Bi-level Coordinated Scheduling and Optimization of Power Systems Based on Stackelberg-GMO

doi:10.16182/j.issn1004731x.joss.26-0115E

Abstract

Abstract:

, To balance the interests of the power grid and the demand side, and achieve coordinated improvements in system economic efficiency, environmental friendliness, and renewable energy accommodation capacity, this paper proposes a bi-level coordinated scheduling model based on the Stackelberg game and the GMO. A leader-follower game model incorporating carbon emission constraints and multi-scenario stochastic constraints for photovoltaic generation is constructed, with the grid operator as the leader and EVs/V2G and energy storage as the followers, resolving the core contradiction between global optimization and individual rationality. The spatio-temporal stochastic characteristics of EV travel, the cycle life of energy storage systems, and user travel comfort constraints are carefully incorporated to reduce the deviation between the model and actual operation.The GMO algorithm is closely adapted to the sequential decision-making logic of the Stackelberg game, and a dedicated solution framework is designedto reliably obtain a SPNE. A virtual electricity price incentive mechanism integrating carbon emission costs and curtailment penalties is designed to guide demand-side resources to match the output characteristics of renewable energy. Results show that the optimization performance of the GMO algorithm is significantly superior to that of the PSO and the GA. Compared with the traditional uncoordinated operation mode, the proposed scheme reduces the total operating cost by up to 50.25%, increases the photovoltaic power accommodation rate to 96.5%, and reduces carbon emissions by up to 51.46%. This research can serve as a theoretical and engineering reference for the coordinated scheduling of flexible resources in new-type power systems.

Key words: new-type power system, coordinated scheduling, Stackelberg game, geometric mean optimizer, demand response, electric vehicle

CLC Number:

TM734

Zhang Yuanxing, Li Jianfeng, Li Taoyong, Zhang Linjuan, Liu Jincheng, Li Bin. Bi-level Coordinated Scheduling and Optimization of Power Systems Based on Stackelberg-GMO[J]. Journal of System Simulation, 2026, 38(8): 2132-2151.

Figures/Tables 12

Fig. 1

Table 1

Core implementation steps

Step	Step description
1	Scenario preprocessing: Generate a set of typical photovoltaic output scenarios and a set of EV spatio-temporal distribution scenarios, and determine the probability of each scenario and the equipment operating parameters
2	Upper-level initialization: Generate a population of virtual electricity prices that satisfy the lower and upper bound constraints, and initialize the agent positions   X_i,₀ and velocities V_i,₀
3	Lower-level initialization: For each upper-level virtual electricity price agent, generate initial EV/V2G/energy storage charging and discharging power schemes that satisfy the technical and user constraints by incorporating the EV spatio-temporal parameters and energy storage life constraints, and set the initial SOC values
4	Calculation of the upper-level objective function: Based on the current virtual electricity price λ_t,_v, calculate the expected fitness value under multiple scenarios and record the individual best and global best solutions
5	Lower-level response optimization: Using the upper-level virtual electricity price as input, construct a DR model incorporating EV spatio-temporal constraints and energy storage life constraints, and solve for the optimal charging and discharging power of each participant
6	Calculation of the DFI in GMO: Collect the individual best fitness values under multiple scenarios, calculate their mean and standard deviation, and then obtain the membership function values and the DFI
7	Generation and mutation of the GMO global guidance vector: Calculate the global guidance vector Y_i_,_k and perform Gaussian mutation
8	Update of GMO agent positions and velocities: Update the velocity V_i,k+₁ and position  X_i,k+₁ , and verify the boundary constraints
9	Update of the individual best and global best solutions: Compare the expected objective values under multiple scenarios after the update. If the updated values are better than the historical values, update the individual best solution. Then, examine all individual best solutions and select the solution with the maximum objective value as the global best solution
10	Convergence assessment: If ‖ $X k + 1, G b e s t$ $-$ $X k, G b e s t$ ‖<ε or the maximum number of iterations is reached, terminate the iterative optimization; otherwise, return to Step 4
11	Equilibrium assessment: Determine whether the game has reached equilibrium. If not, return to Step 4; otherwise, output the optimal solution

Table 1

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Parameter	Value
P_g,max/MW	20
P_g,min/MW	3
R_g,up/down/(MW·h)	2
e_i	0.8 kg CO₂/kW·h
k_cur/(yuan/kW·h)	0.2
E_i,_bat(Energy storage)/(MW·h)	8
P_i,_c/P_i,_d(Energy storage)/MW	4
η_c/η_d(Energy storage /EV)	90%
E_i,_bat(EV)/(kW·h)	60
P_i,_c/P_i,_d(EV)/kW	7

Parameter	Value
α	0.06 yuan/kg CO₂
c_i,_deg/(yuan/(kW·h))	0.08
k_i,_com	20 yuan per SOC deviation unit
α_i,_c	0.8 kg CO₂/kW·h
α_i,_d/(yuan/(kW·h))	0.2
β_i,_c/(yuan/(kW·h))	0.05
β_i,_d/(yuan/(kW·h))	0.1
ω_i,₁	0.5
ω_i,₂	0.3
ω_i,₃	0.2
μ_i,₁	0.7
μ_i,₂	0.3

Indicator	Scheme 1	Scheme 2	Scheme 3	Scheme 4
Total system operating cost/yuan	2 946.12	1 881.67	1 465.7	1 512.3
Photovoltaic power accommodation rate/%	62.1	85.0	96.5	95.8
Daily system carbon emissions/(kg CO₂)	243 264	159 744	118 080	120 520
Power generation cost of conventional units/yuan	2 821.44	1 837.06	1 458.24	1 486.7
PV curtailment penalty cost/yuan	124.68	44.61	7.55	8.92
EV SOC satisfaction rate at departure/%	—	82.6	89.3	100
Number of daily energy storage cycles	—	3.2	2.8	1.7
System curtailment rate volatility/%	—	28.6	22.4	8.7