The basis for the virtual power plant (VPP) pricing algorithm is a joint stochastic process for the power price and the gas price. Instead of defining a stochastic differential equation for the spark spread directly the spark spread is then given by the difference between the power price and the gas price times the VPP heating rate.
The Kluge model will be used to define the power price process , an exponential Ornstein-Uhlenbeck will describe the gas price 
where is a Poisson process with jump intensity . To match the power forward curve the seasonal function is given by :
To be consistent with the gas forward curve the seasonal function is defined by
The Feynman-Kac theorem can be applied to derive the corresponding three-dimensional partial integro differential equation
In general at least one further dimension is needed to keep track of the state of the virtual power plant. Therefore solving this model using finite difference methods will lead to a four-dimensional PIDE problem.
The following diagram shows an one year example path for the power and the gas price based on the freely available Kyos example forward curves. The sample parameterization is affected by  for the power process and  for the gas process.
 T. Kluge, Pricing Swing Options and other Electricity Derivatives
 G. Fusai, A. Roncoroni, Implementing Models in Quantitative Finance: Models and Cases, Chapter 19, ISBN: 978-3-540-22348-1