The impact of monsoon intraseasonal variability on renewable power generation in India

India is increasingly investing in renewable technology to meet rising energy demands, with hydropower and other renewables comprising one-third of current installed capacity. Installed wind-power is projected to increase 5-fold by 2035 (to nearly 100GW) under the International Energy Agency’s New Policies scenario. However, renewable electricity generation is dependent upon the prevailing meteorology, which is strongly influenced by monsoon variability. Prosperity and widespread electrification are increasing the demand for air conditioning, especially during the warm summer. This study uses multi-decadal observations and meteorological reanalysis data to assess the impact of intraseasonal monsoon variability on the balance of electricity supply from wind-power and temperature-related demand in India. Active monsoon phases are characterised by vigorous convection and heavy rainfall over central India. This results in lower temperatures giving lower cooling energy demand, while strong westerly winds yield high wind-power output. In contrast, monsoon breaks are characterised by suppressed precipitation, with higher temperatures and hence greater demand for cooling, and lower wind-power output across much of India. The opposing relationship between wind-power supply and cooling demand during active phases (low demand, high supply) and breaks (high demand, low supply) suggests that monsoon variability will tend to exacerbate fluctuations in the so-called demand-net-wind (i.e., electrical demand that must be supplied from non-wind sources). This study may have important implications for the design of power systems and for investment decisions in conventional schedulable generation facilities (such as coal and gas) that are used to maintain the supply/demand balance. In particular, if it is assumed (as is common) that the generated wind-power operates as a price-taker (i.e., wind farm operators always wish to sell their power, irrespective of price) then investors in conventional facilities will face additional weather-volatility through the monsoonal impact on the length and frequency of production periods (i.e. their load-duration curves).

Long term individual load forecast under different electrical vehicles uptake scenarios

More and more households are purchasing electric vehicles (EVs), and this will continue as we move towards a low carbon future. There are various projections as to the rate of EV uptake, but all predict an increase over the next ten years. Charging these EVs will produce one of the biggest loads on the low voltage network. To manage the network, we must not only take into account the number of EVs taken up, but where on the network they are charging, and at what time. To simulate the impact on the network from high, medium and low EV uptake (as outlined by the UK government), we present an agent-based model. We initialise the model to assign an EV to a household based on either random distribution or social influences - that is, a neighbour of an EV owner is more likely to also purchase an EV. Additionally, we examine the effect of peak behaviour on the network when charging is at day-time, night-time, or a mix of both. The model is implemented on a neighbourhood in south-east England using smart meter data (half hourly electricity readings) and real life charging patterns from an EV trial. Our results indicate that social influence can increase the peak demand on a local level (street or feeder), meaning that medium EV uptake can create higher peak demand than currently expected.

Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Simple piecewise geodesic interpolation of simple and Jordan curves with applications

We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite p -variation for 1⩽p<2.

Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

Bad reduction of genus three curves with complex multiplication

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes p of M such that the stable reduction of C at p contains three irreducible components of genus 1.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.