Nodal Uncertainty Research Articles

Truncated Strategy Based Dynamic Network Pricing for Energy Storage

With the increasing penetration of local renewable energy and flexible demand, the system demand is more unpredictable and causes network overloading, resulting in costly system investment. Although the energy storage (ES) helps reduce the system peak power flow, the incentive for ES operation is not sufficient to reflect its value on the system investment deferral resulting from its operation. This paper designs a dynamic pricing signal for ES based on the truncated strategy under robust operation corresponding to the network charge reduction. Firstly, the operation strategy is designed for ES to reduce the total network investment cost considering the uncertainties of flexible load and renewable energy. These nodal uncertainties are converted into branch power flow uncertainties by the cumulant and Gram-Charlier expansion strategy. Then, a time of use (ToU) pricing scheme is designed to guide the ES operation reflecting its impact on network investment based on the long-run investment cost (LRIC) pricing scheme. The proposed ToU LRIC method allocates the investment costs averagely to network users over the potential curtailment periods, which connects the ES operation with network investment. The curtailment amount and the distribution of power flow are assessed by the truncated strategy considering the impact of uncertainties. As demonstrated in a Grid Supply Point (GSP) distribution network in the UK, the network charges at the peak time reduce more than 20% with ES operation. The proposed method is cost-reflective and ensures the fairness and efficiency of the pricing signal for ES.

Waiting Cost Based Long-Run Network Investment Decision-Making Under Uncertainty

Traditional system investment decision is costly and hard to reverse. This is aggravated by uncertainties from flexible load and renewables (FLR), which impact the accuracy of network investment decisions and could trigger a high asset risk. Thus, system operators have the incentive to postpone network reinforcement, and `wait and see' whether the request of investment can be reduced or delayed with new information. This paper proposes a novel method to evaluate network investment horizon deferral based on the trade-off between waiting profit and waiting cost under FLR uncertainties. Although deferring investment leads to waiting cost, it is worthy to wait if the cost is smaller than the waiting profits. To capture the impact of FLR uncertainties on system investment, nodal uncertainties are converted into branch flow uncertainties based on a combined cumulant and Gram-Charlier expansion method. The waiting cost is quantified by the options' cost based on real options method and waiting profit is from asset present value reduction due to the deferral. Thus, by paying waiting cost, current investment cost can be reserved until uncertainties are reduced to an acceptable level. The waiting time is evaluated by Sharp ratio and expected return, determined by the waiting cost and uncertainty level. The results show that paying waiting cost is an economical way to reduce the impact of uncertainty and avoid hastily investment.

Interval Optimization-Based Unit Commitment for Deep Peak Regulation of Thermal Units

The deep peak regulation of thermal units is an important measure for coping with significant wind power penetration. In this paper, based on interval optimization, a novel multi-objective unit commitment method is proposed considering the deep peak regulation of thermal units. In the proposed method, a thermal power cost model was developed to accurately determine the economic performance of three different peak regulation scenarios, particularly of the deep peak regulation scenario. The midpoint and width of the cost interval are simultaneously considered in the optimization process. The non-dominated sorting GA-II (NSGA-II) algorithm was incorporated into the model for a coordinated control of the midpoint and width of the obtained cost interval for further optimization. Considering that significant wind penetration results in greater nodal variations, the affine arithmetic was employed to solve nodal uncertainties, so that all system variations can be addressed. The method proposed in this paper was validated by a modified IEEE-39 bus system. The results showed that it serves as a useful tool for power dispatchers to obtain robust and economic solutions at different wind power prediction accuracies.

Structural optimization under uncertain loads and nodal locations

This paper presents algorithms for solving structural topology optimization problems with uncertainty in the magnitude and location of the applied loads and with small uncertainty in the location of the structural nodes. The second type of uncertainty would typically arise from fabrication errors where the tolerances for the node locations are small in relation to the length scale of the structural elements. We first review the discrete form of the uncertain loads problem, which has been previously solved using a weighted average of multiple load patterns. With minor modifications, we extend this solution to include loads described by continuous joint probability density functions. We then proceed to the main contribution of this paper: structural optimization under uncertainty in the nodal locations. This optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix. It is shown, however, that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads. By expressing these equivalent loads in terms of continuous random variables, we are able to make use of the extended form of the uncertain loads problem presented in the first part of this paper. The optimization algorithms are developed in the context of minimum compliance (maximum stiffness) design. Simple examples are presented. The results demonstrate that load and nodal uncertainties can have dramatic impact on optimal design. For structures containing thin substructures under axial loads, it is shown that these uncertainties (a) are of first-order significance, influencing the linear elastic response quantities, and (b) can affect designs by avoiding unrealistically optimistic and potentially unstable structures. The additional computational cost associated with the uncertainties scales linearly with the number of uncertainties and is insignificant compared to the cost associated with solving the deterministic structural optimization problem.