling for Epidemic Size in a Spatial Epidemic Model with Mobile Individuals

<div><p>In recent years, serious infectious diseases tend to transcend national borders and widely spread in a global scale. The incidence and prevalence of epidemics are highly influenced not only by pathogen-dependent disease characteristics such as the force of infection, the latent period, and the infectious period, but also by human mobility and contact patterns. However, the effect of heterogeneous mobility of individuals on epidemic outcomes is not fully understood. Here, we aim to elucidate how spatial mobility of individuals contributes to the final epidemic size in a spatial susceptible-exposed-infectious-recovered (SEIR) model with mobile individuals in a square lattice. After illustrating the interplay between the mobility parameters and the other parameters on the spatial epidemic spreading, we propose an index as a function of system parameters, which largely governs the final epidemic size. The main contribution of this study is to show that the proposed index is useful for estimating how parameter scaling affects the final epidemic size. To demonstrate the effectiveness of the proposed index, we show that there is a positive correlation between the proposed index computed with the real data of human airline travels and the actual number of positive incident cases of influenza B in the entire world, implying that the growing incidence of influenza B is attributed to increased human mobility.</p></div

Correlation between the proposed index and the positive incidence of influenza B.

<p>The number of positive cases of influenza B was obtained from the FluNet database [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168127#pone.0168127.ref046" target="_blank">46</a>] and was divided by the total population [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168127#pone.0168127.ref048" target="_blank">48</a>] to eliminate the influence of the population increase. The proposed index was estimated by using the data of the number of passengers in international airlines [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168127#pone.0168127.ref047" target="_blank">47</a>] and the total population. A strong positive correlation between the proposed index and the incidence of influenza B implies that the increased human mobility is responsible for the growing number of the incidence.</p

Interplay between the latent period and the mobility for the final size.

<p>The final size <b><i>r</i></b>_∞ is plotted against the population density <b><i>ρ</i></b>_<b>0</b>. For each parameter value, the results of 100 simulations are plotted. The four cases are compared with respect to the latent period and the mobility, including <b><i>τ</i></b>_<b>E</b> = <b>1</b> and <b><i>α</i></b> = <b>0</b> (blue circles), <b><i>τ</i></b>_<b>E</b> = <b>1</b> and <b><i>α</i></b> = <b>1</b> (orange diamonds), <b><i>τ</i></b>_<b>E</b> = <b>20</b> and <b><i>α</i></b> = <b>0</b> (red squares), and <b><i>τ</i></b>_<b>E</b> = <b>20</b> and <b><i>α</i></b> = <b>1</b> (purple triangles). The other parameter values are set at <b><i>L</i></b> = <b>500</b>, <b><i>τ</i></b>_<b>I</b> = <b>20</b>, <b><i>p</i></b> = <b>1</b>, and .</p

A scaling property for the final size.

<p>The average of the final size <b><i>r</i></b>_∞ over 100 trials with the error bar indicating the standard deviation is plotted against the index <b><i>ϕ</i></b> which is a function of the characteristic length <i>l*</i>, the transmission probability <i>p</i>, and the population density <b><i>ρ</i>₀</b>. The data points correspond to 12600 parameter sets, <i>L =</i> 100 and <i>n =</i> 10³, 10⁴, 10⁵, 10⁶, and <i>L</i> = 500 and <i>n =</i> 10³, 10⁴, 10⁵, for all the combination of <b><i>τ</i>_E = 0,2,4,8,16,32, <i>τ</i>_I = 2,4,8,16,32</b>, <i>p =</i> 0.1, 0.5, 0.9, 1, , and <b><i>α</i> = 0,0.1,0.5,0.9,1</b>.</p

Schematic illustration of the spatial SEIR model with mobile individuals in the square lattice.

<p>The individuals randomly hops from site to site. Each of the susceptible (S), exposed (E), and recovered (R) individuals hops to one of the eight neighbouring sites with the hopping rate λ, while each of the infectious individuals (I) hops similarly with the rate <b><i>λα</i></b> where <b>1−<i>α</i></b> represents the mobility reduction rate.</p

The correlation between the corrected characteristic length and the transport distance of the pathogens in the initial stage.

<p>The numerically computed values of the transport distance <i>d</i> is plotted against the corrected characteristic length <i>l*</i>. The parameter values are the same as those used in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168127#pone.0168127.g004" target="_blank">Fig 4</a>. The straight line indicates the result of line fitting for the data, represented as <i>d</i> = 1.69<i>l*</i> - 0.15.</p

The dependence of the final size on the corrected characteristic length.

<p>The final size <b><i>r</i></b>_∞ computed with 375 parameter sets, including all possible combinations of <b><i>τ</i></b>_<b>E</b> = <b>2,4,8,16,32</b>, , and <b><i>α</i></b> = <b>0,0.1,0.5,0.9,1</b>, are plotted against the corrected characteristic length <i>l*</i> given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168127#pone.0168127.e007" target="_blank">Eq 2</a>.</p

Spatial spreading of an epidemic.

<p>Time evolution of the epidemic spreading in individual-based simulations of the spatial SEIR model is shown. Initially all the individuals are susceptible except for a single infectious individual located at the centre of the lattice space. The parameter values are set at <i>L</i> = 100, <i>n</i> = 10⁴, <i>τ</i>_E = 8, <i>τ</i>_I = 16, <i>p</i> = 1.0, , and α = 0.5. (a)-(d) The snap shots of the spatial distribution of the infectious individuals for (a) <i>t</i> = 100, (b) <i>t</i> = 300, (c) <i>t</i> = 400, and (d) <i>t</i> = 500. The density of the infectious individuals in each site is indicated by the colour strength. (e) The time course of the number <i>n</i>_I(<i>t</i>) of infectious individuals. The diamonds correspond to the patterns (a)-(d).</p