It's natural that investors could be feeling a bit shaken up after the second-biggest bank failure in U.S. history. And given that other banks have been experiencing problems in the wake of that event, those jitters are even more justifiable.

If you're worried about how the banking sector turmoil will impact your investments, let me help ease your mind. Here are three stocks you can add to your portfolio that shouldn't skip a beat even if the situation worsens.

1. Brookfield Renewable 

The sun will keep shining regardless of what happens with the banking industry, and the wind will keep blowing. As a result, investors who own renewable energy stocks shouldn't have anything to worry about. Brookfield Renewable (BEP 0.76%) (BEPC 0.89%) stands out as one of the best renewable energy stocks around.

You can invest in Brookfield Renewable in a couple of ways. The limited partnership trades under the BEP ticker, while the company has a traditional corporate structure that's listed under the BEPC ticker. They're the same business under the hood, though. Both stocks pay attractive dividends.

More importantly, Brookfield Renewable has solid growth prospects. Demand for renewable energy should increase significantly over the coming years and decades as countries and corporations across the world work to reduce their carbon emissions.

Brookfield Renewable is poised to capitalize on this trend. Its operational capacity currently totals around 25 gigawatts, and its development pipeline is close to 110 gigawatts, with a heavy focus on solar.

2. Dollar General

Let's imagine for a second that the recent issues in the banking sector spread and ultimately drag down the entire U.S. economy. I'm not saying that's going to happen, by the way. This is just a hypothetical exercise. But if this scenario did unfold, it would likely impact many Americans financially. That would give people more incentive to shop for bargains on essential products. This is a bleak hypothetical future, but one in which Dollar General (DG -0.24%) would thrive.

The discount retailer operates 19,147 stores across the U.S., and it also recently opened its first store in Mexico. CEO Jeff Owen said on the fourth-quarter conference call last week that Dollar General plans to open another 19 stores in northern Mexico by the end of 2023.

The company projects net sales growth of 5.5% to 6% this year despite macroeconomic challenges and having one less week in its fiscal 2023 than it did in its fiscal 2022. Dollar General's private brands continue to enjoy strong sales growth. These lower-cost brands should experience even higher demand during an economic downturn.

Dollar General doesn't need economic troubles to perform well, though. Its stock trounced the S&P 500 during the boom years of the previous decade. Green noted in the Q4 call that Dollar General has demonstrated over the nearly three decades he's been with the company that it can effectively serve customers regardless of what's going on with the economy.

3. Vertex Pharmaceuticals

Assume that the dire scenario described above happens, with a banking meltdown crippling the rest of the economy. Do you think that patients afflicted with cystic fibrosis, a debilitating genetic disease, would willingly stop taking their medications? Would doctors quit prescribing those drugs or insurers stop paying for them? Of course not. That's why Vertex Pharmaceuticals (VRTX -1.35%) shouldn't be impacted by any spread of the issues that have lately been impacting some banks.

Vertex sells the only approved therapies that treat the underlying cause of cystic fibrosis. There is currently no competition for them. Its closest rivals are at best several years away from even having a shot at challenging Vertex. By that time, Vertex should have an even more powerful therapy on the market for the disease.

The big biotech also has its sights set on indications beyond cystic fibrosis. Vertex and its partner, CRISPR Therapeutics, could soon win regulatory approvals for exa-cel as a treatment for two rare blood disorders -- sickle cell disease and transfusion-dependent beta-thalassemia.

Vertex has a couple of other promising non-cystic fibrosis programs in phase 3 clinical trials. VX-548 is a non-opioid therapy for alleviating acute pain. Inaxaplin targets APOL1-mediated kidney disease, an indication that affects more patients worldwide than cystic fibrosis does. With its growing cystic fibrosis franchise plus multiple promising late-stage candidates, I think that Vertex's share price could at least double over the next seven years