# Load Frequency Control for Multi-Area Power Plants with Integrated Wind Resources
## 1 Introduction
Second, the controller suffers from the chattering problem inherent in the first-order SMC [32; 33; 34]. Therefore, this article focuses on a more realistic LFC design for an MAIPS integrated with a wind plant. Thus, the estimated system state variables (SSVs) from the observer are used in the sliding surface, along with a decentralized second-order SMC, so that the SSVs are not required to be measured. The novelties of the paper are discussed below. * The sliding surface and the decentralized continuous load frequency controller are designed to be fully dependent on the SSVs estimated by the observer; thus, the limitation of using state variables for the feedback of the control (discussed in [23; 24; 25; 26; 27; 28; 29; 30; 31]) has been solved. * The MAIPS state variables and the estimated MAIPS state variables are asymptotically stable with the new linear matrix inequality (LMI) method. * A sliding mode acting under the second-order time derivative is developed to improve the system performance by eliminating the problem of chattering, in contrast with the approaches given in [32; 33; 34]. * The simulation results show that the MAIPS performance is better in terms of overshoot and settling time in comparison with some recent approaches. Therefore, the proposed method is useful for the LFC of real MAIPSs. Multi-Area Interconnected Power System (MAIPS) Model in the State Space Form for Load Frequency Control  
For the purpose of LFC, we first derive an MAIPS model. A power network with three areas is contemplated. Thus, areas 1 and 3 are integrated with a wind plant, whereas area 2 consists of a non-reheat turbine alone, as shown in Figure 1. In general, if \(i\)th area is considered, then the system is re-sketched as shown in Figure 2.  
For simplicity, we have modeled the conventional and wind power networks separately. As we know, the conventional power system considered consists of a speed changer motor, governor, non-reheat turbine and generation. We model each component of the conventional MAIPS in the \(i\)th area, as displayed in Figure 2, in same way as [24,31]. Frequency change is made to be the output of the generator so that LFC can be achieved. Next, we determine the dynamic relations, which consist of a speed changer motor, a governor, a non-reheat turbine and a generator of the \(i\)th area model, as expressed by:  
\[\Delta\dot{f}_{i}(t)=\frac{K_{pi}}{T_{Pi}}\Delta P_{mi}(t)-\frac{K_{pi}}{T_{Pi} }\Delta P_{di}(t)+\frac{K_{pi}}{T_{Pi}}\Delta P_{Wi}(t)-\frac{1}{T_{Pi}}\Delta f _{i}(t)-\frac{K_{pi}}{2\pi T_{Pi}}\sum_{i=1,j\
eq i}^{N}K_{i\parallel}\{ \Delta\delta_{i}(t)-\Delta\delta_{j}(t)\} \tag{1}\]  
\[\Delta\dot{P}_{mi}(t)=\frac{1}{T_{Ti}}\Delta P_{gi}(t)-\frac{1}{T_{Ti}}\Delta P _{mi}(t) \tag{2}\]  
\[\Delta\dot{P}_{gi}(t)=-\frac{1}{R_{i}T_{Gi}}\Delta f_{i}(t)-\frac{1}{T_{Gi}} \Delta P_{gi}(t)+\frac{1}{T_{Gi}}u_{i}(t) \tag{3}\]  
\[\Delta\dot{E}_{i}(t)=K_{Ei}K_{Bi}\Delta f_{i}(t)+\frac{K_{Ei}}{2\pi}\sum_{i=1, j\
eq i}^{N}K_{i\parallel}\{\Delta\delta_{i}(t)-\Delta\delta_{j}(t)\} \tag{4}\]  
Figure 1: A simplified sketch of a three-area integrated wind plant system. Figure 2: Schematic block diagram sketch for \(i\)th area network, including a wind farm. \[\Delta\dot{\delta_{i}}(t)=2\pi\,\Delta f_{i}(t) \tag{5}\]  
where \(\Delta f_{i}(t)\) is the individual area frequency deviation, \(\Delta P_{mi}(t)\) is the mechanical power deviation of each area, \(\Delta P_{gi}(t)\) is each area turbine valve position deviation, \(\Delta P_{di}(t)\) is each unit load deviation, \(R_{i}\) is the individual area droop coefficient and \(K_{ij}\) is the synchronization coefficient. \(\Delta P_{Wi}(t)\) is the wind disturbance, \(\Delta\dot{\delta_{i}}(t)\) and \(\Delta\dot{\delta_{j}}(t)\) are small change in power angle, \(K_{gi}\) and \(K_{Ei}\) are the frequency response coefficient. \(T_{pi}\), \(T_{Gi}\) and \(T_{Ti}\) are the subsystem parameters. \(\Delta E_{i}(t)\) is denoted as the area control error. The system state space form of \(i\)th area is shown as follows. \[