# A Novel Model for Accurate Daily Urban Gas Load Prediction Using Genetic Algorithms
## 3 Mathematic Model  
### Establishment of MWP-DLP Model  
MWP is a combination variable of various weather factors. In the field of gas load, a series of factors such as temperature, solar radiation, wind speed, and the change of building base temperature were comprehensively considered to obtain the MWP index, so that the gas load and MWP index changed linearly, so as to predict the future gas load, which is widely used in local pipeline network specifications in European countries. STD is a commonly used indicator to describe the MWP at present [41; 42; 43; 44; 45]. This indicator is a  
Figure 4: Daily gas load curve of the spring festival and before and after 5 days.  
Figure 3: Comparison of daily gas load curves of the National Day and 5 days before and after three consecutive years.  
measure used to quantify the energy demand required to heat a building, i.e., when the temperature is low, the user needs to heat it.  
The MWP-DLP model is based on the temperature difference between the base temperature of the building and the ambient temperature to determine the energy demand. In the MWP-DLP model, the influences of cumulative temperature, solar radiation, wind, and building foundation temperature on the daily gas load are considered, and the coefficients of cumulative temperature, solar radiation and wind are modified to change the STD value. Thus, the daily gas load is predicted.  
In the MWP-DLP model, the objective function is the daily gas load value, and the calculation formula is shown in Equation (1).  
\[F_{2}=a_{0}+a_{1}(D_{i}+\beta_{1}\cdot WS_{i}\cdot D_{i}) \tag{1}\]  
where \(F_{2}\) is the predicted value of gas daily load, \(10^{4}\) m\({}^{3}\). \(WS_{i}\) is the day wind value, knot. \(D_{i}\) is the degree-day number of the gas network on the second day, \({}^{\circ}\)C. \(a_{0}\), \(a_{1}\), \(\beta_{1}\) is a dimensionless coefficient.  
\(D_{i}\) was used to estimate the control gas consumption. Based on \(D_{i}\), the influence of variable building base temperature was considered using transformation function, and the influence coefficients of solar radiation and wind were improved. The calculation expression is shown in Equation (2).  
\[D_{i}=\begin{cases}0&T_{a,i}>T_{b,low}\\ \frac{\left(T_{a,i}-T_{b,low}\right)^{2}}{2\left(T_{b,low}-T_{b,low}\right)}&T _{b,low}<T_{a,i}<T_{b,up}\\ \left(T_{b,up}+T_{b,low}\right)/2-T_{a,i}&T_{a,i}<T_{b,low}\end{cases} \tag{2}\]  
where \(T_{b,low}\) is the lower limit of building foundation temperature, \({}^{\circ}\)C. \(T_{b,up}\) is the lower limit of building base temperature, \({}^{\circ}\)C. \(T_{a,i}\) is the day \(i\) temperature based on the cumulative effect of solar radiation and temperature, \({}^{\circ}\)C.  
\(T_{a,i}\) can be obtained by Equation (3).  
\[T_{a,i}=T_{sr,i}+T_{eff,i} \tag{3}\]  
where \(T_{sr,i}\) is the temperature of the isothermal effect of solar radiation on day \(i\), \({}^{\circ}\)C. \(T_{eff,i}\) is the temperature generated by the cumulative effect of temperature on day \(i\), \({}^{\circ}\)C. \(T_{sr,i}\) and \(T_{eff,i}\) are calculations such as Equations (4) and (5).  
\[T_{sr,i}=\beta_{2}GR_{i} \tag{4}\]  
\[T_{eff,i}=(1-\varphi_{1})T_{AVG,i}+\varphi_{1}T_{AVG,i-1}\hskip 28.452756 pt0 \leq\varphi_{1}\leq 1 \tag{5}\]  
To sum up, the daily gas load prediction model based on MWP-DLP was established by considering the change of building foundation temperature and modifying the cumulative temperature, solar radiation, and wind coefficient.