6

Design of a Hybrid
混合动力车的设计

Multisource/Multistorage Supervisor
多数据库/多存储管理程序

6.1. Introduction
6.1.介绍

Renewable energy sources such as wind, photovoltaics, small runof-the-river hydropower and marine sources, such as tides, participate either weakly or not at all in the management of the electrical system to which they are connected (see Chapters I and 3). A large quantity of these sources in the energetic mix of the system may cause stability problems [ACK 05, ROB 12b].
风能、光伏发电、小型径流式水力发电和潮汐等海洋能源等可再生能源在其所连接的电力系统的管理中的参与程度很弱或根本不参与（见第一章和第三章）。在系统的能量混合物中，大量的这些源可能会导致稳定性问题[ACK 05，ROB 12 b]。

These problems are particularly present in the case of low-power island electrical systems or those created following the loss of means of interconnection in the case of continental grids. In these situations, a high penetration of variable renewable energy sources in electricity production systems will be possible only if:
这些问题在低功率岛屿电力系统或在大陆电网失去互连手段后产生的电力系统中特别突出。在这些情况下，只有在以下情况下，才有可能在电力生产系统中高度渗透可变可再生能源：

— renewable energy sources (wind, photovoltaic, etc.) are associated with sources whose production is predictable and can therefore be planned and controlled, and/or with storage devices in an integrated management system;
- 可再生能源（风能、光伏等）与其生产是可预测的并且因此可以被计划和控制的源相关联，和/或与集成管理系统中的存储设备相关联;

— renewable energy sources participate in the provision of ancillary services such as voltage and frequency control, blackstart, etc.
- 可再生能源参与提供辅助服务，如电压和频率控制、黑启动等。

The improvement of weather forecasting will also contribute to improve the integration of these services into electric grids. The combined management of charges with this type of production will also contribute to a more harmonious integration of renewable sources. This aspect will not be considered in this chapter; an example of this dual management in the case of electric vehicles is discussed in [BOU 13, BOU 14] and [ROB 15].
天气预报的改进也将有助于改善这些服务与电网的整合。将收费与这类生产相结合的管理也将有助于更和谐地整合可再生能源。本章将不考虑这一方面;[BOU 13，BOU 14]和[ROB 15]中讨论了电动汽车情况下这种双重管理的示例。

The association of multiple different energy sources by means of an integrated management system constitutes a virtual multisource power plant. The objective of this chapter is to propose a methodology for the design of supervision of this new kind of production unit [SPR 09, COU 10].
通过集成管理系统将多个不同的能源相关联，构成了虚拟的多能源发电厂。本章的目的是为这种新型生产单位的监督设计提出一种方法[SPR 09，COU 10]。

The multisource power plant studied in this chapter is composed of a wind turbine coupled with a predictable and controllable source and with two storage systems with different characteristics. The objectives of supervision will be to follow a reference power while maximizing the use of the renewable resource. Moreover, in the case of frequency variation in the electric grid, the multisource plant must participate in the primary control of this frequency (the principle of which is explained in Chapter 3).
本章所研究的多级风力发电厂是由一个风力涡轮机耦合一个可预测和可控的源和两个存储系统具有不同的特性。监管的目标将是遵循一个参考权力，同时最大限度地利用可再生资源。此外，在电网频率变化的情况下，多频电厂必须参与该频率的主要控制（其原理在第3章中解释）。

Fuzzy logic-based supervision seems well adapted for the resolution of this type of problem due to:
基于模糊逻辑的监督似乎很适合解决这类问题，因为：

— the complexity of the system being controlled and the difficulty of obtaining a precise model of it;
- 被控制系统的复杂性和获得精确模型的困难;

— the uncertainty of production of the renewable source;
- 可再生能源生产的不确定性;

— the difficulty of quantifying the grid's response to variations in the productions and charges connected to it.
- 量化电网对产量变化和与之相连的费用的响应的难度。

This chapter will show that the method presented in Chapters 1 and 5 makes it possible to:
本章将说明，第1章和第5章介绍的方法可以：

— avoid the necessity of using precise and complicated models of different sources and storage systems;
- 避免使用不同来源和储存系统的精确和复杂模型的必要性;

— determine the supervisor in a systematic and modular manner;
- 以系统化、模块化的方式确定主管;

— minimize the number of fuzzy laws (from 540 possible laws to 52 relevant laws in the example considered) and simplify real-time implantation.
- 最小化模糊规则的数量（在所考虑的示例中从540个可能的规则到52个相关规则）并简化实时植入。

In section 6.2, the design methodology for the supervision strategy of the hybrid system will be described. Sections 6.3 and 6.4 use simulations to help illustrate the supervisor performances obtained. In section 6.5, the supervisor design methodology will be tested on various multisource system topologies in order to illustrate its systematic and modular character. The performances of different topologies will be compared using quantitative indicators.
在第6.2节中，将描述混合系统的监督策略的设计方法。第6.3节和第6.4节使用模拟来帮助说明所获得的主管绩效。在第6.5节中，将在各种多业务系统拓扑上测试监控器设计方法，以说明其系统性和模块化特征。不同拓扑结构的性能将使用定量指标进行比较。

6.2. Methodology for the construction of a supervisor for a hybrid source incorporating windpower
6.2.混合电源监控器的构建方法

The design methodology of the supervision system applied in this chapter is based on seven stages:
本章所采用的监督系统设计方法基于七个阶段：

determination of system specifications: system characteristics and objectives must be clearly laid out;
系统规格的确定：系统的特点和目标必须明确;

structure of supervisor: the required supervisor inputs and outputs are determined;
主管结构：确定所需的主管输入和输出;

determination of "functional graphs": a graphic representation of the operating modes is proposed based on the knowledge of the system;
确定“功能图”：根据系统的知识提出操作模式的图形表示;

determination of the membership functions of the fuzzy supervisor;
确定模糊监督器的隶属函数;

determination of "operational graphs": a graphic representation of the fuzzy operating modes is proposed;
确定“操作图”：提出了模糊操作模式的图形表示;

fuzzy rules: the characteristics of the fuzzy supervisor are extracted from the operational graphs;
模糊规则：从运算图中提取模糊监督器的特征;

indicators are used to evaluate the achievement of objectives and to compare different cases (different topologies, variants of supervisor, etc.).
指标用于评估目标的实现情况和比较不同的情况（不同的拓扑结构、不同的管理程序等）。

This methodology is developed by applying it to the supervision of a virtual power plant based on renewable energy and including a predictable energy source and two storage systems with different characteristics.
该方法是通过将其应用于基于可再生能源的虚拟发电厂的监管而开发的，该虚拟发电厂包括可预测的能源和具有不同特性的两个存储系统。

In this study, the sizing of storage systems is not addressed; it is assumed to have been made a priori [ROB 12a]. The determination of a real-time supervisor such as the one developed in this chapter may lead to the fine-tuning of the sizing of storage systems with the principal objective of reducing their size.
在这项研究中，存储系统的规模没有解决;它被假定为先验[ROB 12 a]。确定本章中开发的实时监控程序可能会导致对存储系统大小进行微调，其主要目标是减小存储系统的大小。

6.2.1. Determination ofsystem specifications
6.2.1.系统规格的确定

In order to be able to adhere to a reference power and guarantee a reserve stock of power, a windpower plant is connected to a decentralized generator whose production is predictable and can be planned and controlled (e.g. a gas turbine or a diesel generator), and to long-term and short-term storage systems. The whole system is a virtual multisource power plant which will be connected at a point of a power system (Figure 6.1) and will behave like a classic source with regard to the manager of this grid. The principal objectives of a multisource power plant are to:
为了能够坚持参考功率并保证电力储备，风力发电厂连接到分布式发电机，其生产是可预测的并且可以计划和控制（例如燃气涡轮机或柴油发电机），并且连接到长期和短期存储系统。整个系统是一个虚拟的多功能发电厂，它将连接在电力系统的一个点上（图6.1），并将表现得像一个经典的源关于这个电网的管理者。多功能发电厂的主要目标是：

— supply the reference power set by the grid manager, with the obligations of maximizing the use of renewable resources and minimizing fossil fuel consumption;
- 提供电网管理者设定的参考功率，并有义务最大限度地利用可再生资源，最大限度地减少化石燃料消耗;

In a grid, a gap between the power produced and consumed will be compensated for, by a contribution or a kinetic energy storage in rotating masses of machines. This results in a variation in grid power that will be observed by all of the grid's production units. The lower the total inertia of the rotating masses (and therefore the network is small), the higher the frequency variation created by an imbalance of power will be. The participation of a power generation assembly in frequency control consists of the augmentation of its production in the event of a decrease in frequency, and the reduction of its production in the event of an increase in frequency. This contribution is classically represented by the linear relationship shown in Figure 6.2. The characteristic values of this relationship are its slope and the maximum differential P —Pre called the primary reserve (Preserve).
在电网中，生产的电力和消耗的电力之间的差距将通过机器旋转质量中的贡献或动能存储来补偿。这导致电网功率的变化，这将被电网的所有生产单元观察到。旋转质量的总惯性越小（因此网络越小），由功率不平衡产生的频率变化就越大。发电机组参与频率控制包括在频率降低的情况下增加其产量，以及在频率增加的情况下减少其产量。这种贡献典型地由图6.2所示的线性关系表示。这种关系的特征值是其斜率和最大差值P-Pre，称为原始储备（Preserve）。

The size of this stock is defined by the grid manager as a function of economic and technical criteria.
电网管理者根据经济和技术标准确定这一存量的大小。

Figure 6.1. Electrical system studied
图6.1.电气系统研究

re
	Pref P,nax Power PrefP，naxPower

Frequency
频率

[VIZ]

Figure 6.2. Frequency—power characteristic ofa turbo-alternator
图6.2.涡轮发电机的频率功率特性

In order to ensure that the wind turbines do not participate in this adjustment for small variations in frequency, a deadband is introduced by grid operators for this characteristic.
为了确保风力涡轮机不参与频率小变化的这种调整，电网运营商为此特性引入了死区。

Table 6.1 summarizes the objectives, obligations and means of action to be taken into account for the construction of a supervision strategy.
表6.1概述了制定监督战略时应考虑的目标、义务和行动手段。

Table 6.1. Objectives, constraints and means ofaction to be taken into account when designing a supervision strategy
表6.1.设计监督战略时应考虑的目标、限制和手段

6.2.2. Structure ofsupervisor
6.2.2.监事结构

The structure of a supervisor will be organized so as to achieve the two main objectives defined in the previous section.
监督员的结构将按照实现上一节所述两个主要目标的方式安排。

Storage systems will play a fundamental role in obtaining these objectives by:
存储系统将通过以下方式在实现这些目标方面发挥重要作用：

— compensating for fluctuations in the renewable source;
- 补偿可再生能源的波动;

The proper management of these storage systems will be essential to best meet the objectives. Since storage system capacity is limited by technological and economic constraints, however, when these systems are almost completely charged or discharged, the objectives will have to be met by means of other sources:
这些储存系统的适当管理对于最好地实现这些目标至关重要。然而，由于存储系统容量受到技术和经济约束的限制，当这些系统几乎完全充电或放电时，必须通过其他来源来满足目标：

— by degrading windpower when storage systems are saturated;
-当存储系统饱和时，风力发电量会下降;

— using the predictable source when storage systems are discharged.
- 当存储系统放电时使用可预测的源。

At this stage, the inputs required by the supervisor to fulfill its objectives can be defined:
在此阶段，可以定义主管为实现其目标所需的输入：

— in order to follow the reference power (Prey), one supervisor input is the difference AP = P ref —P ms between the total power generated by the multisource power plant Pms and the reference power;
- 为了遵循参考功率（Prey），一个管理器输入是由多频发电厂生成的总功率Pms与参考功率之间的差AP =Pref-Pms;

The outputs of the fuzzy supervisor are references imposed on each element of the multisource power plant:
模糊管理器的输出是施加在多频发电厂的每个元件上的参考：

A block diagram of the supervisor is shown in Figure 6.3.
图6.3显示了监控程序的框图。

In line with the definition of the two principal objectives, the supervisor is divided into two parts:
根据这两个主要目标的定义，监督员分为两部分：

— the frequency control characteristic will be defined separately from the fuzzy supervisor, and this control will be executed as a matter of priority by the storage systems (P
- 频率控制特性将与模糊管理器分开定义，并且该控制将作为优先事项由存储系统（P）执行

Multi-source powerplant supervisor
多源电厂监控器

Figure 6.3. Block diagram ofsupervisor
图6.3.监控器框图

The reference powers of the storage systems are thus the sum of
因此，存储系统的参考功率是以下各项之和：

two terms:
两个术语：

It is important to note that in order to guarantee the availability of energy in the storage systems and to ensure that frequency control actions do not compete with the reference control power Prey, storage levels must be managed by the fuzzy supervisor.
重要的是要注意，为了保证存储系统中的能量的可用性，并确保频率控制动作不与参考控制功率Prey竞争，存储水平必须由模糊管理器管理。

6.2.3. Determination offunctional graphs
6.2.3. 函数图的判定

The strategy of the fuzzy supervisor of a multisource system can be defined graphically, which has the following advantages:
多传感器系统的模糊监控器的策略可以用图形来定义，它具有以下优点：

a literal expression of the objectives and sub-objectives to be achieved, and the obligations and means of action making it possible to:
对要实现的目标和次级目标的文字表述，以及使之有可能：

facilitate exchanges with other disciplinary fields, such as the economy for example, which plays an important role in energy choices;
促进与其他学科领域的交流，例如在能源选择中发挥重要作用的经济;

—a transition between modes determined by the state of certain parts of the system. These states can be described by the fuzzy variables serving as the supervisor inputs, thus enabling smooth transitions between operating modes and the ability of the system to operate in multiple modes simultaneously;
- 由系统某些部分的状态确定的模式之间的转换。这些状态可以用作为管理器输入的模糊变量来描述，从而能够在操作模式之间进行平滑的转换，并且能够使系统同时在多种模式下操作;

— insofar as fuzzy logic integrates Boolean logic, it can be used to revisit more classic approaches such as Petri and Grafcet diagrams.
由于模糊逻辑集成了布尔逻辑，它可以用来重新审视更经典的方法，如Petri和Grafcet图。

The fuzzy logic part of the supervisor shown in Figure 6.3 is represented graphically in Figure 6.4. Operating modes are represented by rectangles with rounded corners and system states by the transitions between these modes.
图6.3所示的监控程序的模糊逻辑部分在图6.4中以图形表示。操作模式由圆角矩形表示，系统状态由这些模式之间的转换表示。

Figure 6.4. Functional graph offuzzy logic-based supervisor
图6.4. 模糊逻辑监控器的功能图

As illustrated in Figure 6.4, the fuzzy logic part of the supervisor is divided into two main operating modes, NI and N2. The objective of the first operating mode (N 1) is to control the output power at the reference power. It is subdivided into three operating submodes. Transitions from one submode to another submode are defined by the state of the storage systems:
如图6.4所示，监控器的模糊逻辑部分分为两个主要操作模式，NI和N2。第一操作模式（N1）的目的是将输出功率控制在参考功率。它被细分为三个操作子模式。从一种子模式到另一种子模式的转换由存储系统的状态定义：

— N 1.1: if the storage system level is medium, the multisource power plant must control the reference power while maximizing the power generated by the wind turbine. The wind turbine therefore functions at its optimal operating point and the storage systems compensate for the difference between the reference power (Prey) and the output power of the multisource power plant (Pms). The functional graph for this operating mode is shown in Figure 6.5;
- N 1.1：如果存储系统水平是中等的，则多级发电厂必须控制参考功率，同时最大化由风力涡轮机产生的功率。因此，风力涡轮机在其最佳操作点处运行，并且存储系统补偿参考功率（Prey）与多级发电站的输出功率（Pms）之间的差。该运行模式的功能图如图6.5所示;

Figure 6.5. Functional graph ofmode NI.I
图6.5. NI.I模式功能图

NI .2: if the storage system level is high, two actions are executed simultaneously by the supervisor. The first action consists of discharging the storage system in order to participate in primary frequency control by absorbing energy. The second action consists of controlling the power of the multisource power plant at the reference power by modifying the calibration angle of the blades (F). The functional graph for this operating mode is shown in Figure 6.6;
NI. 2：如果存储系统级别高，则由管理器同时执行两个动作。第一个动作包括使存储系统放电，以便通过吸收能量参与一次频率控制。第二个动作包括通过修改叶片的校准角度（F）将多频发电设备的功率控制在参考功率。该运行模式的功能图如图6.6所示;

Figure 6.6. Functional graph ofmode NL 2
图6.6. NL 2模式的功能图

The second main operating mode (N2) enables the frequency controller to act via the frequency-power characteristic without entering into conflict with the power controller. In this operating mode, frequency adjustment is prioritized over reference power adjustment. Moreover, in periods of overfrequency and if the storage level is high, the power generated by the wind turbine can be downgraded. Finally, when the predictable source is operational, that is, when the storage level is low, it can also participate in primary frequency regulation. The functional graph for this operating mode is shown in Figure 6.8.
第二主操作模式（N2）使得频率控制器能够经由频率-功率特性而不与功率控制器冲突地起作用。在该操作模式中，频率调整优先于参考功率调整。此外，在过频率的时段中并且如果存储水平高，则可以降低由风力涡轮机产生的功率。最后，当可预测源可操作时，即当存储水平低时，它也可以参与一次频率调节。该运行模式的功能图如图6.8所示。

NI. 1, N 1.2, N 1.3 and N2 are the operating modes of the supervisor and are connected to priority objectives, while the transitions (storage level and frequency differential) can be seen as obligations imposed on the system:
倪N1.1、N1.2、N1.3和N2是管理程序的操作模式，并与优先级目标相关联，而转换（存储级别和频率差）可以被视为对系统施加的义务：

When two storage systems are considered, the three operating modes N 1.1, N 1.2 and N 1.3 are duplicated as shown in Figure 6.9. NI .1ct, NI.2ct and NI.3ct are linked to the short-term storage system and Nl.llt, NI.21t and NI.31t are linked to the long-term storage system. These operating modes are activated simultaneously. Figure 6.9 represents all the operating modes of the fuzzy supervisor as well as the transitions between them.
当考虑两个存储系统时，三种操作模式N 1.1、N 1.2和N 1.3被复制，如图6.9所示。NI.1ct、NI.2ct和NI.3ct与短期存储系统相连，而NI.1lt、NI.21t和NI.31t与长期存储系统相连。这些操作模式同时激活。图6.9表示模糊监控器的所有工作模式以及它们之间的转换。

Figure 6.9. Graphic representation ofdifferent operating modes
图6.9. 不同操作模式的图示

6.2.4. Determination of membership functions
6.2.4.隶属函数的确定

The next stage in the proposed methodology is the determination of the membership functions of the input and output values of the fuzzylogic supervisor. The membership functions of the input values will ensure the transitions between different operating modes (Al, Nivstock
在所提出的方法的下一个阶段是模糊逻辑管理器的输入和输出值的隶属函数的确定。输入值的隶属函数将确保不同操作模式（Al、Nivstock）之间的转换

— sets "S" and "B", for "small" and "big", respectively, ensure the energy reserves necessary for the power plant's contribution to frequency control. In the case considered here, in the event of sub- or super-frequency the same minimal energy reserve of 0.05 per unit is held in the storage systems;
- 设置“S”和“B”，分别用于“小”和“大”，确保发电厂对频率控制的贡献所需的能量储备。在这里考虑的情况下，在亚频率或超频率的情况下，在存储系统中保持每单位0.05的相同的最小能量储备;

Figure 6.10(c) represents the membership functions linked to the frequency differences Af = fref — fmes. Three sets are defined:
图6.10（c）表示与频率差Af=fref-fmes有关的隶属函数。定义了三组：

— two sets "PB" and "NB", for "Positive Big" and "Negative Big", respectively, which are used symmetrically to participate in frequency control.
- 两组“PB”和“NB”，分别用于“正大”和“负大”，它们对称地用于参与频率控制。

Figure 6.10(d) represents the membership functions linked to the power differential AP = P ref —P ms • Because the minimization of this gap is a major objective, five sets are considered to achieve a compromise between the precision of the power generated and the complexity of the supervisor. The sets are called "NB" (Negative Big), "NM" (Negative Medium), "Z" (Zero), "PM" (Positive Medium) and "PB" (Positive Big).
图6.10（d）表示与功率差AP = P ref -P ms相关的隶属函数。由于最小化该差距是一个主要目标，因此考虑了五组，以实现所产生功率的精度和监督程序的复杂性之间的折衷。这些集合被称为“NB”（负大），“NM”（负中），“Z”（零），“PM”（正中）和“PB”（正大）。

The membership functions of the output values are illustrated in
输出值的隶属函数如

Figures 6.11(a)—(d), respectively, for the short-term storage reference power, the long-term storage reference power, the reference angle for the orientation of the wind turbine blades and the reference power of the predictable source.
图6.11（a）-（d）分别针对短期存储参考功率、长期存储参考功率、风力涡轮机叶片定向的参考角度和可预测源的参考功率。

c)
c）、

 d) A P [pul
d）A P [脉冲

Figure 6.10. Membership functions of input values: a) short-term storage level, b) long-term storage level, c) frequency differential and d) power differential. For a color version of the figure, see www.iste.co.uk/robyns/powergrids.zip
图6.10.输入值的隶属函数：a）短期存储水平，B）长期存储水平，c）频率微分和d）功率微分。有关该图的彩色版本，请参见www.iste.co.uk/robyns/powergrids.zip

refstock It pu [pul
RefstockITPU [PUL

ßrefpu [pu
[ Pu ] 普 （ PU ）]

refSP [pul

Figure 6.11. Membership function ofoutput values: a) short-term storage reference power, b) long-term storage reference power, c) reference angle of wind turbine blades and d) reference power ofpredictable source. For a color version of the figure, see www.iste.co.uk/robyns/powergrids.zip
图6.11.输出值的隶属函数：a）短期存储参考功率，B）长期存储参考功率，c）风力涡轮机叶片的参考角度，d）可预测源的参考功率。有关该图的彩色版本，请参见www.example.com

Because storage system power levels can be positive or negative, five sets are considered: "NB", "NM", "Z", "PM" and "PB". The choice of these sets is made so that the output value will be included in the interval [—1, 1] (see section 6.5.1). The link between the angle of orientation of the blades and the reduction of windpower is strongly nonlinear; therefore, the membership functions of the calibration angle are chosen to make the relationship between AP and the reduction of windpower in operating mode N 1.2 more linear. Because the value is always positive [0, l], three sets ("Z", "M" and "B") are chosen so as to achieve a compromise between precision and complexity. In the example considered, the nature of the predictable source is not taken into account, and any choice of three sets has been made ("Z", "M" and "B") so as to supply a reference power of between [0, l ]
因为存储系统功率电平可以是正的或负的，所以考虑五个集合：“NB”、“NM”、“Z”、“PM”和“PB”。这些集合的选择是为了使输出值包含在区间[-1，1]中（见第6.5.1节）。叶片的定向角度与风力减少之间的联系是强烈非线性的;因此，选择校准角度的隶属函数以使操作模式N 1.2中AP与风力减少之间的关系更加线性。因为该值总是正的[0，l]，所以选择三个集合（“Z”、“M”和“B”）以便实现精度和复杂度之间的折衷。在所考虑的示例中，不考虑可预测源的性质，并且已经做出三个集合（“Z”、“M”和“B”）的任何选择，以便提供[0，1]之间的参考功率。.

The number of fuzzy laws associated with each output variable is determined by multiplying the numbers of fuzzy sets for each input variable by one another, or 3 x 3 x 3 x 5 135. In the case being considered, which includes four output variables, the total number of fuzzy laws possible will be 4 ^x 135 — 540. Traditionally, these laws are determined using tables. The table associated with each output variable will thus have five dimensions. The methodology proposed enables the determination of the relevant laws. The associated graphic representation has a double advantage; it facilitates the writing of laws without the use of tables and extracts only the laws that are most relevant to the overall functioning of the system.
与每个输出变量相关联的模糊规则的数量通过将每个输入变量的模糊集的数量彼此相乘或3 x 3 x 3 x 5 135来确定。在所考虑的情况下，它包括四个输出变量，模糊法律的总数可能是4 × 135 - 540。传统上，这些定律是使用表格确定的。因此，与每个输出变量相关联的表格将具有五个维度。所提出的方法有助于确定相关法律。相关的图示具有双重优势：它便于在不使用表格的情况下编写法律，并且只提取与系统整体运作最相关的法律。

6.2.5. Determination ofoperational graphs
6.2.5.运算图的确定

The schema in Figure 6.9 showed that it is possible to break down the system into a group of subsystems. This breakdown is also used for the determination of fuzzy laws. For this, it is necessary to translate the functional graphs into operational graphs that include the membership functions previously defined. Transitions between operational modes will be described by the membership functions of the input values and the actions of the operational modes will be described by the membership functions of the output values. This approach leads us to the operational graph shown in Figure 6.12. The fuzzy sets of the input variables linked to storage and frequency determine the operational modes. A detail of this figure in the case of submode N l . Ict is presented in Figure 6.13. In this mode, the multisource power plant maximizes windpower (ßrefyu is "Z'), does not use the predictable source (Pref_spyu is "Z') and controls output power using the short-term storage system; the larger the output power deficit (APpu), the higher the power generated by the storage system; at the same time, the higher the surplus power, the more power is absorbed by the storage system. The fuzzy sets linked to the power differential can thus be used to define the reference power values of the short-term storage system. A similar approach is used for the other operational submodes
图6.9中的模式表明，将系统分解为一组子系统是可能的。这种故障也用于确定模糊的法律。为此，有必要将功能图转换为包含先前定义的隶属函数的操作图。操作模式之间的转换将由输入值的隶属函数描述，并且操作模式的动作将由输出值的隶属函数描述。这种方法将我们引向图6.12所示的操作图。与存储和频率相关的输入变量的模糊集确定操作模式。该图在子模式Nl的情况下的细节。Ict见图6.13。 在这种模式下，多源发电厂最大化风力（<$refyu是“Z”），不使用可预测的源（Pref_spyu是“Z”），并使用短期存储系统控制输出功率;输出功率赤字（APpu）越大，存储系统产生的功率越高;同时，剩余功率越高，存储系统吸收的功率越多。因此，可以使用与功率微分相关联的模糊集来定义短期存储系统的参考功率值。 类似的方法用于其他操作子模式.

Figure 6.12. Operational graph ofsupervisor
图6.12. Supervisor操作图

Figure 6.13. Operational graph ofmode NL Ict
图6.13. NL Ict模式运行图

6.2.6. Extraction offuzzy laws
6.2.6. 模糊规律提取

Based on the diagram shown in Figure 6.13, it is quite simple to extract the fuzzy laws for operational mode NI. I ct. Certain conditions are inherited from the input conditions of modes NI (IF Afis "Z') and Ni.lct (IF Nivstock_ctyu is "M') and a third condition is linked to the fuzzy reasoning operating in this mode:
根据图6.13所示的图表，提取NI工作方式的模糊规则是相当简单的。我做了CT。某些条件是从模式NI（IFAfis“Z”）和Ni.lct（IFNivstock_ctyu是“M”）的输入条件继承的，第三个条件与在该模式下操作的模糊推理相关联：

-IF Af IS Z AND
- 如果Af是Z并且

ref stock_ct_pu
参考库存_ct_pu 

-IF Af IS Z AND
- 如果Af是Z并且

-IF Af IS Z AND Nivstock_ct.u IS M AND APpu IS Z THEN
- 如果Af是Z且Nivstock_ct.u是M且APPU是Z，则

ref stock_ct_pu
参考库存_ct_pu 

-IF Af IS Z AND
- 如果Af是Z并且

Finally, two laws determining the output variables linked to the wind turbine and the predictable source are entirely defined by membership in operational mode N 1. Ict. These laws are written as:
最后，确定与风力涡轮机和可预测源相关的输出变量的两个定律完全由操作模式N1中的隶属度来定义。Ict。这些法律如下：

IF Afis Z AND
如果Afis Z和

IF Af is Z AND Nivstock_ct.u is M THEN Pref  Z
如果Af是Z且Nivstock_ct.u是M，则Pref Z

Carrying out this operation for all of the modes identified in Figure 6.13, only 52 fuzzy laws are considered instead of the 540 possible laws. A complete list of these laws is given in section 6.5.2. In addition to proposing a systematic construction of the fuzzy supervisor, this methodology enables a significant reduction in the number of laws to be processed, simplifying the real-time implantation of this supervisor.
对图6.13所示的所有模态进行这种运算，只考虑了52条模糊规律，而不是540条可能的规律。这些法律的完整列表见第6.5.2节。除了提出一个系统的模糊监督器的建设，这种方法能够显着减少法律的数量进行处理，简化了实时植入这个监督器。

6.3. Compared performance of different variants of hybrid source
6.3.混合源不同变体的性能比较

To illustrate the efficiency of the supervisor constructed using the proposed methodology, several simulations of the electromechanical system and its supervisor are presented. A modeling of the various system elements is given in this chapter. However, it is important to note that this modeling effort is not necessary for the development of the supervisor; it is rather used to simulate the system and test the supervisor. The structure of the supervisor is independent of the technologies used to create the virtual power plant, but simulations make it possible to adjust certain supervisor parameters such as the numerical limits of the fuzzy sets of the membership functions.
为了说明使用所提出的方法构建的监督的效率，机电系统及其监督的几个模拟。本章给出了各种系统元素的模型。但是，需要注意的是，这种建模工作对于管理程序的开发并不是必需的;它更适合用于模拟系统和测试管理程序。监督者的结构是独立的技术，用于创建虚拟发电厂，但模拟使得有可能调整某些监督者参数，如隶属函数的模糊集的数值限制。

6.3.1. Characteristics ofsimulated system
6.3.1. 模拟系统特性

6.3.1.1. Wind
6.3.1.1.风

The variable-speed wind generator simulated in this example is based on a permanent magnet synchronous generator connected to the grid via two back-to-back AC-DC converters.
本示例中模拟的变速风力发电机基于通过两个背靠背AC-DC转换器连接到电网的永磁同步发电机。

The turbine is modeled by a relationship linking wind speed to the power that can be extracted from it [ACK 05, ROB 12b]:
涡轮机通过将风速与可从其提取的功率联系起来的关系来建模[ACK 05，ROB 12 b]：

1

wind - 2p4Cp
风-2 p4 Cp

where p is the specific density of the air; Ar is the area swept by the blades; is the power coefficient; = ^t is the speed ratio,
其中p是空气的比重;Ar是叶片扫过的面积;是功率系数; =^t是速比，

Qt is the rotation speed of the turbine, Rt is the radius of the turbine, [3 is the angle of orientation of the blades; and v is the wind speed. The dependence of the power factor and [3 is modeled by an analytical expression proposed in [ACK 05]. The model of the simulated wind turbine is presented in [COU 08a] and [COU 08b].
Qt是涡轮机的旋转速度，Rt是涡轮机的半径，β是叶片的定向角;以及v是风速。功率因数和[3]的依赖关系由[ACK 05]中提出的解析表达式建模。模拟风力涡轮机的模型见[COU 08 a]和[COU 08 b]。

6.3.1.2. Predictable source
6.3.1.2.可预测源

A generic predictable source can simply be modeled using a firstorder transfer function between the reference power supplied by the supervisor (Pref sp) and the output power of the source (Psp) [ACK 05]. The equation for this transfer function is given by [6.4], where Tsp is a time constant that depends on the technology chosen:
一般的可预测源可以简单地使用管理器提供的参考功率（Prefsp）和源的输出功率（Psp）之间的一阶传递函数进行建模[ACK 05]。该传递函数的方程由[6.4]给出，其中Tsp是取决于所选技术的时间常数：

1

Il(s) =
Il（s）=

 Tsp s + I [6.4]
Tsp s + I[6.4]

Figure 6.14 represents the model of the predictable source and Psp min and Psp max are the minimum and maximum operating powers of the source, respectively.
图6.14表示可预测源的模型，Pspmin和Pspmax分别是源的最小和最大工作功率。

Figure 6.14. Model ofpredictable source
图6.14.可预报源模型

6.3. I. 3. Storage system
6.3. I. 3.存储系统

The storage system will be represented by a simplified generic model that is structurally identical for long- and short-term storage systems [ABO 05]. The block schema of this model is shown in Figure 6.15, where Pref_stock is the reference power applied by the supervisor to the storage system, W is the energy stored in the system and Pstock is the output power of the system. The characteristic parameters of this model are the maximum charge and discharge powers (Pchmax and Pdchmax , he charge and discharge time constants (Tch and Tdch), the efficiency during charge and discharge (Itch and Qdch), and the maximum and minimum storage levels (wmm and wmax). Note that = O if Wstock wmax where Wstock 0; otherwise, ml = 1.
存储系统将由简化的通用模型表示，该模型在结构上与长期和短期存储系统相同[ABO 05]。此模型的框图如图6.15所示，其中Pref_stock是管理程序应用于存储系统的参考功率，W是系统中存储的能量，Pstock是系统的输出功率。该模型的特征参数是最大充电和放电功率（Pchmax和Pdchmax）、充电和放电时间常数（Tch和Tdch）、充电和放电期间的效率（Itch和Qdch）以及最大和最小存储水平（wmm和wmax）。 注意，如果Wstockwmax（其中Wstock为0），则= 0;否则，ml = 1。

6.3.1.4. Exterior grid
6.3.1.4.外部网格

The exterior grid will be modeled by an equivalent classic production assembly. The elements modeled are:
外部网格将由等效的经典生产组件建模。建模的元素是：

— speed control.
- 速度控制。

Figure 6.16 shows the modeling of the equivalent group when participating in primary and secondary frequency control (a proportional and integral action of speed control) [KUN 97, SAA 99]. TCH and TRH are the time constants of the principal steam input and the heater(s), respectively, and FHP is the fraction of the total power generated by the high-pressure turbine. TG is the time constant of the speed controller, R is the slope of the droop and Kl is the integral gain of the speed loop. AY and APm are the deviations of the sluice gate and the mechanical power, respectively. APL is the difference between the planned power from the generator and the power demand of the grid (pu). H = M/2 is the kinetic inertia constant (s) and D is the mechanical damping factor.
图6.16显示了参与初级和次级频率控制（速度控制的比例和积分作用）时等效组的建模[KUN 97，SAA 99]。TCH和TRH分别是主蒸汽输入和加热器的时间常数，FHP是高压涡轮机产生的总功率的分数。TG是速度控制器的时间常数，R是下垂的斜率，Kl是速度环的积分增益。AY和APm分别为闸门偏差和机械功率。APL是发电机的计划功率与电网的功率需求（pu）之间的差值。H = M/2是动力学惯性常数（s），D是机械阻尼因子。

 Speed control Steam turbine Inertia of the load and of the
速度控制蒸汽涡轮机负载和

rotor of the generator
发电机转子

Figure 6.16. Modeling ofequivalent group participating in primary and secondary control
图6.16.参与初级和次级控制的等效组建模

6.3.2. Simulations of different hybrid source variants
6.3.2.不同混合源变体的模拟

To illustrate the advantages of the graphic design method for fuzzy logic-based supervisors, the methodology is applied to different topologies of multisource power plants. For each topology, the graphic representation is derived from Figure 6.9. The supervisor's objectives remain the same as previously, specifically:
为了说明基于模糊逻辑的监督器的图形设计方法的优点，该方法被应用到不同的拓扑结构的多功能发电厂。对于每一种拓扑结构，其图形表示可从图6.9中得到。主管的目标与以前相同，具体而言：

A comparison of the different topologies using quantitative indicators is given at the end of the section.
在本节的最后，使用定量指标对不同的拓扑结构进行了比较。

6.3.2.1. Simulation of complete multisource power plant (topology A)
6.3.2.1.完整的多功能电厂仿真（拓扑A）

The principal system parameters shown in Figure 6.1 are given in Table 6.2. Ssource is the apparent power of the grid, Ploadl is the active power of load I and Pload2 is the active power of load 2. In order to illustrate a high wind penetration rate in an isolated grid (e.g. an island), the power of the grid is considered to be relatively low. R is chosen in accordance with the performance classically demanded of a conventional power group, and is determined so as to obtain a secondary control with a distinctly larger time constant than the primary control. The control of the grid's voltage is assumed to be executed perfectly by the source. In the test scenario proposed, the reference power of the multisource power plant for the period Oh < t < lh is adjusted to 600 kW, which is close to the average windpower. For the period lh < t < 2h, the reference power is 400 kW, that is, lower than the average windpower; and for the final period 2h < t < 3h, the reference power is higher than the average windpower and is 800 kW. In addition, in order to create frequency variations in the grid, a charge of 800 kW is connected at t = Oh20, t = lh20 and t = lh40 and disconnected at t = Oh40, t = lh40 and t = 2h40.
图6.1所示的主要系统参数见表6.2。Ssource是电网的视在功率，Ploadl是负载I的有功功率，Pload2是负载2的有功功率。为了说明孤立电网（例如，岛）中的高的风穿透率，电网的功率被认为是相对低的。R是根据传统功率组的传统要求的性能来选择的，并且被确定为获得具有比主控制明显更大的时间常数的辅助控制。电网电压的控制被假定为由电源完美地执行。在所提出的测试场景中，将时段Oh < t< lh的多功率发电厂的参考功率调整为600 kW，这接近于平均风力。 对于时段lh< t < 2 h，参考功率为400 kW，即低于平均风力;并且对于最终时段2 h < t < 3 h，参考功率高于平均风力并且为800 kW。此外，为了在电网中产生频率变化，在t = Oh 20、t = lh 20和t = lh 40处连接800 kW的充电，并且在t = Oh 40、t = lh 40和t = 2 h40处断开。

Predictable source 可预测源 750 kW 750千瓦 Tsp		Grid 网格  source 3 MVA 来源3 MVA 800 kW loadi 800 kW负载 800 kW load2 800 kW负载2 4%
Short-term 短期 chmax ct dchmax Ct chmaxctdchmaxCt Tch ct 中国电信 Tdch ct max ct dchctmaxct	storage 存储 300 kW -300 kW -300千瓦 0.5 s 0.5 s 4.17 kWh 4.17千瓦时	Long-term 长期 chmax It chmax It chmaxItchmaxIt Tch It max It max它	storage 存储 230 kW 230千瓦 -230 kW -230千瓦 417 kWh 417千瓦时
		Windpower 750 kW 风力750千瓦

Table 6.2. Parameters ofsimulated grid
表6.2. 模拟网格参数

Figure 6.17 shows the results of the simulation; the output power of the wind turbine is represented as a dotted line (Figure 6.17(a)), while the output power of the multisource power plant is shown as a solid line (Figure 6.17(a)). The other subfigures represent, respectively, the frequency of the grid (Figure 6.17(b)), the long-term storage level (Figure 6.17(c)), the short-term storage level (Figure 6.17(d)), the blade calibration angle (Figure 6.17(e)) and the predictable-source power (Figure 6.17(f)).
图6.17显示了模拟的结果;风力涡轮机的输出功率用虚线表示（图6.17（a）），而多级发电厂的输出功率用实线表示（图6.17（a））。其他子图分别表示电网频率（图6.17（B））、长期蓄能水平（图6.17（c））、短期蓄能水平（图6.17（d））、叶片校准角（图6.17（e））和可预测源功率（图6.17（f））。

Figure 6.17(a) shows that the output power of the multisource power plant follows the reference power despite variations in wind and loads. During the connection of loads, the output power is increased in order to reduce the drop in frequency (Figure 6.17(b)), and the opposite phenomenon occurs when a load is disconnected. A closer look at the first frequency drop is shown in Figure 6.17 as a solid line. This figure also shows a comparison of the behavior of the electric system given charge variations with and without the contribution of the multisource power plant. Frequency excursions are reduced by the action of the multisource power plant. In the considered example, the maximum frequency variation is limited to 0.82 Hz, which corresponds to a 40% reduction compared to the situation without a contribution from the multisource power plant.
图6.17（a）表明，尽管风力和负荷发生变化，但多千瓦发电厂的输出功率仍遵循参考功率。在负载连接期间，输出功率增加，以减少频率下降（图6.17（B）），当负载断开时，出现相反的现象。图6.17用实线表示第一个频率下降。该图还示出了给定电荷变化的电力系统的行为的比较，该电力系统具有和不具有多频发电厂的贡献。多源发电厂的作用减少了频率偏移。在所考虑的示例中，最大频率变化被限制为0.82 Hz，与没有来自多频发电厂的贡献的情况相比，这对应于40%的减少。

A simultaneous examination of Figures 6.17(d) and (e) shows that when the level of energy in the short-term storage system is high, blade angle orientation is used to reduce and smoothen the output power from the wind turbine. Similarly, an examination of Figures 6.17(d) and (f) reveals that when the level of energy in the short-term storage system is low, the predictable source is used to compensate for the lack of windpower
对图6.17（d）和（e）的同时检查表明，当短期存储系统中的能量水平较高时，叶片角度定向用于降低和平滑来自风力涡轮机的输出功率。类似地，对图6.17（d）和（f）的检查表明，当短期存储系统中的能量水平较低时，可预测的来源用于补偿风力的缺乏.

In the simulated case, the predictable source is assumed to be ideal and thus able to generate over the whole range of available power. Depending on the type of source (electric generator, gas microturbine, etc.), a minimum power level and obligations related to startup and shutdown time of this source must be complied with [ALK 09]. Note that this predictable source may also be hydroelectric and may include a water tank [BRE 07, ROB 12b].
在模拟的情况下，假设可预测的源是理想的，因此能够在整个可用功率范围内产生。根据能源的类型（发电机、微型燃气轮机等），必须遵守与该电源的启动和关闭时间相关的最低功率电平和义务[ALK 09]。请注意，该可预测来源也可能是水电，并可能包括水箱[BRE 07，ROB 12b]。

a)
a）、

51

 b) Time lhl
B）时间lhl

 c)
c）、 

d) Time lhl 20
d）时间lhl20

-10

Time [Ill
时间[III

400

Figure 6.17. Behavior ofmultisource power plantfor different reference powers:
图6.17.不同参考功率下多台发电厂的性能：

a) windpower and total power ofvirtual power plant, b) gridfrequency, c) long-term storage energy, d) short-term storage energy, e) wind turbine blade orientation angle,
a）风力和虚拟电站总功率，B）电网频率，c）长期储能，d）短期储能，e）风力涡轮机叶片方位角，

f) predictablepower source. For a color version of the figure, see www.iste.co.uk/robyns/powergrids.zip
f）可预测电源。有关该图的彩色版本，请参见www.iste.co.uk/robyns/powergrids.zip

11

11 11

50

49.5

49

 0.33 0.34 0.35 0.36  0.37 0.38 0.39 0.4
0.330.340.350.360.370.380.39

Time [h]
时间[小时]

Figure 6.18. Contribution to frequency control by multisource power plant: frequency variation without contribution from the multisource power plant (dotted line) and with contributionfrom the multisource power plant (solid line)
图6.18.多源电厂对频率控制的贡献：没有多源电厂贡献的频率变化（虚线）和有多源电厂贡献的频率变化（实线）

Finally, Figure 6.17(c) shows that the main role of long-term storage is to compensate for low-frequency differences between windpower and the reference power of the multisource power plant. Figure 6.17(d) shows that in normal operation, the storage does not reach its maximum value (4.17 kWh) or its minimum value in order to be able to contribute fully to primary frequency control when necessary, that is, to be able to produce and store energy depending on variations in frequency.
最后，图6.17（c）表明，长期蓄能的主要作用是补偿风力发电与多风电场参考功率之间的低频差异。图6.17（d）显示，在正常运行中，存储不会达到其最大值（4.17 kWh）或其最小值，以便能够在必要时完全有助于一次频率控制，即能够根据频率变化产生和存储能量。

6.3.2.2. Combination of a wind turbine and a predictable source
6.3.2.2.风力涡轮机和可预测源的组合

(topology B)
（拓扑B）

The topology considered shown in Figure 6.19 is a multisource power plant composed solely of a wind turbine and a predictable source.
图6.19所示的拓扑结构是一个由一个风力涡轮机和一个可预测的电源组成的多级发电厂。

 Wind turbine Predictable
风力涡轮机可预测

Figure 6.19. Multisource power plant composed ofa wind turbine and a predictable source (topology B)
图6.19.由一台风力涡轮机和一个可预测源组成的多功率发电厂（拓扑B）

Figure 6.20. Graphic representation ofvarious operating modes
图6.20. 各种操作模式的图形表示

Figure 6.20 illustrates the functional graph of the supervisor. This is composed of three operating modes; when the windpower is lower than the reference power, the predictable source supplies the difference. Likewise, when the windpower is higher than the reference power, it must be reduced via the intermediary of the angle of orientation of the wind turbine's blades. Based on this functional graph, we can deduce an operational graph and the relevant fuzzy rules, which number 16. These rules are the ones from sections NI .2ct and NI.3ct of section 6.5.2, which do not draw on the storage reference power and in which the condition having to do with the storage system power level has been removed.
图6.20显示了管理程序的功能图。这是由三个操作模式;当风力低于参考功率，可预测的来源提供的差异。同样，当风力功率高于参考功率时，必须通过风力涡轮机叶片的定向角来降低风力功率。基于此功能图，我们可以推导出一个操作图和相应的模糊规则，其数量为16。这些规则来自第6.5.2节的第NI.2ct和NI.3ct节，它们不利用存储参考功率，并且其中与存储系统功率电平有关的条件已被删除。

Time (h)
时间（h）

Figure 6.21. Output power of the multisource power plant and its reference. For a color version of the figure, see www.iste.co.uk/robyns/powergrids.zip
图6.21.多级电站的输出功率及其参考。有关该图的彩色版本，请参见www.iste.co.uk/robyns/powergrids.zip

Figure 6.21 shows that a multisource power plant without a storage system correctly guarantees the reference power. The windpower profile is the same as the one shown in Figure 6.17(a). Note that frequency variations have not been introduced in this scenario. Moreover, in the absence of a storage system in this topology, primary control in the form of a classic droop (Figure 6.2) must be ensured by the predictable source.
图6.21显示了一个没有储能系统的多千瓦发电厂可以正确地保证参考功率。风力剖面与图6.17（a）所示的相同。注意，在此场景中没有引入频率变化。此外，在这种拓扑结构中没有存储系统的情况下，必须通过可预测的源来确保经典下垂形式的主要控制（图6.2）。

6.3.2.3. Combination of a wind turbine, a predictable source and a short-term storage system (topology C)
6.3.2.3.风力涡轮机、可预测源和短期存储系统的组合（拓扑C）

The topology considered is a multisource power plant composed of a wind turbine, a predictable source and a short-term storage system (Figure 6.21).
所考虑的拓扑结构是一个由一个风力涡轮机、一个可预测的电源和一个短期存储系统组成的多功能发电厂（图6.21）。

Predictable
可预测

Wind Short-term turbine storage source
风力短期涡轮机蓄能源

Figure 6.22. Multisource power plant composed ofa wind turbine, a predictable source and a short-term storage system (topology C)
图6.22. 由风力涡轮机、可预测源和短期存储系统组成的多风电场（拓扑C）

Figure 6.23 shows the functional graph of the supervisor. It is composed of elements N 1.1 and N2 of the supervisor from Figure 6.9. 26 relevant fuzzy rules can be obtained from this graphic representation; these rules are the ones from sections N Ict and N2ct of section 6.5.2, which do not draw on the reference power of the longterm storage system. Figure 6.24 shows that the reference power is properly followed.
图6.23显示了管理程序的功能图。它由图6.9中Supervisor的元素N1.1和N2组成。可以从该图形表示中获得26个相关的模糊规则;这些规则是来自第6.5.2节的第N Ict和N2 ct节的规则，其不利用长期存储系统的参考功率。图6.24显示了参考功率的正确跟随。

Figure 6.23. Graphic representation ofdifferent operating modes
图6.23. 不同操作模式的图示

Time (hours)
时间（小时）

Figure 6.24. Output power ofmultisource plant and its reference. For a color version of thefigure, see www.iste.co.uk/robyns/powergrids.zip
图6.24.多级电站的输出功率及其参考。有关该图的彩色版本，请参见www.iste.co.uk/robyns/powergrids.zip

6.3.2.4. Combination of a wind turbine, a short-term storage system and a long-term storage system (topology D)
6.3.2.4.风力涡轮机、短期存储系统和长期存储系统的组合（拓扑D）

The topology considered is a multisource power plant composed of a wind turbine, a short-term storage system and a long-term storage system (Figure 6.25).
所考虑的拓扑结构是由风力涡轮机、短期存储系统和长期存储系统组成的多源发电厂（图6.25）。

Wind Short-term Long-term turbine storage storage
风能短期长期涡轮机储存

Figure 6.25. Multisource power plant composed ofa wind turbine, a short-term storage system and a long-term storage system (topology D)
图6.25.由一个风力涡轮机、一个短期存储系统和一个长期存储系统组成的多风电场（拓扑D）

The functional graph of the supervisor is quite similar to the one in Figure 6.9, but the operating modes linked to the predictable source have been removed. Operating mode N 1.3, shown in Figure 6.7, is reduced to the operating mode shown in Figure 6.26. The 34 fuzzy rules possible here are the ones from section 6.5.2 that do not draw on the predictable source.
监控器的功能图与图6.9中的非常相似，但是与可预测源相关联的操作模式已被删除。图6.7所示的工作状态N 1.3被简化为图6.26所示的工作状态。这里可能的34条模糊规则是6.5.2节中的那些不利用可预测源的规则。

Figure 6.26. Graphic representation ofoperating modes NI .3ct and NI .31t
图6.26. 操作模式NI .3ct和NI .31t的图示

Figure 6.27 shows that as long as the reference power is less than or equal to the average windpower, the contribution of the storage systems is enough to control the output power at its reference value. However, this is no longer the case in the third part of the scenario (2h < t < 3h), where the reference power is higher than the average windpower (Figure 6.17(a)).
图6.27表明，只要参考功率小于或等于平均风力，储能系统的贡献就足以将输出功率控制在参考值。然而，在情景的第三部分（2h < t < 3h），情况不再如此，其中参考功率高于平均风力（图6.17（a））。

350 0.5 1 1.5 2 2.5 3 Time (hours)
3500.511.522.53时间（小时）

Figure 6.27. Output power ofmultisource plant and its reference.
图6.27.多级电站的输出功率及其参考。

For a color version ofthe figure, see www.iste.co.uk/robyns/powergrids.zip
有关该图的彩色版本，请参见www.iste.co.uk/robyns/powergrids.zip

6.3.2.5. Combination of a wind turbine and a short-term storage system (topology E)
6.3.2.5.风力涡轮机和短期存储系统的组合（拓扑结构E）

The topology considered is a multisource power plant composed solely of a wind turbine and a short-term storage system (Figure 6.28).
所考虑的拓扑结构是一个仅由风力涡轮机和短期存储系统组成的多源发电厂（图6.28）。

Wind Short-term turbine storage
短期涡轮机储存

Figure 6.28. Multisource power plant composed ofa wind turbine and a short-term storage system (topology E)
图6.28.由一台风力涡轮机和一个短期存储系统组成的多功能发电厂（拓扑结构E）

The functional graph of the supervisor is quite similar to the one shown in Figure 6.23, but the operating modes linked to the predictable source have been removed. Operating mode NI .3, shown in Figure 6.7, is reduced to the operating mode shown in Figure 6.26. The 17 remaining fuzzy rules are the ones from sections N Ict and N2ct of section 6.5.2 that do not draw on either the predictable source or the reference power of the long-term storage system.
监控程序的功能图与图6.23中所示的非常相似，但与可预测源相关联的操作模式已被删除。图6.7所示的工况NI .3被简化为图6.26所示的工况。剩余的17个模糊规则是来自第6.5.2节的第N1ct节和第N2ct节的模糊规则，其不利用长期存储系统的可预测源或参考功率。

Figure 6.29 shows that the reference power is well controlled only when it is lower than the average windpower. When the reference power is higher than the average windpower, regulation can occur only within the limits of the storage system capacity.
图6.29表明，只有当参考功率低于平均风功率时，才能很好地控制参考功率。当参考功率高于平均风力时，调节只能在存储系统容量的限制内发生。

Time (hours)
时间（小时）

Figure 6.29. Output power ofmultisource power plant and its reference. For a color version ofthefigure, see www.iste.co.uk/robyns/powergrids.zip
图6.29.多级电站输出功率及其参考。有关该图的彩色版本，请访问www.iste.co.uk/robyns/powergrids.zip

6.3.3. Comparison of performance of different hybrid sources by means of indicators
6.3.3.不同混合源性能指标比较

We will now compare five topologies. Topology A corresponds to the multisource power plant composed of all of its elements and simulated in section 6.3.2.1. Table 6.3 offers several comparison criteria in relation to the objectives defined in Table 6.1: total energy supplied by the multisource power plant; energy generated by the wind turbine and by the predictable source as well as the average and maximum error, with error defined as the absolute value of the difference between the reference power and the output power of the multisource power plant. When the predictable source is present (topologies A, B and O, the same total energy is sent back to the grid and the average error is low. In all three situations, the presence of storage systems reduces the use of predictable source and increases the use of the renewable source (topologies A and C). When the predictable source is not present, the reference power cannot be guaranteed in the presence of a reference power that is higher than the average windpower
现在我们将比较五种拓扑。拓扑A对应于由其所有元件组成并在第6.3.2.1节中模拟的多功能发电厂。表6.3提供了与表6.1中定义的目标相关的几个比较标准：多频发电厂提供的总能量;风力涡轮机和可预测源产生的能量以及平均和最大误差，误差定义为参考功率与多频发电厂输出功率之差的绝对值。当存在可预测源时（拓扑A、B和O），相同的总能量被发送回电网，并且平均误差低。在所有这三种情况下，储存系统的存在减少了可预测能源的使用，增加了可再生能源的使用（拓扑A和C）。 当不存在可预测源时，在存在高于平均风功率的参考功率的情况下，不能保证参考功率.

The topology composed of a wind turbine and a short-term storage system is the one that causes the biggest mistake in the monitoring of the reference, with wind energy that is significantly reduced compared to the optimum in terms of the windpower obtained with topologies A and D.
由风力涡轮机和短期存储系统组成的拓扑结构是在监测参考时引起最大错误的拓扑结构，其中风能与利用拓扑结构A和D获得的风力功率方面的最佳值相比显著减少。

Table 6.3. Comparison ofdifferent topologies
表6.3. 不同拓扑结构的比较

6.4. Conclusion
6.4.结论

In this chapter, a methodology was presented for the development of a fuzzy logic-based supervisor. This method facilitates the analysis and design of the structure of the supervisor and the fuzzy rules intended to supervise multisource systems. The methodology has been illustrated by the development of the supervision strategy for a multisource power plant composed of a wind turbine, a predictable source and storage systems. This approach enables us to avoid using precise and complex models of the sources in play and makes it possible systematically to determine the supervisor while minimizing the number of rules. The performances of this supervisor have been tested using simulations. Finally, the application of this methodology to different topologies of multisource power plants has been used to illustrate its systematic character and to compare the performance of these power plants. In particular, the positive contribution of a storage system and a predictable source combined with a wind turbine has been illustrated.
在这一章中，提出了一种方法的发展模糊逻辑为基础的监督。该方法便于分析和设计监督器的结构和用于监督多机系统的模糊规则。该方法已被说明的监管策略的发展组成的风力涡轮机，一个可预测的源和存储系统的多功能发电厂。这种方法使我们能够避免使用精确和复杂的模型的来源在发挥作用，并使其有可能系统地确定主管，同时尽量减少规则的数量。该监控器的性能已经使用模拟进行了测试。最后，这种方法的应用，以不同的拓扑结构的multisburst电厂已被用来说明其系统的特点，并比较这些电厂的性能。 特别地，已经说明了与风力涡轮机结合的存储系统和可预测源的积极贡献。

6.5. Appendices
6.5.附录

6.5.1. Range of output value variations
6.5.1.输出值变化范围

The range of variations of output values is directly linked to the defuzzification of fuzzy output sets. The most widely used method of defuzzification is based on the calculation of the center of gravity of the resulting membership function as follows [6.5]:
输出值的变化范围与模糊输出集的解模糊化直接相关。最广泛使用的去模糊化方法是基于计算结果隶属函数的重心，如下所示[6.5]：

where U is the universe of discourse of the membership functions of the output values, is the resulting membership function for the output variable y and y* is the output value. The integral of the denominator gives the surface, while the integral of the numerator corresponds to the moment of this surface.
其中U是输出值的隶属函数的论域，是输出变量y的结果隶属函数，y* 是输出值。分母的积分给出曲面，而分子的积分对应于该曲面的矩。

With this method, the range of variation of y* will be smaller than its universe of discourse. For this range of variation to be normalized ([—1, 1] or [0, 1]), it is necessary to extend the membership functions outside this range. In the fuzzy supervisor considered, the extreme fuzzy sets (e.g. NB and PB) are, in the range of variation of the output values ([—1, 1] or [0, 1]), triangular in form. It is therefore proposed here to extend these fuzzy sets by a rectangular form outside the normalized range so as to form a trapezoidal fuzzy set as shown in Figure 6.30. AYR is the base of the rectangle and AY'T is the base of the triangle.
使用这种方法，y* 的变化范围将小于其论述范围。为了使该变化范围被归一化（[-1，1]或[0，1]），有必要将隶属函数扩展到该范围之外。在所考虑的模糊监督器中，在输出值的变化范围（[-1，1]或[0，1]）内，极值模糊集（如NB和PB）是三角形的。因此，这里建议用一个在标准化范围之外的矩形形式来扩展这些模糊集，以便形成一个梯形模糊集，如图6.30所示。AYR是矩形的底边，AY 'T是三角形的底边。

Figure 6.30. Extremefuzzy set
图6.30. 极值模糊集

The extreme values of this range of variation will be reached when the resulting membership function is equal to the extreme fuzzy set. For the center of gravity to be located at the interface between the rectangular and triangular part (Ay = 0), the base of the rectangle AYR, and thus the extension of U beyond the normalized range, must be determined by expression [6.6]:
当所得隶属函数等于极值模糊集时，将达到该变化范围的极值。对于位于矩形和三角形部分之间界面处的重心（Ay = 0），矩形的底边AYR以及U超出规范化范围的延伸必须由表达式[6.6]确定：

AR + AT

[6.6]

where AR = AYR is the area of the rectangle, CR = -AYR/2 is the abscissa of the center of gravity of the rectangle in the point of reference My, AT = AYT/2 is the area of the triangle and CT = AYT/3 is the abscissa of the center of gravity of the triangle. By substituting these expressions in equation [6.6], we obtain expression [6.7]:
其中AR = AYR是矩形的面积，CR = -AYR/2是参考点My处矩形重心的横坐标，AT = AYT/2是三角形的面积，CT = AYT/3是三角形重心的横坐标。通过将这些表达式代入方程[6.6]，我们得到表达式[6.7]：

 AYR.
是 的 ， 我 是 说 

 2 3 2
232

[6.7]
【 6.7 】

After solution, we obtain expression [6.8]:
解出后，我们得到表达式[6.8]：

AYT
月亮

AYR =
º 󍋼/A

[6.8]

In the example considered of the membership functions of the storage system reference power (Figure 6.11(a)), with the base of the triangle (NB) being 0.5, expression [6.8] shows that the universe of discourse U must be [—1.289, 1.289] for the range of variation of
在所考虑的存储系统参考功率的隶属函数的示例中（图6.11（a）），三角形的底（NB）为0.5，表达式[6.8]表明，对于

6.5.2. Fuzzy rules
6.5.2.模糊规则

		NI.1ct	IF Afis Z AND 如果Afis Z和 THEN Pref_Stock_ct_pu is NG 则Pref_Stock_ct_pu为NG		is M AND APpu is NB 是M且APPU是NB
						IF Afis Z AND Nivstock_ctyu THEN Pref Stock ct_pu is PG 如果AfisZ和Nivstock_ctyu，则首选库存ct_pu为PG		is M AND APpu is PB 是M且APPU是PB
						IF Afis Z AND Nivstock is M AND APpu is NM 如果AfisZ且Nivstock为M且APPU为NM THEN Pref Stock ct_pu THEN首选库存ct_pu
						IF Afis Z AND 如果AfisZ和 THEN Pref_Stock_ct_pu 然后Pref_Stock_ct_pu	is M AND APpu is PM is PM 是M和APPU是PM是PM
						IF Afis Z AND 如果AfisZ和 THEN Pref Stock ct_pu THEN首选库存ct_pu	is Z 是Z	is M AND  is Z 是M且是Z
						IF Afis Z AND Nivstock 如果AfisZ和Nivstock		is M THENß ref_pu is Z 是M则ref_pu是Z
						IF Afis Z AND Nivstock 如果AfisZ和Nivstock		is M THEN Pref_SPyu is Z 是M则Pref_SPyu是Z
				NI.2ct	IF Afis Z AND 如果Afis Z和 THEN  is Z 然后是Z		is B AND APpu is Z 是B且APpu是Z
						IF Afis Z AND Nivstock_ctyu 如果AfisZ和Nivstock_ctyu THEN  is Z 然后是Z		is B AND  is NM 是B且是NM
						IF Afis Z AND Nivstock 如果AfisZ和Nivstock THEN  is Z 然后是Z		is B AND APpu is NB 是B且APPU是NB
						IF Afis Z AND 如果Afis Z和 THEN  is M 然后是M		is B AND 是B且	is PM 为PM
						IF Afis Z AND Nivstock_ctyu 如果AfisZ和Nivstock_ctyu		is B AND 是B且	is PB 是PB

THEN  is G 那么G IF Afis Z AND 如果AfisZ和

is B THEN P is Z 是B则P是Z

IF Afis Z AND 如果Afis Z和

ref sp_p 参考sp_pu is B THEN Pref_Stock_ct_pu 是B，则Pref_Stock_ct_pu

is NM 为NM

NI.3ct

IF Afis Z AND 如果Afis Z和 THEN Pref SP_pu IS B 则首选SP_pu为B

is S AND APpu is NB 是S且APPU是NB

IF Afis Z AND  ct_pu 如果AfisZ和ct_pu  THEN P IS M 那么P就是M

is SANDAPpu is NM 是SANDAPPU是NM

IF Afis Z AND 如果AfisZ和  THEN P IS Z 那么P就是Z

is S AND APpu is PB 是S且APPU是PB

IF Afis Z AND 如果Afis Z和 THEN Pref_SP_pu IS Z 则Pref_SP_pu为Z

is S AND APpu is PM 是S且APPU是PM

IF Afis Z AND  ct_pu 如果AfisZ和ct_pu  THEN P IS Z 那么P就是Z IF Afis Z AND 如果AfisZ和

is S AND APpu is Z 是S且APPU是Z  is S THENß  isZ 是S，则是Z

IF Afis Z AND 如果Afis Z和

ref_pu is S THEN Pref_Stock_ct_pu ref_pu是S，则Pref_Stock_ct_pu

is PM 为PM

NIIt

NI.11t

IF Afis Z AND 如果Afis Z和 is M AND  is NB 是M且是NB THEN Pref_Stock_lt_pu_pu is NB 则Pref_Stock_lt_pu_pu为NB

IF Afis Z AND 如果AfisZ和 THEN Pref Stock It_pu THEN Pref StockIt_pu

is M AND APpu is PB 是M且APPU是PB

IF Afis Z AND 如果AfisZ和 THEN Pref_Stock_lt_pu 然后Pref_Stock_lt_pu

is M AND is NM 是M且是NM

is NM 为NM

IF Afis Z AND 如果AfisZ和 THEN Pref_Stock_lt_pu 然后Pref_Stock_lt_pu

is M AND is PM 是M，是PM

is PM 为PM

IF Afis Z AND 如果AfisZ和 THEN Pref Stock It_pu THEN Pref StockIt_pu

is Z 是Z

is M AND APpu is Z 是M且APPU是Z

IF Afis Z AND 如果AfisZ和

is M THEN  is Z 是M，则是Z

IF Afis Z AND 如果Afis Z和

is M THEN Pref_SP_pu IS Z 是M则Pref_SP_pu是Z

NI.21t

IF Afis Z AND 如果Afis Z和  THEN  is Z 然后是Z

is B AND APpu is NB 是B且APPU是NB

IF Afis Z AND THENß ref_pu is Z 如果Δ f是Z，则ref_pu是Z

is B AND APpu is Z 是B且APpu是Z

IF Afis Z AND 如果AfisZ和  THEN  is Z 然后是Z

is B ANDAPpu is NZ 是BANDAPpu是NZ

IF Afis Z AND 如果Afis Z和  THEN  is M 然后是M

is B AND APpu is PM 是B且APPU是PM

IF Afis Z AND 如果AfisZ和 THEN is B 则是B IF Afis Z AND 如果AfisZ和

is B AND APpu is PB 是B且APPU是PB is B THEN P 是B然后是P

IF Afis Z AND Nivstock_ltyu THEN Pref_Stock_lt_pu is NM 如果AfisZ和Nivstock_ltyu，则Pref_Stock_lt_pu为NM

NI.31t

IF Afis Z AND Nivstock THEN Pref_SP_pu is B 如果AfisZ和Nivstock，则Pref_SP_pu为B

is S AND APpu is NB 是S且APPU是NB

IF Afis Z AND 如果Afis Z和 THEN Pref is M 则Pref为M

is S AND 是S且

is NM 为NM

IF Afis Z AND Nivstock 如果AfisZ和Nivstock THEN P 则P

is S AND 是S且

is PB 是PB

IF Afis Z AND 如果Afis Z和 THEN Pref_ SP_pu IS Z 则Pref_SP_pu为Z

is S AND 是S且

is PM 为PM

IF Afis Z AND Nivstock_ltyu is S AND  is Z 如果AfisZ且Nivstock_ltyu是S且是Z THEN P IS Z 那么P就是Z

IF Afis Z AND Nivstock 如果AfisZ和Nivstock

is S THEN  is Z 是S，则是Z

IF Afis Z AND Nivstock 如果AfisZ和Nivstock

is S THEN Pref Stock It_pu is S THEN Pref StockIt_pu

is PM 为PM

N2

N2ct

IF Afis PB OU Afis N THEN Pref Stock ct_pu is Z 如果AfisPB等于AfisN，则首选库存ct_pu为Z

IF Afis NB AND  ct_pu isB THENß ref_pu isZ 如果AfisNB且ct_pu为B，则ref_pu为Z

IF Afis PB AND 如果Afis PB和 is B THEN  is M 是B则是M

IF Afis PB AND 如果Afis PB和 is S THEN Pref_SP_pu is Z 是S则Pref_SP_pu是Z

IF Afis NB AND 如果Afis NB和 is S THEN Pref_SP_pu IS M 是S则Pref_SP_pu是M

N21t

IF Afis PB OU Afis N THEN Pref_Stock_lt_pu is Z 如果AfisPB等于AfisN，则Pref_Stock_lt_pu为Z

IF Afis NB AND Nivstock IF Afis PB AND IFAfisNB ANDNivstockIFAfisPB AND

isB THEN is B THEN is BTHEN is B THEN

is Z is M 是Z是M

IF Afis PB AND 如果AfisPB和

is S THEN P 是S，那么P

IF Afis NB AND Nivstock_ltyu is S THEN Pref_SP_pu is M 如果AfisNB且Nivstock_ltyu为S，则Pref_SP_pu为M

6.6. Bibliography
6.6.书目

[ABO 05] ABOU CHACRA F. , Valorisation et optimisation du stockage d'énergie dans un réseau d'énergie électrique, PhD Thesis, University of Paris-Sud 11, 2005.
[ABO 05] ABBUSINESS CHACRAF.，Valorisationetoptimisationdu stockaged'énergiedans un réseaud'énergieélectrique，PhD Thesis，University of Paris-Sud 11，2005.

[ACK 05] ACKERMANN T., Wind Power in Power Systems, John Wiley & Sons, New York, 2005.
[ACK（ 德国 之 声 中文 网 ） ACKERMANN T . ，《 Wind Power in Power Systems 》 ， John Wiley & Sons ， 2005 年

[ALK 09] ALKHALIL F., DEGOBERT P., COLAS F. et al., "Fuel consumption optimization of a multimachines microgrid by secant method combined with IPPD table", International Conference on Renewable Energy and Power Quality, ICREPQ '09, Valence, 15-17 April 2009.
[ Talk 09 ] 阿 卡利 尔 · F . ，德格 伯特 P 。可乐 F 。et al. ，首页 > 外 文书 > 商业 行销 > 企业 管理 > Fuel Consumption Optimization of A多 机器 MultiMachines" microgrid by secant method combined with IPPD table " ， 可 再生 能源 和 电力 质量 国际 会议 ， ICREPQ ' 09 ， 韦伦 塞 ， 2009 年 4 月 15 - 17 日 。

[BOU 13] BOUALLAGA A., MERDASSI A., DAVIGNY A. et al., "Minimization of energy transmission cost and C02 emissions using coordination of electric vehicle and wind power (W2V)", IEEE PES International Conference POWERTECH 2013, Grenoble, 16-20 June 2013.
[BOU[ 13 ] 布 拉萨 拉 （ Bouallaga A . ）Merdassi A . ，大卫 · A 。et al. ，" 最 小 化 的 能源 传输 成本 和 C02 排放 使用 电力 和 风力 发电 的 协调 （ W2 V ） " ， IEEE PES 国际 会议 POWERTECH 2013 ， 格勒诺布尔 ， 2013 年 6 月 16 - 20 日 。

[BOU 14] BOUALLAGA A., DAVIGNY A., MERDASSI A. et al., "Optimization of fuzzy supervisor for electric vehicle load in distribution grid", 11th International Conference on Modeling and Simulation of Electric Machines, Converters and Systems, ELECTRIMACS '14, Valence, Spain, 20-22 May 2014.
[BOU[ 14 ] Bauallaga A . ，David A . 大卫奔驰 A 。et al. ，" Optimization of fuzzy supervisor for electric vehicle load in distribution grid " ， 11 th International Conference on Modeling and Simulation of Electric Machines ， Converters and Systems ， ELECTRIMACS ' 14 ， 西班牙 瓦朗斯 ， 20 - 22 May 2014 . " 《 优化 配电 网 中 电气 设备 负载 的 模糊 主管 》 ， 第 11 届 电机 建模 与 仿真 国际 会议 ， 转换 器 和 系统 ， ELECTRIMACS ' 14 ， 西班牙 瓦朗斯 ， 2014 年 5 月 20 - 22 日 。

[BRE 07] BREBAN S., NASSER M., ANSEL A. et al., "Variable speed small hydro power plant connected to AC grid or isolated loads", Journal European Power Electronics, vol. 17, pp. 29—36, no. 4, 2007.
[BRE 07] BREBAN S.，NASSER M.，安塞尔A.例如，“连接到交流电网或隔离负载的变速小型水力发电厂”，《欧洲电力电子学杂志》，第17卷，第200页。29-36，第4期，2007年。

[COU 08a] COURTECUISSE V., MOKADEM M.E., ROBYNS B. et al., "Supervision par logique floue d'un systeme éolien å vitesse variable en vue de contribuer au réglage primaire de fréquence", Revue internationale de génie électrique, nos. 4—5, pp. 423—453, July—October 2008.
[COU 08 a] COURTECUISSE五，MOKADEM M.E.，罗宾B。例如，“Supervision parlogiquefloued'unsystemeéolienvitessevariableenvuedecontributerAuréglageprimairedefréquence“，Revueinternationalede génieélectrique，nos.第4-5页。423-453，2008年7月至10月。

[COU 08b] COURTECUISSE V., SPROOTEN J., ROBYNS B. et al., "Experiment of a wind generator participation to frequency control", Journal European Power Electronics, vol. 18, no. 3, pp. 14-24, 2008.
[COU 08b] COURTECUISSE V.，斯普鲁滕·J，罗宾B。例如，“风力发电机参与频率控制的实验”，《欧洲电力电子杂志》，第18卷，第3期，第19页。2008年14-24日。

[COU 10] COURTECUISSE V., SPROOTEN J., ROBYNS B. et al., "Methodology to build fuzzy logic based supervision of hybrid renewable energy systems", Mathematics and Computers in Simulation, Elsevier, vol. 81, pp. 208-224, October 2010.
[COU 10] COURTECUISSE五，斯普鲁滕·J，罗宾B。例如，“方法建立基于模糊逻辑的监督混合可再生能源系统”，数学和计算机模拟，爱思唯尔，第81卷，第100页。208-224，October 2010.

[KUN 97] KUNDUR P. , Power System Stability and Control, WCB/McGrawHill, 1997.
[97] KUNDURP.，电力系统稳定与控制，WCB/McGrawHill，1997。

[ROB12a] ROBOAM X., Integrated Design by Optimization of Electrical Energy Systems, ISTE, London and John & Wiley Sons, New York, 2012.
[ROB 12 a]机器人X，《电能系统优化集成设计》，ISTE，伦敦，John & Wiley Sons，纽约，2012年。

[ROB 12b] ROBYNS B., DAVIGNY A., BRUNO F. et al., Electric power generation from renewable sources, ISTE, London and John & Wiley Sons, New York, , 2012.
[ROB 12 B] ROBYNS B.，大卫尼·A，布鲁诺F.例如，可再生能源发电，ISTE，伦敦和约翰&威利父子公司，纽约，2012年。

[ROB 15] ROBYNS B., SAUDEMONT C., HISSEL D. et al., "Management and valorization of energy storage in transportation and buildings", ISTEWiley, forthcoming, 2015.
[ROB 15] ROBYNS B，Saudemont C.，HISSEL D.例如，“运输和建筑物中储能的管理和价值评估”，ISTEWiley，即将出版，2015年。

[SAA 99] SAADAT H., Power System Analysis, WCB/McGraw-Hi11, 1999.
[SAA 99]萨达特·H.，电力系统分析，WCB/McGraw-Hi 11，1999年。

[SPR 09] SPROOTEN J., COURTECUISSE V., ROBYNS B. et al., "Méthodologie de développement de superviseurs å logique floue de centrales multi sources å base d'énergie renouvelable", European Journal of Electrical Engineering, vol. 12, nos. 5—6, pp. 553-583, 2009.
[SPR 09] SPROOTEN J.，COURTECUISSE V.，罗宾B。例如，“Méthodologiededépémentdesuperviseursprogrammologiqueflouedecentralesmulti sources programming based'énergierenouvelable“，European Journal of Electrical Engineering，vol. 12，nos.第5-6页。553-583，2009年。