U.N. peacekeeping has come a long way in the 20 years since the Rwandan genocide, the U.S. ambassador to the United Nations, Samantha Power, told an audience at the American Enterprise Institute on Friday: “This is not your mother’s, or your grandmother’s, peacekeeping.”

Thank goodness for that, since the image that many Americans have of the international force in blue helmets is of their underfunded unit running out on some 2,000 civilians who sought refuge in the Don Bosco School in Kigali in spring 1994.

Power told the whole horrible story again at the conservative think tank: “Hutu militias had surrounded the school, chanting ‘Hutu power,’ drinking banana beer and brandishing machetes. Yet when orders came for the peacekeepers to evacuate, they followed orders. They had to shoot over the heads of the Tutsis to get out.” And after they did, “militia members walked in, butchering virtually everyone inside.”

But “that was then,’’ said Power, who before she went to work for President Obama wrote the Pulitzer Prize-winning “A Problem from Hell: America and the Age of Genocide.”

“Now,’’ she said, “we have U.N. peacekeeping opening its gates” to more than 100,000 people displaced by the civil war in South Sudan, where people living “foot-deep in filthy water” told her in August that they were just glad to have drinking water and physical safety.

In the old days, peacekeepers went only where they were invited, by mutual consent of all parties, to monitor cease-fire agreements. Now, they’ve been asked to disarm rebel groups in the Democratic Republic of Congo, escort shipments of food and medicine in South Sudan and protect civilians amid 10 ongoing conflicts. There are a record 16 missions around the world, involving 130,000 peacekeepers, up from 75,000 a decade ago.

One thing that hasn’t changed so much is that the United States still pays much of the tab, now 28.3 percent of the total U.N. bill. Why is that, her AEI interlocutor, Danielle Pletka, wanted to know at the outset.

Power had a lot to say about that — and had to speed-walk through her remarks, since she arrived 20 minutes late from a Cabinet meeting, and then had a plane to catch.

Of course, she made the moral case: “We do not want to live in a world where more than 9,000 kids are recruited in less than a year to become child soldiers, as has happened recently in South Sudan. We do not want to live in a world where religious or ethnic communities who lived together for decades in harmony, such as the Muslims and Christians in the Central African Republic, learn to hate and fear one another.”

But she also argued, on practical and financial grounds, that such multi­national efforts are more likely to be seen as legitimate. And they help “address the free-rider problem we see today in so many matters of international security — from the spread of Ebola to the rise of ISIL to the recruitment of foreign terrorist fighters. . . . Peacekeeping gets other countries to stand up, rather than stand by.”

Sometimes, that is. A March report by the U.N.’s internal oversight office found that in 507 attacks on civilians in 2010-2013, peacekeepers almost never used force to intervene. “This is unacceptable,” the ambassador said.

To change that, we have to get more developed countries to deploy more troops — and we might need to send more than the 1,400 we have now in Sinai and Bosnia. And, of course, no talk on the United Nations would be complete without an argument for “bold institutional reforms” and more oversight.

Power only had time to take a few questions, so it’s not surprising she didn’t get one on Ebola, although in closing, she did mention her recent trip to West Africa to assess the international response to the outbreak. “Long before Ebola hit Sierra Leone and Liberia, brutal civil wars did,’’ she said, and we wouldn’t want to imagine the toll of the disease without peacekeeping efforts in both counties, still ongoing in Liberia: “How would Sierra Leone’s military have been able to help build Ebola treatment units or run safe burial operations, as they have done, if they were tied down fighting rebels?”

Power, who tweeted photos of herself having her temperature taken at the airport when she returned from the trip, has been self-monitoring since then.

After she’d left for another airport, Pletka praised Power’s talk but said “the problem is that peacekeeping is a marginal game compared to the challenges we face. And if anyone thinks that it’s going to solve the problems in the Middle East, they’ve got a big surprise coming.”