Thunderbolt 3 offers this already using USB Power Delivery of up to 100W
Thunderbolt 3 was developed by Intel and uses USB-C connectors. It is the first generation to support USB. Compared to Thunderbolt 2, Intel's Thunderbolt 3 controller (codenamed Alpine Ridge) doubles the bandwidth to 40 Gbit/s (5 GB/s), halves power consumption, and simultaneously drives two external 4K displays at 60 Hz (or a single external 4K display at 120 Hz, or a 5K display at 60 Hz when using Apple's implementation for the late-2016 MacBook Pros) instead of just the single display previous controllers can drive. The new controller supports PCIe 3.0 and other protocols, including DisplayPort 1.2 (allowing for 4K resolutions at 60 Hz).
Thunderbolt 3 has limited power delivery capabilities on copper cables and no power delivery capability on optical cables. Using USB-C on copper cables, it can incorporate USB Power Delivery, allowing the ports to source or sink up to 100 watts of power. This eliminates the need for a separate power supply from some devices. Thunderbolt 3 allows backwards compatibility with the first two versions by the use of adapters or transitional cables.
However, your PC would obviously need a Thunderbolt connection.
If your current PC has only DVI or HDMI outputs, as your post seems to suggest, then as neither of those offer sufficient power for a monitor, then your existing setup would not accommodate your request.
HDMI 1.4a can supply power, but the port supplies only 50 mA at 5 V DC over pin 18.
Apart from Apple's 27" Thunderbolt capable monitor, which they have just discontinued (although you may be able to still pick up some discounted remaining stock), there aren't that many on the market. LG recently announced two models:
From LG teases new Apple-compatible Thunderbolt 3 monitors including '5K UltraWide' model:
The 34WK95U is a 34-inch model with 5,120-by-2,160 resolution, high
dynamic range, and LG's "Nano IPS" technology, which is said to boost
the "intensity and purity" of colors. Thunderbolt 3 lets the monitor
handle 5K images at 60 hertz, and connect laptops like the MacBook Pro
without an additional power source.
The 32UK950 will offer a similar featureset, but in a more
conventional aspect ratio and with a slightly smaller 32-inch screen.
The display is said to hit 98 percent of the DCI-P3 color gamut, with
peak brightness of 600 nits, and support a second 4K monitor through