DYNAMIC ACTIVE AND REACTIVE POWER LOAD SHARING IN AN ISLANDED MICROGRID

Abstract

A method of managing a microgrid and control system is provided, in which the virtual resistance control gains (in frame) of each respective inverter is dynamically adjusted based on a variable related to the available power from each of a plurality of renewable distributed generators.

Claims

1. A method of managing a microgrid comprising the steps of: providing the microgrid, the microgrid comprising a plurality of renewable distributed generators, each renewable distributed generator having a respective inverter; determining a variable related to an available power from each of the plurality of renewable distributed generators; controlling each inverter using a virtual impedance load sharing scheme; and, adjusting a plurality of virtual resistance gains of each of the respective virtual impedance load sharing schemes according to a function of the variable from each respective renewable distributed generator.

2. A method of managing a microgrid according to claim 1, in which the virtual resistance gains are in the frame.

3. A method according to claim 1, wherein at least one renewable distributed generator is photovoltaic.

4. A method according to claim 3, wherein all of the plurality of renewable distributed generators are photovoltaic.

5. A method according to claim 2, wherein the variable related to the available power from the photovoltaic renewable distributed generator is proportional to voltage generated by photovoltaic panels of that photovoltaic renewable distributed generator.

6. A method according to claim 5, in which the variable is a maximum active power, P.sub.DC-max, which varies according to P.sub.DC-max k.sub.nV.sub.DC-opt+c.sub.n, where V.sub.DC-opt is the DC voltage at which the available power for a given irradiance is maximum.

7. A method according to claim 1, wherein the variable is an available reactive power Q.sub.available, which is proportional to the square root of the difference of the squares of a power rating of each renewable distributed generator inverter and its output power.

8. A method according to any preceding claim 1, wherein the step of determining the variable comprises: determining the maximum active power (P.sub.DC-max) and the available reactive power (Q.sub.available) of each of the renewable distributed generators.

9. A method according to claim 1, wherein the virtual resistance gains are proportional to the coefficients m.sub.p and n.sub.q.

10. A method according to claim 9, wherein $\left(m_{p.Math..Math.}=\frac{R_{v.Math..Math.}}{1.5.Math..Math.V^{*}}.Math..Math.\mathrm{and}.Math..Math.n_{q.Math..Math.}=\frac{R_{v.Math..Math.}}{1.5.Math.{\left(V^{*}\right)}^2}\right).$

11. A method according to claim 10, wherein the coefficient m.sub.p is adjusted inverse to the maximum active power (P.sub.DC-max) and n.sub.q is adjusted inverse to the available reactive power (Q.sub.available) of each of the renewable distributed generators.

12. A method according to claim 11, wherein in a largely resistive microgrid, $m_{p.Math..Math.}=\frac{.Math..Math.V}{P_{\mathrm{DC}.Math.\text{-}.Math.\max }}.Math..Math.\mathrm{and}.Math..Math.n_{q.Math..Math.}=\frac{.Math..Math.}{Q_{\mathrm{avail}}}$ where V and are the allowed frequency and voltage deviation.

13. A method according to claim 11, wherein in a largely inductive microgrid, $m_p=\frac{.Math..Math.}{P_{\mathrm{DC}.Math.\text{-}.Math.\max }}.Math..Math.\mathrm{and}.Math..Math.n_q=\frac{.Math..Math.V}{Q_{\mathrm{available}}}$ where V and are the allowed frequency and voltage deviation

14. A method according to claim 1, wherein at least one of the plurality of renewable distributed generators is a wind or wave generator comprising a rotor, and wherein the variable related to the available power from each renewable distributed generator is proportional to the cube of the rotor speed.

15. A method according to claim 1, further comprising: reducing the use of an auxiliary power generator in a largely resistive islanded microgrid energy system by adjusting the output impedance of each renewable distributed generator inverter dynamically according to
P.sub.1m.sub.p1=P.sub.2m.sub.p2= . . . =P.sub.Nm.sub.pN=V
Q.sub.1n.sub.q1=Q.sub.2n.sub.q2= . . . =Q.sub.2n.sub.qN=.

16. A control system for a microgrid comprising: a plurality of inverter controllers, wherein each inverter controller is configured to control an inverter for a renewable distributed generator, and each inverter controller is configured to adjust a droop control gain of each respective inverter according to a function of a variable from each renewable distributed generator wherein the variable is related to an available power from each of the plurality of renewable distributed generators.

17. The control system for a microgrid according to claim 16, wherein at least one renewable distributed generator is photovoltaic.

18. A software program, which when executed is configured to carry out the method according to claim 1.

19. A method of managing a microgrid comprising the steps of: providing the microgrid, the microgrid comprising a plurality of renewable distributed generators, each renewable distributed generator having a respective inverter; determining a variable related to an available power from each of the plurality of renewable distributed generators; and adjusting a plurality of gains of each respective inverter according to a function of the variable from each renewable distributed generator, wherein the gains are those utilised in one of the following load sharing schemes: a P-V, Q-f droop scheme; a P-f, Q-V droop with virtual impedance scheme; and, sharing based on the ratio of virtual impedances of units.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0055] An example control system and method according to the present invention will now be described with reference to the accompanying drawings in which:

[0056] FIG. 1 is a graph showing a classic P-f droop scheme;

[0057] FIG. 2 is a graph showing a static virtual impedance droop (V-P);

[0058] FIG. 3 is a schematic of a first microgrid network on which control according to the present invention may be implemented;

[0059] FIGS. 4a and 4b are graphs showing the classical active power-voltage, and reactive power-frequency droops in a resistive microgrid respectively;

[0060] FIG. 5 is an equivalent circuit of parallel-connected DGs with virtual impedance;

[0061] FIG. 6 depicts PV power vs PV voltage characteristic for different solar irradiations (G). The maximum power curve (B) is also shown;

[0062] FIG. 7 is a method to impose curve B (see FIG. 6) on droop/virtual impedance control scheme;

[0063] FIG. 8 is the characteristics of the active power-voltage and reactive power-frequency droops, based on the developed virtual impedance sharing scheme;

[0064] FIGS. 9a and 9b show a dynamic virtual impedance sharing scheme in a resistive MG according to the invention;

[0065] FIGS. 10a and 10b are active power-voltage and reactive power-frequency graphs showing dynamic droop operation for active and reactive power sharing;

[0066] FIG. 11 illustrates the calculation of reactive power that needs to be exchanged with the AG (i.e. Qerror) to protect the inverter's rating;

[0067] FIG. 12, graphs (a) to (f) show simulation results of two DG systems using static virtual impedance load sharing scheme for both Active and Reactive Power Sharing: [0068] (a) available solar power in pu; [0069] (b) static scheme: active power in pu (note that P.sub.2 reduction reduces P.sub.1); [0070] (c) output voltage in pu; [0071] (d) available capacity for reactive power in pu; [0072] (e) Static scheme: reactive power in pu; [0073] (f) Frequency in pu;

[0074] FIG. 13, graphs (a) to (f) show simulation results of two DG systems using virtual impedance load sharing scheme showing dynamic Active power and static Reactive Power Sharing: [0075] (a) available solar power in pu; [0076] (b) Dynamic scheme: active power in pu (note that P.sub.1 increases to compensate for P.sub.2 reductions, hence, P.sub.ag remain zero); [0077] (c) output voltage in pu; [0078] (d) available capacity for reactive power in pu; [0079] (e) Static scheme: reactive power in pu (note that unit 1 generate more active and reactive power than unit 2; while from 10 sec onward Q.sub.avail2>Q.sub.avail1); [0080] (f) Frequency, pu;

[0081] FIG. 14, graphs (a) to (f) show simulation results of two DG systems using the proposed dynamic virtual impedance load sharing scheme for both dynamic Active and Reactive Power Sharing: [0082] (a) available solar power in pu; [0083] (b) Dynamic scheme: active power in pu (note that P.sub.1 increases to compensate for P.sub.2 reductions, hence, P.sub.ag remain zero); [0084] (c) output voltage in pu; [0085] (d) available capacity for reactive power in pu; [0086] (e) Dynamic scheme: reactive power in pu (note that as P.sub.I increases, Q.sub.1 reduces; and as P.sub.2 reduces, Q.sub.2 increases); [0087] (f) Frequency, pu;

[0088] FIG. 15, Bar charts illustrating the output voltage's Total Harmonic Distortion (THD) for the three testing scenarios: [0089] (a) Static P and static Q sharing [0090] (b) Dynamic P and static Q sharing [0091] (c) Dynamic P and dynamic Q sharing (note the significant reduction in THD); and,

[0092] FIG. 16, graphs (a) to (c) show simulation results of two DG systems using the real-time solar data [0093] (a) Available solar power in pu; [0094] (b) AG Energy profiles in pu; [0095] (c) AG Reactive Energy profiles in pu.

DETAILED DESCRIPTION

[0096] The mathematical model of a PV array is described in [28] with P-V characteristic shown in FIG. 6. It was also shown in [6] and [29] that a three-phase inverter (with sinusoidal PWM) can averagely be modelled using - frame transformation techniques:

|V.sub.||m.sub.|V.sub.DC(8)

where V.sub. is the - frame Clarke transform of the DG voltage, |m| is the modulating index (in - frame) and V.sub.DC is the DC link voltage.

[0097] Generally V.sub.DC perturbs in response to irradiance level and demanded load; when there is a reduction in solar irradiance level (hence decreasing V.sub.DC), m must increase to maintain (according to (8)). At m=1; a constant |V.sub.| depends solely on V.sub.DC. Further reduction in V.sub.DC due to irradiance reduction will reduce |V.sub.| d. Hence, in order to accurately control AC bus voltage (|V.sub.| d), minimum DC voltage V.sub.DC-min must ensure (8) while m=1; E.g. for a nominal RMS 230V DGs system explained in [17], VDC650.54V (i.e. operating point limit with modulating index, m=1). Thus, the PV array must be designed such that the DC voltage of the maximum power at a small irradiation (say 0.05 pu)=V.sub.DC-min=650.54V (see FIG. 6).

[0098] In the absence of maximum power tracking, the PV operating point is usually determined by the AC-side load demand; hence the DC link voltage (V.sub.DC) will be perturbed continuously from the minimum operating voltage (V.sub.DC-min) to the PV array's open circuit voltage (V.sub.OC) as the irradiance level or load varies (FIG. 6). The proposed dynamic droop scheme uses the variation in irradiance (i.e. V.sub.DC) in conditioning the conventional static sharing schemes for an efficient load sharing. This will involve a linear approximation of the PV maximum power point characteristic curve (B in FIG. 6) and the subsequent droop gain tracking the irradiance variation within the DG's operating zone. When available solar power is more than the load power, the system operates normally within its operating zone (right hand side of curve B in FIG. 6). As solar irradiation (G) drops, the DG will continue to supply the load, until the available solar power is not enough to meet the demand (point O); AG is thus triggered on (when V.sub.DC becomes less than a threshold) to compensate for the shortage in energy.

[0099] In order to make sure that when the input solar power of one unit drops; the other units do not follow it, the sharing scheme must be sensitive to the input power. However, since measuring solar irradiance is not practical, the present invention makes the sharing scheme vary according to the maximum power curve (i.e. curve B in FIG. 6), which can be linearized as [17], [30]:

P.sub.DC-max-n=k.sub.nV.sub.DC-opt-n+c.sub.n(9)

[0100] Where: [0101] k.sub.n and c.sub.n are gains to get a linear approximation of the maximum power curve of the nth PV array. [0102] V.sub.DC-opt-n is the DC link voltage of the nth PV array when the PV power is maximum (i.e. curve B in FIG. 6).

[0103] Since the PV power P.sub.pv is intermittent, the maximum reactive power, Q.sub.avail that can be exchanged by the inverter is varying as given in [6]:

Q.sub.avail={square root over (S.sub.rated.sup.2P.sub.pv.sup.2)}(10)

[0104] In (10), Q.sub.avail increases for reduction in solar irradiance (G) of a DG unit.

[0105] For a given load (P.sub.Load) and a given solar irradiation (G.sub.1) shown in FIG. 6, the steady state operating point can be, theoretically, anywhere on line OC (AG will be needed on left side of O). However, only point O is located on the maximum power curve B. Therefore, if any point but O is chosen as the steady state operating point, maximum power point tracking will not be possible when it is needed (e.g. when solar irradiation of other unit(s) drops). Hence, an optimized sharing scheme must have the following characteristics: [0106] 1. All units must operate on curve B (FIG. 6); and, [0107] 2. Units with higher P contributions must have lower Q contributions since Q.sub.avail reduces as P.sub.pv increases.

[0108] In order to impose the operation on curve B, FIG. 7 is proposed. In FIG. 7, the measured PV power P.sub.pv is passed through P.sub.pv-V.sub.DC-opt curve explained in [30], to get V.sub.DC-opt which is used in (9) to get P.sub.DC-max. Using FIG. 7 will create a closed loop which makes P.sub.pv=P.sub.DC-max at steady state. P.sub.DC-max will be used for sharing active power and Q.sub.avail will be used for sharing reactive power (explained below). At steady state P.sub.pv=P.sub.DC-max, i.e. the method also ensures that the maximum power from each unit is generated if required by the load, while taking into account the rating, output impedance (in virtual impedance approach) and voltage limits of each unit.

[0109] The present invention is primarily concerned with the application of FIG. 7, (9) and (10) in the dynamic virtual impedance load sharing scheme, as will be discussed below. That said, the present invention can be employed in all three known schemes for the dynamic active and reactive power sharing in a resistive MG as follows:

A. Dynamic P-V and Q-f Droop

[0110] Dynamically, (2) is now set based on (9) and (10) as follows:

[00006]$\begin{array}{cc}{n}_q=\frac{.Math..Math.}{Q_{\mathrm{avail}}};m_q=\frac{.Math..Math.V}{P_{\mathrm{DC}.Math.\text{-}.Math.\max }}& \left(11\right)\end{array}$

[0111] For instance, if solar irradiation of one unit drops, its V.sub.DC-opt and P.sub.DC-max drops causes reduction in P contribution through increasing its m.sub.p. Reduction in P.sub.pv=P.sub.DC-max causes increase in Q.sub.avail which in turn increases Q contribution through reducing n.sub.q. Moreover, other units can compensate for P reduction (assuming there is enough G)

B. Dynamic P-f and Q-V Droop with Virtual Impedance

[0112] Similarly, in the presence of virtual impedance scheme, (3) can be re-written as:

[00007]$\begin{array}{cc}{n}_q=\frac{.Math..Math.}{Q_{\mathrm{avail}}};m_p=\frac{.Math..Math.}{P_{\mathrm{DC}.Math.\text{-}.Math.\max }}& \left(12\right)\end{array}$

[0113] The droop mechanism in (11) and (12) are now sensitive to the available solar power. It should be noted that the droop gains are still proportional to the ratings of their associated units.

C. Dynamic Virtual Impedance Load Sharing Scheme

[0114] Eq. (5) explained the KVL of an inverter voltage and current in frame. As explained above, X.sub.v is used to decouple active and reactive powers through increasing the inductive characteristics of the total output impedance. Therefore, we can use R.sub.v and R.sub.v to control active power (voltage) and reactive power (frequency), respectively, as discussed below:

[0115] Since at steady state the voltage drop due to X, is negligible, (5) can be written as:

v.sub.o=v.sub.*R.sub.vi.sub.o.fwdarw.v.sub.=R.sub.vi.sub.o

v.sub.o=v.sub.*R.sub.vi.sub.o.fwdarw.v.sub.=R.sub.vi.sub.o(13)

[0116] As shown in FIG. 9.b, PLL makes V.sub.q=0 at steady state, hence using Park Transform:

[00008]$\begin{array}{cc}{v}_{a.Math..Math.}=V_{\mathrm{od}}.Math.\cos .Math..Math.-V_{\mathrm{oq}}.Math.\sin .Math..Math..Math.\stackrel{.Math.{\mathrm{PLLV}}_q=0.Math.}{.fwdarw.}.Math.v_{o.Math..Math.}=V_{\mathrm{od}}.Math.\cos .Math..Math..Math..Math.v_{a.Math..Math.}=V_{\mathrm{od}}.Math.\sin .Math..Math.+V_{\mathrm{oq}}.Math.\cos .Math..Math..Math.\stackrel{.Math.{\mathrm{PLLV}}_q=0.Math.}{.fwdarw.}.Math.v_{o.Math..Math.}=V_{\mathrm{od}}.Math.\sin .Math..Math.& \left(14\right)\end{array}$

[0117] Since using X.sub.v the total output impedance is mainly inductive, is relatively small. Thus at steady state, (cos ).fwdarw.1 and (sin ).fwdarw.0, which simplifies (14) as:

[00009]$\begin{array}{cc}{v}_{a.Math..Math.}=V_{\mathrm{od}}.Math.\cos .Math..Math..Math.\stackrel{.Math..fwdarw.0.Math.}{.fwdarw.}.Math..Math.v_{o.Math..Math.}.Math..fwdarw.V_{\mathrm{od}}.Math..Math.v_{a.Math..Math.}=V_{\mathrm{od}}.Math.\sin .Math..Math..Math.\stackrel{.Math..fwdarw.0.Math.}{.fwdarw.}.Math..Math.v_{o.Math..Math.}.Math..fwdarw.V_{\mathrm{od}}.Math.& \left(15\right)\end{array}$

Therefore, the active and reactive powers in frame are:

[00010]$\begin{array}{cc}.Math.P=1.5.Math.\left(v_{o.Math..Math.}.Math.i_{o.Math..Math.}+v_{o.Math..Math.}.Math.i_{o.Math..Math.}\right).Math.\stackrel{.Math.v_{o.Math..Math.}.Math..fwdarw.0.Math..Math.\mathrm{and}.Math..Math..Math.v_{o.Math..Math.}.Math..fwdarw.V_{\mathrm{od}.Math.}.Math.}{.fwdarw.}.Math.P=1.5.Math.\left(V_{\mathrm{od}}.Math.i_{o.Math..Math.}\right).Math..Math.Q=1.5.Math.\left(v_{o.Math..Math.}.Math.i_{o.Math..Math.}-v_{o.Math..Math.}.Math.i_{o.Math..Math.}\right).Math.\stackrel{.Math.v_{o.Math..Math.}.Math..fwdarw.0.Math..Math.\mathrm{and}.Math..Math..Math.v_{o.Math..Math.}.Math..fwdarw.V_{\mathrm{od}.Math.}.Math.}{.fwdarw.}.Math.Q=-1.5.Math.\left(V_{\mathrm{od}}.Math.i_{o.Math..Math.}\right)& \left(16\right)\end{array}$

[0118] Equations (16) shows that active power can be controlled by i.sub.o, and reactive power can be controlled by i.sub.o. Moreover, substituting (15) into (13), gives:

V.sub.od=R.sub.v-i.sub.o

V.sub.od=R.sub.v-i.sub.o(17)

Calculating i.sub.o and i.sub.o from (16), and substituting them into (17) gives:

(1.5V.sub.od)V.sub.od=R.sub.vP

(1.5V.sub.od.sup.2)=R.sub.vQ(18)

[0119] Through using (18), taking into account that =dt, and V.sub.odV*=1 pu (at steady state), one can derive the droop equations based on virtual resistance as (19):

[00011]$\begin{array}{cc}V=V^{*}-m_{p.Math..Math.}.Math.P,m_{p.Math..Math.}=\frac{R_{v.Math..Math.}}{1.5.Math..Math.V^{*}}.Math..Math.={}^{*}+n_{q.Math..Math.}.Math.Q,n_{q.Math..Math.}=\frac{R_{v.Math..Math.}}{1.5.Math..Math.{\left(V^{*}\right)}^2}& \left(19\right)\end{array}$

[0120] Equation (19) is depicted in FIG. 8.

[0121] For a system consisting of N parallel-connected DG, (20) can be written (which is the same as (6) but using m.sub.p and n.sub.q):

P.sub.1m.sub.p1=P.sub.2m.sub.p2= . . . =P.sub.Nm.sub.pN=V

Q.sub.1n.sub.q1=Q.sub.2n.sub.q2= . . . =Q.sub.2n.sub.qN=(20)

where, V and are the allowed voltage and frequency deviations. Using the proposed virtual resistance sharing in a conventional static droop:

[00012]$\begin{array}{cc}{m}_{p.Math..Math.}=\frac{.Math..Math.V}{P_{\mathrm{rated}}}.Math..Math.\mathrm{and}.Math..Math.n_{q.Math..Math.}=\frac{.Math..Math.}{Q_{\mathrm{rated}}}& \left(21\right)\end{array}$

[0122] Combining the proposed dynamic droop with the proposed virtual resistance droop yields:

[00013]$\begin{array}{cc}{m}_{p.Math..Math.}=\frac{.Math..Math.V}{P_{\mathrm{DC}.Math.\text{-}.Math.\max }}.Math..Math.\mathrm{and}.Math..Math.n_{q.Math..Math.}=\frac{.Math..Math.}{Q_{\mathrm{avail}}}& \left(22\right)\end{array}$

Since P and Q are perfectly decoupled through using X.sub.v, a reduction in solar irradiation of one unit increases R.sub.v (through increasing m.sub.p), which in turn reduces P (according (20)). The reduction in P increases Q.sub.avail, which reduces R.sub.v (through reducing n.sub.q), which in turn increases Q (according to (20)). Since other units also are controlled using the proposed dynamic virtual impedance (i.e. (22)), they will adjust their P and Q accordingly to supply the load and to comply with the voltage and frequency standards.

[0123] The available reactive power (Q.sub.avail) of a DG unit increases with decreasing available irradiation according to (10). In the case of static virtual impedance scheme, a fixed Q-droop gain is set irrespective of Q.sub.avail, hence DG unit are not fully optimized for Q.sub.Load sharing leading to excessive switching stress on the inverter. However using the proposed scheme, as shown in FIG. 10a&b, a reduction in P.sub.1 to P.sub.1, causes P.sub.2 to increase (assuming enough G). Hence, Q.sub.avail1 increases and Q.sub.avaial2 reduces which according to (22) and (20) increases Q.sub.1 and reduces Q.sub.2 (see results in FIG. 14). By adopting the proposed approach, significant reduction in the energy demanded from AG is achieved when compared to conventional static scheme (see FIG. 16 for results).

[0124] In a resistive MG, P-V, Q-f droops approach (i.e. section A above) is the simplest, however, has the disadvantage of relatively unstable operation in comparison with the virtual impedance scheme that improves the system stability [21, 22, 25]. Having both droop (P-f & Q-V) and virtual impedance schemes (i.e. section B above), although possible, seems redundant as only virtual impedance scheme can be used for load sharing. Therefore, the preferably embodiment of the present invention as discussed in the following description and the simulation results mainly concentrate on the virtual impedance approach (i.e. section C above); however, a comparison of all three approaches in terms of active and reactive power demanded from AG is also presented (FIG. 16).

[0125] FIGS. 9a and 9b illustrate the proposed dynamic virtual impedance sharing scheme in a resistive MG. The control paradigm is based on the classical cascaded voltage and current control using proportional resonant (PR) controller [21]. Stationary reference frame parameters were generated using Clarke transforms as implemented in [22]. In FIGS. 9a and 9b, the virtual impedance load sharing scheme uses the droop scheme (V vs I) to autonomously respond to changes in connected loads, while a PLL ensures internal frequency synchronization, in order to ensure accurate regulation of P and Q [31, 32].

Auxiliary Generator Control

(i) P Control

[0126] The DC link voltage is used as indicator for regulating the AG (see FIG. 3) to provide active power compensation. When the DC link voltage of either DGs decreases below a threshold (here DC threshold=0.85pu, AG is switched ON to compensate for the energy shortage. The AG reference active power (FIG. 9a) is:

[00014]$\begin{array}{cc}{P}_{\mathrm{aux}}^{*}=-3.Math.\underset{n=1}{\overset{N}{.Math.}}.Math.V_{\mathrm{DC}.Math.\text{-}.Math.n}& \left(23\right)\end{array}$

(ii) Q Control

[0127] The local reactive power difference of DGs is used as indicator for regulating the AG (see FIG. 11) to provide reactive power compensation. When local reactive power of either DG increases above the available reactive power (i.e. QQ.sub.avail), AG is switched ON to provide reactive power compensation. The AG's reference reactive power (FIG. 9a) is:

[00015]$\begin{array}{cc}{Q}_{\mathrm{aux}}^{*}=-5.Math.\underset{n=1}{\overset{N}{.Math.}}.Math.Q_{\mathrm{error}.Math.\text{-}.Math.n}& \left(24\right)\end{array}$

[0128] The proposed method exploits the available capacity of the PV inverter to support the local voltage without violating either the S.sub.rated of the inverter or its voltage limitations [6].

[0129] Thus the PQ control scheme in [33] and [34] was adopted in the AG control for injecting active power and reactive power into the network when needed, where references P and Q are set by (23) and (24).

VI. Simulation Results

[0130] The MG 100 shown in FIG. 3, with parameters explained in Table I, was simulated using Matlab-SIMULINK.

TABLE-US-00001 TABLE I Variable Value Variable Value V.sub.L-L 415 V f* 50 Hz S.sub.rated1/S.sub.rated2 0.6/0.4 (pu) S.sub.Load 0.875 (pu) P.sub.Load/Q.sub.Load 0.75/0.45 (pu) R.sub.line/X.sub.line 7.7 LC filter 4 mH/16 F k.sub.pv/k.sub.iv 0.09/86 k.sub.1 and c.sub.1 (Eq. 9) 76.48 and 50692.01 k.sub.pc/k.sub.ic 0.05/0 k.sub.2 and c.sub.2 (Eq. 9) 43.05 and 28442.60 k.sub.p-pll/k.sub.i-pll 1.2/1200 Length of line 0.5 km C.sub.0 1200 (F)

[0131] The test model consists of two DGs and one AG feeding a three-phase load (demanding both active and reactive power). Each DG has its own control scheme (including virtual impedance loop) and the load sharing scheme is simulated for both conventional and dynamic virtual impedance scheme. The rating of each inverter-based source, S.sub.rated should not be violated. Here S.sub.rated1=S.sub.rated2=1.05 pu.sub.pv (pu.sub.pv denotes pu based on the rating of the associated PV array). The simulation is tested for fixed active power load demand (P.sub.L) and reactive load demand (Q.sub.L) in the presence of variable solar irradiation.

A. Load Sharing Scheme in Resistive Network Using Virtual Impedance Scheme.

[0132] The conventional virtual impedance load sharing scheme was tested for two PV DG sources shown in FIG. 3 in a resistive network, to observe the load sharing interaction feeding both active and reactive load demand. The load sharing was observed between the DGs where solar irradiation of DG2 drops in steps and the load active/reactive power are fixed at 0.75/0.45pu.

[0133] Different load sharing scenarios were simulated in MATLAB/SIMULINK: static-P/static-Q sharing, dynamic-P/static-Q, and dynamic-P/dynamic-Q for the network depicted in FIG. 3. Note that all results are presented in pu based on the total system rating (not each PV system).

i. Static P and Static Q (FIG. 12)

[0134] The network in FIG. 3 was simulated using conventional static virtual impedance i.e. (21). FIG. 12 shows accurate load sharing between the two DGs, which shows the effectiveness of the virtual impedance load sharing scheme.

[0135] Up to 5s, the load is appropriately shared based on their rating since the available solar power (P.sub.avail1 and P.sub.avail2 in FIG. 12.a) on both systems is the same (i.e. 1pu.sub.pv).

[0136] At 5s, as the available power in DG2 (FIG. 12.a) drops due to drops in irradiance level, its local voltage changes to a new operating point resulting in a reduction in power contribution to the load (FIG. 12.b). DG1 complies with this new operating point and reduces its power contribution (FIG. 12.b) although its solar irradiance is constant (FIG. 12.a). As a result, the total generation becomes less than the load which leads to reduction in V.sub.DC. When V.sub.DC<0.85 pu, the AG is triggered on to supply the shortage. It is important to note that over the entire simulation the total available solar power (P.sub.avail1+P.sub.avail2)>P.sub.Load i.e. there should not be any need for AG.

[0137] The available reactive power is shown in FIG. 12.d, it is noted that Q.sub.avail1 and Q.sub.avail2 increase as P1 and P2 decrease, however, due to the fixed sharing ratio, the shared reactive power (based on the fixed sharing ratio) from DG1 and DG2 remain constant for the entire simulation time (FIG. 12.e).

ii. Dynamic P and Static Q (FIG. 13)

[0138] The simulation of the virtual impedance scheme in FIG. 3 was repeated with m.sub.p (i.e. P) varies according to (22) while n.sub.p (i.e. Q) remain constant according to (21). The results in FIG. 13.b shows that the power is shared based on rating when the solar irradiances are the same (up to 5s).

[0139] At 5s, as the available power on DG2 reduces, its m.sub.p increases which in turn reduces the power contribution of DG2 to the overall load. However, the m.sub.p of DG1 proportionally reduces to compensate for the power drop in DG2 (since DG1 has extra capacity to compensate for DG2). Due to DG1 compensation for DG2, the AG power P.sub.ag=0, as shown in FIG. 13.b.

[0140] FIG. 13.d shows Q.sub.available for DG1 and DG2. It is noted that Q.sub.avail1 drops as P.sub.1 increases while Q.sub.avail2 increases as P.sub.2 drops. However, due to fixed n.sub.pp (as shown in FIGS. 13.e), Q.sub.1 and Q.sub.2 remain constant (until 15s) regardless of their Q.sub.available. At 15s, Q.sub.DG1>Q.sub.avail1; hence according to FIG. 11, AG is triggered ON to compensate for the deficiency in reactive power supply (FIG. 13.e). It is noted that although Q.sub.avail2 increases, Q.sub.2 remains constant which demonstrates an inefficient Q sharing.

iii. Dynamic P and Dynamic Q (FIG. 14)

[0141] The simulation was repeated while both m.sub.p and n.sub.p vary according to (22), using the proposed method according to the invention illustrated in FIG. 9a.

[0142] FIG. 14.b shows that P is dynamically shared appropriately based on available generation. In addition, as shown in FIG. 14.e, reactive powers are now dynamically regulated so that contributed reactive power changes proportional to Q.sub.available variations: increase in P.sub.1 to compensate drop in P.sub.2 will result in reduction in Q.sub.avail1; hence the dynamic droop conditions a reduction in Q.sub.1 and an equivalent increase in Q.sub.2 (since Q.sub.avail2 increases as P.sub.2 drops). As a result, the switching stress on each DG's converter is reduced since unit with more P generation has less Q contribution to the load. As it can be seen from FIG. 15, where the THD of the output voltage of the three test scenarios are compared, the THD of case c (i.e. dynamic P and dynamic Q) is much less than the other schemes.

B. Simulation Results with Real-Time Solar Irradiance Variation (FIG. 16)

[0143] The low-voltage network was also tested using real-time (measured) solar irradiation profile (shown in FIG. 16.a) for droop and virtual impedance load sharing scheme. FIG. 16.b shows the energy demand from the AG using different sharing schemes. Energy saving is calculated and shown in Table II by comparing the energy demand of each sharing scheme to the energy demand in static P-f/Q-V droop scheme (this serve as the reference).

TABLE-US-00002 TABLE II Energy Demand Energy Saved Loading Scheme (%) (%) Static P-V/Q-f 67.94 24.68 Dynamic P-V/Q-f 15.62 77.00 Static P-f/Q-V 92.62 0.00 Dynamic P-f/Q-V 15.04 77.58 Static virtual impedance. 59.47 33.15 Dynamic virtual impedance. 5.87 86.75

[0144] FIG. 16.b shows that the dynamic virtual impedance sharing scheme provides more energy saving (up to 87% for the data set studied) from the AG when compared with other load sharing schemes.

[0145] A quantity, similar to energy, is also required to compare the reactive power from the AG for various sharing schemes. Reactive Energy is thus introduced; which is the integral of the AG's reactive power. As shown in FIG. 16.c, the dynamic virtual impedance sharing scheme required the minimum reactive energy from the AG.

[0146] Variations fall within the scope of the present invention. Although the above embodiment discusses varying the virtual resistance in the reference frame, it will be noted that the same system can be applied in the DQ frame.

[0147] The above results utilise closed-loop control of the AG such that P.sub.ag and Q.sub.ag track P*.sub.ag and Q*.sub.ag accurately. It will be understood that feed-forward control could less preferably be used.

[0148] The proposed dynamic active and reactive power sharing method was validated using MATLAB/SIMULINK. Three different sharing schemes for resistive microgrid were outlined, and the application of the proposed dynamic sharing method on them was expressed. Simulation results show that the proposed dynamic virtual impedance provides more energy saving in comparison with the other load sharing approaches. The proposed scheme was validated for multiple PV array with various irradiance conditions; and it was shown that power sharing is proportional to the units' ratings when the irradiance levels are the same. However, if the solar available power on one PV array drops, the other units can generate more power (if the capacity is available) to compensate for the drop, without the need for energy support from local auxiliary generators and thereby providing significant energy saving compared with conventional static droop control techniques. In addition, switching stresses on the inverter-based sources are vastly reduced by dynamically regulating the reactive power demand, through reducing the reactive power contribution of units with higher active power contribution. It was shown that the dynamic reactive power contribution also reduces the demanded reactive power from a local auxiliary generator. The scheme was also validated with real-time (measured) solar irradiation.

REFERENCES

[0149] [1] H. Mahmood, D. Michaelson, and J. Jin, A Power Management Strategy for PV/Battery Hybrid Systems in Islanded Microgrids, IEEE Emerging and Selected Topics in Power Electron., vol. 2, pp. 870-882, October 2014. [0150] [2] K. T. Tan, X. Y. Peng, P. L. So, Y. C. Chu, and M. Z. Q. Chen, Centralized Control for Parallel Operation of Distributed Generation Inverters in Microgrids, IEEE Trans. Smart Grid, vol. 3, pp. 1977-1987, December 2012. [0151] [3] K. Jong-Yul, J. Jin-Hong, K. Seul-Ki, C. Changhee, P. Jine-Ho, K. Hak-Man, and N. Kee-Young, Cooperative Control Strategy of Energy Storage System and Microsources for Stabilizing the Microgrid during Islanded Operation, IEEE Trans. Power Electronics, vol. 25, pp. 3037-3048, December 2010. [0152] [4] L. Yun Wei and K. Ching-Nan, An Accurate Power Control Strategy for Power-Electronics-Interfaced Distributed Generation Units Operating in a Low-Voltage Multibus Microgrid, IEEE Trans. on Power Electronics, vol. 24, pp. 2977-2988, 2009. [0153] [5] M. Fazeli, G. M. Asher, C. Klumpner, and L. Yao, Novel Integration of DFIG-Based Wind Generators Within Microgrids, IEEE Trans. Energy Conversion, vol. 26, pp. 840-850, August 2011. [0154] [6] M. Fazeli, J. B. Ekanayake, P. M. Holland and P. Igic, Exploiting PV Inverters to Support Local Voltage:A Small-Signal Model, IEEE Trans. on Energy Conversion, vol. 29, pp. 453-462, May 2014. [0155] [7] J. M. Guerrero, H. Lijun, and J. Uceda, Control of Distributed Uninterruptible Power Supply Systems, IEEE Trans. Ind. Electron., vol. 55, pp. 2845-2859, July 2008. [0156] [8] S. R. Nandurkar and M. Rajeev, Design and Simulation of three phase Inverter for grid connected Photovoltaic systems, Proceed. Of Third Biennial National Conf, NCNTE, pp. 80-83, February 2012. [0157] [9] Y. A. R. I. Mohamed and E. F. El-Saadany, Adaptive Decentralized Droop Controller to Preserve Power Sharing Stability of Paralleled Inverters in Distributed Generation Microgrids, IEEE Trans. Power Electron., vol. 23, pp. 2806-2816, November 2008. [0158] [10] R. G. Wandhare, S. Thale, and V. Agarwal, Design of a photovoltaic power conditioning system for hierarchical control ofa microgrid, in IEEE 40th Photovoltaic Specialist Conference (PVSC), 2014, pp. 3144-3149. [0159] [11] J. M. Guerrero, H. Lijun, and J. Uceda, Decentralized Control for Parallel Operation of Distributed Generation Inverters Using Resistive Output Impedance, IEEE Trans. Ind. Electron., vol. 54, pp. 994-1004, April 2007. [0160] [12] J. Rocabert, G. M. Azevedo, A. Luna, J. M. Guerrero, J. I. Candela, and P. Rodriguez, Intelligent Connection Agent for Three-Phase Grid-Connected Microgrids, IEEE Trans. Power Electronics, vol. 26, pp. 2993-3005, October 2011. [0161] [13] R. Majumder, C. Balarko, G. Arindam, M. Rajat, L. Gerard and Z. Firuz, Improvement of stability and load sharing in an autonomous microgrid using supplementary droop control loop, IEEE Power and Energy Society General Meeting, pp. 1-1, July 2010. [0162] [14] R. Majumder, A. Ghosh, G. Ledwich, and F. Zare, Load sharing and power quality enhanced operation of a distributed microgrid, IET Renewable Power Generation, vol. 3, pp. 109-119, March 2009. [0163] [15] S. Anand, B. G. Fernandes, and M. Guerrero, Distributed Control to Ensure Proportional Load Sharing and Improve Voltage Regulation in Low-Voltage DC Microgrids, IEEE Trans. Power Electron., vol. 28, pp. 1900-1913, October 2013. [0164] [16] Z. Yixin, Z. Fang, and S. Hongtao, Accurate power sharing strategy for complex microgrid based on droop control method, in IEEE ECCE Asia Downunder (ECCE Asia), 2013, pp. 344-350. [0165] [17] A. M. Egwebe, M. Fazeli, P. Igic, and P. Holland, Implementation and stability study of Dynamic Droop in islanded MicroGrids, IEEE Trans. on Energy Conversion, Vol 31, no. 3, 2016. [0166] [18] Z. Yixin, Z. Fang, L. Baoquan, and Y. Hao, An enhanced load power sharing strategy for low-voltage microgrids based on inverse-droop control method, in Power Electronics International Conference (IPEC-Hiroshima 2014-ECCE-ASIA), 2014, pp. 3546-3552. [0167] [19] K. Jaehong, J. M. Guerrero, P. Rodriguez, R. Teodorescu, and N. Kwanghee, Mode Adaptive Droop Control With Virtual Output Impedances for an Inverter-Based Flexible AC Microgrid, IEEE Trans. on Power Electronics, vol. 26, pp. 689-701, 2011. [0168] [20] H. Jinwei and L. Yun Wei, An Enhanced Microgrid Load Demand Sharing Strategy, IEEE Trans. on Power Electron., vol. 27, pp. 3984-3995, September 2012. [0169] [21] G. Yajuan, J. C. Vasquez, J. M. Guerrero, and E. A. Coelho, Small-signal modeling, analysis and testing of parallel three-phase-inverters with a novel autonomous current sharing controller, in Applied Power Electronics Conference and Exposition (APEC), 2015 IEEE, 2015, pp. 571-578. [0170] [22] G. Yajuan, J. C. Vasquez, J. M. Guerrero, A simple autonomous current-sharing control strategy for fast dynamic response of parallel inverters in islanded microgrids, in IEEE International Energy Conference (ENERGYCON), 2014, pp. 182-188. [0171] [23] A. H. Etemadi, E. J. Davison, R. Iravani, A Generalized Decentralized Robust Control of Islanded Microgrids, IEEE Trans. Power Systems vol. 29, pp. 3102-3113, November 2014. [0172] [24] K. De Brabandere, B. Bolsens, J. V. Keybus, A. Woyte, J. Driesen, R. Belmens, and K. U. Leuven, A voltage and frequency droop control method for parallel inverters, in IEEE 35th Annual Power Electronics Specialists Conference, PESC 2004, pp. 2501-2507 Vol. 4. [0173] [25] H. Jinwei, L. W. Yun, J. M. Guerrero, B. Frede, and V. C. Juan, An Islanding Microgrid Power Sharing Approach Using Enhanced Virtual Impedance Control Scheme. In: IEEE Trans. on Power Electronics, 28.11 (2013), pp. 5272-5282. [0174] [26] H. Jinwei and L. Yun Wei, Generalized Closed-Loop Control Schemes with Embedded Virtual Impedances for Voltage Source Converters with LC or LCL Filters, IEEE Trans. On Power Electronics, vol. 27, pp. 1850-1861, 2012. [0175] [27] L. Zheng, C. Zhuang, J. Zhang, and X. Du, An Enhanced Droop Control Scheme for Islanded Microgrids, International Journal of Control and Automation, vol. 8, pp. 63-74, 2015. [0176] [28] A. Yazdani and P. P. Dash, A Control Methodology and Characterization of Dynamics for a Photovoltaic (PV) System Interfaced With a Distribution Network, IEEE Trans. Power Delivery, vol. 24, pp. 1538-1551, June 2009. [0177] [29] D. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics Converters, Applications, and Design, 3 ed.: John Wiley and Sons, 2003. [0178] [30] M. Fazeli, P. Igic, P. Holland, R. P. Lewis, and Z. Zhuo, Novel Maximum Power Point Tracking with classical cascaded voltage and current loops for photovoltaic systems, in IET Conference on Renewable Power Generation (RPG 2011), pp. 1-5. [0179] [31] K. Kelesidis, G. Adamidis, and G. Tsengenes, Investigation of a control scheme based on modified p-q theory for single phase single stage grid connected PV system, Inter. Conf. Clean Elect. Power pp. 535-540, June 2011. [0180] [32] V. F. Pires, J. F. Martins, and H. Chen, Dual-inverter for grid-connected photovoltaic system: Modeling and sliding mode control, ScienceDirect: Solar Energy, vol. 86, pp. 2106-2115, July 2012. [0181] [33] Z. Bo, Z. Xuesong, and C. Jian, Integrated Microgrid Laboratory System, IEEE Trans. on Power Systems, vol. 27, pp. 2175-2185, 2012. [0182] [34] Z. Shuben, Y. Jian, W. Xiaomin, and Z. Ruiyi, Dynamic power provisioning for cost minimization in islanding micro-grid with renewable energy, in IEEE PES Innovative Smart Grid Technologies Conference (ISGT), 2014, pp. 1-5.