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Table of Contents
💥1 Overview
📚2 Results
🎉3 References
🌈4 Matlab Code, Data, Article
1 Overview
Currently, scholars both domestically and internationally have conducted considerable research on the generation scheduling of virtual power plants (VPPs) from the perspective of single interest entities, focusing on aspects such as bidding models. If more social capital participates in the electricity market, each VPP may belong to different interest entities. Driven by individual rationality, each entity seeks to maximize its own interests, making traditional single-entity optimization scheduling methods difficult to apply. Based on this consideration, existing studies have utilized game theory to analyze the equilibrium relationships between VPPs and the different entities within them. However, most of the aforementioned literature focuses on the game relationships between VPPs under the premise of given trading electricity prices. This paper introduces the distribution system operator (DSO) and establishes a master-slave game optimization model between the DSO and multiple VPPs, studying the mutual influence of DSO dynamic pricing and VPP operational strategies to achieve energy management of multiple virtual power plants. The master-slave game model is a type of equilibrium-constrained optimization problem, where the lower-level game problem serves as a constraint for the upper-level optimization problem, resulting in complexity, nonlinearity, and non-convexity. Currently, the main methods for solving the master-slave game equilibrium solution include numerical optimization methods based on the Karush-Kuhn-Tucker (KKT) conditions and heuristic intelligent algorithms. The KKT condition method can simplify the model but requires the lower-level model to be a convex programming problem and the upper-level to have all parameter information from the lower level, which involves privacy issues. In contrast, heuristic intelligent algorithms only require a small amount of information exchange between the upper and lower levels, protecting lower-level privacy, but they require extensive calls to the lower-level game model, leading to complex calculations and low efficiency. To address these issues, this paper proposes a meta-model-based optimization algorithm, introducing the Kriging meta-model for the first time to solve the master-slave game equilibrium solution, aiming to protect VPP privacy while improving computational efficiency. The meta-model-based optimization algorithm is a mechanism that drives the addition of sample points based on historical data to approximate local or global optimal solutions, improving the shortcomings of traditional heuristic intelligent algorithms that require complex numerical simulations. It is currently widely applied in aerospace fields such as aircraft design and has also seen preliminary applications in power systems. Literature has used the Kriging meta-model to fit random wind speeds and the random response of power system transient simulations. Other studies have replaced power flow calculations with the Kriging meta-model to investigate optimal economic operation and reactive power optimization of active distribution networks. In summary, this paper considers that the DSO and VPPs have different interest demands and establishes a dynamic pricing and energy management model for multiple VPPs based on master-slave game theory. It proposes a game equilibrium algorithm based on the Kriging meta-model, establishing the Kriging meta-model to replace the internal energy management model of VPPs during the solution process, utilizing particle swarm optimization to search for excellent sampling points, updating and correcting the Kriging model, avoiding complex calculations of the lower-level game model, and improving optimization efficiency. Finally, through case analysis, the effectiveness of the model and algorithm proposed in this paper is verified.
For detailed article explanation, see section 4.
2 Results
% Part of the code:
function[P_VPP_s,P_VPP_b,Out]=Fun_VPP1(lambda_DAb,lambda_DAs)% Calculate the lower-level VPP trading subprocess
%% Decision variable initialization
P_VPP_b=sdpvar(1,24); % VPP's purchase electricity from the operator
P_VPP_s=sdpvar(1,24); % VPP's sale electricity to the operator
P_VPP=sdpvar(1,24); % VPP's trading electricity with the operator
P_MT=sdpvar(1,24); % Generation power of MT in VPP
P_ES=sdpvar(1,24); % Charging and discharging power of energy storage in VPP, positive for discharging
P_IL=sdpvar(1,24); % Interruptible load in VPP
P_W=sdpvar(1,24); % Actual wind power output in VPP
S_ES=sdpvar(1,24); % State of charge of energy storage devices in VPP
theta=binvar(1,24); % Trading electricity state variable between VPP and operator
%% Import electricity load and wind power output
P_LD=[2.2,1.8,3,6,5.8,5.2,5.6,3.8,2.5,2.7,3,2.6,2.2,2.1,4.2,5.8,6.2,6.3,6.5,6.6,6.3,6.2,6,5.7];
P_Wmax=[2,1.5,1.6,1.8,1.3,0.6,2.8,3.3,3.9,4,3.3,2.9,2.7,2,0.2,3.2,5.1,3.1,1.8,2,1.3,12,3.8];
%% Import constraints
C=[];
C=[C, P_VPP==P_VPP_b-P_VPP_s, % VPP's trading electricity with the operator, positive for purchase, negative for sale
P_VPP+P_MT+P_ES+P_IL+P_W==P_LD, % Internal power balance constraint of VPP
0<=P_VPP_s<=theta*10, % Set maximum sale electricity of VPP to the operator as 10MW
0<=P_VPP_b<=(1-theta)*10, % Set maximum purchase electricity of VPP from the operator as 10MW
0<=P_MT<=6, % Upper and lower limit of MT's output power
-3.5<=P_MT(2:24)-P_MT(1:23)<=3.5, % MT's ramping constraint
-0.6<=P_ES<=0.6, % Upper and lower limit of charging and discharging power of energy storage
S_ES(1)==0.4-P_ES(1)/1, % SoC constraint of energy storage device for 0-1 time period, initial SoC is 0.4
S_ES(2:24)==S_ES(1:23)-P_ES(2:24)/1, % SoC constraint of energy storage device for 1-24 time periods
0.2<=S_ES<=0.9, % Upper and lower limit of SoC state
S_ES(24)==0.4, % Final SoC of energy storage equals initial value
0<=P_IL<=0.1*P_LD, % Upper and lower limit of interruptible load
0<=P_W<=P_Wmax, % Upper and lower limit of wind power output
];
%% Set objective function
C_MT=0.08*P_MT.^2+0.9*P_MT+1.2; % Generation cost of micro gas turbine
C_ES=0.05*P_ES.^2; % Energy storage cost
C_IL=1.4*P_IL; % Interruptible load cost
C_VPP=sum(lambda_DAb.*P_VPP_b-lambda_DAs.*P_VPP_s)+sum(C_MT+C_ES+C_IL); % Total operating cost of VPP
%% Solver configuration and solving
ops=sdpsettings('solver','cplex','verbose',0,'usex0',0);
ops.cplex.mip.tolerances.mipgap=1e-6;
result=solvesdp(C,C_VPP,ops);
%% Data output
P_VPP_b=double(P_VPP_b);
P_VPP_s=double(P_VPP_s);
Out = [P_VPP;P_MT;P_ES;P_IL;P_W;-P_LD];
end
3References
Some content in this article is sourced from the internet, and references will be noted. If there are any inaccuracies, please feel free to contact us for removal.
[1] Dong Lei, Tu Shuqin, Li Ye, et al. Dynamic Pricing and Energy Management of Multi-Virtual Power Plants Based on Meta-Model Optimization Algorithm. Power System Technology, 2020, 44(03): 973-983. DOI:10.13335/j.1000-3673.pst.2019.2244.
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