(本文)

Recently, the advent of electric power system deregulation and economic growth has brought about the competitive environment and dramatic changes in many countries. Electric supply industry, therefore, has to operate and supply enough electricity to customers in economical and secure manners as well as satisfying technical and social constraints. Optimal power flow (OPF) is a promising tool to fulfill this mission. Generally, conventional OPF aims to determine the control variables such as active power outputs etc. to minimize or maximize a selected objective function while meeting the system constraints simultaneously. Various classical optimization techniques for the conventional OPF problem have been proposed. However, these methods are effective only with convex, smooth, and differentiable objective functions, sensitive to an initial point, and sometimes torturing from insecure convergence properties. The techniques based on derivatives and gradients can lead to a local optimum which is undesirable. When the classical optimization techniques are applied to solve the conventional OPF problem, objective functions and constraints have to be confined into a simplified pattern. Therefore, this dissertation proposes the application of the Evolutionary Programming (EP)-based methods, which provide a great freedom in objective functions and constraints for the OPF problem.

To prevent the transient instability and voltage collapse phenomena, the transient stability and voltage stability issues, which play an important role on blackouts in many countries around the world, are considered in the conventional OPF. In this dissertation, the transient stability issue is treated as the additional constraints of the conventional OPF. The additional constraints are the swing equation, which describes the transient behavior of a synchronous generator, and transient stability limit, which is used to evaluate the stability status of the system. This problem is called Transient Stability Constrained OPF (TSCOPF). Time domain simulation based on the trapezoidal rule is adopted to cope with this swing equation. When the number of the considered contingency is more than 1, the problem is called Multi-Contingency TSCOPF (MC-TSCOPF). Next, the voltage stability issue is considered by adding the value of indicator L into the objective function of the conventional OPF. The indicator L, which is widely used in many applications due to its simplicity of calculation and accuracy, is selected to estimate the voltage stability margin of the system. The larger the indicator L is, the closer the system is to the voltage collapse point. The indicator L at the weakest bus is used as the voltage stability indicator of the whole system. Therefore, the objective function now changes to minimize both indicator L of the weakest bus and the fuel cost simultaneously. The scaling factor is used to weight the importance of voltage stability issue and fuel cost term. The modified objective function brings about the trade-off problem between the financial issue and system security issue. Lastly, OPF with transient and voltage stability considerations is formulated by considering the transient stability issue as the additional constraints and voltage stability issue as one of the objective functions to be minimized.

In this dissertation, two novel EP-based methods are developed to enhance the performance of the conventional EP. The first new method is Improved EP (IEP), which introduces the crossover techniques normally found in Genetic Algorithm (GA) to enhance the offspring generation process. In IEP search template, both mutation and crossover are applied to generate the offspring individuals based on the crossover acceptance rate. The mutation puts emphasis on perturbing the control variables of parent individuals whereas the crossover techniques focus on the information exchange between two parent individuals. The second version of the EP-based methods is Adaptive EP (AEP). The AEP reduces the parameters required to pre-define when the EP method is selected to solve the OPF problem. The reduced parameter is the population size, which normally plays a crucial role on the quality of solution and execution time. The population size starts with one single individual at the beginning and then it will change adaptively according to the adaptation rule adopted from an idea that the population having many improved individuals can reduce its size whereas the population having few improved individuals should increase its size.

In TSCOPF problem, time domain simulation used to assess transient stability leads to very long computational time when the EP-based methods are applied. To alleviate the above problem, this dissertation proposes the combination of time domain simulation and artificial neural network to evaluate the system transient stability. The neural network, which is less time-consuming, is first used to classify the individual into three regions, namely stable, unstable, and critical regions using pre-set thresholds and then time domain simulation will be performed with only individual classified in the critical region. The reduction of computational time of TSCOPF can be expected from this proposed strategy.

The effectiveness of the proposed EP-based methods is tested on WSCC 9-bus and IEEE 30-bus systems with three types of cost functions representing the approximated cost model and detailed cost model of the thermal unit. The results show that, for almost all OPF problems, IEP and AEP can obtain the better solutions with the shorter computational time than the conventional EP. When the neural network is incorporated into the EP-based methods, the computational time of TSCOPF and MC-TSCOPF is dramatically reduced while the quality of solution is almost the same as the methods without the neural network. The results of different OPF problems show that the solution from the conventional OPF problem provides the cheapest operating point among all OPF problems. However, it cannot guarantee the transient stability after some possible contingencies and cannot provide a satisfactory voltage stability margin. The solution from TSCOPF can guarantee transient stability after the considered contingency with the significant increases in fuel cost and computational time. The solution from OPF considering voltage stability provides the larger voltage stability margin than that from the conventional OPF. The increase in stability margin is gained by setting the voltage magnitudes of generator buses at a high value. The computational time of this problem is not as long as that of TSCOPF. The reason is that the calculation time of indicator L is much shorter than time domain simulation. Lastly, the solution from OPF considering both transient and voltage stabilities can provide transiently-stable operating point with a satisfactory voltage stability margin. As expected, the fuel cost and computational time of this problem are the most significant among all OPF problems.

本論文は「Development of an Efficient Calculation Method Based on Evolutionary Programming for Optimal Power Flow Considering Transient and Voltage Stabilities(過度安定度と電圧安定度を考慮した進化的プログラミングに基づいた効果的な最適潮流計算手法の開発)」と題し、6章よりなる。

第1章は「Introduction(序論)」で、まず進化的プログラミング(EP)の一般的な概念について述べ、次に、最適潮流計算などの電力系統の最適化問題へのEPの適用例を紹介している。また、一般的な最適潮流計算について、目的関数、制約条件、制御変数などを説明している。

第2章は「Optimal Power Flow (OPF) Problem with Transient and Voltage Stability Considerations(過度安定度と電圧安定度を考慮した最適潮流計算)」と題し、「従来型最適潮流計算」、「過度安定度を考慮した最適潮流計算」、「電圧安定度を考慮した最適潮流計算」、「過度安定度と電圧安定度を考慮した最適潮流計算」の4つの最適化問題についてそれぞれ定式化をしている。過度安定度は、発電機の動揺方程式と過渡安定度制約を「従来型最適潮流計算」の制約条件に加え、電圧安定度は、よく使われるindicator Lという電圧安定性指標を「従来型最適潮流計算」の目的関数に加えることによって考慮している。

第3章は「Evolutionary Programming (EP)-Based Methods(進化的プログラミングに基づいた最適化手法)」と題し、従来型EPについて述べ、改良型EP(IEP)、適応型EP(AEP)の2つの進化的プログラミングに基づいた最適化手法を提案している。まず本論文で用いる従来型EPについて、全体のアルゴリズムおよび突然変異(mutation)や淘汰(selection)などの主な個別計算手法を述べ、突然変異に加えて遺伝的アルゴリズム(GA)における交叉(crossover)を適用しEPの新たな個体を生成することで、従来型EPに比べて高速で求解が可能なIEPを提案している。最後に、EPにおける個体数を適応的に変化させることで、従来型EPと比べて設定するパラメータ数が少なく、計算負荷の小さい適応型EP (AEP)を提案している。

第4章は「Artificial Neural Network (ANN) for Transient Stability Assessment(人工ニューラルネットワークによる過度安定度評価)」と題し、第2章で述べた「過度安定度を考慮した最適潮流計算」における発電機の動揺方程式と過渡安定度制約条件をニューラルネットワークによって考慮することで、最適潮流計算における過度安定度の評価時間を短縮する手法を提案している。また、第3章で提案したEPに基づいた最適化手法と提案したニューラルネットワークを組み合わせた「過度安定度を考慮した最適潮流計算」の新たな解法全体について説明し、提案したニューラルネットワークの有効性を示すため、2通りのニューラルネットワーク学習法によるシミュレーションを行っている。

第5章は「Numerical Results and Discussion(シミュレーション結果および考察)」と題し、第3章で提案した従来型EP、IEP、AEPを第2章で設定した4つの最適化問題に対して適用し、数値シミュレーションによって評価している。そのシミュレーション結果から、新たに提案したIEP、AEPは、従来型EPと比較して、よりよい解を、より短い計算時間で得られることを示している。AEPは、計算負荷が小さいだけでなく、設定するパラメータ数が少ないことも大きな利点であることがわかった。また、「過度安定度を考慮した最適潮流計算」に対して、ニューラルネットワークと組み合わせた従来型EP、IEP、AEPを適用することで計算時間が大幅に削減できることが明らかとなった。過度安定度と電圧安定度の両方を考慮した場合は考慮しない場合と比較して、最適化の制約がより厳しくなっているため、目的関数である発電機の燃料費が高くなり、また計算時間が長くなることも明らかとなった。

第6章は「Conclusions(結論)」で、各章の結論をまとめている。

以上を要するに、従来の最適化手法では最適解を求めるのが難しい過度安定度と電圧安定度を考慮した最適潮流計算問題に対して、ニューラルネットワークを融合した改良型進化的プログラミングに基づいた最適化手法を提案し、さまざまな種類の最適化問題に対してこの提案手法が、求解性が高くかつ計算負荷が小さいことをシミュレーションによって明らかにしたもので、電気工学、特に電力システム工学に貢献するところが少なくない。

よって本論文は博士(工学)の学位請求論文として合格と認められる。