Proposed control scheme

5. Coordinated Control Scheme for EV Charging and Volt/Var Devices Scheduling to Regulate Voltages of Active Distribution Networks

where PEV is the charging/discharging power of EV

y(k+ 1) =soc(k+ 1) (5.6)

where A=I;B=_B^η∆t

cap;C=I.

Smart PV inverters can affect the feeder voltage with their active as well as reactive power pro- duction. This work assumes that the PV inverter is oversized to enable injection of at least 44% PV reactive power, even with 100% active power production. Further, due to economic considerations, the curtailment of PV active power is limited to 20% of its active power production. The reactive power set-points of the PV inverters, obtained from the centralized control are further adjusted according to an autonomous volt/var curve. Depending on the local voltage magnitudes, the volt/var curve determines the reactive power.

5.3 Proposed control scheme

Three-Stage VVC

First Stage VVC

Second Stage VVC

Hourly Dispatch of OLTC

Set PV and EV reactive power set-points, PV active power set- point every one minute

}

{

ts=1 hour

ts=1 minute Time

Objective function [eq. (15)] EV charging/discharging decisions half-hourly Third Stage VVC

Objective function [eq. (8)]

}

ts=0.5 hour

Objective function [eq. (7)]

Figure 5.2: Coordinated centralized controller: three-stage MPC.

5.3.1 Three stages of MPC in the proposed scheme

To coordinate different voltage regulation devices with different operation time characteristics, the proposed control scheme is operated at three stages. In the first stage, the slow discrete devices’

operation is optimized to bring the voltage levels within the desired limit. The optimal control problem at this stage is solved at every hour to minimize the switching operations of OLTC. The second stage aims at scheduling different fast volt/var devices at every one-minute interval. It is mainly designed to coordinate the reactive and active power injections of power electronics interfaced devices to deal with short-term voltage variations. The third stage deals with the economic charging of EVs to satisfy the EV users’ demand. As the real-time electricity price is received by the EV aggregator of each area at half-hour interval, the charging/discharging decisions of EVs are taken half hourly. The optimization problem is formulated in such a way that it fits into the framework of economic MPC.

5.3.2 Problem formulation

Let, the incremental control inputs over the horizon be denoted by [∆u(k),∆u(k+ 1), ....,∆u(k+N_C−1)]

and inputs be

[u(k), u(k+ 1), ...., u(k+N_C−1)].

The outputs over the prediction horizon are represented as [y(k+ 1), y(k+ 2), ...., y(k+NP)].

5. Coordinated Control Scheme for EV Charging and Volt/Var Devices Scheduling to Regulate Voltages of Active Distribution Networks

The voltage magnitudes [V(k)] and state-of-charge of the EVs [soc(k)] are the outputs of MPC for all the stages. The OLTC reference voltage [Vtap(k)] is input for the first stage, active and reactive power of PV and reactive power of EV [P_{P V}(k), Q_{P V}(k), Q_ev(k)] are the second stage inputs, and charging/discharging power of EV [P_EV(k)] is input for the third stage.

Similarly, incremental input vectors [∆u(k)] for first, second and third stage are:

[∆V_tap(k)],

[∆P_{P V}(k),∆Q_{P V}(k),∆Q_EV(k)], [∆P_EV(k)], respectively.

The MPC problem for the first stage can be formulated as min

NP

X

i=1

[||V_ref(k+i|k)−V(k+i|k)||²_Q+||σ||²_S] +

NC−1

X

i=0

||∆V_tap(k+i)||²_Rtap

(5.7)

The MPC problem for the second stage can be formulated as min

NP

X

i=1

[||V_ref(k+i|k)−V(k+i|k)||²_Q+||σ||²_S] +

NC−1

X

i=0

[||∆P_{P V}(k+i)||²_R

P Vp

+||∆Q_{P V}(k+i)||²_R

P Vq +||∆Q_EV(k+i)||²_R

EVq] (5.8)

The above objective functions are subjected to the following constraints:

∆u^min≤∆u(k+i)≤∆u^max (5.9)

u^min ≤u(k+i)≤u^max (5.10)

In eqs. (5.9)-(5.10), u and ∆u are changed according to the stage of operation.

Q_{P V} =± q

S_{P V}²−P_{P V}² (5.11)

QEV =± q

SEV2−PEV2 (5.12)

fori= 0,1, ...N_C −1

It is to be noted that the active power of PV is curtailed to 20% of its rated capacity.

5.3 Proposed control scheme

fori= 1,2, ..., NP.

V(k+i|k) =V(k+i−1|k) + δV

δu^T∆u(k+i−1) (5.14)

fori= 1,2, ..., N_P.

The objective function to be minimized in the third stage is a linear programming problem with economic considerations.

min

NP

X

i=1

[||V_ref(k+i|k)−V(k+i|k)||²_Q+||σ||²_S] +

NC−1

X

i=0

[RT P.∆PEV(k) +py.ν]

(5.15)

where, RT P is real-time price of electricity consumption and p_y is the penalty associated with the violation of output variable (SoC of EV battery). Eq. (5.15) is subjected to inequality and equality constraints as in (5.16)-(5.19) along with (5.13) and (5.14).

∆P_EV^min ≤∆P_EV(k+i)≤∆P_EV^max (5.16) P_EV^min ≤PEV(k+i)≤P_EV^max (5.17)

−ν₁1 +soc^min(k+i)≤soc(k+i|k)≤soc^max(k+i) +ν₂1 (5.18) soc(k+i|k) =soc(k+i−1|k)−PEV(k+i−1)

B_cap^max ∆t (5.19)

fori= 1,2, ..., N_P.

There are basically three types of MPC constraints: plant manipulated variable (MV); plant output variable (OV), and MV increment constraints. The physical limits on the plant MVs are included in MPC as hard MV bounds. The MV increment bounds are included when there is a known physical limit on the rate of change, or the application requires preventing large increments for some other reason.

Eqs. (5.16) and (5.17) are MV increments and MV constraints, respectively. Here, the charging /discharging power of EV is considered as the MV. They are hard constraints and are handled by the algorithm that the solver uses. However, due to varying charging power available at each sampling instant, the input variables and rate of inputs can be out of bounds. To cope with this situation, several rules are formulated to the MPC problem. They are:

ˆ Rule 1: If at any time, the input constraints are violated due to the sudden changing available charging power from the aggregated EVs, the minimum/maximum value at that sampling instant

5. Coordinated Control Scheme for EV Charging and Volt/Var Devices Scheduling to Regulate Voltages of Active Distribution Networks

is automatically considered as discharging/charging power for the next sampling instant.

ˆ Rule 2: The charging/discharging power is adjusted at every sampling instant to keep the storage constraints within desired bounds.

A popular method for handling state and output constraints in a MPC algorithm is to use “soft constraints”, in which penalty terms are added directly to the objective function. Here, eq. (5.18) is the output constraint (soc being the OV). Slack variables,µ are added to OV with the aim to soften the constraint so as to diminish the possibility of infeasibility. These variables are heavily penalized by the penalty variable py.

Eq. (5.19) is the equality constraint that describes how the SoC of EV battery is updated at each sampling instant. This is the plant model for MPC and is thus, handled at each sampling instant.

Reaching the final SoC by all EVs at time of departure,t_dis one of the important constraints that needs to be satisfied. This is described in eq. (5.20).

soc(td)≥socreq. (5.20)

Further, with the manipulation of lower bound constraint, soc^min(k) of (5.18), constraint (5.20) can be satisfied. soc^min(k) needs to be updated at every sampling instant. Using eqs. (5.18) and (5.20), the required constraint can be represented as:

soc^min(k) =max[socreq−max(0,{k_out−k)ηP_EV^max

B_cap^max}, soc_low] (5.21) Here,soc_low is limited to 0.2 due to physical considerations of the EV battery.

5.3.3 Local level control

The reactive power is dispatched by the centralized controller to the local control layer embedded in each DG unit. The PV and EV inverters need to have their local controller as per the recent distributed energy resources integration standards. A piecewise linear Q(V) characteristic is proposed as local control for each DG unit. This local characteristic is adjusted according to the set-points received from the centralized MPC as per Table. 5.1. The reactive power set-point received from the centralized control is denoted by Q₀.