CN116111614B - 一种基于模糊pid的电解铝负荷参与孤网调频的方法 - Google Patents
一种基于模糊pid的电解铝负荷参与孤网调频的方法 Download PDFInfo
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Abstract
本发明涉及高耗能工业负荷调频控制技术，具体涉及一种基于模糊PID的电解铝负荷参与孤网调频的方法，包括建立电解铝负荷参与的孤立电网调频模型；采集系统频率变化量∆f和频率变化率df/dt；建立模糊PID控制器并计算出需要调节的负荷量；建立电解铝负荷特性模型并根据该模型计算出电解铝负荷相应控制参数调整量，以调节电解铝负荷功率。该方法利用模糊PID控制参数应外界环境变化自动调节，且调节规则可以人为制定以保证控制系统的稳定性的特性，提升了电网频率控制的可靠性和电力系统运行的稳定性。
Description
技术领域
本发明属于高耗能工业负荷调频控制技术领域，特别涉及一种基于模糊PID的电解铝负荷参与孤网调频的方法。
背景技术
近年来随着我国可再生能源装机容量的逐步提高，可再生能源消纳问题愈发严重，同时大规模可再生能源的接入给电力系统运行和控制造成了巨大压力，传统的火电机组的调频能力难以因对由新能源波动造成的电网频率波动问题。高耗能工业负荷具有热蓄能特性，其功率可以在较大范围内连续调节，因此，引入高耗能负荷如电解铝负荷参与电网互动调节能有效减少因负荷波动对电网频率造成的冲击。
电网系统中，负荷参与电网调频通常采用PID控制，传统的PID控制虽然能使电力系统的动态响应得到一定的改善，但是传统PID控制同样存在易引起超调，产生积分饱和现象，稳态误差较大，可能引起系统振荡等众多问题。所以这里提出用模糊PID控制器代替传统PID控制器，模糊PID控制具有自适应性，其控制参数在控制过程中可以根据人为制定的调节规则动态变化，选择合适的隶属函数和模糊规则可以较好的改善控制效果。
发明内容
针对背景技术存在的问题，本发明提供一种基于模糊PID的电解铝负荷参与孤网调频的方法。
为解决上述技术问题，本发明采用如下技术方案：一种基于模糊PID的电解铝负荷参与孤网调频的方法，包括：
建立电解铝负荷参与的孤立电网调频模型；
采集系统频率变化量∆f和频率变化率df /dt；
建立模糊PID控制器并计算出需要调节的负荷量；
建立电解铝负荷特性模型并根据该模型计算出电解铝负荷相应控制参数调整量，以调节电解铝负荷功率。
在上述基于模糊PID的电解铝负荷参与孤网调频的方法中，建立电解铝负荷参与的孤立电网高频模型包括以下步骤：
步骤1.1、建立发电机组传递函数模型包括：
构建调速器传递函数模型：
(1)
式中，T G为调速器时间常数，s为拉普拉斯算子；
构建汽轮机传递函数模型：
(2)
式中，为汽轮机时间常数，/>为再热器时间常数，/>为汽轮机再热器增益；
步骤1.2、建立发电机-电力系统模型：
(3)
式中，M表示等效惯量系数，D表示等效阻尼系数；
步骤1.3、建立电解铝负荷等效传递函数：
(4)
式中，表示电解铝实际负荷功率变化，/>表示电解铝负荷功率变化的控制信号，s表示拉普拉斯算子，/>和b均为电解铝负荷动态响应模型的等效参数。
在上述基于模糊PID的电解铝负荷参与孤网调频的方法中，系统频率变化量Δf的绝对值的变化范围为0 .2～0 .5Hz。
在上述基于模糊PID的电解铝负荷参与孤网调频的方法中，建立模糊pid控制器并计算出需要调节的功率包括以下步骤：
步骤3.1、对系统频率变化量Δf和频率变化率df/dt进行模糊化处理；
定义系统频率变化量Δf和频率变化率df/dt的模糊子集均为{负大[NB]、负中[NM]、负小[NS]、零[ZO]、正小[PS]、正中[PM]、正大[PB]}，并定义系统频率变化量Δf和频率变化率df/dt的模糊集对应的论域为{-3, -2, -1, 0, 1, 2, 3}；将采集到的系统频率变化量Δf和频率变化率df/dt数据分别映射至论域的相对位置；
步骤3.2、确定隶属度函数；
采用三角隶属函数作为输入量隶属度函数；
步骤3.3、建立模糊化规则表；
比例控制参数KP的模糊规则如下：
if Δf is NB and df/dt is NB then ∆KPis PB
if Δf is NB and df/dt is NM then ∆KPis PB
if Δf is NB and df/dt is NS then ∆KPis PM
if Δf is NB and df/dt is ZO then ∆KPis PM
if Δf is NB and df/dt is PS then ∆KPis PS
if Δf is NB and df/dt is PM then ∆KPis ZO
if Δf is NB and df/dt is PB then ∆KPis ZO
if Δf is NM and df/dt is NB then ∆KPis PB
if Δf is NM and df/dt is NM then ∆KPis PB
if Δf is NM and df/dt is NS then ∆KPis PM
if Δf is NM and df/dt is ZO then ∆KPis PS
if Δf is NM and df/dt is PS then ∆KPis PS
if Δf is NM and df/dt is PM then ∆KPis ZO
if Δf is NM and df/dt is PB then ∆KPis NS
if Δf is NS and df/dt is NB then ∆KPis PM
if Δf is NS and df/dt is NM then ∆KPis PM
if Δf is NS and df/dt is NS then ∆KPis PM
if Δf is NS and df/dt is ZO then ∆KPis PS
if Δf is NS and df/dt is PS then ∆KPis ZO
if Δf is NS and df/dt is PM then ∆KPis NS
if Δf is NS and df/dt is PB then ∆KPis NS
if Δf is ZO and df/dt is NB then ∆KPis PM
if Δf is ZO and df/dt is NM then ∆KPis PM
if Δf is ZO and df/dt is NS then ∆KPis PS
if Δf is ZO and df/dt is ZO then ∆KPis ZO
if Δf is ZO and df/dt is PS then ∆KPis NS
if Δf is ZO and df/dt is PM then ∆KPis NM
if Δf is ZO and df/dt is PB then ∆KPis NM
if Δf is PS and df/dt is NB then ∆KPis PS
if Δf is PS and df/dt is NM then ∆KPis PS
if Δf is PS and df/dt is NS then ∆KPis ZO
if Δf is PS and df/dt is ZO then ∆KPis NS
if Δf is PS and df/dt is PS then ∆KPis NS
if Δf is PS and df/dt is PM then ∆KPis NM
if Δf is PS and df/dt is PB then ∆KPis NM
if Δf is PM and df/dt is NB then ∆KPis PS
if Δf is PM and df/dt is NM then ∆KPis ZO
if Δf is PM and df/dt is NB then ∆KPis NS
if Δf is PM and df/dt is NB then ∆KPis NM
if Δf is PM and df/dt is NB then ∆KPis NM
if Δf is PM and df/dt is NB then ∆KPis NM
if Δf is PM and df/dt is NB then ∆KPis NB
if Δf is PB and df/dt is NB then ∆KPis ZO
if Δf is PB and df/dt is NB then ∆KPis ZO
if Δf is PB and df/dt is NB then ∆KPis NM
if Δf is PB and df/dt is NB then ∆KPis NM
if Δf is PB and df/dt is NB then ∆KPis NM
if Δf is PB and df/dt is NB then ∆KPis NB
if Δf is PB and df/dt is NB then ∆KPis NB
微分控制参数KD的模糊规则如下：
if Δf is NB and df/dt is NB then ∆KDis PS
if Δf is NB and df/dt is NM then ∆KDis NS
if Δf is NB and df/dt is NS then ∆KDis NB
if Δf is NB and df/dt is ZO then ∆KDis NB
if Δf is NB and df/dt is PS then ∆KDis NB
if Δf is NB and df/dt is PM then ∆KDis NM
if Δf is NB and df/dt is PB then ∆KDis PS
if Δf is NM and df/dt is NB then ∆KDis PS
if Δf is NM and df/dt is NM then ∆KDis NS
if Δf is NM and df/dt is NS then ∆KDis NB
if Δf is NM and df/dt is ZO then ∆KDis NM
if Δf is NM and df/dt is PS then ∆KDis NM
if Δf is NM and df/dt is PM then ∆KDis NS
if Δf is NM and df/dt is PB then ∆KDis ZO
if Δf is NS and df/dt is NB then ∆KDis ZO
if Δf is NS and df/dt is NM then ∆KDis NS
if Δf is NS and df/dt is NS then ∆KDis NM
if Δf is NS and df/dt is ZO then ∆KDis NM
if Δf is NS and df/dt is PS then ∆KDis NS
if Δf is NS and df/dt is PM then ∆KDis NS
if Δf is NS and df/dt is PB then ∆KDis ZO
if Δf is ZO and df/dt is NB then ∆KDis ZO
if Δf is ZO and df/dt is NM then ∆KDis NS
if Δf is ZO and df/dt is NS then ∆KDis NS
if Δf is ZO and df/dt is ZO then ∆KDis NS
if Δf is ZO and df/dt is PS then ∆KDis NS
if Δf is ZO and df/dt is PM then ∆KDis NS
if Δf is ZO and df/dt is PB then ∆KDis ZO
if Δf is PS and df/dt is NB then ∆KDis ZO
if Δf is PS and df/dt is NM then ∆KDis ZO
if Δf is PS and df/dt is NS then ∆KDis ZO
if Δf is PS and df/dt is ZO then ∆KDis ZO
if Δf is PS and df/dt is PS then ∆KDis ZO
if Δf is PS and df/dt is PM then ∆KDis ZO
if Δf is PS and df/dt is PB then ∆KDis ZO
if Δf is PM and df/dt is NB then ∆KDis PB
if Δf is PM and df/dt is NM then ∆KDis NS
if Δf is PM and df/dt is NB then ∆KDis PS
if Δf is PM and df/dt is NB then ∆KDis PS
if Δf is PM and df/dt is NB then ∆KDis PS
if Δf is PM and df/dt is NB then ∆KDis PS
if Δf is PM and df/dt is NB then ∆KDis PB
if Δf is PB and df/dt is NB then ∆KDis PB
if Δf is PB and df/dt is NB then ∆KDis PM
if Δf is PB and df/dt is NB then ∆KDis PM
if Δf is PB and df/dt is NB then ∆KDis PM
if Δf is PB and df/dt is NB then ∆KDis PS
if Δf is PB and df/dt is NB then ∆KDis PS
if Δf is PB and df/dt is NB then ∆KDis PB
积分控制参数KI的模糊规则如下：
if Δf is NB and df/dt is NB then ∆KIis NB
if Δf is NB and df/dt is NM then ∆KIis NB
if Δf is NB and df/dt is NS then ∆KIis NM
if Δf is NB and df/dt is ZO then ∆KIis NM
if Δf is NB and df/dt is PS then ∆KIis NS
if Δf is NB and df/dt is PM then ∆KIis ZO
if Δf is NB and df/dt is PB then ∆KIis ZO
if Δf is NM and df/dt is NB then ∆KIis NB
if Δf is NM and df/dt is NM then ∆KIis NB
if Δf is NM and df/dt is NS then ∆KIis NM
if Δf is NM and df/dt is ZO then ∆KIis NS
if Δf is NM and df/dt is PS then ∆KIis NS
if Δf is NM and df/dt is PM then ∆KIis ZO
if Δf is NM and df/dt is PB then ∆KIis ZO
if Δf is NS and df/dt is NB then ∆KIis NB
if Δf is NS and df/dt is NM then ∆KIis NM
if Δf is NS and df/dt is NS then ∆KIis NS
if Δf is NS and df/dt is ZO then ∆KIis NS
if Δf is NS and df/dt is PS then ∆KIis ZO
if Δf is NS and df/dt is PM then ∆KIis PS
if Δf is NS and df/dt is PB then ∆KIis PS
if Δf is ZO and df/dt is NB then ∆KIis NM
if Δf is ZO and df/dt is NM then ∆KIis NM
if Δf is ZO and df/dt is NS then ∆KIis NS
if Δf is ZO and df/dt is ZO then ∆KIis ZO
if Δf is ZO and df/dt is PS then ∆KIis PS
if Δf is ZO and df/dt is PM then ∆KIis PM
if Δf is ZO and df/dt is PB then ∆KIis PM
if Δf is PS and df/dt is NB then ∆KIis NM
if Δf is PS and df/dt is NM then ∆KIis NS
if Δf is PS and df/dt is NS then ∆KIis ZO
if Δf is PS and df/dt is ZO then ∆KIis PS
if Δf is PS and df/dt is PS then ∆KIis PS
if Δf is PS and df/dt is PM then ∆KIis PM
if Δf is PS and df/dt is PB then ∆KIis PB
if Δf is PM and df/dt is NB then ∆KIis ZO
if Δf is PM and df/dt is NM then ∆KIis ZO
if Δf is PM and df/dt is NB then ∆KIis PS
if Δf is PM and df/dt is NB then ∆KIis PS
if Δf is PM and df/dt is NB then ∆KIis PM
if Δf is PM and df/dt is NB then ∆KIis PB
if Δf is PM and df/dt is NB then ∆KIis PB
if Δf is PB and df/dt is NB then ∆KIis ZO
if Δf is PB and df/dt is NB then ∆KIis ZO
if Δf is PB and df/dt is NB then ∆KIis PS
if Δf is PB and df/dt is NB then ∆KIis PM
if Δf is PB and df/dt is NB then ∆KIis PM
if Δf is PB and df/dt is NB then ∆KIis PB
if Δf is PB and df/dt is NB then ∆KIis PB；
步骤3.4、解模糊处理；
采用重心法进行解模糊处理，具体公式如下：
(5)
式中，Fi为模糊化量值，Mi为对应Fi的隶属度，N为模糊子集元素的个数，V o为模糊控制器输出量解模糊后的精确值；
在获得相应增量后，对原参数进行相应调整，公式如下：
(6)
(7)
(8)
其中，，/>，/>分别为由模糊PID控制器计算出的对应比例系数，微分系数和积分系数的调整量，α、β、γ分别为设定的对应/>、/>、/>的修正系数，/>为修正前的比例调节系数，/>为修正前的微分调节系数，/>为修正前的积分调节系数，/>为修正后的比例调节系数，/>为修正后的微分调节系数，/>为修正后的积分调节系数。
在上述基于模糊PID的电解铝负荷参与孤网调频的方法中，建立电解铝负荷特性模型并根据该模型计算出电解铝负荷相应控制参数调整量，以调节电解铝负荷功率包括以下步骤：
步骤4.1、根据修正后的PID参数确定电解铝负荷调整量：
(9)；
其中，为电解铝负荷调整量，/>，/>，/>分别为比例调节系数，微分调节系数和积分调节系数。
步骤4.2、根据各电解铝厂可调容量分配调节任务；
(10)
其中，Ai为第i个电解铝厂的可调容量，N为参与调频的电解铝厂数量，为电解铝负荷调节总量，/>为第i个电解铝厂需要调节的负荷；若调节容量超过电解铝厂可调范围，则电解铝厂采用最大负荷或最小负荷工况运行；
步骤4.3、建立电解铝负荷的有功-电压外特性模型，通过调整相应参数来实现对负荷功率的控制；
电解铝负荷的有功-电压外特性数学模型如下：
(11)
(12)
式中，P Load为电解铝负荷的有功功率，V B为电解槽直流电压，R为电解铝负荷等效阻抗，E为电解铝负荷等效反电动势，V AH为负荷母线高压侧母线电压，k为铝厂降压变压器变比，L SR为饱和电抗器的电感值，ω为电网频率，I d为电解槽的直流电流；
得到PID控制器给出的负荷功率调节量后，通过式（11）、式（12）计算饱和电抗器需要调整的数值后进行操作，实现调节电解铝有功负荷。
与现有技术相比，本发明的有益效果：
1.本发明为电网频率控制提供了一种调频策略，可以有效遏制新能源接入电网后引起的频率波动。
2.模糊PID控制在运行中不断检测Δf和df/dt，根据模糊控制原理，来对比例控制参数KP、微分控制参数KD和积分控制参数KI进行在线修改以满足Δf和df/dt对控制参数的不同要求，而使被控制对象相较于传统PID控制有良好的动、静态性能，使频率控制更加的稳定与可靠。
3.利用模糊PID控制参数应外界环境变化自动调节，且通过制定调节规则保证控制系统的稳定性，提升了电网频率控制的可靠性和电力系统运行的稳定性。
4.模糊PID控制器结构简单，鲁棒性较强，调整速度较快且精度较高。
附图说明
图1为本发明实施例电解铝负荷参与孤网调频的控制方法的流程示意图；
图2为本发明实施例含电解铝负荷的孤立电网控制框网；
图3为本发明实施例三角形隶属度函数图；
图4为本发明实施例电解铝负荷的有功-电压外特性数学模型图。
具体实施方式
下面将结合本发明实施例对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动的前提下所获得的所有其他实施例，都属于本发明保护的范围。
需要说明的是，在不冲突的情况下，本发明中的实施例及实施例中的特征可以相互组合。
下面结合具体实施例对本发明作进一步说明，但不作为本发明的限定。
本实施例一种基于模糊PID控制的电解铝负荷参与孤立电网的调频方法，主要通过对电解铝负荷的控制来实现对电网频率的调节，该控制方法包括建立孤立电网调频模型，搭建模糊PID控制器以及建立电解铝负荷特性模型，利用模糊PID控制参数应外界环境变化自动调节，且通过制定调节规则保证控制系统的稳定性，提升了电网频率控制的可靠性和电力系统运行的稳定性。
本实施例是通过以下技术方案来实现的，如图1所示，一种基于模糊PID控制的电解铝负荷参与孤立电网的调频方法，包括以下步骤：
S1.建立电解铝负荷参与的孤立电网调频模型；
S2.采集系统频率变化量∆f和频率变化率df/dt(即d∆f/dt)；
S3.建立模糊pid控制器并计算出需要调节的功率；
S4.建立电解铝负荷特性模型并根据该模型计算相应参数调整量，调整该参数以调节电解铝负荷功率。
S1具体包括：实时监测电网频率及频率变化率；
S1.1 建立发电机组传递函数模型；
构建调速器传递函数模型：
(1)
式中，TG为调速器时间常数，s为拉普拉斯算子；
构建汽轮机传递函数模型：
式中，TCH为汽轮机时间常数，TR为再热器时间常数，FH为汽轮机再热器增益；
(2)
S1.2 建立发电机-电力系统模型；
(3)
式中M表示等效惯量系数，D表示等效阻尼系数；
S1.3 建立电解铝负荷等效传递函数；
式中，表示电解铝实际负荷功率变化，/>表示电解铝负荷功率变化的控制信号，s表示拉普拉斯算子，a和b均为电解铝负荷动态响应模型的等效参数；
(4)
具体的控制流程图如附图2所示，其中ΔPs(s)为发电机组二次调频量，ΔPL(s)为其它负荷波动量。
S2中，系统频率变化量Δf的绝对值的变化范围为0 .2～0 .5Hz。
S3的具体步骤包括：根据频率变化量Δf和频率变化率df/dt计算出PID控制器各参数相应调整量；
S3.1对输入量Δf和df/dt进行模糊化处理；
定义频率变化量Δf和频率变化率df/dt的模糊子集均为{负大[NB]、负中[NM]、负小[NS]、零[ZO]、正小[PS]、正中[PM]、正大[PB]}，并定义频率变化量Δf和频率变化率df/dt模糊集对应的论域为{-3, -2, -1, 0, 1, 2, 3}。将采集到的频率变化量Δf和频率变化率df/dt数据分别映射至论域的相对位置。
S3.2 确定隶属度函数；
对输入进行模糊量化后还要计算它们在模糊子集上的隶属度。隶属度是一个介于0和1之间的值，用以描述对应一个输入属于某一个模糊子集的程度。这里采用最常用的三角隶属函数，其函数关系如附图3所示；
S3.3 建立模糊化规则表；
计算输入量隶属度之后需要根据相应模糊规则得到被整定量在模糊子集上的隶属度。
模糊规则表的确定与控制器调节效果密切相关，合理的确定模糊化规则表能够使参数在随输入参数变化而动态变化的过程中对系统产生较好的控制效果，这种自动调整的能力是传统PID控制器所不具备的，具体的模糊规则如下：
比例控制参数KP，增大参数KP可以提升系统响应速度并降低稳态误差，但过大的参数KP会产生较大的超调量，使系统产生振荡。因此在整个控制过程中，在控制初期系统偏差较大时选取较大的参数KP以加快系统的响应速度，使频率偏差尽快缩小，在控制中期为防止产生过大超调适当减小参数KP，在控制末期为减小稳态误差再适当调大参数KP。基于以上规则设计出比例控制参数KP的模糊规则表：
表1.比例控制参数KP的模糊规则表
微分控制参数KD，增大参数KD可以减小系统超调量但同时会延长调整时间。在控制初期应选取较大的参数KD使系统超调量减小。在控制中期由于调节特性对参数KD值的变化比较敏感，应选取一个合适的值并保持不变。在控制末期则应该减小参数KD值，以减小被控过程的制动作用，进而补偿在调节过程初期由于KD值较大所造成的调节过程的时间延长。基于以上规则设计出KD的模糊规则表：
表2. 微分控制参数KD的模糊规则表
积分控制参数KI，增大参数KI可以减小甚至消除稳态误差但同时会造成积分饱和现象，故在控制初期选取较小的参数KI以减弱饱和现象，在控制末期选取较大的参数KI以减小稳态误差。基于以上规则设计出积分控制参数KI的模糊规则表：
表3.积分控制参数KI的模糊规则表
S3.4. 进行解模糊处理；
这里采用重心法进行解模糊处理，具体公式如下：
(5)
式中，Fi为模糊化量值，Mi为对应Fi的隶属度，N为模糊子集元素的个数，Vo为模糊控制器输出量解模糊后的精确值；
在获得相应增量后，我们需要对原参数进行相应调整，具体实现公式如下：
(6)
(7)
(8)
其中，，/>，/>分别为由模糊PID控制器计算出的对应比例系数，微分系数和积分系数的调整量，α、β、γ分别为设定的对应/>、/>、/>的修正系数，/>为修正前的比例调节系数，/>为修正前的微分调节系数，/>为修正前的积分调节系数，/>为修正后的比例调节系数，/>为修正后的微分调节系数，/>为修正后的积分调节系数。
S4具体步骤包括：
S4.1.根据修正后的PID参数确定电解铝负荷调整量：
(9)
S4.2.根据各电解铝厂可调容量分配调节任务：
(10)
其中，Ai为第i个电解铝厂的可调容量，N为参与调频的电解铝厂数量，为电解铝负荷调节总量，/>为第i个电解铝厂需要调节的负荷；若调节容量超过电解铝厂可调范围，则令铝厂相应采用最大负荷或最小负荷工况运行。
S4.3.建立电解铝铝的有功-电压外特性模型，如图4所示，通过调整相应参数来实现对负荷功率的控制。电解铝负荷的有功-电压外特性数学模型如下：
(11)
(12)
式中，P Load为电解铝负荷的有功功率，V B为电解槽直流电压，R为电解铝负荷等效阻抗，E为电解铝负荷等效反电动势，V AH为负荷母线高压侧母线电压，k为铝厂降压变压器变比，L SR为饱和电抗器的电感值，ω为电网频率，I d为电解槽的直流电流。
现代工业生产中多用调节饱和电抗器来调整负荷功率，故在拿到PID控制器给出的负荷功率调节量后，通过上述数学表达式计算出饱和电抗器需要调整的数值后进行相应操作以实现调节电解铝有功负荷的目的。
以上仅为本发明较佳的实施例，并非因此限制本发明的实施方式及保护范围，对于本领域技术人员而言，应当能够意识到凡运用本发明说明书内容所作出的等同替换和显而易见的变化所得到的方案，均应当包含在本发明的保护范围内。
Claims (1)
1.一种基于模糊PID的电解铝负荷参与孤网调频的方法，其特征在于，包括：
建立电解铝负荷参与的孤立电网调频模型；
采集系统频率变化量∆f和频率变化率df /dt；
建立模糊PID控制器并计算出需要调节的负荷量；
建立电解铝负荷特性模型并根据该模型计算出电解铝负荷相应控制参数调整量，以调节电解铝负荷功率；
建立电解铝负荷参与的孤立电网高频模型包括以下步骤：
步骤1.1、建立发电机组传递函数模型包括：
构建调速器传递函数模型：
(1)
式中，为调速器时间常数，s为拉普拉斯算子；
构建汽轮机传递函数模型：
(2)
式中，为汽轮机时间常数，/>为再热器时间常数，/>为汽轮机再热器增益；
步骤1.2、建立发电机-电力系统模型：
(3)
式中，M表示等效惯量系数，D表示等效阻尼系数；
步骤1.3、建立电解铝负荷等效传递函数：
(4)
式中，表示电解铝实际负荷功率变化，/>表示电解铝负荷功率变化的控制信号，s表示拉普拉斯算子，/>和b均为电解铝负荷动态响应模型的等效参数；
系统频率变化量Δf的绝对值的变化范围为0 .2～0 .5Hz；
建立模糊pid控制器并计算出需要调节的功率包括以下步骤：
步骤3.1、对系统频率变化量Δf和频率变化率df/dt进行模糊化处理；
定义系统频率变化量Δf和频率变化率df/dt的模糊子集均为{负大[NB]、负中[NM]、负小[NS]、零[ZO]、正小[PS]、正中[PM]、正大[PB]}，并定义系统频率变化量Δf和频率变化率df/dt的模糊集对应的论域为{-3, -2, -1, 0, 1, 2, 3}；将采集到的系统频率变化量Δf和频率变化率df/dt数据分别映射至论域的相对位置；
步骤3.2、确定隶属度函数；
采用三角隶属函数作为输入量隶属度函数；
步骤3.3、建立模糊化规则表；
比例控制参数KP的模糊规则如下：
if Δf is NB and df/dt is NB then ∆KP is PB
if Δf is NB and df/dt is NM then ∆KP is PB
if Δf is NB and df/dt is NS then ∆KP is PM
if Δf is NB and df/dt is ZO then ∆KP is PM
if Δf is NB and df/dt is PS then ∆KP is PS
if Δf is NB and df/dt is PM then ∆KP is ZO
if Δf is NB and df/dt is PB then ∆KP is ZO
if Δf is NM and df/dt is NB then ∆KP is PB
if Δf is NM and df/dt is NM then ∆KP is PB
if Δf is NM and df/dt is NS then ∆KP is PM
if Δf is NM and df/dt is ZO then ∆KP is PS
if Δf is NM and df/dt is PS then ∆KP is PS
if Δf is NM and df/dt is PM then ∆KP is ZO
if Δf is NM and df/dt is PB then ∆KP is NS
if Δf is NS and df/dt is NB then ∆KP is PM
if Δf is NS and df/dt is NM then ∆KP is PM
if Δf is NS and df/dt is NS then ∆KP is PM
if Δf is NS and df/dt is ZO then ∆KP is PS
if Δf is NS and df/dt is PS then ∆KP is ZO
if Δf is NS and df/dt is PM then ∆KP is NS
if Δf is NS and df/dt is PB then ∆KP is NS
if Δf is ZO and df/dt is NB then ∆KP is PM
if Δf is ZO and df/dt is NM then ∆KP is PM
if Δf is ZO and df/dt is NS then ∆KP is PS
if Δf is ZO and df/dt is ZO then ∆KP is ZO
if Δf is ZO and df/dt is PS then ∆KP is NS
if Δf is ZO and df/dt is PM then ∆KP is NM
if Δf is ZO and df/dt is PB then ∆KP is NM
if Δf is PS and df/dt is NB then ∆KP is PS
if Δf is PS and df/dt is NM then ∆KP is PS
if Δf is PS and df/dt is NS then ∆KP is ZO
if Δf is PS and df/dt is ZO then ∆KP is NS
if Δf is PS and df/dt is PS then ∆KP is NS
if Δf is PS and df/dt is PM then ∆KP is NM
if Δf is PS and df/dt is PB then ∆KP is NM
if Δf is PM and df/dt is NB then ∆KP is PS
if Δf is PM and df/dt is NM then ∆KP is ZO
if Δf is PM and df/dt is NB then ∆KP is NS
if Δf is PM and df/dt is NB then ∆KP is NM
if Δf is PM and df/dt is NB then ∆KP is NM
if Δf is PM and df/dt is NB then ∆KP is NM
if Δf is PM and df/dt is NB then ∆KP is NB
if Δf is PB and df/dt is NB then ∆KP is ZO
if Δf is PB and df/dt is NB then ∆KP is ZO
if Δf is PB and df/dt is NB then ∆KP is NM
if Δf is PB and df/dt is NB then ∆KP is NM
if Δf is PB and df/dt is NB then ∆KP is NM
if Δf is PB and df/dt is NB then ∆KP is NB
if Δf is PB and df/dt is NB then ∆KP is NB
微分控制参数KD的模糊规则如下：
if Δf is NB and df/dt is NB then ∆KD is PS
if Δf is NB and df/dt is NM then ∆KD is NS
if Δf is NB and df/dt is NS then ∆KD is NB
if Δf is NB and df/dt is ZO then ∆KD is NB
if Δf is NB and df/dt is PS then ∆KD is NB
if Δf is NB and df/dt is PM then ∆KD is NM
if Δf is NB and df/dt is PB then ∆KD is PS
if Δf is NM and df/dt is NB then ∆KD is PS
if Δf is NM and df/dt is NM then ∆KD is NS
if Δf is NM and df/dt is NS then ∆KD is NB
if Δf is NM and df/dt is ZO then ∆KD is NM
if Δf is NM and df/dt is PS then ∆KD is NM
if Δf is NM and df/dt is PM then ∆KD is NS
if Δf is NM and df/dt is PB then ∆KD is ZO
if Δf is NS and df/dt is NB then ∆KD is ZO
if Δf is NS and df/dt is NM then ∆KD is NS
if Δf is NS and df/dt is NS then ∆KD is NM
if Δf is NS and df/dt is ZO then ∆KD is NM
if Δf is NS and df/dt is PS then ∆KD is NS
if Δf is NS and df/dt is PM then ∆KD is NS
if Δf is NS and df/dt is PB then ∆KD is ZO
if Δf is ZO and df/dt is NB then ∆KD is ZO
if Δf is ZO and df/dt is NM then ∆KD is NS
if Δf is ZO and df/dt is NS then ∆KD is NS
if Δf is ZO and df/dt is ZO then ∆KD is NS
if Δf is ZO and df/dt is PS then ∆KD is NS
if Δf is ZO and df/dt is PM then ∆KD is NS
if Δf is ZO and df/dt is PB then ∆KD is ZO
if Δf is PS and df/dt is NB then ∆KD is ZO
if Δf is PS and df/dt is NM then ∆KD is ZO
if Δf is PS and df/dt is NS then ∆KD is ZO
if Δf is PS and df/dt is ZO then ∆KD is ZO
if Δf is PS and df/dt is PS then ∆KD is ZO
if Δf is PS and df/dt is PM then ∆KD is ZO
if Δf is PS and df/dt is PB then ∆KD is ZO
if Δf is PM and df/dt is NB then ∆KD is PB
if Δf is PM and df/dt is NM then ∆KD is NS
if Δf is PM and df/dt is NB then ∆KD is PS
if Δf is PM and df/dt is NB then ∆KD is PS
if Δf is PM and df/dt is NB then ∆KD is PS
if Δf is PM and df/dt is NB then ∆KD is PS
if Δf is PM and df/dt is NB then ∆KD is PB
if Δf is PB and df/dt is NB then ∆KD is PB
if Δf is PB and df/dt is NB then ∆KD is PM
if Δf is PB and df/dt is NB then ∆KD is PM
if Δf is PB and df/dt is NB then ∆KD is PM
if Δf is PB and df/dt is NB then ∆KD is PS
if Δf is PB and df/dt is NB then ∆KD is PS
if Δf is PB and df/dt is NB then ∆KD is PB
积分控制参数KI的模糊规则如下：
if Δf is NB and df/dt is NB then ∆KI is NB
if Δf is NB and df/dt is NM then ∆KI is NB
if Δf is NB and df/dt is NS then ∆KI is NM
if Δf is NB and df/dt is ZO then ∆KI is NM
if Δf is NB and df/dt is PS then ∆KI is NS
if Δf is NB and df/dt is PM then ∆KI is ZO
if Δf is NB and df/dt is PB then ∆KI is ZO
if Δf is NM and df/dt is NB then ∆KI is NB
if Δf is NM and df/dt is NM then ∆KI is NB
if Δf is NM and df/dt is NS then ∆KI is NM
if Δf is NM and df/dt is ZO then ∆KI is NS
if Δf is NM and df/dt is PS then ∆KI is NS
if Δf is NM and df/dt is PM then ∆KI is ZO
if Δf is NM and df/dt is PB then ∆KI is ZO
if Δf is NS and df/dt is NB then ∆KI is NB
if Δf is NS and df/dt is NM then ∆KI is NM
if Δf is NS and df/dt is NS then ∆KI is NS
if Δf is NS and df/dt is ZO then ∆KI is NS
if Δf is NS and df/dt is PS then ∆KI is ZO
if Δf is NS and df/dt is PM then ∆KI is PS
if Δf is NS and df/dt is PB then ∆KI is PS
if Δf is ZO and df/dt is NB then ∆KI is NM
if Δf is ZO and df/dt is NM then ∆KI is NM
if Δf is ZO and df/dt is NS then ∆KI is NS
if Δf is ZO and df/dt is ZO then ∆KI is ZO
if Δf is ZO and df/dt is PS then ∆KI is PS
if Δf is ZO and df/dt is PM then ∆KI is PM
if Δf is ZO and df/dt is PB then ∆KI is PM
if Δf is PS and df/dt is NB then ∆KI is NM
if Δf is PS and df/dt is NM then ∆KI is NS
if Δf is PS and df/dt is NS then ∆KI is ZO
if Δf is PS and df/dt is ZO then ∆KI is PS
if Δf is PS and df/dt is PS then ∆KI is PS
if Δf is PS and df/dt is PM then ∆KI is PM
if Δf is PS and df/dt is PB then ∆KI is PB
if Δf is PM and df/dt is NB then ∆KI is ZO
if Δf is PM and df/dt is NM then ∆KI is ZO
if Δf is PM and df/dt is NB then ∆KI is PS
if Δf is PM and df/dt is NB then ∆KI is PS
if Δf is PM and df/dt is NB then ∆KI is PM
if Δf is PM and df/dt is NB then ∆KI is PB
if Δf is PM and df/dt is NB then ∆KI is PB
if Δf is PB and df/dt is NB then ∆KI is ZO
if Δf is PB and df/dt is NB then ∆KI is ZO
if Δf is PB and df/dt is NB then ∆KI is PS
if Δf is PB and df/dt is NB then ∆KI is PM
if Δf is PB and df/dt is NB then ∆KI is PM
if Δf is PB and df/dt is NB then ∆KI is PB
if Δf is PB and df/dt is NB then ∆KI is PB；
步骤3.4、解模糊处理；
采用重心法进行解模糊处理，具体公式如下：
(5)
式中，Fi为模糊化量值，Mi为对应Fi的隶属度，N为模糊子集元素的个数，V o为模糊控制器输出量解模糊后的精确值；
在获得相应增量后，对原参数进行相应调整，公式如下：
(6)
(7)
(8)
其中，，/>，/>分别为由模糊PID控制器计算出的对应比例系数，微分系数和积分系数的调整量，α、β、γ分别为设定的对应/>、/>、/>的修正系数，/>为修正前的比例调节系数，/>为修正前的微分调节系数，/>为修正前的积分调节系数，/>为修正后的比例调节系数，/>为修正后的微分调节系数，/>为修正后的积分调节系数；
建立电解铝负荷特性模型并根据该模型计算出电解铝负荷相应控制参数调整量，以调节电解铝负荷功率包括以下步骤：
步骤4.1、根据修正后的PID参数确定电解铝负荷调整量：
(9)；
其中，为电解铝负荷调整量，/>，/>，/>分别为比例调节系数，微分调节系数和积分调节系数；
步骤4.2、根据各电解铝厂可调容量分配调节任务；
(10)
其中，Ai为第i个电解铝厂的可调容量，N为参与调频的电解铝厂数量，为电解铝负荷调节总量，/>为第i个电解铝厂需要调节的负荷；若调节容量超过电解铝厂可调范围，则电解铝厂采用最大负荷或最小负荷工况运行；
步骤4.3、建立电解铝负荷的有功-电压外特性模型，通过调整相应参数来实现对负荷功率的控制；
电解铝负荷的有功-电压外特性数学模型如下：
(11)
(12)
式中，P Load为电解铝负荷的有功功率，V B为电解槽直流电压，R为电解铝负荷等效阻抗，E为电解铝负荷等效反电动势，V AH为负荷母线高压侧母线电压，k为铝厂降压变压器变比，L SR为饱和电抗器的电感值，ω为电网频率，I d为电解槽的直流电流；
得到PID控制器给出的负荷功率调节量后，通过式（11）、式（12）计算饱和电抗器需要调整的数值后进行操作，实现调节电解铝有功负荷。
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