obsidian_backup/多体+耦合求解器/稳态运行载荷/Control of variable speed pitch turbine/auto/Control of variable speed pitch turbine.md

8.3.2 Control of variable-speed, pitch-regulated turbines

A variable-speed generator is decoupled from the grid frequency by a power converter, which can control the load torque at the generator directly, so that the speed of the turbine rotor can be allowed to vary between certain limits. An often-quoted advantage of variable-speed operation is that below rated wind speed, the rotor speed can be adjusted in proportion to the wind speed so that the optimum tip speed ratio is maintained. At this tip speed ratio the power coefficient, C_{p} , is a maximum, which means that the aerodynamic power captured by the rotor is maximised. This is often used to suggest that a variable-speed turbine can capture much more energy than a fixed-speed turbine of the same diameter. In practice it may not be possible to realise all of this gain, partly because of losses in the power converter and partly because it is not possible to track optimum C_{p} perfectly.
变速发电机通过功率转换器与电网频率解耦，该转换器可以直接控制发电机上的负载转矩，从而允许涡轮机转子的转速在一定范围内变化。变速运行的一个常被引用的优点是，在额定风速以下，转子转速可以按比例调整以适应风速，从而保持最佳叶尖速度比。在该叶尖速度比下，功率系数 C_{p} 达到最大值，这意味着涡轮机叶片捕获的空气动力学功率被最大化。这常被用来表明，与相同直径的定速涡轮机相比，变速涡轮机可以捕获更多的能量。然而，在实践中，由于功率转换器中的损耗以及无法完美跟踪最佳 $C_{p}$，可能无法实现全部的增益。

Maximum aerodynamic efficiency is achieved at the optimum tip speed ratio \lambda=\lambda_{\mathrm{opt}} , at which the power coefficient C_{p} has its maximum value C_{p(\mathrm{max})} . Because the rotor speed \varOmega is then proportional to wind speed U. , the power increases with U^{3} and \varOmega^{3} , and the torque with U^{2} and \varOmega^{2} . The aerodynamic torque is given by
最大空气动力学效率在最佳叶尖速度比 \lambda=\lambda_{\mathrm{opt}} 时实现，此时功率系数 C_{p} 达到其最大值 C_{p(\mathrm{max})} 。由于转子转速 \varOmega 此时与风速 U 成正比，因此功率随 U^{3} 和 \varOmega^{3} 增大，而扭矩随 U^{2} 和 \varOmega^{2} 增大。空气动力学扭矩的表达式为

Q_{a}=\frac{1}{2}\rho A C_{q}U^{2}R=\frac{1}{2}\rho\pi R^{3}\frac{C_{p}}{\lambda}U^{2}

Since U\!=\!\varOmega R/\lambda we have

Q_{a}=\frac{1}{2}\rho\pi R^{5}\frac{C_{p}}{\lambda^{3}}\varOmega^{2}

In the steady state therefore, the optimum tip speed ratio can be maintained by setting the load torque at the generator, Q_{g} , to balance the aerodynamic torque, that is,
稳态条件下，可以通过在发电机处设置负载转矩 $Q_{g}$，以平衡气动转矩，从而维持最佳叶片尖速比，即：

{\it Q}_{g}=\frac{1}{2}\frac{\pi\rho R^{5}C_{p}}{\lambda^{3}G^{3}}\omega_{g}^{2}-{\it Q}_{L}

Here Q_{L} represents the mechanical torque loss in the drive train (which may itself be a function of rotational speed and torque), referred to the high-speed shaft. The generator speed is \omega_{\mathrm{g}}=G2 , where G is the gearbox ratio.
这里，Q_{L} 表示传递到高速轴上的驱动系机械扭矩损耗（本身可能旋转速度和扭矩的函数）。发电机转速为 $\omega_{\mathrm{g}}=G\varOmega$，其中 G 为齿轮箱传动比。

This torque-speed relationship is shown schematically in Figure 8.3 as the curve B1–C1. Although it represents the steady-state solution for optimum C_{p} , it can also be used dynamically to control generator torque demand as a function of measured generator speed. In many cases, this is a very benign and satisfactory way of controlling generator torque below rated wind speed.
图 8.3 示意性地显示了转矩-转速关系曲线 B1–C1。虽然它代表了最佳 C_{p} 的稳态解，但也可以动态地用于控制与测得的发电机转速相关的发电机转矩需求。在许多情况下，这是一种在额定风速以下控制发电机转矩的温和且令人满意的方案。

For tracking peak C_{p} below rated in a variable-speed turbine, the quadratic algorithm of Eq. (8.4) works well and gives smooth, stable control. However, in turbulent winds, the large rotor inertia prevents it from changing speed fast enough to follow the wind, so rather than staying on the peak of the C_{p} curve it will constantly fall off either side, resulting in a lower mean C_{p} . This problem is clearly worse for heavy rotors, and also if the C_{p}-\lambda curve has a sharp peak. Thus, in optimising a blade design for variable-speed operation, it is not only important to try to maximise the peak C_{p} , but also to ensure that the C_{p}-\lambda curve is reasonably flat-topped. 为了跟踪额定转速以下的最大 C_{p} 值，公式(8.4)中的二次算法效果良好，能提供平稳、稳定的控制。然而，在湍流风况下，大型转子的惯性阻碍了其快速改变转速以跟踪风速，因此它无法始终保持在 C_{p} 曲线的峰值上，而是会不断偏离两侧，导致平均 C_{p} 值降低。这种问题对于重型转子尤其明显，并且当 C_{p}-\lambda 曲线具有尖锐峰值时也会加剧。因此，在优化用于可变速运行的叶片设计时，不仅要努力最大化峰值 $C_{p}$，还要确保 C_{p}-\lambda 曲线具有较为平坦的峰顶。

It is possible to manipulate the generator torque to cause the rotor speed to change faster when required, so staying closer to the peak of the C_{p} curve. One way to do this is to modify the torque demand by a term proportional to rotor acceleration (Bossanyi 1994):
在需要时，可以通过调整发电机转矩，使转子转速变化更快，从而更接近 C_{p} 曲线的峰值。一种方法是，通过一个与转子加速度成比例的项来修改转矩需求（Bossanyi 1994）：

Figure 8.3 Schematic torque-speed curve for a variable-speed pitch-regulated turbine
图 8.3 可变速调桨涡轮机示意扭矩-转速曲线

\mathcal{Q}_{g}=\frac{1}{2}\frac{\pi\rho R^{5}C_{p}}{\lambda^{3}G^{3}}\omega_{g}^{2}-Q_{L}-B\dot{\omega}_{g}

where B is a gain that determines the amount of inertia compensation. For a stiff drive train, and ignoring frequency converter dynamics, the torque balance gives
其中，B 是一个增益，用于确定惯性补偿量。对于刚性驱动系统，且忽略变频器动力学，扭矩平衡方程为：

I\dot{\boldsymbol\Omega}=Q_{a}-G Q_{g}

where I is the total inertia (of rotor, drive train and generator, referred to the low-speed shaft) and \varOmega is the rotational speed of the rotor. Hence
其中，I 为总惯量（转子、传动装置和发电机的总惯量，参考低速轴），\varOmega 为转子的转速。因此，

(I-G^{2}B)\dot{\Omega}=Q_{a}-\frac{1}{2}\frac{\pi\rho R^{5}C_{p}}{\lambda^{3}G^{2}}\omega_{g}^{2}+G Q_{L}

Thus, the effective inertia is reduced from I to I-G^{2}B , allowing the rotor speed to respond more rapidly to changes in wind speed. The gain B should remain significantly smaller than I/G^{2} otherwise the effective inertia will approach zero, requiring huge power swings to force the rotor speed to track closely the changes in wind speed.
因此，有效惯量从 I 降低到 I-G^{2}B ，使得转子速度能够更快地响应风速变化。增益 B 应该显著小于 $I/G^{2}$，否则有效惯量将趋近于零，需要巨大的功率波动才能使转子速度紧密跟踪风速变化。

Another possible method is to use available measurements to make an estimate of the wind speed, calculate the rotor speed required for optimum C_{p} , and then use the generator torque to achieve that speed as rapidly as possible. The aerodynamic torque can be expressed as
另一种可行的方法是利用现有的测量数据来估算风速，计算出实现最佳 C_{p} 所需的转子转速，然后利用发电机扭矩以尽可能快的速度达到该转速。空气动力学扭矩可以表示为：

Q_{a}=\frac{1}{2}\rho A C_{q}R U^{2}=\frac{1}{2}\rho\pi R^{5}\varOmega^{2}C_{q}/\lambda^{2}

where R is the turbine radius, \varOmega the rotational speed, and C_{q} the torque coefficient. If drive train torsional flexibility is ignored, a simple estimator for the aerodynamic torque is
其中，R 为涡轮半径，\varOmega 为转速，C_{q} 为扭矩系数。如果忽略驱动系扭转柔性，一个简单的气动扭矩估算方法是：

{Q_{a}}^{*}=G Q_{g}+I\dot{\varOmega}=G Q_{g}+I\dot{\omega}_{g}/G

where I is the total inertia. A more sophisticated estimator could take into account drive train torsion, etc. From this it is possible to estimate the value of the function F(\lambda)=C_{q}(\lambda)/\lambda^{2} as
其中，I 为总惯性矩。更复杂的估计器可以考虑驱动系扭矩等因素。由此，可以估算出函数 F(\lambda)=C_{q}(\lambda)/\lambda^{2} 的值，如：

F^{*}(\lambda)=\frac{Q_{a}^{*}}{\frac{1}{2}\rho\pi R^{5}(\omega_{g}/G)^{2}}

Knowing the function F(\lambda) from steady state aerodynamic analysis, one can then deduce the current estimated tip speed ratio \lambda^{*} (see also Section 8.3.16 for a better estimation method). The desired generator speed for optimum tip speed ratio can then be calculated as
了解通过稳态气动分析得到的函数 F(\lambda) 后，就可以推导出当前的估计叶尖速度比 $\lambda^{*}$（参见第 8.3.16 节以获得更好的估计方法）。然后，可以计算出为了获得最佳叶尖速度比所需的发电机转速，如下所示：

\omega_{d}=\omega_{g}\widehat{\lambda}/\lambda^{*}

where \widehat{\lambda} is the optimum tip speed ratio to be tracked. A simple PI controller can then be used, acting on the speed error \omega_{\mathrm{g}}-\omega_{\mathrm{d}} , to calculate a generator torque demand that will track \omega_{\mathrm{d}} . The higher the gain of PI controller, the better will be the C_{p} tracking, but at the expense of larger power variations. Simulations for a particular turbine showed that a below rated energy gain of almost 1\% could be achieved, with large but not unacceptable power variations.
其中，\widehat{\lambda} 为需要跟踪的最佳叶片尖速比。 随后，可以使用一个简单的 PI 控制器，基于转速误差 \omega_{\mathrm{g}}-\omega_{\mathrm{d}} ，计算出能够跟踪 \omega_{\mathrm{d}} 的发电机扭矩需求。 PI 控制器的增益越高，C_{p} 跟踪效果越好，但会以更大的功率波动为代价。 对特定风机的仿真表明，可以在额定功率以下实现近 1\% 的能量增益，同时伴随较大的，但尚可接受的功率波动。

Holley et al. (1999) demonstrated similar results with a more sophisticated scheme, and also showed that a perfect C_{p} tracker could capture 3\% more energy below rated, but only by demanding huge power swings of plus and minus three to four times rated power, which is totally unacceptable.
霍利等人在1999年的研究中，使用一种更为复杂的方案也得出了相似的结果，并且表明一个完美的$C_{p}$跟踪器可以在额定功率以下捕获3%更多的能量，但这需要正负三到四倍于额定功率的巨大功率波动，这是完全不可接受的。

Because such large torque variations are required to achieve only a modest increase in power output, it is usual to use the simple quadratic law, possibly augmented by some inertia compensation as in Eq. (8.5) if the rotor inertia is large enough to justify it.
由于为了仅实现温和的功率输出提升，需要如此大的扭矩变化，通常采用简单的二次律，如果转子惯性足够大，可以考虑通过惯性补偿（如公式(8.5)所示）进行修正。

As turbine diameters increase in relation to the lateral and vertical length scales of turbulence, it becomes more difficult to achieve peak C_{p} anyway because of the non-uniformity of the wind speed over the rotor swept area. Thus if one part of a blade is at its optimum angle of attack at some instant, other parts will not be. 随着涡轮机直径相对于湍流的横向和纵向尺度不断增大，由于扫风面积的风速不均匀性，即使如此，要实现峰值 C_{p} 变得越来越困难。因此，如果叶片的一部分在某一时刻处于最佳攻角，那么其他部分就不会如此。

In most cases, it is actually not practical to maintain peak C_{p} from cut-in all of the way to rated wind speed. Although some variable-speed systems can operate all of the way down to zero rotational speed, this is not the case with limited range variable-speed systems based on the widely used doubly fed induction generators. These systems only need a power converter rated to handle a fraction of the turbine power, which is a major cost saving. This means that in low wind speeds, just above cut-in, it may be necessary to operate at an essentially constant rotational speed, with the tip speed ratio above the optimum value.
在大多数情况下，维持峰值 C_{p} 从启动风速一直到额定风速实际上并不现实。虽然一些变速系统可以运行到零转速，但基于广泛使用的双馈感应发电机（DFIG）的限幅变速系统则不行。这类系统只需要一个能够处理风机功率一部分的功率转换器，这能节省大量成本。这意味着在低风速下，略高于启动风速时，可能需要以一个基本恒定的转速运行，并且叶片速度比高于最佳值。

At the other end of the range, it is usual to limit the rotational speed to some level, usually determined by aerodynamic noise constraints or blade leading-edge erosion, which is reached at a wind speed that is still some way below rated. It is then cost-effective to increase to torque demand further, at essentially constant rotational speed, until rated power is reached. Figure 8.3 illustrates some typical torque-speed trajectories, which are explained in more detail below. Turbines designed for noise-insensitive sites may be designed to operate along the optimum C_{p} trajectory all of the way until rated power is reached. The higher rotational speed implies lower torque and in-plane loads, but higher out-of-plane loads, for the same rated power. This strategy might be of interest for offshore wind turbines.
在转速范围的另一端，通常需要将旋转速度限制在某个水平，这个水平通常由气动噪声约束或叶片前缘侵蚀决定，而达到该速度的风速仍然低于额定风速。此时，在基本恒定的旋转速度下，进一步增加扭矩需求是经济有效的，直至达到额定功率。图 8.3 说明了一些典型的扭矩-转速轨迹，将在下面更详细地解释。为噪声不敏感场地设计的风机，可以设计成沿着最佳 C_{p} 轨迹运行，直至达到额定功率。更高的旋转速度意味着在相同额定功率下，扭矩和面内载荷降低，但面外载荷增加。这种策略可能对海上风力涡轮机具有吸引力。