电气工程学报, 2018, 13(7): 40-48 doi: 10.11985/2018.07.006

基于VSG的光储双向变流器关键特性研究

陶鸿飞1, 孙丽敬2, 崔健2, 杨才明1, 金渊文1, 谢栋1

1. 国网绍兴供电公司 绍兴 312000

2. 中国电力科学研究院有限公司 北京 100192

Research on Key Characteristics of Optical-Storage Bidirectional Converter Based on Virtual Synchronous Generator Technology

Tao Hongfei1, Sun Lijing2, Cui Jian2, Yang Caiming1, Jin Yuanwen1, Xie Dong1

1. State Grid Shaoxin Power Supply Company Shaoxing 312000 China

2. China Electric Power Research Institute Beijing 100192 China

收稿日期: 2017-09-12   网络出版日期: 2018-07-25

Received: 2017-09-12   Online: 2018-07-25

作者简介 About authors

陶鸿飞 男 1966年生,高级工程师,长期从事电力系统及自动化工作。

孙丽敬 女 1981年生,高级工程师,长期从事分布式电源、微电网和交直流配电方面的工作。

摘要

介绍了基于虚拟同步发电机技术的光储双向变流器的拓扑结构与工作原理,基于虚拟同步发电机控制策略进行小信号模型建模,给出虚拟惯性、有功-频率与无功-电压控制的关键参数设计方法,并分析了这些参数对装置性能的影响。最后针对30kW光储一体虚拟同步发电机原理样机,利用PSACD/EMTDC仿真结果和硬件实验结果验证了控制策略、参数设计的有效性。

关键词: 虚拟同步发电机 ; 有功频率控制 ; 惯量控制 ; 参数影响

Abstract

The topology and working principle of the optical-storage bidirectional converter based on virtual synchronous generator technology is introduced, the small signal model modeling based on the control strategy of virtual synchronous generator is carried out, the design method of key parameters of virtual inertia, active frequency and reactive voltage control is given, and the influence of these parameters on the performance of the device is analyzed. Finally, for the prototype of 30kW virtual synchronous generator integrated with optical and storage, PSACD / EMTDC simulation results and hardware experiment results are used to verify the effectiveness of the control strategy and parameter design.

Keywords: Virtual synchronous generator ; P-f control ; inertia control ; parameter influence

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本文引用格式

陶鸿飞, 孙丽敬, 崔健, 杨才明, 金渊文, 谢栋. 基于VSG的光储双向变流器关键特性研究. 电气工程学报[J], 2018, 13(7): 40-48 doi:10.11985/2018.07.006

Tao Hongfei. Research on Key Characteristics of Optical-Storage Bidirectional Converter Based on Virtual Synchronous Generator Technology. Journal of Electrical Engineering[J], 2018, 13(7): 40-48 doi:10.11985/2018.07.006

1 引言

“十三五”期间,光伏扶贫将成为我国光伏产业发展的重要部分。随着光伏扶贫计划的深入推广,分布式光伏高密度接入县域电网后,因其运行特性受环境影响较大且具有明显的随机性和波动性,给配电网带来诸多问题,如潮流大量倒送、电压越限、电压偏差严重和电压波动等[1,2,3]。另一方面,分布式光伏最本质特征就是分散、小型和自发自用,从电网运行和调度层面来解决大规模分布式光伏接入问题较为困难[4],因此,研制自适应电网、友好接入的分布式光伏并网装备是解决县域电网应对高渗透率分布式光伏接入问题的有效解决思路之一。光储一体虚拟同步发电机是在上述背景下衍生出的可代替逆变器的一种光伏友好并网装置。

虚拟同步发电机(Virtual Synchronous Generator,简称VSG)技术是指通过模拟同步发电机组的机电暂态特性,使采用变流器的电源具有同步发电机组的惯量、阻尼、一次调频和无功调压等并网运行外特性的技术。近年来,国内外对VSG的研究成果多集中在建模与控制策略、稳定分析和应用等方面。文献[11]分析了虚拟惯量和阻尼系数对VSG并网稳定性的影响,并综合动态响应时间和超调量对参数进行选择分析;文献[12]在一阶环节虚拟惯量的虚拟同步发电机并网PQ控制系统中,增加一个超前环节,形成超前滞后惯性环节,通过调节超前滞后环节的零极点参数,优化系统运行性能。文献[13]基于一种光储共交流母线的光储虚拟同步发电机拓扑结构分析了虚拟同步发电机在负载功率扰动、光伏阵列功率扰动时的响应特性以及并网模式下的动态特性。文献[14]根据光伏出力曲线与特征值分析得到光伏电源稳定运行区域,设计了光伏电源附加控制策略,防止因光伏电源最大可用功率不足而造成的直流电压跌落,进而直接通过虚拟同步发电机接入光伏电源实现了离网与并网的灵活可靠运行。在工程应用方面,2016年,国家电网公司在张北风光储输基地开展示范工程建设,对现有风机、光伏发电的逆变器和控制系统进行改造,2017年完成一期改造,虚拟同步发电机容量达到140MW,是目前世界上规模最大的虚拟同步发电机示范工程。综合诸多团队的科研成果来看,对虚拟同步电机关键参数对性能影响的实用化分析较少。因此,本文首先在分析一种光储一体虚拟同步发电机的拓扑结构与工作原理的基础上,基于虚拟同步发电机控制策略,给出了调频控制、无功控制的关键参数取值方法,并分析了关键参数对虚拟同步发电机性能的影响。最后,基于30kW光储一体虚拟同步发电机样机,利用PSCAD/EMTDC仿真和硬件试验平台验证了控制策略、参数设计的有效性、可行性。

2 拓扑结构与工作原理

2.1 拓扑结构

光储一体虚拟同步发电机拓扑结构如图1所示,由两个三相全桥模块通过直流支撑电容组成一个背靠背结构。其中,VgaVgbVgc为电网三相相电压,UoaUobUoc为虚拟同步发电机交流侧输出电压,E为逆变器桥臂输出目标相电压有效值;Udc为直流母线电压,iaibic为流经滤波电感L2的电流。

图1

图1   光储一体虚拟同步发电机拓扑结构

Fig.1   Topology of VSG integrated with photovoltaic and battery


本结构中,一个三相全桥模块作为并网同步逆变器,将直流侧微源提供的直流电变换成三相交流电,经LCL型滤波器并入电网。

另一个三相全桥模块分解为3个DC/DC变换器,分别进行控制。每个Buck/Boost变换器均可以实现光伏或者储能的接入,将光伏侧/储能侧直流电压升压为并网同步逆变器所需的直流电压。

2.2 工作原理

本文设计的光储一体虚拟同步发电机直流源设计为2路光伏、1路储能,分别接入图1拓扑图中①~③接入点。

同步逆变器实现虚拟同步发电机控制,表现为受控交流电压源特性。

所配置的一路储能作为虚拟同步发电机的惯量单元,通过充放电能来模拟同步发电机转子存储或释放的动能。储能用DC/DC变换器采用电压-电流双环控制实现直流稳压控制。

光伏用DC/DC变换器工作在最大功率点跟踪MPPT(maximum power point tracking)模式,实现光伏最大功率输出。

3 建模与参数设计

光储一体虚拟同步发电机具备有功–频率、无功–电压两个本质控制功能,体现惯量、阻尼两个标志性特性。

3.1 有功–频率控制

有功–频率控制环源自同步发电机一次调频与惯性特性。通过调节虚拟机械转矩Tm实现同步逆变器有功指令Pset的调节;通过调频控制器实现对电网频率偏差的响应。其中,Tm由机械转矩指令T0和频率偏差反馈指令ΔT两部分组成,可以表示为

$T_{0} = \frac {P_{set}}{\omega}$
$△T = k_{f} (w_{ref} - \omega_{n})$

式中,ω为虚拟同步发电机实际角频率;ωn为公共母线角频率;ωref为电网基准频率;kf为调频系数。

引入同步发电机转子运动方程,得到有功–频率控制器如式(3)所示,控制框图如图2所示。

图2

图2   有功–频率控制框图

Fig.2   Block diagram of P-f control


$P_{set} \frac {1}{\omega_{n}} + k_{f} (\omega_{ref}-\omega_{n}) - P_{out} \frac {1}{\omega_{n}} - D(w-w_{n}) = J\omega \frac {dw}{dt}$

式中,Pout为实际输出有功功率;θ为实际电角度;D为阻尼系数;J为转动惯量。

在稳态时,ω≈ωref,根据控制理论与数学原理,调频系数kf和阻尼系数D归一,以有功环下垂系数Dp表示,得到有功–频率控制器为

$P_{set} \frac {1}{\omega_{n}} + D_{p}(\omega-\omega_{n}) - P_{out} \frac {1}{\omega_{n}} = J\omega \frac {d\omega}{dt}$

3.2 无功–电压控制

无功–电压控制环源自同步发电机一次调压与励磁特性,通过调节虚拟同步发电机的虚拟电势E来调节虚拟同步发电机交流侧电压和无功功率。无功–电压控制器如式(5)所示,控制框图如图3所示。

$Q_{set} + D_{q} (U_{ref} - U_{o}) - Q_{e} = K \frac {dE}{dt}$

式中,Qe为实际输出的无功功率;Qset为设定的无功功率给定值;Dq为无功–电压下垂系数;UrefUo为同步逆变器机端电压有效值的指令值与实际输出值;K为励磁惯性系数。

图3

图3   无功–电压控制框图

Fig.3   Block diagram of Q-V control


3.3 虚拟同步机小信号建模

图4为虚拟同步发电机整体控制框图,首先根据采集的电压电流信号得到实际输出的有功功率、无功功率,同时采集的电网电压经SPLL得到电网角速度,再经过有功–频率控制、无功–电压控制、目标调制电压生成及SVPWM调制后得到逆变器开关管的触发脉冲,控制逆变器最终实现虚拟同步发电机控制目标。

同步逆变器进入稳态工作时,其输出的有功功率和无功功率为

$P_{out} = \frac {3EU_{g}} {X_{s}}sin d$
$Q_{e} = \frac {3(E-U_{g} cos d)E}{X_{s}}$

根据式(4)、式(5)和图4,可以得到虚拟同步发电机在s域内的小信号模型,如图5所示。

图4

图4   虚拟同步发电机控制框图

Fig.4   Block diagram of VSG


其中,Xs为逆变器输出阻抗与线路阻抗之和;Ug为电网三相相电压有效值;δ为VSG桥臂中点电压与电网电压之间的角度差,也称为功角。

图5a可得虚拟同步发电机有功环的开环传递函数OP(s)和闭环传递函数CP(s)分别如式(8)和式(9)所示。

图5

图5   虚拟同步发电机控制的小信号模型

Fig.5   Small signal model of VSG control


$O_{p} (s) = \frac {3U_{g}E_{n}}{\omega_{n}JX_{s}s^{2} + \omega_{n} D_{p} X _{s} s}$
$C_{p}(s) = \frac 3U_{g} E_{n} {\omega_{n}JX_{s}s^{2} + \omega_{n}D_{p}X_{s}s + 3U_{g} E_{n}}$

图5b可得虚拟同步发电机无功环的开环传递函数OQ(s)和闭环传递函数CQ(s)分别如式(10)和式(11)所示。

$O_{Q}(s)= \frac {2.121 (2E_{n} - U_{g})} {KX_{s}s + D_{q} X_{s}}$
$C_{Q} (s) = \frac {2.121(2E_{n} - U_{g})}{KX_{s}s + D_{q}X_{s} + 2.121(2E_{n} - U_{g})}$

3.4 参数设计

从上述建模分析可知,虚拟同步发电机关键控制参数有:有功环下垂系数Dp,无功环下垂系数Dq;有功环惯性系数J,无功环惯性系数K

标准EN 50438规定逆变器接入电网连续运行电网条件为:电网电压频率在49~51Hz,电网电压幅值在90%~110%额定电压幅值。根据该标准的要求,DpDq的最大值设计为:电网电压频率变化1Hz,虚拟同步发电机输出有功功率变化100%;电网电压幅值变化10%,虚拟同步发电机输出无功功率变化100%。如果以10kW虚拟同步发电机,接入三相电压为380V电网情况为例分析,那么有:Dp≤5,Dq≤321。

选择虚拟同步机主电路参数见表1。将电路参数分别代入虚拟同步机有功环与无功环的传递函数,将有功环与无功环的稳态性能指标要求与动态性能指标要求作为约束条件,可得在各约束条件下DpJDqK的取值范围见表2

表1   虚拟同步机主电路参数

Tab.1  Main circuit parameters of VSG

参 数取 值参 数取 值
额定容量/kV·A10滤波电感L2/mH3
直流电压/V700网侧电感L3/mH1
直流侧电容/μF1 000滤波电容/μF10
电网相电压/V220

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表2   虚拟同步机控制参数取值范围

Tab.2  Control parameters range of VSG

参 数有功环无功环
DpJDqK
取值范围0~50~0.10~3210~8

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4 参数变化对虚拟同步机性能的影响

4.1 DpJ的变化对有功环性能的影响

Xs为逆变器输出阻抗与线路阻抗之和,通常线路电感值远小于网侧电感L2,可忽略,因此有Xs = ωn(L2 + L3)。将表1所示参数代入式(8)和式(9),可得有功环的闭环传递函数为

$C_{p}(s) = \frac {145200}{394.384 J s^{2} + 394.384 D_{p}s+145200}$

图6图7分别为参数DpJ变化时有功环的闭环极点分布图。由图6可知,在参数Dp变化时,有功环的闭环极点逐渐远离实轴,即有功环的稳定裕度随着Dp的增大而增大。在动态性能方面,随着Dp的增大,有功环的闭环极点均为共轭复数,所以系统为欠阻尼系统。且闭环极点实部绝对值增大,虚部绝对值减小,即有功环的阻尼比增大,所以超调量减小,上升时间增大,调节时间减小,振荡频率减小。随着Dp的增大,有功环的闭环极点均匀分布,所以Dp的变化对有功环的稳态性能以及动态性能的影响是持续的。

图6

图6   Dp 变化时闭环极点分布图

Fig.6   Close loop pole map when Dp changing


图7所示为有功环惯性系数J变化时的闭环极点分布图。J变化时,有功环闭环极点均为共轭复根,所以为欠阻尼系统。随着J的增大,有功环的闭环极点靠近虚轴,所以稳定裕度减小;在动态性能方面,随着J的增大,有功环的闭环极点实部绝对值减小,虚部绝对值减小,阻尼比减小,所以有功环超调量增大,上升时间增大,调节时间增大,振荡频率减小。J的增大使得有功环的响应变慢。随着J的增大,有功环的闭环极点分布越来越密集,即J的变化对有功环的影响随着J的增大而变弱。

图7

图7   J 变化时闭环极点分布图

Fig.7   Close loop pole map when J changing


4.2 DqK的变化对无功环性能的影响

表1中参数代入式(11)可得无功环的闭环传递函数为

$C_{Q}(s) = \frac{466.62}{1.256Ks + 1.256D_{q} + 466.62}$

图8为无功环在参数K一定、Dq变化时的闭环极点分布图。随着Dq的增大,无功环的闭环极点逐渐远离虚轴,动态性能方面,随着Dq的增大,无功环的闭环极点绝对值增大,所以无功环的响应变快,响应时间变短。随着Dq的增大,无功环的闭环极点均匀分布,所以Dq的变化对无功环的影响是持续的。

图8

图8   Dq 变化时无功环极点分布图

Fig.8   Pole map when Dq changing


图9为无功环在参数Dq一定、K变化时的闭环极点分布图。随着K的增大,无功环的闭环极点逐渐靠近虚轴,动态性能方面,随着K的增大,无功环的闭环极点绝对值减小,所以无功环的响应变慢,响应时间变长。随着K的增大,无功环的闭环极点分布越来越密集,所以K的变化对无功环的影响随着K的增大逐渐变弱。

图9

图9   K 变化时极点分布图

Fig.9   Pole map when K changing


5 仿真与实验验证

为验证光储一体虚拟同步发电机拓扑结构、控制算法和参数分析的有效性,在PSCAD/EMTDC中搭建了30kW光储一体虚拟同步发电机模型。仿真参数与研制的样机参数一致,见表3

表3   光储一体虚拟同步发电机参数

Tab.3  Parameters of VSG integrated with photovoltaic and battery

技术参数技术指标
直流最大输入电压/V1 000
直流电压范围/V200~1 000
直流最大输入功率/kW37.5
直流最大输入电流/A34
交流额定工作电压380V,三相三线
交流电压范围/V300~400
交流额定输出电流/A45
储能配置10kW、0.5h
直流滤波电感L1 /mH1
直流侧电容C1 /μF100
交流侧电感L2 /mH1.5
直流侧电容C2 /μF10
交流侧电感L3 /mH0.1
有功环下垂系数Dp5
无功环下垂系数Dq1
有功环惯性系数J0.1
无功环惯性系数K7

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5.1 惯量特性验证

设置电网侧频率在标称电压下输出频率按照图10所示的曲线变化,在t0~t1t2~t3t4~t5t6~t7内频率变化率保持为0.5Hz/s,t4 - t3≥2min、t6 - t5 = t2 - t1 = 1min。频率变化区间和稳态区间中虚拟同步发电机交流侧电压与电流的波形如图11所示,在电网频率波动时,虚拟同步机输出电压基本保持稳定,为给定值380V。当电网频率降低时,虚拟同步发电机输出有功功率增大;当频率升高时,虚拟同步发电机输出有功功率减小。

图10

图10   电网频率变化曲线

Fig.10   Curve of power grid frequency


图11

图11   虚拟同步机交流侧电压电流波形

Fig.11   Curve of voltage and current of VSG on AC side


以每20ms为一点计算响应于惯量的有功功率平均值,有功功率响应曲线如图12所示。当电网频率跌至48.1Hz时,有功功率快速调整至26kW,有功功率变化率为2.89kW/s,近似为额定功率的10%,如图12中30~33.8s阶段所示;当电网频率由50Hz上升至51.4Hz时,有功功率快速调整至5kW,调整速率为2.64kW/s,近似为额定功率的10%,如图12中217.6~220.4s阶段所示。有功功率能够快速响应电网频率变化,减缓频率变化速度,进行惯量控制。

图12

图12   VSG 有功功率响应曲线

Fig.12   Curve of active power for VSG


5.2 有功–频率控制验证

在虚拟同步发电机轻载输出(30%额定有功时),与重载输出(100%额定有功时)两种工况下,分析电网频率阶跃至48.5Hz、50.4Hz时的有功–频率控制响应,如图13图14所示。由图读取有功–频率响应的各项动态指标列于表4

图13

图13   轻载时有功功率响应曲线

Fig.13   Curve of active power when load is light


图14

图14   重载时有功功率响应曲线

Fig.14   Curve of active power when load is heavy


表4   系统性能指标

Tab.4  Performance of system

f/Hz响应时间tr /s调节时间ts /s误差/kW
轻载48.50.501.00.55
50.40.251.00.30
重载48.50.500.90.50
50.40.201.00.20

新窗口打开| 下载CSV


表4可知,轻载或重载时,当电网频率发生阶跃降低或阶跃升高时,系统有功功率均能迅速响应,并快速过渡到稳态。最大稳态控制误差不大于额定功率的1.83%,响应时间不大于500ms,调节时间不大于1s。

5.3 无功功率控制验证

在额定电压条件下,设置光储一体虚拟同步发电机从无功功率为零开始,以10%额定功率为变化步长运行60s并逐步降低至最小无功输出值(-30%的额定有功),运行60s后,无功功率回到零,以10%额定功率为变化步长运行60s并逐步升高至最大无功输出值(-30%的额定有功)。

无功功率响应波形如图15所示,无论无功功率给定值是正阶跃还是负阶跃,输出值均能跟随给定值,响应时间不大于1s,几乎没有无功控制误差。

图15

图15   无功功率响应波形

Fig.15   Curve of reactive power


5.4 实验验证

设计了光储一体虚拟同步发电机试验平台,采用艾美泰克RS-270型交流可调电源作为模拟电网,容量为270kW;采用日本拓普康(Topcon)的直流模拟电源TC.GSS.32.500.400.S.HMI模拟光伏列阵,其输出功率在整个测试期间稳定在规定的功率等级,偏差±1%;采用10kW、0.5h的锂电池作为储能单元。

图16为30kW光储一体虚拟同步发电机有功–频率控制波形。三相正弦波形为输出电流波形,锯齿状波形为电池电流波形。电网频率由50Hz阶跃为49.9Hz,频率变化前设备输出有功功率7kW,频率变化后电池放电,设备输出电流增大,有功功率增加量与理论计算值相差100W,控制误差小于1%。

图16

图16   有功功率响应曲线

Fig.16   Curve of active power


图17为30kW光储一体虚拟同步发电机惯量特性试验波形。三相正弦波形为输出电流波形,锯齿状波形为电池电流波形。电网频率由50Hz按照1Hz/s变为48.1Hz,电池放电,有功功率增大,快速响应电网频率变化。

图17

图17   有功功率响应曲线(惯量特性测试时)

Fig.17   Curve of active power for inertia test


图18为30kW光储一体虚拟同步发电机无功控制试验中三相电流波形。有功功率输出8kW,无功功率设置值为5kvar,无功功率实测值为4.95kvar,无功功率控制误差小于0.5%。

图18

图18   无功功率控制曲线

Fig.18   Curve of Reactive power control


6 结论

本文以光储一体虚拟同步发电机为分析原型,给出虚拟同步发电机控制策略以及小信号模型,并分析了关键参数对虚拟同步发电机性能的影响。最后,基于30kW光储一体虚拟同步发电机样机,利用PSCAD/EMTDC仿真和硬件试验平台验证了控制策略、参数设计的有效性、可行性。

(1)惯量特性方面,有功环惯量系数J的增大会使得有功环响应变慢,为有功环注入一定的“惯量”,但同时会使得有功环的超调量增大,稳定裕度减小,K的增大同样可为无功环注入一定的“惯量”,使得无功环的响应变慢。

(2)一次调频特性方面,有功环下垂系数Dp的增加会增大有功环的稳定裕度,减小超调量,增大上升时间,使有功环响应的振荡减弱。

(3)无功功率控制特性方面,无功环下垂系数Dq的增大使得无功环的响应变快,响应时间变短。

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