4. EL ANÁLISIS EXPERIMENTAL DE LA CONDUCTA APLICADO A LA
4.2. El aprendizaje y la enseñanza desde la perspectiva experimental
Fig. 5.1 depicts a typical line having resistance R and reactance X. The sending end voltage is VS
∠δ
ο where the receiving voltage is VR∠0
o. Ps and Qs denote the sending end real and reactive power flow in the line, and PR and QR denote the net receiving end real and reactive power. A Distributed Generator (DG) is connected at the end of the line where the aggregated load is also connected. The line current is I∠
θo. The complex power flow ÍÎÎÎ in the line at the receiving end is expressed as:Figure 5.1 A two bus network.
Í
ÎÎÎ = %+ w. = MÎÎÎ.~ Ð,− − − − − − − − − − − − − − − − − − − − − − − − (5.1)∗
|, ÍÎÎÎ = %∗ − w. = M
∗
ÎÎÎ. ~̅ − − − − − − − − − − − − − − − − − − − − − (5.2) The real power loss in the line Ploss is given by:
%Årr = ~2. = . (% 2+ . 2) M2 Ò − − − − − − − − − − − − − − − − − − − −(5.3) where, ~ = v(%2M+ .2) 2 , Í = ?% 2+ . 2 , MÎÎÎ = M∗ ÎÎÎ = M ∠0.
By neglecting the line charging of the overhead line, the receiving end voltage can be expressed as:
M
∠
0° = MÍ∠
Z° − ~̅( + wY) − − − − − − − − − − − − − − − − − − − − − (5.4)M2 = MÍ 2− 2. 1± 6(MÍ2− 2. 1)2− 4. (12+ 22) 2 , − − − − − − − − − − − − (5.5) +,-, Z = tan−1Ó 2 M2+ 1Ô − − − − − − − − − − − − − − − − − − − − − −(5.6) where, 1 = (%. + .. Y), +,-, 2 = (%. Y − .. )
The receiving end power PR, QR is the net power consumption at the receiving end:
% = (%Å − %), +,-, . = (.Å− .) Therefore, (5.3) becomes: %Årr = ~2. = . /(%Å− %) 2+ (. Å− .)20 M2 Ò − − − − − − − − − − − − − (5.7) Using the positive quantity before the radical in the receiving end voltage expression of (5.5) [175], the loss can be found from (5.7) as follows:
%Årr = ~2. = 2. /(%Å− %)
2+ (.Å− .)20
MÍ2− 2. 1+ 6(MÍ2− 2. 1)2− 4. (12+ 22)
− − − − − − − −(5.8) where, K1 and K2can be rewritten as
: = /(%P− %Õ). + (.P− .Õ). Y0, +,-, = /(%P− %Õ). Y − (.P− .Õ). 0
It is evident that Ploss=f(PL,QL,VS,R,X, PG,QG), where all the quantities are constant for a given network with known DG power generation and loads. Thus by variation of ‘QG’ the loss can be varied. The receiving end voltage VRalso changes with the variation of ‘QG’ as seen from (5.5). Therefore, an optimal VR can be determined for which the loss becomes a minimum.
The derivative of ‘Ploss’ with respect to ‘QG’ in (5.8) is equated to zero, which returns an optimal value of ‘QG’. Inserting this ‘QG’ into (5.5) gives the optimal set point of the voltages VR for minimum system loss. Therefore, this optimal VR is achieved by controlled reactive power exchange with the PV-STATCOM.
The above analysis is for a simplistic network. It is obvious that for a more complex network an Optimal Power Flow (OPF) solution is required which provides the voltage set point for minimum line loss. According to OPF formulation the voltage magnitudes
and the angles at each bus acts as state variables, real and reactive powers acts as the control variables [203].
There are also some internal losses for operating the DGs. For power inverter based DGs like PV solar farms these losses, Ploss_inv,are associated with IGBT conduction, switching and snubber losses which can be expressed in terms of a polynomial expression [176]- [178]:
%ºrr _(,' = ¿Í+ ¿M. Í + ¿. Í2 ( Ö. ×. ) − − − − − − − − − − − − − − − − − −(5.9) where, S is the apparent power output from the DG inverter expressed in p.u., CS is associated with the standby fixed losses, CV is associated with voltage dependent losses and CR is associated with resistive losses for IGBT conduction. The efficiency, η, of the inverter can be expressed as:
Ø = Í Í + %Ò ºrr _(,'− − − − − − − − − − − − − − − − − − − − − − − − − (5.10)
Therefore, for a typical inverter efficiency curve [179] having an efficiency of 98%, by using the curve fitting technique of MATLAB with (5.9) and (5.10), the values of CS, CV, and CRare determined to be 0.2414%, 0.00364% and 0.0002%, respectively.
5.3 System Model
5.3.1
System Description
As network losses are associated with steady state operation of the power system, the study is performed using load flow software PowerWorld Simulator [180]. However, for a better understanding of the control concepts of the PV-STATCOM, the system is simulated in EMTDC/PSCAD and the output is validated with the PowerWorld Simulator output. In PowerWorld Simulator the PV solar farm is modeled as a P-Q bus providing zero reactive power, while acting as conventional PV system. However, when the PV solar farm operates as PV-STATCOM, it is modeled as a P-V bus considering that the PV solar farm is producing power P (based on its maximum power point- MPP) at the optimal voltage VR to result in minimum loss.
On the other hand, in EMTDC/PSCAD, the conventional PV solar farm along with the Maximum Power Point Tracking (MPPT) feature is modeled as given in Chapter 2.
5.3.2
PV System Control
Fig. 5.2 depicts the detailed diagram for a conventional PV solar farm to act as PV- STATCOM with an auxiliary PV-STATCOM voltage controller, and the optimal power flow (OPF) unit.
2
CDC
2
CDC VDC
Figure 5.2 Detailed PV-STATCOM configuration in the study system (a) PV array model, (b) IGBT matrix of inverter, (c) L-C-L filter, (d) MPPT module, (e) conventional inverter controller, (f) PCC voltage regulator and (g) Optimal Power Flow unit.
5.3.2.1
Conventional PV System Control
The conventional PV solar farm controller regulates the reactive power output of the inverter such that it can perform unity power factor operation along with the DC link voltage control, as demonstrated in Chapter 2. The d-axis current control loop regulates the DC voltage and the real power transfer through two PI regulators (PI-1 and PI-3), as shown in Fig. 5.2 (e). However, the q-axis current control loop regulates the reactive
power to zero through a single PI controller (PI-2), as shown in Fig. 5.2 (e). The DC link voltage reference is set by the MPPT output as shown in Fig. 5.2 (d) such that, corresponding to MPP voltage, all of the available real power output from the PV modules is transferred to the network through the inverter.
5.3.2.2
PV-STATCOM with PCC Voltage Controller
To operate the PV system as PV-STATCOM and to control the PCC bus voltage, a ‘PCC voltage control module’, as shown in Fig. 5.2 (f), is added to the q-axis current control loop by adding an additional PI controller PI-4 [62],[108]. It regulates the voltage at the Point of Common Coupling (PCC) by comparing the measured voltage signal at PCC, VPCC, with the reference voltage value of PCC, VPCC_ref. The output of this module sets the reference value of ‘Iq’ which ultimately controls the reactive power flow from the inverter using the remnant capacity of the inverter after real power generation. The Id current control loop serves the same purpose of the DC link voltage control as in a conventional PV solar system control. The rest of the controller is the same as the conventional controller. In the proposed novel control, the “optimal” set point voltage of the PCC, VPCC_ref, is determined locally by the DG operator, by running an optimal power flow program as shown in Fig. 5.2 (g). This utilizes system data which includes real power, Pi and reactive power Qi of all ‘i’ generators, loads Pj, Qj at all ‘j’ bus, network resistance R, inductance, X, succeptance, B values, and the slack bus voltage Vs, and angle