本文選題：潮流計(jì)算 + 牛頓法　； 參考：《天津大學(xué)》2014年博士論文

【摘要】：潮流計(jì)算是電力系統(tǒng)分析的一項(xiàng)基本工作。隨著電力系統(tǒng)的快速發(fā)展，電網(wǎng)的規(guī)模與復(fù)雜度日益增加，電力系統(tǒng)的非線性程度越來越高（重載情況下尤為明顯），傳統(tǒng)潮流算法經(jīng)常遇到不收斂的情況。因此有必要發(fā)展魯棒并高效的潮流計(jì)算方法。本文研究了以非線性動(dòng)力系統(tǒng)理論為基礎(chǔ)的潮流方法。主要工作分為以下幾個(gè)方面： （1）首先研究了牛頓潮流算法的狀態(tài)空間收斂域特性。采用數(shù)值仿真的方法對牛頓法的收斂域進(jìn)行了刻畫，分析了牛頓法收斂域在基態(tài)和負(fù)荷變化時(shí)的特性，從收斂域的角度揭示了牛頓法對初值的敏感性和負(fù)荷條件對牛頓法收斂性的影響機(jī)理。 （2）研究了基于動(dòng)力系統(tǒng)軌跡的潮流方法，將潮流計(jì)算問題轉(zhuǎn)換為動(dòng)力系統(tǒng)的求解問題，，通過追蹤動(dòng)力系統(tǒng)軌跡獲得穩(wěn)定平衡點(diǎn)來得到潮流方程的解。首先介紹了基于動(dòng)力系統(tǒng)軌跡的潮流方法的基本思想，分析了該方法的特點(diǎn)及優(yōu)勢。然后介紹了幾種典型動(dòng)力系統(tǒng)方程的構(gòu)造形式，給出動(dòng)力系統(tǒng)穩(wěn)定平衡點(diǎn)和潮流解之間的關(guān)系，以及不同潮流問題下動(dòng)力系統(tǒng)的適用情況。然后，介紹了該方法用于計(jì)算潮流多解問題時(shí)的求解思路。最后對這種方法進(jìn)行了數(shù)值測試。測試結(jié)果表明基于動(dòng)力系統(tǒng)軌跡的潮流方法可以用于計(jì)算初值問題和病態(tài)問題引起的牛頓法不收斂的情況，表明了這種方法的有效性和魯棒性。 （3）基于動(dòng)力系統(tǒng)軌跡的潮流法，潮流解的收斂域?qū)?yīng)著動(dòng)力系統(tǒng)穩(wěn)定平衡點(diǎn)的穩(wěn)定域。本文首先通過數(shù)值方法刻畫了幾種典型動(dòng)力系統(tǒng)的穩(wěn)定域，分析了穩(wěn)定域在負(fù)荷變化時(shí)的特性，從穩(wěn)定域的角度揭示了基于動(dòng)力系統(tǒng)軌跡的潮流法具有鄰近收斂性，同時(shí)說明選取合適的動(dòng)力系統(tǒng)形式（如QGS形式）時(shí)基于動(dòng)力系統(tǒng)軌跡的潮流方法不會受到初值和病態(tài)條件的影響。其次證明了QGS形式的動(dòng)力系統(tǒng)滿足穩(wěn)定邊界的刻畫定理，并依據(jù)定理設(shè)計(jì)了QGS形式動(dòng)力系統(tǒng)的穩(wěn)定邊界的系統(tǒng)化刻畫方法。 （4）本文結(jié)合靜態(tài)方法和動(dòng)態(tài)方法的特點(diǎn)，提出了基于動(dòng)態(tài)軌跡的統(tǒng)一性潮流法（TraJectory-based Unified Power Flow Method，簡稱TJU潮流法）。首先介紹了基于動(dòng)態(tài)軌跡的統(tǒng)一性潮流法的基本思想，以及求解的三個(gè)階段：準(zhǔn)確軌跡、近似軌跡和快速求解。在此基礎(chǔ)上根據(jù)靜態(tài)方法和動(dòng)態(tài)方法的結(jié)合情況設(shè)計(jì)了兩種整體實(shí)現(xiàn)方案。其次，針對SDF形式和QGS形式的動(dòng)力系統(tǒng)特點(diǎn)，提出了基于這兩種動(dòng)力系統(tǒng)的TJU潮流法。最后總結(jié)得出了TJU潮流法的特性。TJU潮流法兼具動(dòng)態(tài)方法和靜態(tài)方法的優(yōu)點(diǎn)，具有良好的收斂性、鄰近收斂性、魯棒性和計(jì)算速度。 （5）基于動(dòng)態(tài)軌跡的統(tǒng)一性潮流法算法層的主要內(nèi)容有：首先探討了TJU潮流算法的設(shè)計(jì)中動(dòng)態(tài)方法和靜態(tài)方法的選取，根據(jù)TJU算法的基本思想和數(shù)值方法的特點(diǎn)，靜態(tài)方法采用牛頓法，動(dòng)態(tài)方法采用Pseudo-Transient方法。根據(jù)TJU潮流法的整體設(shè)計(jì)方案，提出了TJU基本潮流算法和TJU增強(qiáng)潮流算法，并詳細(xì)介紹了具體的實(shí)現(xiàn)流程。然后通過數(shù)值計(jì)算的方式分析了TJU潮流算法中幾個(gè)因素對計(jì)算速度的影響，對具體實(shí)現(xiàn)時(shí)參數(shù)的選取有一定的指導(dǎo)意義。最后，通過測試算例對TJU潮流算法進(jìn)行了評估。測試結(jié)果表明TJU潮流算法具有良好的收斂性和計(jì)算速度，可以有效地求解初值問題和病態(tài)問題，并且對大系統(tǒng)同樣有效。
[Abstract]:Power flow calculation is a basic work of power system analysis. With the rapid development of the power system, the scale and complexity of the power grid are increasing, the nonlinear degree of the power system is getting higher and higher (especially in the heavy load case). The traditional power flow algorithm often meets the situation of non convergence. Therefore, it is necessary to develop a robust and efficient power flow meter. The power flow method based on nonlinear dynamic system theory is studied in this paper. The main work is divided into the following aspects:
(1) first, the properties of the state space convergence domain of the Newton flow algorithm are studied. The numerical simulation method is used to characterize the convergence domain of the Newton method. The characteristics of the Newton's convergence domain in the ground state and the load change are analyzed. The sensitivity of the Newton method to the initial value and the convergence of the Newton method are revealed from the angle of the convergence domain. Influence mechanism.
(2) the power flow method based on the power system trajectory is studied. The power flow calculation problem is converted to the solution of the dynamic system. The solution of the power flow equation is obtained by tracking the trajectory of the power system to obtain the solution of the power flow equation. First, the basic idea of the power flow method based on the dynamic system trajectory is introduced, and the characteristics and advantages of the method are analyzed. After introducing the structural forms of several typical dynamic system equations, the relationship between the stable equilibrium point of the power system and the solution of the power flow, and the application of the power system under different power flow problems are given. Then, the solution of this method is introduced when it is used to calculate the multi solution of the power flow. Finally, the numerical test of this method is carried out. The results show that the power flow method based on the dynamic system trajectory can be used to calculate the non convergence of Newton method caused by the initial value problem and the ill conditioned problem, which shows the effectiveness and robustness of the method.
(3) based on the power system trajectory method, the convergence domain of the power flow solution is corresponding to the stable equilibrium of the dynamic system. In this paper, the stability domain of several typical dynamic systems is depicted by numerical method, the characteristics of the stable domain in the load change are analyzed, and the power flow method based on the dynamic system trajectory is revealed from the angle of the stable domain. At the same time, it shows that the power system based power flow method based on the dynamic system path is not affected by the initial value and the ill conditioned condition when selecting the appropriate dynamic system form (such as QGS form). Secondly, it is proved that the dynamic system of QGS form satisfies the stable boundary characterization theorem, and the stable boundary of the power system of QGS form is designed according to the theorem. A systematic portrayed method.
(4) in this paper, combining the characteristics of static and dynamic methods, the unified power flow method (TraJectory-based Unified Power Flow Method, called TJU tidal current method) based on dynamic trajectory is proposed. First, the basic idea of the unified tidal current method based on dynamic trajectory is introduced, and the three stages of the solution are described, the exact trajectory, the approximate trajectory and the fast track. Two overall implementation schemes are designed on the basis of the combination of static and dynamic methods. Secondly, based on the characteristics of SDF and QGS dynamic systems, the TJU flow method based on these two power systems is proposed. Finally, the special.TJU flow method of the TJU flow method is concluded with both dynamic and static methods. The advantages of the method are good convergence, convergence, robustness and computation speed.
(5) the main contents of the algorithm layer of the unified power flow method based on dynamic trajectory are as follows: first, the selection of dynamic and static methods in the design of TJU power flow algorithm is first discussed. According to the basic ideas of the TJU algorithm and the characteristics of the numerical method, the static method adopts the Newton method, the dynamic square method adopts the Pseudo-Transient method. The whole method is based on the TJU tidal current method. The TJU basic power flow algorithm and the TJU power flow algorithm are proposed, and the concrete implementation process is introduced in detail. Then, the influence of several factors on the calculation speed in the TJU flow algorithm is analyzed by numerical calculation, and the parameters are selected as a guide for the specific implementation. Finally, a test example is given to the TJU. The test results show that the TJU power flow algorithm has good convergence and calculation speed, and can effectively solve the problem of initial value and ill condition, and it is also effective for large systems.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TM744

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