Dispatchable load (DL) participating in demand response will reduce system power deviation and promote renewable energy consumption. But with limited regulation capability

the response of DL is uncertain

which is undesirable to the market participators. A punishment mechanism for response deviation can be formulated. But a loose punishment is not effective

and a severe punishment will reduce the enthusiasm of DL supplier. Taking the response deviation as a random contributing factor

a stochastic optimization model of DL response amount and punishment price is proposed based on the relationship between response price and amount

punishment price and response deviation. With the expectation model

it is transformed to deterministic optimization model. Finally

the effectiveness of the proposed models is verified by numerical results.