Transient Stability-Constrained Optimal Power Flow Calculation With Extremely Unstable Conditions Using Energy Sensitivity Method

Xia, Shiwei; Ding, Zhaohao; Shahidehpour, Mohammad; Chan, Ka Wing; Bu, Siqi; Li, Gengyin

doi:10.1109/tpwrs.2020.3003522

Cited by 25 publications

(23 citation statements)

References 23 publications

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“…Generators in the traditional four-machine two-area system are replaced with PMSGs for verification to verify the influence on FIGURE 14 Line potential energy of auto-correlation mode 1 FIGURE 15 Main oscillation path of the four-machine system with the permanent magnet synchronous generator system and the generators' energy angle FIGURE 16 Mode potential energy of different modes and generators' energy angle the oscillation characteristics of high penetrated-PMSG power system (Figure 7A). A three-phase short-circuit fault is applied at the bus 7, and the fault time is 0-0.05 s. When a smallsignal disturbance occurs in the system, the energy in the generator and the system network fluctuates.…”

Section: Numerical Results 51 Case 1: Four-machine Two-area System Co...mentioning

confidence: 99%

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Dominant inter‐area oscillation path analysis of power systems with a high penetration of permanent magnet synchronous generator by using network mode energy

Liu

Zhang

et al. 2021

IET Generation Trans & Dist

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In this study, a network mode energy (NME) method is used to analyse the low‐frequency oscillation (LFO) of a power system with a high penetration of a permanent magnet synchronous generator (PMSG). This method is also utilized to determine the dominant inter‐area oscillation path. NME comes from a network potential energy based on a small signal mode, which includes a generator internal node mode potential energy and a line mode potential energy (LMPE). The exchange process and distribution of NME in the power system containing the PMSG are studied by analysing the composition of LMPE. A sensitivity index is constructed to determine the state variables of the generator and the PMSG, which remarkably influences energy distribution. Then, the path characteristics of LFO are analysed. The dominant inter‐area oscillation paths and energy interaction of the system connecting to the PMSG are determined. The proposed NME can be calculated on the basis of measurement information, and network energy decomposition is carried out using the measured line mode oscillation index. The mechanism of PMSG participating in oscillation is revealed from the network perspective to provide a basis for network‐based regulation. The correctness analysis and simulation of a four‐machine two‐area system with the PMSG and the New England 10‐machine 39‐bus system with the PMSG are carried out.

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Section: Numerical Results 51 Case 1: Four-machine Two-area System Co...mentioning

confidence: 99%

“…The direct method has been used in power systems, so many energy functions have been proposed [1,[12][13][14][15][16][17]. However, this method is utilized to analyse the transient stability of power systems and obtain good application results.…”

Section: Introductionmentioning

confidence: 99%

Dominant inter‐area oscillation path analysis of power systems with a high penetration of permanent magnet synchronous generator by using network mode energy

Liu

Zhang

et al. 2021

IET Generation Trans & Dist

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“…There is no voltage instability, only rotor angle instability. By controlling high sensibility generators with respect to the dominant FIGURE 11 Voltage of buses and rotor angle after transient stability calculation under fault 1 before and after rescheduling for 39-bus standard system FIGURE 12 Rotor angle after transient stability calculation under fault 2 before and after rescheduling for 39-bus standard system unstable generator and the generator with the highest swing, each unstable generator can be quickly adjusted to be stable. In addition, by mapping the action of DRL to the power rescheduling of generators and capacitors/reactors at the same time, rotor angle instability and transient voltage instability under fault 1 and fault 2 are controlled to be stable at the same time.…”

Section: Ieee 39-bus Systemmentioning

confidence: 99%

“…On the one hand, it improves numerical differentiation with interior point methods (IPM), such as reduced space IPM [6], two-level parallel decomposition [7], and primal-dual Newton IPM [8]. On the other hand, transient stability constraints are transformed into other forms, such as transient sensitivity analysis [9], independent transient stability assessment [10], OMIB reference trajectory [11], and energy sensitivity method [12]. However, for TSCOPF, transient voltage stability constraint is rarely considered, while static voltage stability constraint is studied chiefly [13,14].…”

Section: Introductionmentioning

confidence: 99%

Data‐model driven rescheduling considering both rotor angle stability and transient voltage stability constraints

Wang

Tang

2022

IET Renewable Power Gen

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Facing the problem of workforce and time costs caused by the rescheduling of large‐scale power grids with renewable energy penetration, and the lack of parallel control research on rotor angle instability and transient voltage instability, a rescheduling method based on trajectory sensitivity and deep reinforcement learning (DRL) is proposed to meet the requirements of rotor angle stability and transient voltage stability at the same time. By introducing the process of rescheduling to meet the transient stability constraint, the Markov decision‐making process of rescheduling is first constructed. Then, a simple dominant instability type identification method is proposed according to the occurrence time, location, voltage pattern, and position of the oscillation centre. Moreover, a rescheduling strategy is formulated based on the dominant instability mode identification, trajectory sensitivity calculation, actionable device selection, action amount computation, and action of the device. Next, according to the improved distributed distributive deep deterministic policy gradients (D4PG), a DRL model is established to map the action to actionable generator pairs and capacitors/reactors, so as to realize parallel rescheduling of rotor angle instability and transient voltage instability. Finally, the improved New England 39‐bus system and an actual power grid are used to verify the effectiveness and advantages of the method.

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“…T RANSIENT stability-constrained optimal power flow (TSCOPF) is an optimization problem that offers a comprehensive approach to power system optimization by simultaneously addressing economic and operational objectives while considering both static and dynamic stability constraints. TSCOPF has recently received increasing attention [1], [2] because system operators are forced to operate power systems close to their operational limits owing to the high penetration of non-programmable renewable generation, liberalized electricity markets, and environmental restrictions.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Numerical Methods for TSCOPF in a Large Interconnected System

et al. 2022

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Transient stability-constrained optimal power flow (TSCOPF) models comprehensively analyze the security and economic operation of power systems. However, they require a high computational effort and can suffer from convergence problems when applied to large systems. This study analyzes the performance of eleven numerical integration algorithms applied to ordinary differential equations that represent power system dynamics in a TSCOPF model. The analyzed algorithms cover a range of explicit and implicit methods, including the recently published semi-explicit and semi-implicit Adams-Bashforth-Moulton formulas, together with several initialization techniques. The integration methods are applied to a model of the Iberian Peninsula power system, and their performance is discussed in terms of convergence, accuracy, and computational effort. The results show that most implicit methods converge to the solution, even for large time steps. In particular, the Adams-Moulton method of order two and Simpson's rule, both initialized with RK4, outperform the trapezoidal rule, which is the default method in TSCOPF models.INDEX TERMS numerical methods, optimal power flow, power system stability, transient stability,Number of synchronous generators and buses, respectively. c iCost coefficient of the synchronous generator at bus i (in e M W h ). P g,i,0 , Q g,i,0Steady-state active and reactive power generated by the synchronous generator at bus i (in p.u.). P g,i,t , Q g,i,tActive and reactive power generated by the synchronous generator at bus i and time t (in p.u.).Active and reactive load at bus i and time t (in p.u.). P e,i,t , Q e,i,tElectric output active and reactive power in the rotor of the synchronous generator at bus i and time t (in p.u.). P m,iMechanical input power of the synchronous generator at bus i (in p.u.).V i,0 , α i,0 Steady state voltage magnitude and angle at bus i (in p.u. and rad, respectively). V i,t , α i,tVoltage magnitude and angle at bus i and time t (in p.u. and rad, respectively). I brSteady state current of branch br (in p.u.). Y i,j , θ i,jMagnitude and angle of the element (i, j) in the bus admittance matrix Y (in p.u. and rad, respectively). Y L,br,j , θ L,br,j Magnitude and angle of the element (br, j) in the line admittance matrix Y L (in p.u. and rad, respectively). δ i,tRotor angle of synchronous generator i at time t in synchronously rotating reference frame (in rad). δ COI,tThe rotor angle corresponds to the center of inertia (COI) at time t (in rad). ω s Synchronous rotor speed (in rad s ). ∆ω i,0Steady-state rotor speed deviation of the

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Transient Stability-Constrained Optimal Power Flow Calculation With Extremely Unstable Conditions Using Energy Sensitivity Method

Cited by 25 publications

References 23 publications

Dominant inter‐area oscillation path analysis of power systems with a high penetration of permanent magnet synchronous generator by using network mode energy

Dominant inter‐area oscillation path analysis of power systems with a high penetration of permanent magnet synchronous generator by using network mode energy

Data‐model driven rescheduling considering both rotor angle stability and transient voltage stability constraints

Evaluation of Numerical Methods for TSCOPF in a Large Interconnected System

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