Modeling of inverter based Ac microgrids for control development

Optimal and Decentralized Control Strategies for Inverter-Based AC Microgrids

“…The AC output voltages of the jth inverter (v a,j , v b,j , v c,j ) are controlled by the duty cycles (d 1,j , d 2,j , d 3,j ). An additional energy storage device is collocated with the load (u B,a , u B,b , u B,c ) [10,17]. The time-varying nature of the state equations can be removed by utilizing the Parks power-invariant reference frame transformation, yielding a DC-like system, as shown in Figure 2.…”

“…The time-varying nature of the state equations can be removed by utilizing the Parks power-invariant reference frame transformation, yielding a DC-like system, as shown in Figure 2. This reference frame transformation has been done by [17] to create a dq0 reference frame model for a two inverter microgrid, as shown in Figure 2 with N = 2. The dq0 state equations for the jth AC inverter are given in (1), where a DC capacitor (C dc ), which was introduced as in [10], provides the ability to control the DC input voltage to the inverter [10,17]:…”

“…where φ j = jth inverter output voltage angle relative to current, β = 1 2 3 2 , ω = AC angular frequency, cφ j = cos φ j , sφ j = sin φ j , v j = DC voltage source to the jth inverter, v dc,j = DC input voltage of the jth inverter, v d,j = βλ j cφ j v dc,j = d-axis output voltage of the jth inverter, v q,j = βλ j sφ j v dc,j = q-axis output voltage of the jth inverter, v ds = d-axis AC bus voltage, v qs = q-axis AC bus voltage, i d,j = d-axis current of the jth inverter, i q,j = q-axis current of the jth inverter, R dc,j = equivalent inverter input resistances of the jth inverter, C dc,j = capacitor on the DC side of the jth inverter, λ j = depth-of-modulation of the jth inverter, L j = power line LR filter inductance for the jth inverter, R j = power line LR filter resistance for the jth inverter, u j = ideal voltage storage for the jth inverter, u Bd = ideal current storage on the d-axis bus load, u Bq = ideal current storage on the q-axis bus load. The corresponding bus equations in the dq0 reference frame are [17] C Bd dv ds dt =…”

“…. , u N , u Bd , u B,q ) were used in [10,17] as control inputs to develop a feedback controller, utilizing Hamiltonian surface shaping and power flow control (HSSPFC) techniques, which ensures stability while satisfying time-varying bus loads [10,17,18]. The state variable model of [17], which was modified by [10] by the addition of C dc,j , has been expanded to N inverters, where x is the 3N + 2 state vector, v is the N stochastic source vector, and u is the N + 2 input vector [10,17]:…”

“…The significance of [10] in adding C dc into the microgrid architecture of [17] shows up mathematically in (4), where the βλ j sφ j and βλ j cφ j terms are all contained inR. Without C dc , the βλ j sφ j and βλ j cφ j terms are in both D T and B T .…”