# Advanced Control and Fault Detection Strategies for District Heating and Cooling Systems--A Review
## 2 State of the Art Control Strategies for District Heating (DH) and District Cooling (DC) Systems
### Heat/Cold Load Forecasting in DHC Networks
To set the best hyper-parameter of these models in this work, the authors used an exhaustive search over specified values, whereas in the following paper [36], they used the tree-structured Parzen estimator, that is, a Bayesian optimization algorithm. Assessing almost the same models on the same dataset, it results that all the models improved their performance a lot, but the best one is still the deep ANN that achieved a MAPE of 8.08%. Considering the assessment of the same models on the DH network in Karlshann (peak capacity of about 50-60 MW) that is much larger than the one in Rottne, the performance of all the models improves, and the MAPE is more or less reduced by half. In the framework of the OPTi project [33], ML-based black-box models (random forest) to forecast the load of buildings connected to the DH system of Lulea (Sweden) have been studied in [37], whereas grey-box models have been developed in [38]. SVM, multiple linear regression (MLR), and feed-forward ANN performed similarly and better than regression trees in [PERSON] et al. (2016) [39] where on average worse results have been obtained in  
Figure 3: Heat load of a DH system located in Northern Italy for two consecutive weeks from 10 to 24 January 2016.  
forecasting loads of commercial buildings with respect to residential ones using these black-box ML models. [PERSON] et al. (2016) [40] achieved better results using SVM for hourly load forecasting concerning partial least square (PLS) and random forest (RF). The mean absolute percentage error (MAPE) over the testing dataset of one week achieved with SVM was 3.43%. In [41], an adaptive neuro-fuzzy inferences system (ANFIS) has been developed using only previous values of thermal load, whereas a different approach has been adopted in [42], where it has been demonstrated that a feature fusion long short-term memory (FFLSTM) deep neural network model outperforms seven different ML state-of-art models. Regarding the load forecast in district cooling (DC) systems, [PERSON] et al. (2008) [43] demonstrated the improvement achieved using a recurrent neural network (RNN) with respect to a three-layered neural network (TLNN) at the expenses of a slightly higher processing time. The RNN architecture employs the sigmoid activation function in both inner and output layers and the 33 inputs consist of the previous 24h values of the cooling load, day of the week, and daily minimum and maximum forecasted ambient temperature. In the past, statistical time series forecasting methods have been also successfully applied to DHC systems. For instance, statistical and physical models have been combined in [PERSON] and [PERSON] (2006) [44] according to a grey-box approach. Auto-regressive models with exogenous inputs (ARX) has been used by [PERSON] (2008) [45], whereas a seasonal autoregressive integrated moving average (SARIMA) model have been developed in [PERSON] et al. (2011) [46] and incorporated into a state space framework where on-line load forecasting is obtained exploiting a Kalman filter. Another solution has been adopted by [PERSON] (2010) [47] that applied the Box-Jenkins method to model the stochastic behavior of the social component of a DH load and a cubic function for the outdoor temperature-dependent component. At the substation level, a linear regression algorithm is proposed in [48] to disaggregate the SH and DHW parts from the total load to be used for forecasting purposes in the framework of the H2020 RELATED project [49]. However, this model performed worse than an ensemble of decision trees (DT) model. Similarly, a compact black-box model of the building based on a linear system has been developed in [PERSON] et al. (2019) [50]. The latter uses the predicted average temperature of the day, the average and the minimum and maximum temperature of the previous day as inputs, and it is able to provide the peak and steady-state load and the peak duration as outputs.