With the exponential growth of the Power IoT, the dynamic access of massive terminal devices and their resource-constrained nature poses dual challenges to secure communication systems. Traditional key exchange protocols, relying on high-complexity computations and centralized architectures, struggle to meet the real-time and low-Power requirements of terminals like smart meters. This paper proposes a lightweight dynamic key exchange protocol based on Chebyshev polynomials. By leveraging the recursive and semigroup properties of Chebyshev polynomials, the protocol simplifies key negotiation into three polynomial computations, replacing traditional complex operations. This significantly reduces computational load on terminals, and ensures terminal anonymity. Formal security analysis under the random oracle model rigorously verifies the protocol's security. Compared to typical elliptic curve schemes, the computational load on terminal devices is reduced by approximately 70%. This solution provides a highly adaptable, low-energy-consumption security infrastructure for Power IoT.