称号及び氏名

博士（工学）

学位授与の日付

2007 年 3 月 31 日

論文

名

張建

「Nonlinear Generator Control Based on Equilibrium
Point Analysis and Voltage Stability Considering
Dynamic Load for Power System」（電力システムの平衡点解析による非線形発電機制御と動的負荷を考慮した電圧安定性）

審

査

委

員

主査

川本俊治

副査

森本

茂雄

副査

小亀秀己

論文要旨

Modern electric power systems are characterized by extensive systeminterconnections and increasing dependence. The supply of reliable and economic
electric energy is a major determinant of industrial progress and consequent rise in thestandard of living.
Moreover, as the deregulation of the electric power industry moves forward,“Decentralized Power Sources” has been a focus of constant attention. Technologies ofsolar energy, wind power and fuel cells are extensively studied. Although these are thepotential for a major portion of the electric power supply, significant issues remain
limiting the widespread use of these technologies, including generation control andsystem stability. Also, because of the complexity of power systems with these
distributed generators, the more flexible and overloaded operation of power systems isnecessary, and the higher safety and reliability have been strongly required. Therefore,
the transient stability of power system and the nonlinear generator control are thought tobe important research subjects despite the stability analysis is quite difficult, since thegenerator has a strong nonlinearity.
Especially, generators play a crucial role in the power systems, which have two
important inputs, field voltage and mechanical power. The field voltage is supplied by agenerator driven by a motor or by the shaft of the turbine-generator. Rectifier andthyristor units converting ac to dc in various ways are also common. In any case, theunits are called exciters, and the voltage control system, including an error detector andvarious feedback loops, is usually called an excitation system or Automatic Voltage
Regulator (AVR). For providing supplemental damping to the oscillation ofsynchronous machine rotors through the generator excitation, Power System Stabilizer(PSS), which is installed in the AVR, can improve the power system stability. This
supplementary control is beneficial during line outages and large power transfers.

However, power system instabilities can arise in certain circumstances due to negative
damping effects of the PSS on the rotor. The reason is that PSS is always designed
around a steady-state operating point: their damping effect is only valid for small
excursions around this operating point, but during severe disturbances, power systems
are modeled as large nonlinear highly structured systems. Therefore, PSS is limited
since it is not available for the swing in the nonlinear region and may actually cause thegenerator under its control to lose synchronism in an attempt to control its excitation
field. The design of a nonlinear controller is a quite important subject.
At the same time, the significance of load modeling for voltage stability studies hasbeen emphasized by several disturbances, which have taken place in the past years. As aresult of these disturbances, new investigations have come up to better understand thenature of the load. Actually, accurate models for generators, lines and transformers areavailable today, whereas load models are usually simplified. Static load models are notaccurate enough for capturing the dynamics of the network. Despite power system loads
keep being very difficult to model, accurate dynamic load models are indispensable
because an accurate one will provide a better understanding of the load dynamics and its
representation, making it possible to optimizing the economy and reliability of thesystem operation by voltage stability analysis.
In this thesis, firstly, an analysis based on equilibrium points has been proposed, andapplied to a nonlinear controller design of the Japanese standard one-machine
infinite-bus system model by adding a nonlinear complementary control input for theAVR in place of the linear controller PSS. In the analysis, the system model isformulated by the twelfth order nonlinear differential equations, and is analyzed on abasis of the proposed analysis without any approximation, where the limiters are also
considered in the numerical simulation.
In the case of PSS, there exists the unstable equilibrium point in the inside of theAVR limiter, and it does not go away from the stable one by changing the variable
parameters of the PSS. Therefore, the Critical Clearing Time (CCT) is not improved
because the unstable equilibrium point restricts the transient stability.
On the other hand, for the proposed controller, the unstable equilibrium point of thesystem can be moved or eliminated. So, in this case, the limiter restricts the transientstability since the unstable equilibrium point is eliminated. Here, the unstable point canbe eliminated by the feedback of the proposed nonlinear controller, and the excitation
current is rapidly increased in comparison with PSS. Thus, the proposed method is valid
for the nonlinear region. By adding the complementary control input ua to the AVR, theunstable equilibrium point goes away from the stable one and disappears depending onthe feedback gain, and the CCT and Available Transfer Capability (ATC) are fairlyimproved.
For the investigation on the voltage stability of the Japanese standard one-machine
infinite-bus system model, the dynamic load model is also necessary, and is studied inthis thesis. Dynamic load modeling and stability analysis are important subjects under
the deregulation of electric power industry and the complexity of power systems with
distributed generators. However, it has been said that a realistic dynamic modeling ofcomposite loads is one of the great unsolved (possibly unsolvable) problems ofelectric power field. On the other hand, the dynamic load model proposed by Ihara, Taniand Tomiyama is constructed on a basis of the measured load characteristics, and isgiven in the polynomial form with a differential equation.

The Japanese standard one-machine system model with a dynamic load is treated forthe derivation of the system P-V curve in this thesis. Next, the load model including astatic and a dynamic load terms is introduced, and the measured data of V2, PL, and QL
in Japan and Sweden are expressed by exponential functions. Then, the model can be
expressed in an algebraic form. The coefficient parameters are estimated by using thedata and the least squares method for the modeling. Therefore, the intersection of thesystem P-V curve and the load P-V gives an operation point.
The details of this thesis will be discussed in each Chapter.
In Chapter1, the objectives and the backgrounds of this study are introduced simply.
In Chapter2, the basic concepts of power system, e. g., synchronous generator, powersystem stability are briefly described for an easy understanding.
In Chapter3, the Japanese standard system model used in this thesis is introduced.
The models of IEEE are known, and are also used in Japan for the evaluation of a new
analytical technique of the electric power system. However, the characteristic
phenomena of the Japanese power systems have not been well considered, andsometimes the control system models treated in Japan are also not handled in the systemmodels. Therefore, the technical committee of the Institute of Electrical Engineers inJapan (IEEJ) developed the Japanese standard system models to answer the needs ofthe Japanese electric power engineers. Then, the standard one-machine system model isformulated by the twelfth order nonlinear differential equations, and in the end of thechapter, the power flow is also calculated.
In Chapter4, a nonlinear controller is designed by the equilibrium point analysis. The
proposed nonlinear complementary control input based on the analysis for AVR isconstructed, and equilibrium points of the model are analyzed in comparison with PSS.
Also, CCT, ATC and the simulation results of the system model are discussed. As aresult, by using the proposed nonlinear controller, the system transient stability can bequite improved.
In Chapter5, the dynamic load model proposed by Ihara et al. is introduced, and isverified by two types of measured data in Japan and Sweden. The data of terminal
voltage, active power and reactive power at a load-bus are expressed by approximatedfunctions. Then, the least squares method is used for the estimation of parameters of thedynamic load model. Since the dynamic load model introduced in this thesis has a form
with a differential equation, it is difficult to apply it to the voltage stability analysis.
Therefore, the solution of the differential equation is approximated by a simple
polynomial form, and then the dynamic load model can be rewritten in a simple
polynomial form of the load-bus voltage. So, the load P-V curves can be constructed,
and the voltage stability can be analyzed by the system P-V curves derived from thestandard system and the load P-V curves.
Finally, in Chapter6, the main results of this thesis are concluded, and a future subject
is given by explaining the correlation of generator control and load.
審査結果の要旨
本論文は、電力システムの安全性および信頼性を向上させることを目的として、発電機の非線形制御の方法を新しく提案し、分散型電源が混在する負荷のモデルを構成することにより、電力システムの解析および電圧安定性の向上についての研究をまとめたものであり、次のような成果を得ている。

（１） 標準 1 機無限大系統モデルの動揺方程式を 12 次元の非線形連立微分方程式で定式化し、平衡点解析により近似することなくモデルの平衡点を求め、非線形発電機制御の新しい方法を提案した。
（２） 実電力システムで用いられている線形制御器および提案法について、臨界故障除去時間および制御応答をシミュレーションにより比較し、特性をかなり改善できることを検証した。
（３） 標準 1 機無限大系統モデルの一般的な負荷を取り扱い、実測データに基づいて負荷の電圧低下および負荷脱落を考慮し、分散型電源などによる動的負荷を含む P-V 曲線を導出することにより、実測の負荷の構成を明らかにした。
（４） 系統モデルの P-V 曲線および導出した負荷 P-V 曲線との交点から送電の運転点を求め、負荷の構成に依存する電圧安定度を解析できること、さらに非線形発電機制御により電圧安定度を向上させることができることを示した。
以上の研究成果は、電力自由化および分散型電源が急進展する中で、強く求められている非線形発電機制御および電圧安定度の解析と向上に関する指針と知見を与えるものであり、今後の電力システムの安全性および信頼性の向上に貢献するところは大きい。また、申請者が自立して研究活動を行うために必要な能力と学識を有していることを証したものである。