# Joint Acquisition Time Design and Sensor Association for Wireless Sensor Networks in Microgrids
## 3 System Model  
In this section, we describe the system model. As shown in Figure 1, we consider a microgrids system based on a smart factory. The system includes five types of facilities: a workshop, a central energy plant, a wind generator, an integrated data network, photovoltaics and offices. New energy facilities such as wind generators and photovoltaics intermittently generate electricity to reduce the impact on the center-dependence of the grid. To ensure the stable operation of the entire microgrid system, a WSN consisting of \(N\) sensors is deployed. The set of sensors are denoted as \(\mathcal{N}\), where \(|\mathcal{N}|=N\). Due to the randomness of the deployment location in the practical scene, all sensor nodes are deployed through the Poisson point process (PPP) with a density of \(\rho\) in this paper, including temperature, voltage, current, light intensity and wind speed, etc., which presents a relatively random sensor deployment to cover more application scenarios. Of course, wind speed sensors and light intensity sensors are mainly deployed near wind generators and photovoltaics, respectively, in actual scenarios. In order to obtain effective topology control, all sensor nodes are divided into \(K\) clusters. The sensor nodes in each cluster will select one of them to become the CH, and the other sensor nodes will become CMs. The set of CHs are denoted as \(\mathcal{K}\), where \(|\mathcal{K}|=K\) and \(\mathcal{Z}=\left\{\mathcal{Z}_{1},\cdots\mathcal{Z}_{j},\cdots,\mathcal{Z}_ {K}\right\}\), \(\sum_{m\in\mathcal{K}}|\mathcal{Z}_{m}|=N-K\). The CMs collect data and transmit it to the CH. The CH is responsible for collecting the data from the CMs and transmitting them to the BS via the uplink channel after fusion. Therefore, we have the following assumptions for the entire WSN. First, once the sensor is deployed, the location will no longer change. Secondly, all sensors are homogeneous and have the same data processing capacity and energy consumption model, but the size of the data packets generated by each sensor in each round is different, which is related to the data acquisition time. Finally, all sensors contain the same initial energy, and the energy of the data transmission gradually decreases. When the energy is exhausted, the node is considered to be dead. Energy Consumption Model  
The sensor operating time is mainly divided into two parts. The first part is data acquisition. At this stage, each sensor collects a certain bit of data and waits to be transmitted to the CH; the second part is the data transmission and reception stage, the CMs upload  
Figure 1: A microgrids state detection system based on WSN. the collected data through the wireless channel, and CH receives the data and processes data from CMs. In the data acquisition stage, the energy consumption of the sensor node \(n\) can be expressed as follows:  
\[E_{n,c}=p_{c}*t_{n}, \tag{1}\]  
where \(p_{c}\) is the acquisition power, and \(t_{n}\) is the acquisition time of sensor node \(n\). In addition, the longer the acquisition time of the sensor, the smaller the probability of data distortion and the higher the satisfaction level that can be obtained. Therefore, the satisfaction level of sensor node \(n\) can be defined as the utility function of time \(t\):  
\[\sigma U_{n}(t_{n}), \tag{2}\]  
where \(\sigma>0\) is a coefficient of the satisfaction function. The utility function is a monotonic increasing function of time \(t_{n}\). This function can be modeled as a logarithmic function and is also used in [21; 22]. Of course, the algorithm and simulation results presented in this paper can be easily implemented when sensor nodes have different utility functions. However, as the acquisition time of the sensor is longer, more amount of data are generated correspondingly. The maximum acquisition time of data is defined as \(T_{\max}\). In the data transmission stage, the energy model in [23] was used. The energy model mainly includes two parts: transmission power consumption and circuit power consumption.