Fast and revenue-oriented protection of radial
LV cables with smart battery operation
Sara Ramezani
aNicolas H¨oning
aHan La Poutr´e
aba
Centrum Wiskunde en Informatica, Science Park 123, 1098 XG Amsterdam
bUtrecht University, Princetonlaan 4, 3511 CC Utrecht
Abstract
Increasing demand and generation in the low-voltage part of our electricity grids challenge existing infras-tructure. A battery installed at the end of often-overheated cables can protect them from overheating, if it is operated intelligently. In addition, it can be crucial to also optimize the battery’s revenue. We propose two robust heuristic online strategies, which reach up to 83% of the approximated theoretical optimum1.
1
Problem
Too much aggregated load or generation can overheat an LV cable. Replacement of cables is expensive and cannot happen in all streets at the same time due to budget constraints. We propose that the network operator can prolong the operation time of an often-overheated cable by installing a smart battery at its end. This battery can react to most overheated situations by charging or discharging, thereby protecting the cable. As a battery is also expensive, it is important to consider that it can make profits during non-overheated times, by buying and selling electricity, and thus (partly) pay for itself. Therefore, we are dealing with multiple objectives, for which expectations of future conditions are important.
In order to evaluate costs of overheating, we assume a cost function v that assigns a value to each time step based on how much the cable was overheated in that time step. It is most realistic to take into consideration that consecutive overloaded intervals are more damaging to the cable:
v(x, k) =
ckh x > C 0 otherwise
where x is the magnitude of the maximum flow on the cable and k is the order of the time step in the set of consecutive overheated time steps that contain it (it is k for the k-th consecutive overheated interval). Also, ch> 1 is a constant and C is the current capacity of the cable, above which it is considered overheated.
We aim to minimize ωV − R, where R is the total revenue of the battery, V is total cost added over all time steps, and ω is a constant weight. For all considered time steps t ∈ T , the offline optimization solution aims to find the battery charges c1, . . . , cT and discharges d1, . . . , dT, such as to minimize ωV − R:
min c1,...,cT,d1,...,dT ωV − R = ω T X t=1 v(xt, kt) − T X t=1 pt(dt− ct)
where ptis the market price of electricity in t (which we assume also gives us approximative information
about the behavior of loads and generators along the cable) and the battery size and its charge and discharge
limits are fixed constraints to this problem. Note that because of the exponential factor in the v function and the structure of kt, this function is very complicated to compute analytically. However, we can formulate a
linear program (LP) to approximate the optimal solution to this problem.
2
Heuristic strategies
We present two heuristic strategies, H1and H2, for solving the online problem. Both make two general
assumptions about overheated time steps, namely that resolving overheating takes precedence and that low-ering overheating as much as possible is worthwhile. These assumptions make the algorithms robust, while their implementation is straightforward and their computation time is low.
The first heuristic strategy, H1, is purely reactive - it does not rely on expectations of future states (it
does not use expectations of prices and cable flows in the intervals after the current interval). If the cable exhibits overheating, H1resolves it as much as is feasible given the battery charge level and its charge and
discharge rates. Otherwise, H1always tries to bring the charge in the battery to half of its capacity. This
is a robust preparation for resolving both kinds of overheated intervals: the ones during which charging is needed to protect and the ones during which discharging is needed (recall that H1does not know which one
to expect). The H1algorithm does not attempt to optimize revenue other than to avoid overheating costs.
The second heuristic strategy, H2, prepares for the future if possible - it uses an expectation of future
prices in order to estimate the maximal and minimal levels on the cable for the remaining time steps (without battery activity). H2tries to resolve overheated intervals but also optimizes revenue. If the current step is
overheated, H2 resolves overheating according to H1. If it is not, H2 plans its expected schedule ahead
until time T to find the best action for the current time step t. This happens in two stages: First, a “wish list” is made, such that expected overheating is resolved as much as possible (using H1), and otherwise the
most possible profit is made (according to expected prices). To achieve this, independence between time steps is assumed. In the second step, the ”wish list“ is adjusted, now taking the dependence of each step i ∈ [t, T ] on the steps preceding it into account, such that the whole schedule becomes feasible given battery limits. At the same time, the precedence to avoid overheating is implemented by adjusting planned battery actions during non-overheated time intervals such that overheating in following intervals is reduced as much as possible. All adjustments in the second step happen with revenue management in mind.
3
Simulation results
We model a scenario (a street with 20 connections) that can be expected to be realistic several years from now. Household demand is comparable to today, with several electric vehicles and solar panels added. The behavior of households partly follows market prices, and is partly determined by sun patterns (time of day). The battery is assumed to be an electric vehicle battery. Price data is adapted from 2012 wholesale data of the APX UK power market (with weekends removed). Results are average performances from 20 stochastic settings, which are each determined by a random day drawn from the price data.
Next to a scenario with no battery, we run the linear program with either complete knowledge about future prices (LP-ActPrice, the approximated theoretical optimum) or expected prices (LP-ExpPrices). Of course, we also run H1and H2. Expected prices are an average daily price series of the month in which the
current price sample happened. We found in simulations that both H1and H2do better than LP-ExpPrices,
while both (particularly H1) produce more stable results. H2does better than H1, and comes as close as
83% to the performance of LP-ActPrice.
References
[1] Sara Ramezani, Nicolas H¨oning, and Han La Poutr´e. Fast and revenue-oriented protection of radial LV cables with smart battery operation. In Proceedings of the 2nd IEEE Symposium on Computational Intelligence Applications in Smart Grids (CIASG), pages 107–114, Singapore, 2013.
