Probabilistic Power Flow Simulation allowing Temporary Current Overloading Wander Sybe Wadman CWI Amsterdam The Netherlands w.wadman@cwi.nl Gabri¨ el Bloemhof DNV KEMA Energy & Sustainability Arnhem, the Netherlands gabriel.bloemhof@kema.com Daan Crommelin CWI Amsterdam The Netherlands daan.crommelin@cwi.nl Jason Frank CWI Amsterdam The Netherlands j.e.frank@cwi.nl Abstract—This paper presents a probabilistic power flow model subject to connection temperature constraints. Renewable power generation is included and modelled stochastically in order to reflect its intermittent nature. In contrast to conventional models that enforce connection current constraints, short-term current overloading is allowed. Temperature constraints are weaker than current constraints, and hence the proposed model quantifies the overload risk more realistically. Using such a constraint is justified the more by the intermittent nature of the renewable power source. Allowing temporary current overloading necessitates the incor- poration of a time domain in our model. This substantially influences the choice of model for the renewable power source, as we explain. Wind power is modelled by use of an ARMA model, and appropriate accelerations of the power flow solution technique are chosen. Several IEEE test case examples illustrate the more realistic risk analysis. An example shows that a current constraint model may overestimate these risks, which may lead to unnecessary over-investments by grid operators in grid connections. Keywords- Probabilistic power flow, renewable generation, Monte Carlo, reliability analysis I. I NTRODUCTION Renewable energy generation is increasingly integrated, but high penetration of renewable generators is expected to strain the power grid. The limited predictability of distributed renewable sources implies that substantial implementation in the grid will result in a significantly increased risk of power imbalances. Uses of storage, trade or unit commitment may mitigate these risks. Above all, a quantitative uncertainty analysis of the power flow has to be performed, which is the topic of this paper. An electricity network should fulfill the following constraints: • The absolute voltage should be between acceptable bounds at all nodes. Formally stated, V min < |V (t)| <V max (1) should hold at all nodes for all times t. • The reactive power should be between acceptable bounds at all generation nodes: Q min <Q(t) <Q max , (2) should hold at all nodes for all times t. • The temperature of each connection should be bounded: T (t) <T max , (3) should hold at all node connections for all times t. T max is assumed to be the critical temperature of the connection above which operation failure or degradation over time may occur. A straightforward method to satisfy the latter constraint, is to ensure that the current never exceeds a certain maximum. That is, |I (t)| <I max , (4) should hold at all node connections for all times t. In this paper, we assume that I max corresponds to T max in the sense that if I (t)= I max for all times t, then lim t→∞ T (t)= T max . (5) These maxima depend on the material and thickness of the connection. Tables displaying this correspondence for cables can be found in [1], for example. However, the transient temperature adjustment incurs some lag time, so a mild violation of a given current maximum—with a short duration—may not lead to violation of the temperature constraint. Hence, directly imposing the current constraint may be too restrictive. In fact, the grid dimensioning should anticipate the most extreme event, which may very well be accidental and of short duration. Underestimating the connec- tion capacities in this way, may lead to over-investments in grid connections. Therefore, this article will treat an improved “soft” current constraint, which basically demands that the current be not too high for too long, by focusing on constraint (3) instead of (4). To include renewable generation units, one must model their uncertain nature. The choice of model should be consistent with available data. Often, and especially when considering investments in new infrastructure, power generation data are scarce, and data of their meteorological sources (e.g. wind speed, solar radiation) are preferred because of their wide availability. Further, the power generation and therefore the connection currents exhibit time correlation. This means that checking for short-term current overloading necessitates the inclusion of chronology in our model, which discourages the Proceedings of PMAPS 2012, Istanbul, Turkey, June 10-14, 2012 494