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| An Extended Power Flow Calculation Model Based on Power Droop Bus and Two-Step Analysis |
| Feng Zhuocheng1, Jiang Tong1, Wan Kaiyao2, Li Qinxin2 |
1. State Key Laboratory of Alternative Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China;
2. China Electric Power Research Institute Beijing 100192 China |
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Abstract Power flow calculation (PFC) is the basis of power system analysis. Ensuring the convergence of power flow plays an important role in the planning and operation of power network. Mathematically, the essence of PFC is to solve nonlinear equations, whose convergence is influenced by many factors. When improper initial value selection and unreasonable mode arrangement occur, the PFC cannot converge. The non-convergence of PFC indicates that the equation has no solution or the equation has solution but cannot be obtained due to the limitations of the solving algorithm. If the solution exists, a robust pathological power flow algorithm should be used to find the flow solution. Otherwise, the boundary conditions of power flow equations should be changed and the operating mode should be adjusted to make the power flow equations solvable and find the solution. At present, the main method of power flow adjustment is expert experience, which consumes a lot of human resources and requires a large amount of calculation. Therefore, an efficient and stable power flow adjustment strategy is urgently needed to ensure the reliable convergence of power flow. To address these issues, this paper proposed an extended power flow calculation model based on power droop bus and two-step analysis.
Firstly, the power droop bus is defined to restore power flow solvability. The principle of restoring power flow solvability by bus type conversion is to intersect the characteristic curve of the converted bus with the original solvable domain manifold. The boundary of the solvable domain is composed of saddle node bifurcation (SNB) points, which is a closed curve containing the origin. According to the definition of power droop bus, the new manifold will pass through the origin of the coordinate system, and the new manifold will still pass through the original feasible region, which explains its effectiveness towards restoring solvability.
An extended power flow calculation model considering power droop buses is given. The extended system is developed to restore power flow solvability by introducing power droop bus. A two-step analysis method is proposed to determine the bus conversion logic. Based on the bus voltage equation, it divides the network into PQ subnet and PV subnet. Buses need to be converted are determined by analyzing the PQ and PV subnet individually. The adjustment scheme is determined in the state backtracking procedure, which determines the action generator through calculating the left eigenvector at the backtracking point.
The algorithm is tested in IEEE 118 bus system and TEXAS 2000 bus system, and compared with methods including optimal power flow (OPF) based on interior point method. In the specific scenes, 23 out of 25 unsolvable cases are adjusted into solvable cases. To verify the effectiveness and applicability of the proposed strategy, 50 unsolvable cases are constructed by increasing load randomly, and 48 cases are adjusted successfully.
The simulation results indicate that proposed method achieve 92% success rate for most unsolvable cases. It can adapt to a variety of power flow situations without solutions. Further improvement should be focus on PFC problems considering direct current transmission.
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Received: 03 August 2022
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2023, Vol. 38 
