Volume One, Chapter 12: The Weibull Distribution

Page (1/3)

The so-called "Weibull distribution" is a continuous probability distribution model widely used to describe the distribution of random variables. In the design and layout of wind farms, the Weibull distribution enables the characterization of wind speed frequency distribution based on wind speed data, optimizing the placement and spacing of turbines to maximize wind energy utilization.

Essentially, the wind speed frequency distribution is the statistical probability distribution of wind speeds. It serves as a core indicator measuring the characteristics of wind energy resource distribution, intuitively reflecting the probability distribution of various wind speed values over a given period within a wind farm.

During the layout design process of a wind farm, optimization must be based on precise wind speed distribution data to ensure the efficiency and economic viability of the project reach their optimal levels.

The practical application of the Weibull distribution involves first collecting a year’s worth of wind speed data for the region. Then, using statistical methods such as Maximum Likelihood Estimation (MLE) or linear regression, two key parameters of the Weibull distribution—the shape parameter (k) and the scale parameter (A)—are estimated.

Accurate estimation of these two parameters is critical for the subsequent calculation of wind energy density. Once these parameters are obtained, the Weibull function can be employed to calculate wind energy density, thereby providing a more precise scientific basis for wind farm layout design and wind energy assessment.

Maimaiti, who had participated in wind farm planning and layout work before, was naturally no stranger to the Weibull distribution. However, in his era, wind power theory had long matured in China. Coupled with the rapid development of computer computing power and the Internet of Things, the tedious and complex task of data calculation was directly delegated to computers. They only needed to provide practical advice based on the resulting data.

Accustomed to the computer technology of later generations, this was Maimaiti's first time witnessing the grand scene of manually calculating the Weibull distribution, and he couldn't help but gain a newfound respect for Ma Wenbin.

Watching Ma Wenbin, his forehead beaded with sweat, painstakingly calculating the final step of the scale parameter—“taking the mean of the wind speed data raised to the power of the shape parameter, then raising that mean to the inverse of the shape parameter to obtain a preliminary estimate of the scale parameter”—Maimaiti hesitated to interrupt his train of thought.

Although he had noticed that Ma Wenbin neglected the important factor of wind energy density in the Weibull distribution calculation, under the current circumstances, it wasn't a major issue.

After about fifteen more minutes, Ma Wenbin suddenly exhaled deeply, exasperated yet gallantly tossing the nearly worn-down pencil onto the ground. Standing up, he pointed to a set of data he had derived and proudly declared:

Page (2/3)

“I wasn’t wrong, right, junior sister? Here are the data: the shape parameter for Zone I is 2.28, which is significantly higher than the 1.98 in Zone IV B, proving that the wind speed in this area is more stable. Its scale parameter is 11.966 meters per second. But I don’t know what the wind speed is in Zone IV B that you mentioned?”

Zhang Yan was equally astonished by Ma Wenbin’s manual handling of the function equations, her mouth agape in surprise. After watching her senior’s delight for a long while, she finally uttered, “Alright… you win, senior brother.”

Yet, seeing her senior’s triumphant expression, Zhang Yan’s mind swiftly turned, and with a mischievous smile, she said, “But this only proves that Zone I is more suitable for installing wind turbines compared to Zone IV B. Senior brother, did you forget one thing?”

“What thing?” Ma Wenbin blinked in surprise.

Zhang Yan giggled playfully, blinking coquettishly as she scrutinized Ma Wenbin for a moment before saying, “Zone I borders Chaiwopu Lake, right? The Chaidong Substation’s grid seems to only connect as far as the forest farm over there, doesn’t it? You’d have to bypass the forest farm to lay new circuits, then install another transformer and build a new substation to supply power for your grid connection and testing. Are you sure you’ve coordinated this with the Electric Power Bureau in advance?”

“This…” Ma Wenbin stammered, turning to Wang Xiquan beside him. From Wang’s disappointed glance, the earlier joy vanished, replaced by a long sigh and an impatient grumble: “Forget it then!”

Only then did Ma Wenbin notice the black, round head beside Wang Xiquan. Upon focusing, he realized Maimaiti had quietly stood there all along and said somewhat irritably, “When did you suddenly show up here, Balangzi?”

“I’ve been here since you started calculating the Weibull distribution,” Maimaiti answered earnestly.

If he hadn’t mentioned it, Ma Wenbin might have been spared further embarrassment. But now, his face grew even longer. “We’re discussing serious matters here. Why come to stir up trouble?”

“I’m here to observe and learn,” Maimaiti smiled. “I just happened to pass by and saw Teacher Ma giving an on-site demonstration of the Weibull distribution calculation. Such a rare opportunity—I definitely couldn’t miss it!”

Uninformed onlookers might think Maimaiti was paying a compliment, but Wang Xiquan immediately caught the sarcasm in his words.

Taking the role of an instigator, Wang chuckled, “Ha ha, Wenbin, you always say Maimaiti is just a technical school worker, lacking formal systematic education. Now he’s come specially to learn from you. How can you just chase him away? And you’re a teacher, no less.”

“Well, that’s different… that was at university. Now we’re discussing… hey!”

Page (3/3)

Ma Wenbin, a straightforward man from Northwest China, was never known for slick words. In such an awkward situation, his verbal skills faltered, and after a few complaints of “Forget it, forget it!” he stowed the papers and the pencil he’d dropped on the ground into the bag on the tractor’s rear seat and retreated alone to a crooked tree to smoke in solitude.

Seeing this, all but Maimaiti shared a smile—Zhang Yan and Wang Xiquan exchanging knowing glances.

“Senior brother, really, when will you ever change that temper of yours?” Zhang Yan called out playfully. When he turned his back and ignored her, she laughed again, casting a curious glance at Maimaiti, who remained indifferent.

“Oh? So you’re Maimaiti? I just heard Teacher Wang mention you. He said you have an international perspective and are an indispensable talent! From what he said, I thought you’d be like my senior brother—some old scholar. Didn’t expect you to be so young.”

Zhang Yan greeted him warmly, unaware of any impropriety in her words.

Maimaiti didn’t mind at all. After all, in this era, certain words had yet to acquire the ambiguous meanings they would in later times.

“Ah, I just graduated from technical school… Zhang, Sister Zhang, nice to meet you. I’m just interested in this stuff; professionally, I’m no match for you.”

“Oh, still humble! But I like being called ‘Sister.’” Zhang Yan covered her mouth, chuckling, then gave a sly smile. “You say you’re interested in this—then tell me, where is the best spot to place the experimental wind turbine?”

Maimaiti’s expression immediately turned difficult.

It wasn’t that he had no idea, but without actual data, a topographic map of the entire area, or a wind rose diagram for reference, it was like a cook trying to make a meal without any ingredients.

Even if he wanted to offer advice, he didn’t know where to begin, so he tactfully replied, “Well… Sister Zhang, you’re making it hard for me. How could I dare to show off in front of you?”