优化配电网参数:考虑负荷不确定性下的区间灵敏度分析与计算加速方法

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本文主要探讨了在考虑负荷不确定性的情况下,对电力分配网络参数进行区间敏感性分析和优化的方法。作者Zhigang Lu等人提出了一种先进的策略,其核心是利用一种创新的区间敏感性模型。这些模型允许研究人员处理线路上的导纳(包括线路和变压器)变化对网络损耗的影响,同时考虑到实际操作中的不确定性和变异性。 首先,文章构建了一个基于区间分析的框架,通过引入区间前向后向功率流算法。这种方法不同于传统的单值分析,它能够提供一个关于参数变化对系统性能影响的全面范围,而非单一的点估计。这在面对负荷波动或设备老化等难以精确预测的状况时显得尤为重要,因为它们可能导致网络损耗的上下限变化。 为了提高计算效率,研究者采用简化集模型来快速计算系统损失的区间敏感性。这种简化意味着在保持精度的同时,降低了计算的复杂度,使得大规模的网络优化成为可能。这种方法借鉴了细菌群体化学趋化行为的概念,将复杂的网络动态简化为易于处理的数学模型,从而实现了对参数空间的高效搜索和优化。 具体而言,研究过程包括以下步骤: 1. 区间敏感性模型设计:开发出能适应负荷不确定性的一套模型,这些模型能够捕捉到参数变化对网络损耗的可能影响范围。 2. 区间功率流算法:构建一个能够处理区间变量的前向和后向迭代流程,用于求解网络的区间状态,包括电压、电流和功率分布。 3. 优化策略:利用区间分析的结果,确定最优的线路和变压器参数组合,既能满足安全性要求,又能最大限度地减少网络损耗的可能性。 4. 计算速度提升:通过简化模型降低计算负担,确保在实际应用中能迅速找到有效的解决方案。 这项研究对于提高电力分配系统的可靠性、经济性和适应性具有重要意义,因为它不仅提供了理论上的支持,还为实际工程中的网络参数调整提供了实用的工具。通过结合区间分析和优化技术,电力公司可以更好地应对负荷波动带来的挑战,提升整体电网运营效率。

(a) Consider the case of a European Vanilla Call option which is path independent. Examine the convergence of the Monte Carlo Method using the programme given in ‘MC Call.m’. How does the error vary with the number of paths nP aths? The current time is t = 0 and the Expiry date of the option is t = T = 0.5. Suppose that the current value of the underlying asset is S(t = 0) = 100 and the Exercise price is E = 100, with a risk free interest rate of r = 0.04 and a volatility of σ = 0.5. (b) Now repeat part (a) above but assume that the volatility is σ = 0.05. Does the change in the volatility σ influence the convergence of the Monte Carlo Method? (c) Now repeat part (a) but instead of taking one big step from t = 0 to t = T divide the interval into nSteps discrete time steps by using the programme given in ‘MC Call Small Steps.m’. Confirm that for path independent options, the value of nP aths determines the rate of convergence and that the value of nSteps can be set to 1. (d) Now let us consider path dependent options. The programme given in ‘MC Call Small Steps.m’ is the obvious starting point here. We assume that the current time is t = 0 and the expiry date of the option is t = T = 0.5. The current value of the underlying asset is S(t = 0) = 100 and the risk free interest rate is r = 0.05 and the volatility is σ = 0.3. (i) Use the Monte Carlo Method to estimate the value of an Arithematic Average Asian Strike Call option with Payoff given by max(S(T) − S, ¯ 0). (ii) Use the Monte Carlo Method to estimate the value of an Up and Out Call option with Exercise Price E = 100 and a barrier X = 150. (iii) Comment on the the rate of convergence for part (i) and (ii) above with respect to the parameters nP aths and nP aths使用matlab编程

2023-06-11 上传

Algorithm 1: The online LyDROO algorithm for solving (P1). input : Parameters V , {γi, ci}Ni=1, K, training interval δT , Mt update interval δM ; output: Control actions 􏰕xt,yt􏰖Kt=1; 1 Initialize the DNN with random parameters θ1 and empty replay memory, M1 ← 2N; 2 Empty initial data queue Qi(1) = 0 and energy queue Yi(1) = 0, for i = 1,··· ,N; 3 fort=1,2,...,Kdo 4 Observe the input ξt = 􏰕ht, Qi(t), Yi(t)􏰖Ni=1 and update Mt using (8) if mod (t, δM ) = 0; 5 Generate a relaxed offloading action xˆt = Πθt 􏰅ξt􏰆 with the DNN; 6 Quantize xˆt into Mt binary actions 􏰕xti|i = 1, · · · , Mt􏰖 using the NOP method; 7 Compute G􏰅xti,ξt􏰆 by optimizing resource allocation yit in (P2) for each xti; 8 Select the best solution xt = arg max G 􏰅xti , ξt 􏰆 and execute the joint action 􏰅xt , yt 􏰆; { x ti } 9 Update the replay memory by adding (ξt,xt); 10 if mod (t, δT ) = 0 then 11 Uniformly sample a batch of data set {(ξτ , xτ ) | τ ∈ St } from the memory; 12 Train the DNN with {(ξτ , xτ ) | τ ∈ St} and update θt using the Adam algorithm; 13 end 14 t ← t + 1; 15 Update {Qi(t),Yi(t)}N based on 􏰅xt−1,yt−1􏰆 and data arrival observation 􏰙At−1􏰚N using (5) and (7). i=1 i i=1 16 end With the above actor-critic-update loop, the DNN consistently learns from the best and most recent state-action pairs, leading to a better policy πθt that gradually approximates the optimal mapping to solve (P3). We summarize the pseudo-code of LyDROO in Algorithm 1, where the major computational complexity is in line 7 that computes G􏰅xti,ξt􏰆 by solving the optimal resource allocation problems. This in fact indicates that the proposed LyDROO algorithm can be extended to solve (P1) when considering a general non-decreasing concave utility U (rit) in the objective, because the per-frame resource allocation problem to compute G􏰅xti,ξt􏰆 is a convex problem that can be efficiently solved, where the detailed analysis is omitted. In the next subsection, we propose a low-complexity algorithm to obtain G 􏰅xti, ξt􏰆. B. Low-complexity Algorithm for Optimal Resource Allocation Given the value of xt in (P2), we denote the index set of users with xti = 1 as Mt1, and the complementary user set as Mt0. For simplicity of exposition, we drop the superscript t and express the optimal resource allocation problem that computes G 􏰅xt, ξt􏰆 as following (P4) : maximize 􏰀j∈M0 􏰕ajfj/φ − Yj(t)κfj3􏰖 + 􏰀i∈M1 {airi,O − Yi(t)ei,O} (28a) τ,f,eO,rO 17 ,建立了什么模型

2023-05-12 上传