Algorithms on Minimizing the Maximum Sensor Movement for Barrier Coverage of a Linear Domain

In this paper, we study the problem of moving $n$ sensors on a line to form a barrier coverage of a specified segment of the line such that the maximum moving distance of the sensors is minimized. Previously, it was an open question whether this problem on sensors with arbitrary sensing ranges is solvable in polynomial time. We settle this open question positively by giving an $O(n^2 \log n)$ time algorithm. For the special case when all sensors have the same-size sensing range, the previously best solution takes $O(n^2)$ time. We present an $O(n \log n)$ time algorithm for this case; further, if all sensors are initially located on the coverage segment, our algorithm takes $O(n)$ time. Also, we extend our techniques to the cycle version of the problem where the barrier coverage is for a simple cycle and the sensors are allowed to move only along the cycle. For sensors with the same-size sensing range, we solve the cycle version in $O(n)$ time, improving the previously best $O(n^2)$ time solution.Comment: This version corrected an error in the proof of Lemma 2 in the previous version and the version published in DCG 2013. Lemma 2 is for proving the correctness of an algorithm (see the footnote of Page 9 for why the previous proof is incorrect). Everything else of the paper does not change. All algorithms in the paper are exactly the same as before and their time complexities do not change eithe

Reliability-based Probabilistic Network Pricing with Demand Uncertainty

The future energy system embraces growing flexible demand and generation, which bring large-scale uncertainties and challenges to current deterministic network pricing methods. This paper proposes a novel reliability-based probabilistic network pricing method considering demand uncertainty. Network reliability performance, including probabilistic contingency power flow (PCPF) and tolerance loss of load (TLoL), are used to assess the impact of demand uncertainty on actual network investment cost, where PCPF is formulated by the combined cumulant and series expansion. The tail value at risk (TVaR) is used to generate analytical solutions to determine network reinforcement horizons. Then, final network charges are calculated based on the core of the Long-run incremental cost (LRIC) algorithm. A 15-bus system is employed to demonstrate the proposed method. Results indicate that the pricing signal is sensitive to both demand uncertainty and network reliability, incentivising demand to reduce uncertainties. This is the first-ever network pricing method that determines network investment costs considering both supply reliability and demand uncertainties. It can guide better sitting and sizing of future flexible demand in distribution systems to minimise investment costs and reduce network charges, thus enabling a more efficient system planning and cheaper integration.</p

Cournot oligopoly game-based local energy trading considering renewable energy uncertainty costs

Facilitated by advanced information and communication technologies (ICTs), local energy trading develops rapidly, playing an important role in the energy supply chain. Thus, it is essential to develop local trading models and strategies that can benefit participants, not only stimulating local balancing but also promoting renewable penetration. This paper proposes a new local energy trading decision-making model for suppliers by using the Cournot Oligopoly game, considering the uncertainty costs of renewable energy. Four types of representative energy providers are modelled, traditional thermal generation, wind power, photovoltaic (PV) power, and electricity storage. The revenue of these technologies is extensively formulated according to their operation cost, investment cost, and income from selling energy. The uncertainty cost of renewable generation is integrated into the trading, modelled as a penalty for potential energy shortage that is derived from output probability distribution function (PDF). This trading model is formulated as a non-cooperative Cournot oligopoly game to enable energy suppliers to maximize their profits through local trading considering price. The response of the customer to energy price variations, i.e. demand elasticity, is also included in the model. A unique Nash equilibrium (NE) and optimum strategies are derived by the proposed Optimal-Generation-Plan (OGP) Algorithm. As demonstrated in a typical local market, the proposed approach can effectively model and resolve multiple suppliers’ competition in local energy trading. It can work as a vehicle to facilitate the trading between various generation technologies and customers, realising local balancing and benefiting all market participants with enhanced revenue and reduced energy bills.</p

LMP-based Pricing for Energy Storage in Local Market to Facilitate PV Penetration

Increasing Photovoltaic (PV) penetration and low-carbon demand can potentially lead to two different flow peaks, generation, and load, within distribution networks. This will not only constrain PV penetration but also pose serious threats to network reliability. This paper uses energy storage (ES) to reduce system congestion cost caused by the two peaks by sending cost-reflective economic signals to affect ES operation in responding to network conditions. First, a new charging and discharging (C/D) strategy based on binary search method is designed for ES, which responds to system congestion cost over time. Then, a novel pricing method, based on locational marginal pricing (LMP), is designed for ES. The pricing model is derived by evaluating ES impact on the network power flows and congestions from the loss and congestion components in LMP. The impact is then converted into an hourly economic signal to reflect ES operation. The proposed ES C/D strategy and pricing methods are validated on a real local grid supply point area. Results show that the proposed LMP-based pricing is efficient to capture the feature of ES and provide signals for affecting its operation. This work can further increase network flexibility and the capability of networks to accommodate increasing PV penetration.</p

Network pricing for customer-operated energy storage in distribution networks

Network pricing is essential for electricity system operators to recover investment and operation costs from network users. Current pricing schemes are only for generation and demand that purely withdraws or injects power from/into the system. However, they cannot properly price energy storage (ES), which has the dual characteristics of injecting and withdrawing power. This paper develops a novel pricing scheme for ESs in distribution systems operated by customers to reflect their impact on network planning and operation. A novel charging and discharging methodology is designed for ESs to respond to time of use tariffs for maximising electricity cost savings. The long-term incremental cost for ES is designed based on future reinforcement horizon and short-term operation cost is quantified by system congestion. Then, a novel pricing scheme for ES is designed by integrating the two costs. The pricing signals can guide ES operation to benefit both distribution network operators and ES owners. The new methodology is demonstrated on a small system with an ES of different features and then on a practical Grid Supply Point (GSP) area.</p