Simulating customer behavior for demand response

摘要

Methods are disclosed that teach two simulators used with demand response management systems. The first simulator generates load patterns from historical customer consumption data and generates customer loads from the generated load patterns. The second simulator generates customer response to changing electricity prices using an econometric characterization of the customer response.

主权项

1. A customer electrical load curve simulation method that uses historical customer load patterns to generate customer load curves comprising:
inputting pattern parameters {circumflex over (μ)}0, {circumflex over (σ)}0, {circumflex over (μ)}=[{circumflex over (μ)}0+Δt, . . . ,{circumflex over (μ)}24] and {circumflex over (σ)}=[{circumflex over (σ)}0+Δt, . . . , {circumflex over (σ)}24], and simulation parameters P{tilde over (t)}start, nsim and [{tilde over (t)}start,{tilde over (t)}end,Δ{tilde over (t)}] wherein P{tilde over (t)}start is the desired starting load level, nsim is the number of simulated load curves that will be generated, {tilde over (t)}start is the desired starting time of the simulation, {tilde over (t)}end is the desired ending time of the simulation and Δ{tilde over (t)} is the desired time resolution for the simulation, {circumflex over (μ)}0 and {circumflex over (σ)}0 are the mean and standard deviation of the starting load level of estimated pattern parameters and {circumflex over (μ)} and {circumflex over (σ)} are vectors which represent the mean and the standard deviation of the load changes between each load sample Δt, wherein the pattern parameters {circumflex over (μ)}0, {circumflex over (σ)}0, {circumflex over (μ)}=[{circumflex over (μ)}0+Δt, . . . , {circumflex over (μ)}24] and {circumflex over (σ)}=[{circumflex over (σ)}0+Δt, . . . , {circumflex over (σ)}24] are calculated from historical electrical load data comprising:
inputting historical electrical load data {circumflex over (P)}ti for each time interval tε[0,24] and observation i=1, 2, . . . , N;calculating the mean {circumflex over (μ)}0=Σi=1N{circumflex over (P)}0i/N and the standard deviation {circumflex over (σ)}0=√{square root over (Σi=1N({circumflex over (P)}0i−{circumflex over (μ)}0)2/(N−1))} of starting load level P0; and calculating the mean {circumflex over (μ)}t=Σi=1NΔ{circumflex over (P)}ti/N and the standard deviation {circumflex over (σ)}t=√{square root over (Σi=1N(Δ{circumflex over (P)}ti−{circumflex over (μ)}t)2/(N−1))} of the load change ΔPt between time t−Δt and t; if P{tilde over (t)}start ≠μ{tilde over (t)}start,where μ{tilde over (t)}startis a desired starting time, determining a scaling parameter α=P{tilde over (t)}start/μ{tilde over (t)}start and multiplying the mean {circumflex over (μ)} and variance {circumflex over (σ)} parameters by the scaling parameter α; generating random numbers that are distributed according to a standard normal distribution, wherein generating u{tilde over (t)} that are uniformly distributed in [0,1] and converting the u{tilde over (t)} to standard normal random numbers by inverse transform sampling Φ−1(u)); calculating the load Pj,{tilde over (t)}=Pj,{tilde over (t)}−Δ{tilde over (t)}+μ{tilde over (t)}+Φ−1(u{tilde over (t)})σ{tilde over (t)} for each simulation replication jε{1, . . . , nsim} and time point {tilde over (t)}ε[{tilde over (t)}start,{tilde over (t)}end]; calculating a load matrixP=[Pj,t~]∈Rnsim×(t~end-t~startΔ⁢⁢t~+1)  as output; and simulating the customer electrical load curve using the load matrix.