Optimized design of voltage control rules for distributed energy sources at substation inverter interfaces

By constructing a parallel microgrid system [26] containing N distributed power source and M loads, defined ℕs={1,2,⋯,N}$${\mathbb{N}_s} = \{ 1,2, \cdots ,N\}$$ and ℕL={1,2,⋯,M}$${\mathbb{N}_L} = \{ 1,2, \cdots ,M\}$$, the output current of the distributed power source is connected to the common DC bus via a DC/DC converter, and the loads are connected in parallel to the common DC bus. The microgrid system model is shown in Fig. 1.

Figure 1.

Microgrid system model

The communication network topology graph of the microgrid system is designed as Ω=(ℕS,H,A)$$\Omega = \left( {{\mathbb{N}_S},H,A} \right)$$, where ℕS$${\mathbb{N}_S}$$ is a network node; H∈ℕs×ℕs$$H \in {\mathbb{N}_s} \times {\mathbb{N}_s}$$ is an edge of the network; and A=(aij)N×N$$A = {\left( {{a_{ij}}} \right)_{N \times N}}$$ is a network neighbor link matrix. When the distributed power supply DG_i can obtain information from the distributed power supply DG_j, a_ij > 0; conversely, if DG_i cannot obtain DG_j obtain information, a_ij = 0. If i ≠ j, the Laplace matrix L=(lij)N×N$$L = {\left( {{l_{ij}}} \right)_{N \times N}}$$ of the network topology graph can be defined as l_ij = −a_ij, otherwise, lij=∑n=1,n≠iNain$${l_{ij}} = \sum\limits_{n = 1,n \ne i}^N {{a_{in}}}$$. Definition N_i is the set containing neighboring nodes i, and the information flow is connected if there exists a network pathway between any two nodes. In order to equalize the output current of each distributed power source and ensure bus voltage recovery, the microgrid system current and voltage sufficiency conditions are defined as follows: (1)Iidi=Ijdj$$\frac{{{I_i}}}{{{d_i}}} = \frac{{{I_j}}}{{{d_j}}}$$ (2)Vcom=Vref$${V_{com}} = {V_{ref}}$$

Where I_i and I_j are the distributed voltage output current controlled by the converter; d is the current ratio, the value of which is inversely proportional to the rated current of the distributed power supply in which it is located; V_com is the common bus voltage; and V_ref is the rated voltage of the common bus.

A hierarchical control architecture is designed for the above microgrid system to effectively achieve the voltage restoration and current equalization objectives. Each distributed power supply contains a local controller, which consists of primary control and secondary control. The primary control consists of a sag control and a voltage-current dual-loop controller, which is responsible for regulating the converter output to ensure that the converter output voltage can track the system voltage rating V_ref. The secondary controller outputs a compensation term u_i to achieve the microgrid system voltage restoration and current equalization objectives. The control strategy is shown below: (3)Vi(t)=Vref−RdIi(t)−δi(t)$${V_i}(t) = {V_{ref}} - {R_d}{I_i}(t) - {\delta_i}(t)$$ (4)δ̇i(t)=ui(t)$${\dot \delta_i}(t) = {u_i}(t)$$

where R_d is the sag factor; I_i(t) is the converter output current; and u_i(t) is the secondary controller compensation term.

The distributed iterative strategy [27] is applied to the secondary controller design, for each distributed iterative secondary controller, the control system can be equated to an intelligent body, which interacts with the microgrid system environment and develops the corresponding control strategy by obtaining the neighboring distributed power supply current information. In this control strategy, the sag control virtual resistance R_d is set to 0, i.e., the intelligent body is a no-sag distributed control scheme, and the secondary control directly provides voltage reference values for the voltage-current double-loop control in the primary control. Therefore, defining t₁, t₂, t₃, ⋯ characterized as a discrete sequence h = t_k+1 − t_k containing time interval h, the above control strategy can be characterized as: (5)Vi(t)=Vref−δi(t)$${V_i}(t) = {V_{ref}} - {\delta_i}(t)$$ (6)δi(k+1)=δi(t)+h×ui(k)$${\delta_i}(k + 1) = {\delta_i}(t) + h \times {u_i}(k)$$

where u_i(k) is the secondary controller output compensation value at moment t_k. The microgrid system output power flow is represented as follows: (7)Vcom=1∑i∈ℕsGi+∑i∈ℕL(1RLi)∑i∈NsGiVi$${V_{com}} = \frac{1}{{\sum\limits_{i \in {\mathbb{N}_s}} {{G_i}} + \sum\limits_{i \in {\mathbb{N}_L}} {\left( {\frac{1}{{{R_{Li}}}}} \right)} }}\sum\limits_{i \in {N_s}} {{G_i}} {V_i}$$ (8)Ii=Gi(Vi−Vcom)$${I_i} = {G_i}\left( {{V_i} - {V_{com}}} \right)$$

where G_i is the conductance of the line connecting the ind converter to the common bus V_com; R_Li is the ith load impedance. In order to effectively achieve the voltage recovery and current equalization objectives, the current sharing deviation and voltage recovery deviation of the ith distributed power supply are defined as e_Ii(k) and e_v(k). i.e: (9)eIi(k)=∑j∈Niaij(Iidi−Ijdj)$${e_{Ii}}(k) = \sum\limits_{j \in {N_i}} {{a_{ij}}} \left( {\frac{{{I_i}}}{{{d_i}}} - \frac{{{I_j}}}{{{d_j}}}} \right)$$ (10)ev(k)=Vcom−Vref$${e_v}(k) = {V_{com}} - {V_{ref}}$$

Distributed power current sharing deviation can be characterized as e_li(k) = −LD⁻¹I(k), where D=diag{d1,d1,⋯,dN}$$D = diag\left\{ {{d_1},{d_1}, \cdots ,{d_N}} \right\}$$, the zero space of LD⁻¹ can be characterized as span{d1,d1,⋯,dN}$$span\left\{ {{d_1},{d_1}, \cdots ,{d_N}} \right\}$$ when and only when Ω is connected. therefore, e_li(k) = 0 can be represented as I_i/d_i = I_j/d_j, and voltage restoration and current equalization objectives are achieved when and only when the information flow of the microgrid system is connected e_li(k) = 0, e_v(k) = 0. Then the voltage restoration deviation and current equalization deviation dynamics are characterized as: (11)eh(k+1) = eh(k)+hϖiGiui(k) +h∑j∈NjajGjuj(k)dj+hϑ∑j∈Njaijdj∑k∈ℕs/{ij}Gjul(k)$$\begin{array}{rcl} {e_h}(k + 1) &=& {e_h}(k) + h{\varpi_i}{G_i}{u_i}(k) \\ &&+ h\sum\limits_{j \in {N_j}} {{a_j}} \frac{{{G_j}{u_j}(k)}}{{{d_j}}} + h\vartheta \sum\limits_{j \in {N_j}} {\frac{{{a_{ij}}}}{{{d_j}}}} \sum\limits_{k \in {\mathbb{N}_s}/\{ ij\} } {{G_j}} {u_l}(k) \\ \end{array}$$ (12)ev(k+1)=ev(k)+hϑ∑i∈Ni(Giui(k))$${e_v}(k + 1) = {e_v}(k) + h\vartheta \sum\limits_{i \in {N_i}} {\left( {{G_i}{u_i}(k)} \right)}$$

where ϑ=1/∑j∈NsGi+∑j∈Ns(1/RLi)$$\vartheta = 1/\sum\limits_{j \in {N_s}} {{G_i}} + \sum\limits_{j \in {N_s}} {\left( {1/{R_{Li}}} \right)}$$; σi=(lii(ϑ−1)/di−∑j∈Niϑaij/dj)$${\sigma_i} = \left( {{l_{ii}}(\vartheta - 1)/{d_i} - \sum\limits_{j \in {N_i}} \vartheta {a_{ij}}/{d_j}} \right)$$. It can be seen that the microgrid system error dynamics are affected by multiple intelligences, and considering that each intelligence can make control decisions based on its own optimal value gain in a game-theoretic network, the microgrid system distributed power performance index function can be defined as: (13)Ji=∑k=0∞γk(aeii2(k)+bev2(k)+rui2(k))$${J_i} = \sum\limits_{k = 0}^\infty {{\gamma^k}} \left( {ae_{ii}^2(k) + be_v^2(k) + ru_i^2(k)} \right)$$

where a, b, r is the positive weight; γ is the performance metric function discount factor γ ∈ (0, 1]; then both the dynamic characteristics and the performance factor of the distributed power supply performance metric function depend on the controller actions. By introducing the definition of Nash equilibrium, the control actions of the remaining intelligences except the ith intelligence are defined as u−i={uj|j∈ℕS,j≠i}$${u_{ - i}} = \left\{ {{u_j}|j \in {\mathbb{N}_S},j \ne i} \right\}$$. Based on this, the voltage recovery deviation and current equalization deviation controller compensation term u_i(k) provided by each intelligence should ensure that the realization of the N intelligences achieves Nash equilibrium, and in order to efficiently illustrate such issues, two definitions are provided as follows:

Definition 1. u_i(k) is an optimal control action if the control action u_i(k) stabilizes Eqs. (10) and (11) and is guaranteed J_i to be finite.

Definition 2. There should exist a Nash equilibrium solution for a N-subject dynamic boonet system containing multiple control decision groups {u1#,u2#,⋯,uN#}$$\left\{ {u_1^\# ,u_2^\# , \cdots ,u_N^\# } \right\}$$ for all i ∈ N (14)Ji#≜Ji(ui#,u−i#)≤Ji(ui,u−i#)$$J_i^\# \triangleq {J_i}\left( {u_i^\# ,u_{ - i}^\# } \right) \leq {J_i}\left( {{u_i},u_{ - i}^\# } \right)$$

where N tuple {J1#,J2#,…JN#}$$\left\{ {J_1^\# ,J_2^\# , \ldots J_N^\# } \right\}$$ is referred to as the Nash equilibrium solution for N subjects. According to the above definition, the microgrid system distributed secondary controller control action u_i(k) not only realizes the system voltage recovery and current equalization, but also ensures that the microgrid system realizes the Nash equilibrium solution.

Distributed optimization [29] is commonly used to minimize the additive sum type function as its optimization objective function, each self-subject within the optimization system corresponds to a node, data information can be transmitted between nodes, nodes transmitting data information to each other are called neighbors of another node. As shown in the following equation: (15)minx∈Rf(x)≜∑i=1nfi(x)$${\min _{x \in R}}f(x) \triangleq \mathop \sum \limits_{i = 1}^n {f_i}(x)$$

x is the node data information variable; f(x) is the data information variable function of node i; n is the set of all nodes of the optimization system.

The self-subject nodes are first weighted based on the data information of neighboring nodes, and then the gradient-assisted computation is used to update their own data information: (16)xi(k+1)=xi(k)+∑i∈Niaij(xj(k)−xi(k))−ρi(k)∇fi(xi(k))$$x_i^{(k + 1)} = x_i^{(k)} + \sum\limits_{i \in {N_i}} {{a_{ij}}} \left( {x_j^{(k)} - x_i^{(k)}} \right) - \rho_i^{(k)}\nabla {f_i}\left( {x_i^{(k)}} \right)$$

xi(k+1)$$x_i^{(k + 1)}$$ is the node data information of the k + 1rd iteration of the self-subject node i; xi(k)$$x_i^{(k)}$$ is the node data information of the kth iteration of the self-subject node i; N_i is the set of neighboring nodes of the self-subject node i; xj(k)$$x_j^{(k)}$$ is the node data information of the kth iteration of the self-subject node j; xj(k)−xi(k)$$x_j^{(k)} - x_i^{(k)}$$ is the information of the kth data interaction between the self-subject node i and the self-subject node j; a_ij is the weighting coefficient of the information interaction between the self-subject node i and the self-subject node j; ∇fi(xi(k))$$\nabla {f_i}\left( {x_i^{(k)}} \right)$$ is the self-subject node i’s own gradient: ρ_i^(k) denotes the gradient coefficient for the krd iteration from the subject node i.

On the basis of the typical distributed gradient descent algorithm, a distributed gradient algorithm that considers the relative state of the self-subject nodes is proposed with full consideration of the relative state of the self-gradient, as follows: (17)xi(k+1)=xi(k)+∑i∈Niaijsgn(xj(k)−xi(k))−ρi(k)∇fi(xi(k)) sgn(x)={ 1 ifx≥0 −1 ifx<0$$\begin{array}{l} x_i^{(k + 1)} = x_i^{(k)} + \sum\limits_{i \in {N_i}} {{a_{ij}}} \operatorname{sgn} \left( {x_j^{(k)} - x_i^{(k)}} \right) - \rho_i^{(k)}\nabla {f_i}\left( {x_i^{(k)}} \right) \\ \operatorname{sgn} (x) = \left\{ {\begin{array}{*{20}{l}} 1&{ if\ x \geq 0} \\ { - 1}&{ if\ x < 0} \end{array}} \right. \\ \end{array}$$

sgn is a relative state function which has only 1 and -1.

Fig. 3 shows the information interaction diagram of distributed generation clusters. Distributed power plants, distributed power sources, and load users in a grid are divided into distributed clusters, each of which has its own leader.

Figure 3.

Distributed generation cluster information interaction diagram

1)

Objective function

The minimum operating cost of the system is used as the objective function, and the operating cost includes the active output operating cost and the reactive output operating cost: (18)minOC=∑i∈NPxPDGiADGi+∑j∈NPcPDGjADGj+∑x∈NQurQDGxADGx+∑y∈NQxQDGyADGy$$\min {O_C} = \sum\limits_{i \in {N_{Px}}} {{P_{DGi}}} {A_{DGi}} + \sum\limits_{j \in {N_{Pc}}} {{P_{DGj}}} {A_{DGj}} + \sum\limits_{x \in {N_{Qur}}} {{Q_{DGx}}} {A_{DGx}} + \sum\limits_{y \in {N_{Qx}}} {{Q_{DGy}}} {A_{DGy}}$$

O_C is the system operating cost; N_Puc is the uncontrollable, N_Pc is the controllable, N_Quc is the uncontrollable reactive distributed energy pool; N_Qc is the controllable reactive distributed energy pool; P_DGi is the uncontrollable distributed energy i node active output. A_DGi is the energy operating cost coefficient; P_DGj is the energy j node active output; Q_DGx is the energy x node reactive output; ADGj$${A_{DG_j}}$$ is the controllable active distributed energy operating cost coefficient; Q_DGy is the controllable distributed energy y node reactive output; A_DGY is the controllable active distributed energy operating cost coefficient. 2)

Distributed generation cluster constraint

Controllable distributed energy output constraints: (19){ PDGmin≤PDGj≤PDGmax∀j∈NPc QDGmin≤QDGy≤QDGmax∀y∈NQc$$\left\{ {\begin{array}{*{20}{l}} {{P_{DG\min }} \leq {P_{DGj}} \leq {P_{DG\max }}\forall j \in {N_{{P_c}}}} \\ {{Q_{DG\min }} \leq {Q_{DGy}} \leq {Q_{DG\max }}\forall y \in {N_{{Q_c}}}} \end{array}} \right.$$

Cluster system voltage constraints: (20)Uimin≤Ui≤Uimax$${U_{i\min }} \leq {U_i} \leq {U_{i\max }}$$

U_i is the voltage value at node i when the system is running; U_imin and U_imax are the minimum and maximum values of the voltage at node i, respectively. 3)

Information interaction variables

In order to coordinate and optimize the voltage control of distributed generation clusters. Set the objective function of information interaction between clusters I_V: (21)IVi=∂Oc∂Pi+∂Oc∂Qi$${I_{Vi}} = \frac{{\partial {O_c}}}{{\partial {P_i}}} + \frac{{\partial {O_c}}}{{\partial {Q_i}}}$$

I_V is the inter-cluster information interaction objective function: O_C is the system operation cost; P is the distributed energy active output, Q is the distributed energy reactive output; i is the node number. For easy representation, the inter-cluster information interaction objective function is rewritten as: (22)IV=ξi+δi$${I_V} = {\xi_i} + {\delta_i}$$

ξ_i denotes the distributed energy active information interaction variable at node i; δ_i denotes the distributed energy reactive information interaction variable at node i. Namely: (23)IVi=ξi+δi$${I_{Vi}} = {\xi_i} + {\delta_i}$$

Active information interaction variable:

Between distributed generation clusters, the load customers use the same amount of electricity as the distributed generation units generate, i.e., the power inequality is zero: (24)limt→∞‖ΔPi‖=0,∀i∈N$$\mathop {\lim }\limits_{t \to \infty } \left\| {\Delta {P_i}} \right\| = 0,\forall i \in N$$

ΔP_i denotes the cluster i active power inequality measure, and N denotes the distributed generation cluster. The leader of each cluster I_V needs to reach a consistent equilibrium point: (25)limt→∞‖ξlead,i−ξi*‖=0,∀i∈N$$\mathop {\lim }\limits_{t \to \infty } \left\| {{\xi_{lead,i}} - \xi_i^*} \right\| = 0,\forall i \in N$$

ξ_lead,i denotes the leader distributed energy active information interaction variable of cluster i; ξi*$$\xi_i^*$$ denotes the I_V consistent equilibrium point of cluster i.

According to the distributed optimization theory, the cluster distributed power active output operating cost model is a quadratic cost function: (26)ξi=∂Ci(PGi)/∂PGi=up1PGi+up2$${\xi_i} = {{\partial {C_i}\left( {{P_{Gi}}} \right)} \mathord{\left/ {\vphantom {{\partial {C_i}\left( {{P_{Gi}}} \right)} {\partial {P_{Gi}}}}} \right. } {\partial {P_{Gi}}}} = {u_{p1}}{P_{Gi}} + {u_{p2}}$$

The power imbalance reference value corresponding to the distributed generation cluster can be expressed as: (27)ΔPi=(ξi*−uP2)/(2up1)−Pi$$\Delta {P_i} = {{\left( {\xi_i^* - {u_{P2}}} \right)} \mathord{\left/ {\vphantom {{\left( {\xi_i^* - {u_{P2}}} \right)} {\left( {2{u_{p1}}} \right)}}} \right. } {\left( {2{u_{p1}}} \right)}} - {P_i}$$

When the system converges to the mean consistent point ΔP_i = 0, i.e., Pi*=(ξi*−uP2)/2uP1$${P_i}^* = \left( {\xi_i^* - {u_{P2}}} \right)/2{u_{P1}}$$. P_i^* is the active power of the distributed generation units in cluster i when the system reaches the optimal equilibrium point.

Reactive power information interaction variable:

The reactive power output of the distributed generation cluster can be expressed as: (28)Q=UIsinΘ=UIXsinΘX=UEcosσ−UX$$Q = UI\sin \Theta = U\frac{{IX\sin \Theta }}{X} = U\frac{{E\cos \sigma - U}}{X}$$

Make the reactive power inequality of the cluster zero: (29)limt→∞‖ΔQi‖=0,∀i∈N$$\mathop {\lim }\limits_{t \to \infty } \left\| {\Delta {Q_i}} \right\| = 0,\forall i \in N$$

Leader I_V of each cluster needs to reach a consistent equilibrium point: (30)limt→∞‖δlead,i−δi*‖=0,∀i∈N$$\mathop {\lim }\limits_{t \to \infty } \left\| {{\delta_{lead,i}} - \delta_i^*} \right\| = 0,\forall i \in N$$

Interaction variable: δ_i^* denotes the I_V-consistent equilibrium point of cluster i.

The cluster distributed power reactive operating cost is modeled as a quadratic cost function: (31)δi=∂Ci(QGi)/∂QGi=uq1QGi+uq2$${\delta_i} = \partial {C_i}\left( {{Q_{Gi}}} \right)/\partial {Q_{Gi}} = {u_{q1}}{Q_{Gi}} + {u_{q2}}$$

The power imbalance reference value corresponding to the distributed generation cluster can be expressed as: (32)ΔQi=(δi*−uQ2)/(2uQ1)−Qi$$\Delta {Q_i} = {{\left( {\delta_i^* - {u_{Q2}}} \right)} \mathord{\left/ {\vphantom {{\left( {\delta_i^* - {u_{Q2}}} \right)} {\left( {2{u_{Q1}}} \right)}}} \right. } {\left( {2{u_{Q1}}} \right)}} - {Q_i}$$

When the system converges to the mean consistent point ΔQ_i = 0, i.e., Qi*=(δi*−uQ2)/2uQ1$${Q_i^*} = {{\left( {{\delta_i^*} - {u_{Q2}}} \right)} \mathord{\left/ {\vphantom {{\left( {{\delta_i^*} - {u_{Q2}}} \right)} {2{u_{Q1}}}}} \right. } {2{u_{Q1}}}}$$.

After the individual cluster hold-up expectation points have been determined, the power inequality measure for each cluster can be determined based on the hold-up equilibrium points: (33)ΔPi=Pi*−Pi,∀i∈N ΔQi=Qi*−Qi,∀i∈N$$\begin{array}{l} \Delta {P_i} = P_i^* - {P_i},\forall i \in N \\ \Delta {Q_i} = Q_i^* - {Q_i},\forall i \in N \\ \end{array}$$

1)

Intra-cluster active information interaction

Based on the amount of active power inequality assigned to each cluster, the update strategy for the active information interaction variable of each cluster leader unit is as follows: (34)ξi(k+1)=∑j=1ndijξj(k)+εΔPi(k)$$\xi_i^{(k + 1)} = \sum\limits_{j = 1}^n {{d_{ij}}} \xi_j^{(k)} + \varepsilon \Delta P_i^{(k)}$$

When ΔP > 0, it means that the power used by the load is greater than the power generated, so the current ξ should be increased and vice versa.

The active information variable update strategy is: (35)ξi(k+1)=ξi(k)+∑j=1ndijξj(k)$$\xi_i^{(k + 1)} = \xi_i^{(k)} + \sum\limits_{j = 1}^n {{d_{ij}}} \xi_j^{(k)}$$

d_ij denotes the active information interaction right value between nodes i and j, d_ij ≠ 0 if there is a communication line connection between nodes i and j, and d_ij = 0 otherwise; n is the number of nodes neighboring node i. 2)

Intra-cluster reactive information interaction

The update strategy of reactive information interaction variables for each cluster leader unit is as follows: (36)δi(k+1)=δi(k)−ρi(k)∇fi(δi(k))+γΔQi(k)$$\delta_i^{(k + 1)} = \delta_i^{(k)} - \rho_i^{(k)}\nabla {f_i}\left( {\delta_i^{(k)}} \right) + \gamma \Delta Q_i^{(k)}$$

The reactive information variable update strategy is: (37)δi(k+1)=δi(k)+∑i=1nδijsgn(δj(k)−δi(k))$$\delta_i^{(k + 1)} = \delta_i^{(k)} + \sum\limits_{i = 1}^n {{\delta_{ij}}} \operatorname{sgn} \left( {\delta_j^{(k)} - \delta_i^{(k)}} \right)$$

Fig. 4 shows the distributed generation intra-cluster drafting control strategy. i_d, i_q, u_d, and u_q are abc/dq converted to obtain the current-voltage dq components after the leader unit is updated I_V and the distributed power sources within each cluster follow the leader to update their respective I_V until the constraints are satisfied.

Figure 4.

Control strategy of the distributed generation cluster

Due to the access of distributed power in the new energy distribution network, the volatility of the grid voltage becomes stronger, the traditional deterministic criterion is no longer applicable to the current scheduling and control decision-making, and the introduction of probabilistic decision-making analysis is more relevant to the new energy grid. In this paper, the node voltage retention index (NVRI) is used as the evaluation index of voltage fluctuation, which indicates the ability of node voltage to maintain stability after accessing distributed power supply, and the index reflects the situation of nodes near a certain voltage value through the form of probability, and provides guidance for the work of the grid control center in regulating the voltage, and the formula is shown below: (38)ZNVRI=m(Φ)M$${Z_{NVRI}} = \frac{{m(\Phi )}}{M}$$ (39)Φ={Vi,t||Vi,t−Vt−1|≥αVt−1}$$\Phi = \left\{ {{V_{i,t}}\left| {\left| {{V_{i,t}} - {V_{t - 1}}} \right|} \right. \geq \alpha {V_{t - 1}}} \right\}$$

where m(Φ) denotes the number of elements in the set, M is the total number of samples, V_i,t and V_i,t are the voltage amplitudes of node i in the grid at moments t and t − 1, respectively, and α is the threshold of the voltage fluctuation range, which can be specified according to the evaluation needs.

Z_NVRI actually reflects the probability of the change of voltage fluctuation at the moment before and after the node after the DG access, and a large probability indicates a large voltage fluctuation, and vice versa, a small voltage fluctuation.

The evaluation process of ESS and DR for coordinated voltage in new energy distribution network is as follows: 1)

Simulated in MATLAB to the relevant distributed power supply output data and sampling of output.

This paper verifies and analyzes the impact of ESS and DR on the coordinated voltage control of new energy distribution networks. Among the examples in this section of the algorithm only in node 10 access to the wind power generation system consisting of three wind turbines whose capacities are all 500kW, the operating parameters of the wind turbine are shown in Table 1. The scale parameter c in the stochastic model parameters of the wind turbine is a parameter reflecting the average wind speed size in the region, so assume that c=8.52m/s at the moment of t-1, take the expected power at this time as the actual output power at the time of t-1, and then compute = t-1V 0.9527, while set c=7.013m/s at the moment of t, and use the Monte Carlo simulation method to Calculate the probabilistic current of the system, and then analyze the voltage fluctuation between the two moments due to the change of wind power output, and α is taken as 1% for NVRI calculation.

In this paper, we mainly analyze the effects of ESS and DR on coordinated voltage fluctuation, so we simultaneously access ESS at node 10, and node 9 and node 11 as DR user nodes participating in grid operation scheduling. The role of ESS and DR on coordinated voltage fluctuation is analyzed by analyzing the following two operation scenarios at time t: 1)

Without considering ESS and DR, the distribution grid operates in a wind power access environment.

Fig. 5 shows the probability density (PDF) of the voltage distribution of node 10 in two operation cases, where (a) and (b) are the PDF without considering ESS and DR and the PDF considering ESS and DR, respectively.Fig. 6 shows the cumulative probability distribution (CDF) of the voltage at node 10.

Figure 5.

The probability density of the voltage distribution under two kinds of strips

Figure 6.

The voltage cumulative probability distribution of node 10

From the figure, it can be seen that in the operation state of (1), due to the random fluctuation of the fan output, the possibility of the voltage fluctuation range of node 10 at the moment of t is in the range of 0.91338~1.03796p.u., while in the operation state of (2), due to the consideration of the coordinated voltage effect of ESS and DR, it can be seen that the possibility of the voltage fluctuation range of the node 10 at this time is in the range of 0.93934~1.03914p.u. The CDFs of node 10 are shown in Fig. 6. 1.03914p.u., and the fluctuation probability is greater in the interval of voltage value of 0.94659~0.9997p.u., which makes the transition of the node voltage between t-1 and t moments smoother. The node voltage retention index NVRI can be seen that the value of the evaluation index of node 10 after considering ESS and DR (0.63975) is smaller than the value when ESS and DR are not considered (0.33757). The above analysis can prove the effectiveness of ESS and DR in smoothing the voltage fluctuation caused by DG.