Intelligent integration strategies of wind farms in a super grid

1 Introduction

Wind energy already represents a significant part in international energy supply concepts. More than ever, it is our duty to meet the challenges of a stable energy production, with a large proportion of wind energy. In the coming years, wind energy is expected to cover an increasing share of global needs. These prerequisites depend mainly among others capacity of wind power technology to be integrated into existing network topologies. To do this, an intelligent and flexible technology is required for the challenges facing network managers on wind turbines and wind farms with the power plant behavior.

The increasing demand for electric power in a global economy characterized by an alarming recession of global fossil fuel reserves, imperatively induced a collapse in energy generation balance.

The procedures for renewable energy survey made by the research teams around the world are only partially successful. Given these circumstances, it is imperative to explore new operational and technical management of these grids are generally subject to adverse events likely to affect the quality of the services requested by customers, even partially[10].

Various procedures for controlling the stability of super networks, with the guarantee of balance of energy balance were proposed. In this context, some works [1] were based on the medium-term dynamic simulation to see the impact of the action to be taken and selecting appropriate control systems. This is based on the application of a modal analysis of the voltage combined with the assessment of the sensitivity of different power plants with respect to the wind farms.

Indeed, controlling the behaviour of a conventional power plant could be affected by a dysfunction in one or more wind farms requires instantaneous acquisition of active and reactive powers of the power plants and the magnitude of this impact in the order to take an appropriate decision ensuring a strengthening of the stability of these plants through intelligent control strategy acting so as to restore the level of voltage and powers required in any node of the electrical network studied.

Other authors [2–4] became interested in the study of dynamical models of the frequency to simulate the impact of the most important system parameters on the frequency response due to disturbances and consequently determine the optimal number of steps in the procedure of grid stabilisation.

Some done studies [5] are interested in developing techniques to control the vulnerability of a power system through a combined approach incorporating fuzzy logic and neural to avoid the collapse of the voltage.

In this context and in order to ensure a perfect stability of voltage and frequency throughout the network, we are interested to the implementation of a new smart strategy to achieve optimal integration of wind farms to a large network. Indeed, we have paid particular attention to assessing the sensitivity of the different power plants especially at moments of connection or disconnection of one or more wind farms wf ^k  ; k ={ 1, …,  n }.

The sensitivity of different power plants induced by the connection of wind farms in the studied network will be processed through a new smart strategy to guarantee a perfect stability in frequency and voltage of this network. Indeed, we evaluated the quality of active and reactive powers developed by each production plant according to those injected by the various wind farms, specially at the instants of connection and disconnection of these wind farms. Specifically, the based strategy takes into account voltage fluctuations at different nodes and fluctuations of active and reactive powers induced by the connection or disconnection of wind farms. Based on the sensitivity of each production plant to the impact of wind farms connected or disconnected, we proceeded by appropriate adjustment of powers and voltages applied in each network node.

2 Study design of a large network

The matrix of nodal admittances of a n network nodes is constructed as follows: Y ¯ n = [ Y ¯ ( n 1 , n 1 ) Y ¯ ( n 1 , n 2 ) … Y ¯ ( n 1 , n n ) Y ¯ ( n 2 , n 1 ) Y ¯ ( n 2 , n 2 ) … Y ¯ ( n 2 , n n ) . . … . Y ¯ ( n n , n 1 ) Y ¯ ( n n , n 2 ) … Y ¯ ( n n , n n ) ](1)

The injected apparent power in a node n _k is expressed as follows [17]: S ¯ n k = Y ( n k , n k ) . V n k 2 . e - j . θ n k n k + ∑ j = 1 ; j ≠ k j = N → k Y ( n k , n j ) . V n k . V n j . e j . ( α n k - α n j - θ n k n j )(2)

N_→k is the number of nodes connected to the node n _k .

Therefore: { P inj - n k = Y ( n k , n k ) . V n k 2 . cos ( θ n k n k ) + ∑ j = 1 ; j ≠ k j = N → k Y ( n k , n j ) . V n k . V n j . cos ( α n k - α n j - θ n k n j ) Q inj - n k = - Y ( n k , n k ) . V n k 2 . sin ( θ n k n k ) + ∑ j = 1 ; j ≠ k j = N → k Y ( n k , n j ) . V n k . V n j . sin ( α n k - α n j - θ n k n j )(3)

We define the specific active and reactive powers P_{spec-n k} , Q_{spec-n k} at any network node n _k as follows: { P spec - n k = P Gn k - P Cn k Q spec - nk = Q Gn k - Q Cn k(4)

The active and reactive powers P _{Gn k} ,  Q _{Gn k} will only be considered in case of connection of a power plant in this node n _k . P _{Cn k} ,  Q _{Cn k} are the active and reactive powers consumed in this node. Similarly, we define the functions of active and reactive power at any node in the network to be studied:

The Jacobian matrix [J (P _Vα , Q _Vα )] is constructed as follows: [ J P V ] = [ ∂ FP n 1 ∂ V n 1 ∂ FP n 1 ∂ V n 2 … ∂ FP n 1 ∂ V n n - 1 ∂ FP n 1 ∂ V n n ∂ FP n 2 ∂ V n 1 ∂ FP n 2 ∂ V n 2 … ∂ FP n 2 ∂ V n n - 1 ∂ FP n 2 ∂ V n n . . . . . . . . . . . . . . . ∂ FP n n - 1 ∂ V n 1 ∂ FP n n - 1 ∂ V n 2 … ∂ FP n n - 1 ∂ V n n - 1 ∂ FP n n - 1 ∂ V n n ∂ FP n n ∂ V n n 1 ∂ FP n n ∂ V n n 2 … ∂ FP n n ∂ V n n - 1 ∂ FP n n ∂ V n n ](5)[ J P α ] = [ ∂ FP n 1 ∂ α n 1 ∂ FP n 1 ∂ α n 2 … ∂ FP n 1 ∂ α n n - 1 ∂ FP n 1 ∂ α n n ∂ FP n 2 ∂ α n 1 ∂ FP n 2 ∂ α n 2 … ∂ FP n 2 ∂ α n n - 1 ∂ FP n 2 ∂ α n n . . . . . . . . . . . . . . . ∂ FP n n - 1 ∂ α n 1 ∂ FP n n - 1 ∂ α n 2 … ∂ FP n n - 1 ∂ α n n - 1 ∂ FP n n - 1 ∂ α n n ∂ FP n n ∂ α n 1 ∂ FP n n ∂ α n 2 … ∂ FP n n ∂ α n n - 1 ∂ FP n n ∂ α n n ](6)[ J Q V ] = [ ∂ FQ n 1 ∂ V n 1 ∂ FQ n 1 ∂ V n 2 … ∂ FQ n 1 ∂ V n n - 1 ∂ FQ n 1 ∂ V n n ∂ FQ n 2 ∂ V n 1 ∂ FQ n 2 ∂ V n 2 … ∂ FQ n 2 ∂ V n n - 1 ∂ FQ n 2 ∂ V n n . . . . . . . . . . . . . . . ∂ FQ n n - 1 ∂ V n 1 ∂ FQ n n - 1 ∂ V n 2 … ∂ FQ n n - 1 ∂ V n n - 1 ∂ FQ n n - 1 ∂ V n n ∂ FQ n n ∂ V n 1 ∂ FQ n n ∂ V n 2 … ∂ FQ n n ∂ V n n - 1 ∂ FQ n n ∂ V n n ](7)[ J Q α ] = [ ∂ FQ n 1 ∂ α n 1 ∂ FQ n 1 ∂ α n 2 … ∂ FQ n 1 ∂ α n n - 1 ∂ FQ n 1 ∂ α n n ∂ FQ n 2 ∂ α n 1 ∂ FQ n 2 ∂ α n 2 … ∂ FQ n 2 ∂ α n n - 1 ∂ FQ n 2 ∂ α n n . . . . . . . . . . . . . . . ∂ FQ n n - 1 ∂ α n 1 ∂ FQ n n - 1 ∂ α n 2 … ∂ FQ n n - 1 ∂ α n n - 1 ∂ FQ n n - 1 ∂ α n n ∂ FQ n n ∂ α n 1 ∂ FQ n n ∂ α n 2 … ∂ FQ n n ∂ α n n - 1 ∂ FQ n n ∂ α n n ](8)

The partial derivatives ∂ P inj - n k ∂ V n k , ∂ P inj - n k ∂ V n j of the active power injected into a node n _k relative to voltages (V _nk ,  V _nj ) j = { 1, …,  n }, and the partial derivatives ∂ P inj - n k ∂ α n k , ∂ P inj - n k ∂ α n j relative to the angle (α _{n k} , α _{n j} ) are calculated from the following relationships [17]: { ∂ P inj - n k ∂ V n k = Y ( n k , n k ) . V n k . cos ( θ n k n k ) + ∑ j = 1 j = n Y ( n k , n j ) . V n j . cos ( α n k - α n j - θ n k n j ) ∂ P inj - n k ∂ α n j = Y ( n k , n j ) . V n k . cos ( α n k - α n j - θ n k n j )(9){ ∂ P inj - n k ∂ α n k = - Y ( n k , n k ) . V n k 2 . sin ( θ n k n k ) - ∑ j = 1 j = n Y ( n k , n j ) . V n k . V n j . sin ( α n k - α n j - θ n k n j ) ∂ P inj - n k ∂ α n j = Y ( n k , n j ) . V n k . V n j . sin ( α n k - α n j - θ n k n j )(10)

Likewise, ∂ Q inj - n k ∂ V n k , ∂ Q inj - n k ∂ V n j and ∂ Q inj - n k ∂ α n k , ∂ Q inj - n k ∂ α n j are given by the following relationships [17]: { ∂ Q inj - n k ∂ V n j = - Y ( n k , n k ) . V n j . sin ( θ n k n k ) + ∑ j = 1 j = n Y ( n k , n j ) . V n k . sin ( α n k - α n j - θ n k n j ) ∂ Q inj - n k ∂ V n j = Y ( n k , n j ) . V n k . sin ( α n k - α n j - θ n k n j )(11){ ∂ Q inj - n k ∂ α n k = - Y ( n k , n k ) . V n k 2 . cos ( θ n k n k ) + ∑ j = 1 j = n Y ( n k , n j ) . V n k . V n j . cos ( α n k - α n j - θ n k n j ) ∂ Q inj - n k ∂ α n j = - Y ( n k , n j ) . V n k . V n k . cos ( α n k - α n j - θ n k n j )(12)

Formulas 9, 10, 11 and 12 are exclusively news set by us after extremely laborious tests and with those, we are able to simulate the behavior of a network of what size it is by the mean of an outstanding software under Matlab environment done by our self.

The equivalent circuit diagram of a single wind generator connected to an electrical grid as indicated by Fig. 3: I ¯ wg k = ( Y ¯ wg k + Y ¯ tr + Y ¯ 1 ) . ( E ¯ wg k - V ¯ n i )(13)

Given that the studied wind farm is made up of r wind generator, we obtain the following equivalent circuit:

Referring to Fig. 4, we write:

I ¯ wg = ( Y ¯ tr + Y ¯ l ) . ( V ¯ wg - V ¯ n i )(14)

On the other hand, the admittance Y ¯ wg k represents a proportion K _{wg k} of the total equivalent admittance Y ¯ wg eq, therefore: Y ¯ wg k = K wg k . Y ¯ wg eq(15)

So: I ¯ wg = Y ¯ wg eq . ∑ k = 1 k = r K wg k . E ¯ wg k - V ¯ wg . ∑ k = 1 k = r Y ¯ wg k(16)

Finally: I ¯ wg = Y ¯ wg eq . [ E ¯ wg eq - V ¯ wg ](17)

Where: { Y ¯ wg eq = ∑ k = 1 k = r Y ¯ wg k E ¯ wg eq = ∑ k = 1 k = r K wg k . E ¯ wg k(18)

Knowing that E ¯ wg eq is the total equivalent electromotive force (e.m.f) and Y ¯ wg eq the total equivalent admittance of the wind farm. The current through the bus k becomes:

where: Y ¯ wg eqt = Y ¯ wg eq + Y ¯ tr + Y ¯ l(19)

The active and reactive powers generated by the equivalent wind farm at the bus n _i : { P wg eq = Y wg eqt . E wg eq 2 . cos ( θ wg eqt ) - Y wg eqt . E wg eq . V n i . cos ( α wg eq - α n i - θ wg eqt ) Q wg eq = - Y wg eqt . E wg eq 2 . sin ( θ wg eqt ) - Y wg eqt . E wg eq . V n i . sin ( α wg eq - α n i - θ wg eqt )(20)

knowing that: { E ¯ wg eq = E wg eq . e j . α wg eq Y ¯ wg eqt = Y wg eqt . e j . θ wg eqt V ¯ n i = V n i . e j . α n i

Moreover, the active and reactive powers injected into the bus n _i are expressed as follows [17, 18]: { P i n j − n i = V n i . ∑ j = 1 j = N → i Y ( n i , n j ) . V n j . cos ( α n i − α n j − θ n i n j ) Q i n j − n i = V n i . ∑ j = 1 j = N → i Y ( n i , n j ) . V n j . sin ( α n i − α n j − θ n i n j )(21)

N_→i is the number of nodes connected to the node n _i .

We proposed in this paper to implement an intelligent integration strategy of wind farms in a super grid. This strategy is mainly based on the calculation of the sensitivities of active and reactive powers P _{M i} and Q _{M i} generated by each power plant, at a bus n _i , versus the active and reactive powers P_{inj-n x} and Q_{inj-n x} injected at a bus n _x . { P M i = ∑ j = 1 j = N → i Y ( n i , n j ) . V n i . V n j . cos ( α n i - α n j - θ n i n j ) Q M i = ∑ j = 1 j = N → i Y ( n i , n j ) . V n i . V n j . sin ( α n i - α n j - θ n i n j )(22)

N_→i is the number of nodes connected to the node n _i .

And the voltage level V _{n x} at bus n _x is written as follows [17]: { V n x = P inj - n x ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . cos ( α n x - α n j - θ n x n j ) V n x = Q inj - n x ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . sin ( α n x - α n j - θ n x n j )(23)

Relationships (22) and (23) give: { P M i = Y ( n i , n x ) . V n i . V n x . cos ( α n i - α n x - θ n i n x ) + ∑ j = 1 ; j ≠ x j = N → i Y ( n i , n j ) . V n i . V n j . cos ( α n i - α n j - θ n i n j ) Q M i = Y ( n i , n x ) . V n i . V n x . sin ( α n i - α n x - θ n i n x ) + ∑ j = 1 ; j ≠ x j = N → i Y ( n i , n j ) . V n i . V n j . sin ( α n i - α n j - θ n i n j )(24) Even yet: { P M i = Y ( n i , n x ) . V n i . V n x . cos ( α n i - α n x - θ n i n x ) + Γ n i → n j ( j ≠ x ) P inj Q M i = Y ( n i , n x ) . V n i . V n x . sin ( α n i - α n x - θ n i n x ) + Γ n i → n j ( j ≠ x ) Q inj(25)

Where:

Γ n i → n j ( j ≠ x ) P inj = ∑ j = 1 ; j ≠ x j = N → i Y ( n i , n j ) . V n i . V n j . cos ( α n i - α n j - θ n i n j ) Γ n i → n j ( j ≠ x ) Q inj = ∑ j = 1 ; j ≠ x j = N → i Y ( n i , n j ) . V n i . V n j . sin ( α n i - α n j - θ n i n j )(26)

Hence: { P M i = Y ( n i , n x ) . V n i . P inj - n x ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . cos ( α n x - α n j - θ n x n j ) . cos ( α n i - α n x - θ n i n x ) + Γ n i → n j ( j ≠ x ) P inj P M i = Y ( n i , n x ) . V n i . Q inj - n x ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . sin ( α n x - α n j - θ n x n j ) . cos ( α n i - α n x - θ n i n x ) + Γ n i → n j ( j ≠ x ) P inj Q M i = Y ( n i , n x ) . V n i . Q inj - n x ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . sin ( α n x - α n j - θ n x n j ) . sin ( α n i - α n x - θ n i n x ) + Γ n i → n j ( j ≠ x ) Q inj Q M i = Y ( n i , n x ) . V n i . P inj - n x ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . cos ( α n x - α n j - θ n x n j ) . sin ( α n i - α n x - θ n i n x ) + Γ n i → n j ( j ≠ x ) Q inj(27)

We focus only on the sensitivity of the of active and reactive powers P _{M i} and Q _{M i} generated by each power plant, at a bus n _i , versus the active and reactive powers P _{wg x} and Q _{wg x} generated at a bus n _x . { P M i = Y ( n i , n x ) . V n i . P inj - n x ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . cos ( α n x - α n j - θ n x n j ) . cos ( α n i - α n x - θ n i n x ) + Γ n i → n j ( j ≠ x ) P inj Q M i = Y ( n i , n x ) . V n i . Q inj - n x ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . sin ( α n x - α n j - θ n x n j ) . sin ( α n i - α n x - θ n i n x ) + Γ n i → n j ( j ≠ x ) Q inj(28)

Where: { P inj - n x = P wg x - P Cn x Q inj - n x = Q wg x - Q Cn x(29)

Then, the sensitivity of a machine M _i to the real P_{inj-n x} and reactive Q_{inj-n x} powers injected in a bus n _x is expressed as follow: { ∂ P M i ∂ P inj - n x = Y ( n i , n x ) . V n i . cos ( α n i - α n x - θ n i n x ) ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . cos ( α n x - α n j - θ n x n j ) ∂ Q M i ∂ Q inj - n x = Y ( n i , n x ) . V n i . sin ( α n i - α n x - θ n i n x ) ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . sin ( α n x - α n j - θ n x n j )(30)

In the case where the node n _i is not directly connected to a wind farm, then we write: { P M i = Y ix . V i . cos ix ∑ j = 1 j = N → x Y xj . V j . cos xj . P inj - n x + Γ n i → n j ( j ≠ x ) P inj Q M i = Y ix . V i . sin ix ∑ j = 1 j = N → x Y xj . V j . sin xj . Q inj - n x + Γ n i → n j ( j ≠ x ) Q inj(31)

Where: { Y ix . V i . cos ix = Y ( n i , n x ) . V n i . cos ( α n i - α n x - θ n i n x ) Y ix . V i . sin ix = Y ( n i , n x ) . V n i . sin ( α n i - α n x - θ n i n x )(32)

On the path to the wind farm: { P M i = Y ix . V i . cos ix Y xy . P inj - n y Γ n y → n j Y yj . V j . cos yj . cos xy + Γ n x → n j ( j ≠ y ) Y xj . V j . cos xj . P inj - n x + Γ n i → n j ( j ≠ x ) P inj Q M i = Y ix . V i . sin ix Y xy . Q inj - n y Γ n y → n j Y yj . V j . sin yj . sin xy + Γ n x → n j ( j ≠ y ) Y xj . V j . sin xj . Q inj - n x + Γ n i → n j ( j ≠ x ) Q inj(33)

Where: { Γ n x → n j ( j ≠ y ) Y xj . V j . cos xj = ∑ j = 1 j = N → x Y xj . V j . cos xj ( j ≠ y ) Γ n x → n j ( j ≠ y ) Y xj . V j . sin xj = ∑ j = 1 j = N → x Y xj . V j . sin xj ( j ≠ y )(34)

And: { Γ n y → n j Y yj . V j . cos yj = Y yt . P inj - n t Γ n t → n j Y tj . V j . cos tj . cos yt + Γ n y → n j ( j ≠ t ) Y yj . V j . cos yj Γ n y → n j Y yj . V j . sin yj = Y yt . Q inj - n t Γ n t → n j Y tj . V j . sin tj . sin yt + Γ n y → n j ( j ≠ t ) Y yj . V j . sin yj(35)

So: { P M i = Y ix . V i . cos ix Y xy . P inj - n y Y yt . P inj - n t Γ n t → n j Y tj . V j . cos tj . cos yt + Γ n y → n j ( j ≠ t ) Y yj . V j . cos yj . cos xy + Γ n x → n j ( j ≠ y ) Y xj . V j . cos xj . P inj - n x + Γ n i → n j ( j ≠ x ) P inj Q M i = Y ix . V i . sin ix Y xy . Q inj - n y Y yt . Q inj - n t Γ n t → n j Y tj . V j . sin tj . sin yt + Γ n y → n j ( j ≠ t ) Y yj . V j . sin yj . sin xy + Γ n x → n j ( j ≠ y ) Y xj . V j . sin xj . Q inj - n x + Γ n i → n j ( j ≠ x ) Q inj(36){ ∂ P M i ∂ P inj - n x = Y ( n i , n x ) . V n i . cos ( α n i - α n x - θ n i n x ) ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . cos ( α n x - α n j - θ n x n j ) ∂ Q M i ∂ Q inj - n x = Y ( n i , n x ) . V n i . sin ( α n i - α n x - θ n i n x ) ∑ j = 1 j = N → x Y ( n x , n j ) . V n j . sin ( α n x - α n j - θ n x n j )(37) In the case where the node n _i is not directly connected to a wind farm, then we write: { P M i = Y ix . V i . cos ix ∑ j = 1 j = N → x Y xj . V j . cos xj . P inj - n x + Γ n i → n j ( j ≠ x ) P inj Q M i = Y ix . V i . sin ix ∑ j = 1 j = N → x Y xj . V j . sin xj . Q inj - n x + Γ n i → n j ( j ≠ x ) Q inj(38)