US 12,261,433 B2
Method and system for collaborative regulation of multi-component power distribution network with high proportion of distributed power sources
Tianguang Lv, Jinan (CN); Molin An, Jinan (CN); Xueshan Han, Jinan (CN); Jian Chen, Jinan (CN); and Shumin Sun, Jinan (CN)
Assigned to SHANDONG UNIVERSITY, Jinan (CN)
Filed by SHANDONG UNIVERSITY, Shandong (CN)
Filed on Apr. 26, 2022, as Appl. No. 17/729,202.
Claims priority of application No. 202111067640.0 (CN), filed on Sep. 13, 2021.
Prior Publication US 2023/0093345 A1, Mar. 23, 2023
Int. Cl. H02J 3/00 (2006.01); G05B 6/02 (2006.01); G05B 13/04 (2006.01)
CPC H02J 3/00 (2013.01) [G05B 6/02 (2013.01); G05B 13/042 (2013.01); H02J 2203/20 (2020.01)] 7 Claims
OG exemplary drawing
 
1. A method for collaborative regulation of a multi-component power distribution network with a high proportion of distributed power sources, comprising:
measuring, in real-time, a user voltage on a user side by a measuring apparatus mounted on the user side, and sending information of the measured user voltage to a regulation center of the multi-component power distribution network;
based on the information of the measured user voltage and an optimization model comprising a calculation part of a user side and a calculation part of the regulation center of the multi-component power distribution network, performing, by the regulation center of the multi-component power distribution network, a first iterative calculation process of corresponding preset control objectives for the calculation part of the regulation center of the multi-component power distribution network in the optimization model by a Lagrange algorithm, simultaneously controlling errors of the corresponding preset control objectives in the first iterative calculation process by a Proportional-Integral-Differential (PID) controller, and adjusting parameters of the PID controller of the regulation center to change a speed of the first iterative calculation according to different situations, to achieve convergence of the first iterative calculation process, so as to output and send a regulation signal of a local load of the user side to the user side;
performing, by the user side, a second iterative calculation process of corresponding preset control objectives based on the regulation signal of the local load of the user side and the calculation part of the user side in the optimization model, simultaneously controlling the errors of the corresponding preset control objectives in the second iterative calculation process by the PID controller, and adjusting parameters of the PID controller of the user side to change a speed of the second iterative calculation according to different situations, to achieve convergence of the second iterative calculation process, and output a load regulating physical value of the local load of the user side; and
regulating the local load of the user side by a regulating apparatus to the load regulating physical value of the local load of the user side, so the multi-component power distribution network meets requirements of a minimum economic cost and a minimum deviation between the user voltage on the user side and a standard voltage at the same time; wherein
the optimization model is:

OG Complex Work Unit Math
constraint conditions of the optimization model comprise:

OG Complex Work Unit Math
wherein γt ∈ R+ represents a coefficient of balance between an economic cost objective of a user and a voltage level objective of the multi-component power distribution network; αit and βit respectively represent regulation signals of the active power and reactive power generated by the regulation center of the multi-component power distribution network to a distributed power source of the user at a time t; pit and qit respectively represent that a distributed power source at a node i will inject active power and reactive power to the multi-component power distribution network at the time t; pit and qit represent vectors composed of the active power and reactive power injected by all nodes in the multi-component power distribution network; vt represents a voltage level of the multi-component power distribution network; Cit(pit, qit) represents the economic cost for the user side; Dt(vt) represents the voltage level objective of the multi-component power distribution network; vt and vt represent upper and lower limit requirements of the voltage level of the multi-component power distribution network; R and X represent coefficient matrixes corresponding to active power and reactive power in an approximate linearized power flow calculation formula of the multi-component power distribution network, and a represents a constant; bit represents a function symbol; i represents a node of the multi-component power distribution network, and N represents a node set; fit represents a function symbol; :=represents the meaning of definition; Zit represents a user load set;
the load of the user is regulated, and a calculation formula is:
after the user receives a regulation signal sit(k), according to a current user load zit(k) and the economic cost Cit(zit(k)) of a local user, the load is regulated by the following formula:
zit(k+1)=zit(k)−ε1(∇zCit(zit(k))−sit(k))
wherein during calculation, (pit, qit) ∈ Zit is ensured, the symbol ∇ represents a gradient, and subscripts represent corresponding variables when the gradient is calculated;
the regulation center of the multi-component power distribution network collects the user voltage information and calculates a regulation signal according to the collected voltage information and the calculation formulas are:

OG Complex Work Unit Math
wherein during calculation, μt(k+1)≥0 and μt(k+1)≥0 are ensured; ε1 and ε2 represent step sizes of the iterative calculation; μt and μt represent Lagrange multipliers corresponding to inequality constraints; k represents a number of iterations in an algorithm calculation process;
in the process of controlling the errors of the corresponding preset control objectives in the iterative calculation process by the PID controller, the control objectives are:
 
 
 
 control objective 1 ∇xrL(x*,λ*,μ*) = 0, r = 1,2,...,n
 
 control objective 2 hi(x*) = 0, i = 1,2,...,m
 
 control objective 3 μj*gj(x*) = 0, j = 1,2,...,l
 
 constraint 1 gj(x*) ≤ 0, j = 1,2,...,l
 
 constraint 2 μj* ≥ 0, j = 1,2,...,l
 
 
 
 wherein the superscript * represents an optimal solution;
the PID controller defines the errors in the control process for three control objectives, and the errors are respectively:
the error of the control objective 1:
e(k)∇xr=0−∇xrL(x,λ,μ)|x(k),λ(k),μ(k)=−∇xrL(x,λ,μ)|x(k),λ,(k)μ(k)
the error of the control objective 2:
e(k)∇λi=∇λiL(x,λ,μ)|x(k+1)−0=∇λiL(x,λ,μ)|x(k+1)=hi(x)|x(k+1)
the error of the control objective 3:
e(k)∇μj=∇μjL(x,λ,μ)|x(k+1)−0=∇μjL(x,λ,μ)|x(k+1)=gj(x)|x(k+1)
a Lagrange function corresponding to the optimization model is constructed:

OG Complex Work Unit Math
wherein λi represents a Lagrange multiplier corresponding to an equality constraint hi(x), μj represents a Lagrange multiplier corresponding to an inequality constraint gj(x), and all Lagrange multipliers are written as vectors, represented by vectors λ and μ; f(x) represents an objective function; the subscripts xr, λi, μj of the numerical symbol ∇ represent corresponding variables when the gradient is calculated; and
based on the three defined errors, an expression of a PID controller corresponding to the PID controller is:
u(k+1)=u(k)+KpΔe(k)+K1e(k)+KD[Δe(k)−Δe(k−1)]
wherein Δe(k)=e(k)−e(k−1), and u represents the output of the PID controller.