# An Energy-Distance-Balanced Cluster Routing Protocol for Smart Microgrid IoT Sensing Networks
## 3 Framework Architectures
### Static Node Energy Framework  
This paper utilizes an enhanced wireless communication energy consumption model that incorporates key transmission parameters, as depicted in Figure 3. The complete energy expenditure for transmitting \(m\) bits over distance \(d\) is given by  
\[E_{TX}(m,d)=\frac{P_{t}}{r}\times m+\frac{P_{\text{circ}}}{r}\times m +E_{\text{retx}}(m,d,\text{PER}) \tag{1}\] \[\text{where }P_{t}=P_{\text{min}}\times\text{PL}(d)\times\text{SNR }_{\text{margin}}\] (2) \[\text{PL}(d)=\text{PL}_{0}+10n\log_{10}(d/d_{0})\] (3) \[E_{\text{retx}}=E_{TX}(m,d)\times\frac{\text{PER}}{1-\text{PER}} \tag{4}\]
* Transmission parameters:
* \(P_{t}\): the transmission power (W), calculated from minimum required power \(P_{\text{min}}\) at receiver sensitivity;
* \(r\): the data rate (bps), dependent on modulation scheme;
* PER: the packet error rate, derived from BER and the packet size. * Channel parameters:
* \(\text{PL}(d)\): the path loss model with reference loss \(\text{PL}_{0}\) at \(d_{0}=1\) m;
* \(n\): the path loss exponent (2.7-4.1 for substations);
* \(\text{SNR}_{\text{margin}}\): the fading margin (3-6 dB for 95% reliability). Simplified Model Justification: For microgrid WSNs operating at fixed a fixed speed of 250 kbps with BPSK modulation, the comprehensive model reduces to our baseline formulation:  
\[E_{TX}(m,d)=med^{n}+mE_{PX} \tag{5}\]  
where \(\epsilon\) encapsulates \(P_{t}/r\) and \(E_{PX}\) subsumes circuit energy and PER effects. This simplification is validated for low-power IoT scenarios [14; 22], with PER < 1% at \(d<100\) m. For harsh environments (e.g., 600 V substations), we incorporate PER effects through \(\epsilon\) variance (\(\sigma^{2}=0.8\)-1.2). In this study, a specific radio model was adopted to serve as the energy consumption model, expressed as \(E=kd^{m}\), where \(E\) denotes the energy expenditure, \(k\) represents the data size in bits, \(d\) is the distance of transmission, and \(n\) is the path loss exponent. The exponent \(n\) varies based on the network's adherence to either a multipath fading model (\(n=4\)) or a free-space propagation model (\(n=2\)) within the channel model. The total energy \(E_{TX}(m,d)\) required by a node for transmitting information is divided into two components: \(E_{AX}(m,d)\) for signal amplification and \(E_{TPX}(t)\) for circuit operation during transmission time \(t\):  
Figure 3: Energy model. \[E_{\rm TX}(m,d) =E_{\rm AX}(m,d)+E_{\rm TPX}(t)\] \[E_{\rm AX}(m,d) =med^{2}\] \[E_{\rm TPX}(t) =P_{\rm circuit}\cdot t \tag{6}\] \[E_{TX}(m,d)=\frac{P_{t}}{r}\times m+\frac{P_{\text{circ}}}{r}\times m +E_{\text{retx}}(m,d,\text{PER}) \tag{1}\]0 \[E_{TX}(m,d)=\frac{P_{t}}{r}\times m+\frac{P_{\text{circ}}}{r}\times m +E_{\text{retx}}(m,d,\text{PER}) \tag{1}\]1  
where \(t=\frac{m}{r}\) (transmission time) and \(r=\) the data rate (bps). This model assumes constant transmission power and data rate, which align with standard WSN practice using fixed modulation schemes. In this context, \(E_{AX}\) signifies the energy utilized in transmitting information across the path, highlighting that \(E_{AX}\) directly correlates with the square of distance \(d\). The parameter \(m\) quantifies the data packet size emitted by the node in bits; \(\varepsilon\) is the energy efficiency coefficient, and \(E_{PX}\) indicates the per-unit data energy usage within the node's hardware, with \(E_{TPX}(m)\) relating to the hardware energy use for data with \(m\) bits. The energy \(E_{RX}(m)\) required to receive \(m\) bits of data is formulated as  
\[E_{TX}(m,d)=\frac{P_{t}}{r}\times m+\frac{P_{\text{circ}}}{r}\times m +E_{\text{retx}}(m,d,\text{PER}) \tag{1}\]2  
where \(E_{RX}\) defines the energy cost per unit of data received by the node. While the current model assumes homogeneous environments, real-world microgrid deployments face challenges such as communication noise and spatial heterogeneity.