Scheduling method for power system based on flexible HVDC

Abstract

The present disclosure provides a scheduling method for a power system based on flexible HVDC (high-voltage direct current) and a pumped storage power station, which belongs to a field of power system control technologies. The method is applicable in a power system having a flexible HVDC system and a pumped storage power station. By establishing a scheduling model for the power system, which contains an objective function and multiple constraints, and solving the scheduling model, a capability of the pumped storage power station is used to adjust the unstable output of the renewable energy power generator and stabilize fluctuant of the renewable energy power generation, such that a power incoming into a load center presents a stable ladder pattern and an optimal scheduling scheme can be obtained.

Claims

1. A scheduling method for a power system based on flexible high-voltage direct current (HVDC), comprising: establishing a scheduling model for the power system based on flexible HVDC, the power system including a pumped storage power station for stabilizing fluctuant of renewable energy power stations, the scheduling model comprising an objective function and a plurality of constraints; wherein the objective function of the scheduling model is configured for minimizing a total cost S.sub.SUM of the power system, and the objective function is expressed by: $\min \left[S_{\mathrm{SUM}}=\underset{i\in I}{.Math.}{A}_i\left(P_i\right)+\underset{i\in G}{.Math.}{G}_i\left(P_{\mathrm{Gi}}\right)+S_{\mathrm{pun}}\right]$ wherein the total cost contains a transmission cost, an electricity cost and a penalty term, the transmission cost is represented by $\underset{i\in I}{.Math.}{A}_i\left(P_i\right);$ where A.sub.i represents a transmission cost function on an i-th transmission line in the power system, P.sub.i represents an active power on the i-th transmission line, and I represents a set of flexible direct current transmission branches; A.sub.i=R.sub.iP.sub.i.sup.2; where R.sub.i represents line loss on the i-th transmission line; wherein the electricity cost is represented by $\underset{i\in G}{.Math.}{G}_i\left(P_{\mathrm{Gi}}\right);$ where G represents a set of nodes connected to electric generators in the power system, and G.sub.i represents an electricity cost function of an electric generator at an i-th node, P.sub.Gi represents an active power of the electric generator at the i-th node; G.sub.i=a.sub.iP.sub.Gi.sup.2+b.sub.iP.sub.Gi+c.sub.i; where a.sub.i,b.sub.i,c.sub.i represent electricity cost parameters of the electric generator at the i-th node, respectively; wherein the penalty term is a sum of an electricity abandoning penalty and a load tracking offset penalty, and is represented by S.sub.pun=S.sub.1+S.sub.2; wherein the plurality of constraints comprises a pumped storage power station constraint expressed by:
w.sub.u,t+1−w.sub.u,t=w.sub.h,t−w.sub.g,t
w.sub.u,min≤w.sub.u,t≤w.sub.u,max
w.sub.l,t+1−w.sub.l,t=w.sub.g,t−w.sub.h,t
w.sub.l,min≤w.sub.l,t≤w.sub.l,max
w.sub.h,t=η.sub.hp.sub.h,t
p.sub.g,t=η.sub.gw.sub.g,t
p.sub.ch.t=B(t)p.sub.g,t
p.sub.dis.t=B(t)p.sub.g,t
p.sub.ch.t≥0
p.sub.dis.t≥0 where p.sub.g,t represents a generating power of the pumped storage power station at the time point t, w.sub.g,t represents a water-use power of the pumped storage power station at the time point t, η.sub.g represents a generating efficiency of the pumped storage power station, p.sub.h,t represents an electricity-use power of the pumped storage power station at the time point t, w.sub.h,t represents a water-store power of the pumped storage power station at the time point t, η.sub.h represents a pumping efficiency of the pumped storage power station, w.sub.u,t represents a water storage of an upstream water reservoir at the time point t, w.sub.u,t+1 represents a water storage of the upstream water reservoir at a time point t+1, w.sub.u,max represents a maximum water storage of the upstream water reservoir, w.sub.u,min represents a minimum water storage of the upstream water reservoir, w.sub.l,t represents a water storage of a downstream water reservoir at the time point t, w.sub.l,t+1 represents a water storage of the downstream water reservoir at the time point t+1, w.sub.l,max represents a maximum water storage of the downstream water reservoir, w.sub.l,min represents a minimum water storage of the downstream water reservoir, p.sub.ch.t represents an incoming power of the pumped storage power station at the time point t, p.sub.dis.t represents an outgoing power of the pumped storage power station at the time point t, B represents a Boolean function; solving the scheduling model to acquire an optimal active power P.sub.Gi of each electric generator at each node, an optimal power set value w.sub.i,0 of each renewable energy power station at each node, an optimal generating power p.sub.g,t of the pumped storage power station at the time point t and an optimal transmission power l.sub.z of a flexible direct current transmission line connected to a flexible direct current bus Z; and operating the power system based on the optimal P.sub.Gi, w.sub.i,0, p.sub.g,t, l.sub.z.

2. The scheduling method of claim 1, wherein the electricity abandoning penalty is represented by $S_1=\alpha \left[\underset{j\in J}{.Math.}{\left(P_j-p_j\right)}^2\right],$ where P.sub.j represents an actual output of a j-th renewable energy power station, p.sub.j represents a predictive output of the j-th renewable energy power station; J represents of a set of renewable energy power stations; α represents a coefficient for the electricity abandoning penalty of the renewable energy power station.

3. The scheduling method of claim 1, wherein the load tracking offset penalty is represented by S.sub.2=γ(P.sub.b.t−P.sub.b.t−1).sup.2, t∈T, where γ represents a coefficient for the load tracking offset penalty, T represents a controlled time period, P.sub.b.t represents a load tracking value at the time point t, P.sub.b.t−1 represents a load tracking value at a time point t−1.

4. The scheduling method of claim 1, wherein the plurality of constraints further comprise an electric generator's power constraint; wherein the electric generator's power constraint is expressed by:
P.sub.Gi,min≤P.sub.Gi−α.sub.i(u.sub.max−u.sub.0)
P.sub.Gi−α.sub.i(u.sub.min−u.sub.0)≤P.sub.Gi,max where i is one element from a set G representing a set of nodes connected to electric generators, P.sub.Gi,min, P.sub.Gi,max represent a minimum output and a maximum output of the electric generator at an i-th node, respectively, P.sub.Gi represents an active power of the electric generator at the i-th node, α.sub.i represents an adjustment coefficient for an automatic generation control of the electric generator at the i-th node, u.sub.max represents a maximum output of a renewable energy power station, u.sub.min represents a minimum output of the renewable energy power station, u.sub.0 represents an actual output of the renewable energy power station.

5. The scheduling method of claim 1, wherein the plurality of constraints further comprise a renewable energy power station's power constraint; wherein the renewable energy power station's power constraint is expressed by: $w_{i,\min }\le \underset{\_}{w}$ $w_{i,\max }\le \stackrel{\_}{w}$ $0\le w_{i,\min }\le w_{i,0}\le w_{i,\max }$ $u_0=\underset{i\in N_W}{.Math.}{w}_{i,0}$ $u_{\max }=\underset{i\in N_W}{.Math.}{w}_{i,\max }$ $u_{\min }=\underset{i\in N_W}{.Math.}{w}_{i,\min }$ where N.sub.w represents a set of nodes connected to renewable energy power stations, w.sub.i,0 represents a power set value of a renewable energy power station at an i-th node, w.sub.i,min represents a minimum output of the renewable energy power station at the i-th node, w.sub.i,max represents a maximum output of the renewable energy power station at the i-th node, w represents an lower limit of fluctuant of a renewable energy, w represents an upper limit of fluctuant of the renewable energy, u.sub.max represents a maximum output of the renewable energy power station, u.sub.min represents a minimum output of the renewable energy power station, u.sub.0 represents an actual output of the renewable energy power station.

6. The scheduling method of claim 1, wherein the plurality of constraints further comprise a whole system power balance constraint; wherein the whole system power balance constraint is expressed by: $\underset{i\in N_G}{.Math.}{P}_{\mathrm{Gi}}+\underset{i\in N_W}{.Math.}{w}_{i,0}=\underset{i\in N_D}{.Math.}{P}_{\mathrm{Di}}$ where N.sub.D represents a set of nodes connected to loads, N.sub.G represents a set of nodes connected to traditional energy power stations, N.sub.w represents a set of nodes connected to renewable energy power stations, P.sub.Gi represents an active power of the electric generator at an i-th node connected to a traditional energy power, P.sub.Di represents a load power of an i-th node connected to a load, w.sub.i,0 represents a power set value of a renewable energy power station at an i-th node connected to a renewable energy power station.

7. The scheduling method of claim 1, wherein the plurality of constraints further comprise a transmission power capacity constraint; wherein the transmission power capacity constraint is expressed by: $-{\stackrel{\_}{P}}_L\le \underset{i\in N_G}{.Math.}{G}_i^L\left(P_{\mathrm{Gi}}+{\alpha }_i{u}_0\right)+\underset{i\in N_W,{\mathrm{AG}}_i^L>0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\min }+\underset{i\in N_W,{\mathrm{AG}}_i^L<0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\max }+\underset{i\in N_D}{.Math.}{G}_i^L{P}_{\mathrm{Di}}$ $\underset{i\in N_G}{.Math.}{G}_i^L\left(P_{\mathrm{Gi}}+{\alpha }_i{u}_0\right)+\underset{i\in N_W,{\mathrm{AG}}_i^L>0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\max }+\underset{i\in N_W,{\mathrm{AG}}_i^L<0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\min }+\underset{i\in N_D}{.Math.}{G}_i^L{P}_{\mathrm{Di}}\le {\stackrel{\_}{P}}_L$ where N.sub.G represents a set of nodes connected to traditional energy power stations, N.sub.w represents a set of nodes connected to renewable energy power stations, N.sub.D represents a set of nodes connected to loads, G.sub.i.sup.L, G.sub.j.sup.L represent power transfer distribution factors of an L-th transmission branch relative to an i-th node and a j-th node, respectively, AG.sub.i.sup.l represents a sensitivity of the L-th transmission branch to the active power of an i-th node connected to a renewable energy power station, P.sub.Gi represents an actual output of an electric generator at an i-th node connected to a traditional energy power station, α.sub.i represents an adjustment coefficient for an automatic generation control of the electric generator at the i-th connected to traditional energy power station, w.sub.i,min represents a minimum output of the renewable energy power station at the i-th node connected to a renewable energy power station, w.sub.i,max represents a maximum output of the renewable energy power station at the i-th node connected to a renewable energy power station, u.sub.0 represents an actual output of the renewable energy power station, P.sub.Di represents a load power of the i-th node connected to a load; ${\mathrm{AG}}_i^L=G_i^L-\underset{j\in N_G}{.Math.}{G}_j^L{\alpha }_j,$ where P.sub.L represents a maximum allowable power of the L-th transmission branch, α.sub.j represents an adjustment coefficient for an automatic generation control of the electric generator at the j-th node.

8. The scheduling method of claim 1, wherein the plurality of constraints further comprise a flexible direct current constraint; wherein the flexible direct current constraint is expressed by:
p.sub.z=p.sub.z.i+p.sub.z.o
p.sub.z+l.sub.z=0
p.sub.z≤S.sub.z
r≥|l.sub.z/S.sub.zl|
r≤1 where p.sub.z.i, p.sub.z.o represent an incoming power and an outgoing power of a flexible direct current bus Z, respectively, p.sub.z represents a direct current power of the flexible direct current bus Z, l.sub.z represents a transmission power of a flexible direct current transmission line connected to the flexible direct current bus Z, r represents a maximum load rate of the flexible direct current line, S.sub.z represents a capacity of a convertor station at the flexible direct current bus Z, S.sub.zl represents a capacity of the flexible direct current line connected to the flexible direct current bus Z.

9. A scheduling apparatus for a power system based on flexible high-voltage direct current (HVDC), comprising: a processor; a memory having executable instructions stored therein, wherein when the instructions are executed by the processor, the processor is caused to perform the scheduling method for a power system based on flexible HVDC comprising: establishing a scheduling model for the power system based on flexible HVDC, the power system including a pumped storage power station for stabilizing fluctuant of renewable energy power stations, the scheduling model comprising an objective function and a plurality of constraints; wherein the objective function of the scheduling model is configured for minimizing a total cost S.sub.SUM of the power system, and the objective function is expressed by: $\min \left[S_{\mathrm{SUM}}=\underset{i\in I}{.Math.}{A}_i\left(P_i\right)+\underset{i\in G}{.Math.}{G}_i\left(P_{\mathrm{Gi}}\right)+S_{\mathrm{pun}}\right]$ wherein the total cost contains a transmission cost, an electricity cost and a penalty term, the transmission cost is represented by $\underset{i\in I}{.Math.}{A}_i\left(P_i\right);$ where A.sub.i represents a transmission cost function on an i-th transmission line in the power system, P.sub.i represents an active power on the i-th transmission line, and I represents a set of flexible direct current transmission branches; A.sub.i=R.sub.iP.sub.i.sup.2; where R.sub.i represents line loss on the i-th transmission line; wherein the electricity cost is represented by $\underset{i\in G}{.Math.}{G}_i\left(P_{\mathrm{Gi}}\right);$ where G represents a set of nodes connected to electric generators in the power system, and G.sub.i represents an electricity cost function of an electric generator at an i-th node, P.sub.Gi represents an active power of the electric generator at the i-th node; G.sub.i=a.sub.iP.sub.Gi.sup.2+b.sub.iP.sub.Gi+c.sub.i; where a.sub.i,b.sub.i,c.sub.i represent electricity cost parameters of the electric generator at the i-th node, respectively; wherein the penalty term is a sum of an electricity abandoning penalty and a load tracking offset penalty, and is represented by S.sub.pun=S.sub.1+S.sub.2; wherein the plurality of constraints comprises a pumped storage power station constraint expressed by:
w.sub.u,t+1−w.sub.u,t=w.sub.h,t−w.sub.g,t
w.sub.u,min≤w.sub.u,t≤w.sub.u,max
w.sub.l,t+1−w.sub.l,t=w.sub.g,t−w.sub.h,t
w.sub.l,min≤w.sub.l,t≤w.sub.l,max
w.sub.h,t=η.sub.hp.sub.h,t
p.sub.g,t=η.sub.gw.sub.g,t
p.sub.ch.t=B(t)p.sub.g,t
P.sub.dis.t=B(t)p.sub.g,t
p.sub.ch.t≥0
p.sub.dis.t≥0 where p.sub.g,t represents a generating power of the pumped storage power station at the time point t, w.sub.g,t represents a water-use power of the pumped storage power station at the time point t, η.sub.g represents a generating efficiency of the pumped storage power station, p.sub.h,t represents an electricity-use power of the pumped storage power station at the time point t, w.sub.h,t represents a water-store power of the pumped storage power station at the time point t, η.sub.h represents a pumping efficiency of the pumped storage power station, w.sub.u,t represents a water storage of an upstream water reservoir at the time point t, w.sub.u,t+1 represents a water storage of an upstream water reservoir at a time point t+1, w.sub.u,max represents a maximum water storage of the upstream water reservoir, w.sub.u,min represents a minimum water storage of the upstream water reservoir, w.sub.l,t represents a water storage of a downstream water reservoir at the time point t, w.sub.l,t+1 represents a water storage of a downstream water reservoir at the time point t+1, w.sub.l,max represents a maximum water storage of the downstream water reservoir, w.sub.l,min represents a minimum water storage of the downstream water reservoir, p.sub.ch.t represents an incoming power of the pumped storage power station at the time point t, p.sub.dis.t represents an outgoing power of the pumped storage power station at the time point t, B represents a Boolean function; solving the scheduling model to acquire an optimal active power P.sub.Gi of each electric generator at each node, an optimal power set value w.sub.i,0 of each renewable energy power station at each node, an optimal generating power p.sub.g,t of the pumped storage power station at the time point t and an optimal transmission power l.sub.z of a flexible direct current transmission line connected to a flexible direct current bus Z; and operating the power system based on the optimal P.sub.Gi, w.sub.i,0, p.sub.g,t, l.sub.z.

10. The scheduling anuaratus of claim 9, wherein the electricity abandoning penalty is represented by $S_1=\alpha \left[\underset{j\in J}{.Math.}{\left(P_j-p_j\right)}^2\right],$ where P.sub.j represents an actual output of a j-th renewable energy power station, p.sub.j represents a predictive output of the j-th renewable energy power station; J represents of a set of renewable energy power stations; α represents a coefficient for the electricity abandoning penalty of the renewable energy power station.

11. The scheduling apparatus of claim 9, wherein the load tracking offset penalty is represented by S.sub.2=γ(P.sub.b.t−P.sub.b.t−1).sup.2, t∈T, where γ represents a coefficient for the load tracking offset penalty, T represents a controlled time period, P.sub.b.t represents a load tracking value at the time point t, P.sub.b.t−1 represents a load tracking value at a time point t−1.

12. The scheduling apparatus of claim 9, wherein the plurality of constraints further comprise an electric generator's power constraint; wherein the electric generator's power constraint is expressed by:
P.sub.Gi,min≤P.sub.Gi−α.sub.i(u.sub.max−u.sub.0)
P.sub.Gi−α.sub.i(u.sub.min−u.sub.0)≤P.sub.Gi,max where i is one element from a set G representing a set of nodes connected to electric generators, P.sub.Gi,min, P.sub.Gi,max represent a minimum output and a maximum output of the electric generator at an i-th node, respectively, P.sub.Gi represents an active power of the electric generator at the i-th node, α.sub.i represents an adjustment coefficient for an automatic generation control of the electric generator at the i-th node, u.sub.max represents a maximum output of a renewable energy power station, u.sub.min represents a minimum output of the renewable energy power station, u.sub.0 represents an actual output of the renewable energy power station.

13. The scheduling apparatus of claim 9, wherein the plurality of constraints further comprise a renewable energy power station's power constraint; wherein the renewable energy power station's power constraint is expressed by: $w_{i,\min }\le \underset{\_}{w}$ $w_{i,\max }\le \stackrel{\_}{w}$ $0\le w_{i,\min }\le w_{i,0}\le w_{i,\max }$ $u_0=\underset{i\in N_W}{.Math.}{w}_{i,0}$ $u_{\max }=\underset{i\in N_W}{.Math.}{w}_{i,\max }$ $u_{\min }=\underset{i\in N_W}{.Math.}{w}_{i,\min }$ where N.sub.w represents a set of nodes connected to renewable energy power stations, w.sub.i,0 represents a power set value of a renewable energy power station at an i-th node, w.sub.i,min represents a minimum output of the renewable energy power station at the i-th node, w.sub.i,max represents a maximum output of the renewable energy power station at the i-th node, w represents an lower limit of fluctuant of a renewable energy, w represents an upper limit of fluctuant of the renewable energy, u.sub.max represents a maximum output of the renewable energy power station, u.sub.min represents a minimum output of the renewable energy power station, u.sub.0 represents an actual output of the renewable energy power station.

14. The scheduling apparatus of claim 9, wherein the plurality of constraints further comprise a whole system power balance constraint; wherein the whole system power balance constraint is expressed by: $\underset{i\in N_G}{.Math.}{P}_{\mathrm{Gi}}+\underset{i\in N_W}{.Math.}{w}_{i,0}=\underset{i\in N_D}{.Math.}{P}_{\mathrm{Di}}$ where N.sub.D represents a set of nodes connected to loads, N.sub.G represents a set of nodes connected to traditional energy power stations, N.sub.w represents a set of nodes connected to renewable energy power stations, P.sub.Gi represents an actual output of the electric generator at an i-th node connected to a traditional energy power, P.sub.Di represents a load power of an i-th node connected to a load, w.sub.i,0 represents a power set value of a renewable energy power station at an i-th node connected to a renewable energy power station.

15. The scheduling apparatus of claim 9, wherein the plurality of constraints further comprise a transmission power capacity constraint; wherein the transmission power capacity constraint is expressed by: $-{\stackrel{\_}{P}}_L\le \underset{i\in N_G}{.Math.}{G}_i^L\left(P_{\mathrm{Gi}}+{\alpha }_i{u}_0\right)+\underset{i\in N_W,{\mathrm{AG}}_i^L>0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\min }+\underset{i\in N_W,{\mathrm{AG}}_i^L<0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\max }+\underset{i\in N_D}{.Math.}{G}_i^L{P}_{\mathrm{Di}}$ $\underset{i\in N_G}{.Math.}{G}_i^L\left(P_{\mathrm{Gi}}+{\alpha }_i{u}_0\right)+\underset{i\in N_W,{\mathrm{AG}}_i^L>0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\max }+\underset{i\in N_W,{\mathrm{AG}}_i^L<0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\min }+\underset{i\in N_D}{.Math.}{G}_i^L{P}_{\mathrm{Di}}\le {\stackrel{\_}{P}}_L$ where N.sub.G represents a set of nodes connected to traditional energy power stations, N.sub.w represents a set of nodes connected to renewable energy power stations, N.sub.D represents a set of nodes connected to loads, G.sub.i.sup.L, G.sub.j.sup.L represent power transfer distribution factors of an L-th transmission branch relative to an i-th node and a j-th node, respectively, AG.sub.i.sup.l represents a sensitivity of the L-th transmission branch to the active power of an i-th node connected to a renewable energy power station, P.sub.Gi represents an actual output of an electric generator at an i-th node connected to a traditional energy power station, α.sub.i represents an adjustment coefficient for an automatic generation control of the electric generator at the i-th connected to traditional energy power station, w.sub.i,min represents a minimum output of the renewable energy power station at the i-th node connected to a renewable energy power station, w.sub.i,max represents a maximum output of the renewable energy power station at the i-th node connected to a renewable energy power station, u.sub.0 represents an actual output of the renewable energy power station, P.sub.Di represents a load power of the i-th node connected to a load; ${\mathrm{AG}}_i^L=G_i^L-\underset{j\in N_G}{.Math.}{G}_j^L{\alpha }_j,$ where P.sub.L represents a maximum allowable power of the L-th transmission branch, α.sub.j represents an adjustment coefficient for an automatic generation control of the electric generator at the j-th node.

16. The scheduling apparatus of claim 9, wherein the plurality of constraints further comprise a flexible direct current constraint; wherein the flexible direct current constraint is expressed by:
p.sub.z=p.sub.z.i+p.sub.z.o
p.sub.z+l.sub.z=0
p.sub.z≤S.sub.z
r≥|l.sub.z/S.sub.zl|
r≤1 where p.sub.z.i, p.sub.z.o represent an incoming power and an outgoing power of a flexible direct current bus Z, respectively, p.sub.z represents a direct current power of the flexible direct current bus Z, l.sub.z represents a transmission power of a flexible direct current transmission line connected to the flexible direct current bus Z, r represents a maximum load rate of the flexible direct current line, S.sub.z represents a capacity of a convertor station at the flexible direct current bus Z, S.sub.zl represents a capacity of the flexible direct current line connected to the flexible direct current bus Z.

17. A non-transitory computer-readable storage medium having instructions stored therein, wherein when the instructions are executed by a processor, the processor is caused to perform the scheduling method for a power system based on flexible high-voltage direct current (HVDC), comprising: establishing a scheduling model for the power system based on flexible HVDC, the power system including a pumped storage power station for stabilizing fluctuant of renewable energy power stations, the scheduling model comprising an objective function and a plurality of constraints; wherein the objective function of the scheduling model is configured for minimizing a total cost S.sub.SUM of the power system, and the objective function is expressed by: $\min \left[S_{\mathrm{SUM}}=\underset{i\in I}{.Math.}{A}_i\left(P_i\right)+\underset{i\in G}{.Math.}{G}_i\left(P_{\mathrm{Gi}}\right)+S_{\mathrm{pun}}\right]$ wherein the total cost contains a transmission cost, an electricity cost and a penalty term, the transmission cost is represented by $\underset{i\in I}{.Math.}{A}_i\left(P_i\right);$ where A.sub.i represents a transmission cost function on an i-th transmission line in the power system, P.sub.i represents an active power on the i-th transmission line, and I represents a set of flexible direct current transmission branches; A.sub.i=R.sub.iP.sub.i.sup.2; where R.sub.i represents line loss on the i-th transmission line; wherein the electricity cost is represented by $\underset{i\in G}{.Math.}{G}_i\left(P_{\mathrm{Gi}}\right);$ where G represents a set of nodes connected to electric generators in the power system, and G.sub.i represents an electricity cost function of an electric generator at an i-th node, P.sub.Gi represents an active power of the electric generator at the i-th node; G.sub.i=a.sub.iP.sub.Gi.sup.2+b.sub.iP.sub.Gi+c.sub.i; where a.sub.i,b.sub.i,c.sub.i represent electricity cost parameters of the electric generator at the i-th node, respectively; wherein the penalty term is a sum of an electricity abandoning penalty and a load tracking offset penalty, and is represented by S.sub.pun=S.sub.1+S.sub.2; wherein the plurality of constraints comprises a pumped storage power station constraint expressed by:
w.sub.u,t+1−w.sub.u,t=w.sub.h,t−w.sub.g,t
w.sub.u,min≤w.sub.u,t≤w.sub.u,max
w.sub.l,t+1−w.sub.l,t=w.sub.g,t−w.sub.h,t
w.sub.l,min≤w.sub.l,t≤w.sub.l,max
w.sub.h,t=η.sub.hp.sub.h,t
p.sub.g,t=η.sub.gw.sub.g,t
p.sub.ch.t=B(t)p.sub.g,t
p.sub.dis.t=B(t)p.sub.g,t
p.sub.ch.t≥0
p.sub.dis.t≥0 where p.sub.g,t represents a generating power of the pumped storage power station at the time point t, w.sub.g,t represents a water-use power of the pumped storage power station at the time point t, η.sub.g represents a generating efficiency of the pumped storage power station, p.sub.h,t represents an electricity-use power of the pumped storage power station at the time point t, w.sub.h,t represents a water-store power of the pumped storage power station at the time point t, η.sub.h represents a pumping efficiency of the pumped storage power station, w.sub.u,t represents a water storage of an upstream water reservoir at the time point t, w.sub.u,t+1 represents a water storage of an upstream water reservoir at a time point t+1, w.sub.u,max represents a maximum water storage of the upstream water reservoir, w.sub.u,min represents a minimum water storage of the upstream water reservoir, w.sub.l,t represents a water storage of a downstream water reservoir at the time point t, w.sub.l,t+1 represents a water storage of a downstream water reservoir at the time point t+1, w.sub.l,max represents a maximum water storage of the downstream water reservoir, w.sub.l,min represents a minimum water storage of the downstream water reservoir, p.sub.ch.t represents an incoming power of the pumped storage power station at the time point t, p.sub.dis.t represents an outgoing power of the pumped storage power station at the time point t, B represents a Boolean function; solving the scheduling model to acquire an optimal active power P.sub.Gi of each electric generator at each node, an optimal power set value w.sub.i,0 of each renewable energy power station at each node, an optimal generating power p.sub.g,t of the pumped storage power station at the time point t and an optimal transmission power l.sub.z of a flexible direct current transmission line connected to a flexible direct current bus Z; and operating the power system based on the optimal P.sub.Gi, w.sub.i,0, p.sub.g,t, l.sub.z.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flowchart of a scheduling method for a power system based on flexible HVDC and a pumped storage power station according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

(2) The present disclosure provides a scheduling method for a power system based on flexible HVDC and a pumped storage power station, which will be described in detail below in combination with specific embodiments.

(3) A scheduling method for a power system based on flexible HVDC and a pumped storage power station is provided. As illustrated in FIG. 1, the method includes the followings.

(4) (1) Establishing a scheduling model for the power system based on flexible HVDC and the pumped storage power station, the scheduling model including an objective function and a plurality of constraints. The step has following sub steps (1-1) to (1-2).

(5) In the present disclosure, the power system includes several renewable energy power stations (typically, wind power generation stations and PV power stations), a large pumped storage power station, several traditional energy power stations, and a load center.

(6) (1-1) determining the objective function of the scheduling model for minimizing a total cost S.sub.SUM of the power system:

(7) $\min \left[S_{\mathrm{SUM}}=\underset{i\in I}{.Math.}{A}_i\left(P_i\right)+\underset{i\in G}{.Math.}{G}_i\left(P_{\mathrm{Gi}}\right)+S_{\mathrm{pun}}\right]$

(8) The total cost contains a transmission cost, an electricity cost and a penalty term, the transmission cost is represented by

(9) 0$\underset{i\in I}{.Math.}{A}_i\left(P_i\right);$
where A.sub.i represents a transmission cost function on an i-th transmission line in the power system, P.sub.i represents an active power on the i-th transmission line, which is a quantity to be solved, and I represents a set of flexible direct current transmission branches, which is a known quantity.

(10) The transmission cost function on the i-th transmission line can be expressed by:
A.sub.i=R.sub.iP.sub.i.sup.2;

(11) where R.sub.i represents line loss on the i-th transmission line, which is a known quantity.

(12) The electricity cost is represented by

(13) $\underset{i\in G}{.Math.}{G}_i\left(P_{\mathrm{Gi}}\right);$
where G.sub.i represents an electricity cost function of an electric generator at an i-th node of the power system, P.sub.Gi represents an active power of the electric generator at the i-th node, which is a quantity to be solved, and G represents a set of nodes connected to electric generators in the power system, which can be obtained from connected positions of all the electric generators in the power system, and is a known quantity.

(14) The electricity cost function of the electric generator at the i-th node can be expressed by:
G.sub.i=a.sub.iP.sub.Gi.sup.2+b.sub.iP.sub.Gi+c.sub.i

(15) where a.sub.i,b.sub.i,c.sub.i represent electricity cost parameters of the electric generator at the i-th node, respectively, which are known quantities.

(16) The penalty term is a sum of an electricity abandoning penalty and a load tracking offset penalty, and is represented by S.sub.pun=S.sub.1+S.sub.2.

(17) The electricity abandoning penalty is represented by

(18) $S_1=\alpha \left[\underset{j\in J}{.Math.}{\left(P_j-p_j\right)}^2\right],$
where P.sub.i represents an actual output of a renewable energy power station j, which is a quantity to be solved, p.sub.j represents a predictive output of the renewable energy power station j; J represents of a set of renewable energy power stations; a represents a coefficient for the electricity abandoning penalty of the renewable energy power station

(19) The load tracking offset penalty is represented by S.sub.2=γ(P.sub.b.t−P.sub.b.t−1).sup.2, t∈T , where γ represents a coefficient for the load tracking offset penalty, which is a known quantity. T represents a controlled time period, which is a known quantity. P.sub.b.t represents a load tracking value at a time point t.

(20) (1-2) determining the plurality of constraints, including:

(21) (1-2-1) an electric generator's power constraint:
P.sub.Gi,min≤P.sub.Gi−α.sub.i(u.sub.max−u.sub.0)
P.sub.Gi−α.sub.i(u.sub.min−u.sub.0)≤P.sub.Gi,max

(22) where i is one element from a set G representing a set of nodes connected to electric generators, P.sub.Gi,min, P.sub.Gi,max represent a minimum output and a maximum output of the electric generator at the i-th node, respectively, which are known quantities. P.sub.Gi represents an actual output of the electric generator at the i-th node, which is a quantity to be solved. α.sub.i represents an adjustment coefficient for an automatic generation control of the electric generator at the i-th node, which is a known quantity. u.sub.max represents a maximum output of the renewable energy power station, u.sub.min represents a minimum output of the renewable energy power station, u.sub.0 represents an actual output of the renewable energy power station.

(23) (1-2-2) a renewable energy power station's power constraint:

(24) $w_{i,\min }\le \underset{\_}{w}$$w_{i,\max }\le \stackrel{\_}{w}$$0\le w_{i,\min }\le w_{i,0}\le w_{i,\max }$$u_0=\underset{i\in N_W}{.Math.}{w}_{i,0}$$u_{\max }=\underset{i\in N_W}{.Math.}{w}_{i,\max }$$u_{\min }=\underset{i\in N_W}{.Math.}{w}_{i,\min }$

(25) where N.sub.w represents a set of nodes connected to renewable energy power stations, w.sub.i,0 represents a power set value of the renewable energy power station at the i-th node, which is a quantity to be solve. w.sub.i,min represents a minimum output of the renewable energy power station at the i-th node, which is a known quantity. w.sub.i,max represents a maximum output of the renewable energy power station at the i-th node, which is a known quantity. w represents an lower limit of fluctuant of a renewable energy, w represents an upper limit of fluctuant of the renewable energy;

(26) (1-2-3) a whole system power balance constraint:

(27) $\underset{i\in N_G}{.Math.}{P}_{\mathrm{Gi}}+\underset{i\in N_W}{.Math.}{w}_{i,0}=\underset{i\in N_D}{.Math.}{P}_{\mathrm{Di}}$

(28) where N.sub.D represents a set of nodes connected to loads, N.sub.G represents a set of nodes connected to traditional energy power stations, N.sub.w represents a set of nodes connected to renewable energy power stations, P.sub.Di represents a load power of an i-th node connected to the load, which is a known quantity.

(29) (1-2-4) a transmission power capacity constraint:

(30) $-{\stackrel{\_}{P}}_L\le \underset{i\in N_G}{.Math.}{G}_i^L\left(P_{\mathrm{Gi}}+{\alpha }_i{u}_0\right)+\underset{i\in N_W,{\mathrm{AG}}_i^L>0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\min }+\underset{i\in N_W,{\mathrm{AG}}_i^L<0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\max }+\underset{i\in N_D}{.Math.}{G}_i^L{P}_{\mathrm{Di}}$$\underset{i\in N_G}{.Math.}{G}_i^L\left(P_{\mathrm{Gi}}+{\alpha }_i{u}_0\right)+\underset{i\in N_W,{\mathrm{AG}}_i^L>0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\max }+\underset{i\in N_W,{\mathrm{AG}}_i^L<0}{.Math.}{\mathrm{AG}}_i^L{w}_{i,\min }+\underset{i\in N_D}{.Math.}{G}_i^L{P}_{\mathrm{Di}}\le {\stackrel{\_}{P}}_L$

(31) where G.sub.i.sup.L, G.sub.j.sup.L represent power transfer distribution factors of an L-th transmission branch relative to the i-th node and the j-th node, respectively, AG.sub.i.sup.l represents a sensitivity of the L-th transmission branch to the active power of the i-th node.

(32) ${\mathrm{AG}}_i^L=G_i^L-\underset{j\in N_G}{.Math.}{G}_j^L{\alpha }_j,$
where P.sub.L represents a maximum allowable power of the L-th transmission branch, which is a known quantity.

(33) (1-2-5) a pumped storage power station constraint:
w.sub.u,t+1−w.sub.u,t=w.sub.h,t−w.sub.g,t
w.sub.u,min≤w.sub.u,t≤w.sub.u,max
w.sub.l,t+1−w.sub.l,t=w.sub.g,t−w.sub.h,t
w.sub.l,min≤w.sub.l,t≤w.sub.l,max
w.sub.h,t=η.sub.hp.sub.h,t
p.sub.g,t=η.sub.gw.sub.g,t
p.sub.ch.t=B(t)p.sub.g,t
p.sub.dis.t=B(t)p.sub.g,t
p.sub.ch.t≥0
p.sub.dis.t≥0

(34) where p.sub.g,t represents a generating power of the pumped storage power station at the time point t, w.sub.g,t represents a water-use power of the pumped storage power station at the time point t, η.sub.g represents a generating efficiency of the pumped storage power station, p.sub.h,t represents an electricity-use power of the pumped storage power station at the time point t, w.sub.h,t represents a water-store power of the pumped storage power station at the time point t, η.sub.h represents a pumping efficiency of the pumped storage power station, w.sub.u,t represents a water storage of an upstream water reservoir at the time point t, w.sub.u,t+represents a water storage of the upstream water reservoir at a time point t+1, w.sub.u,max represents a maximum water storage of the upstream water reservoir, w.sub.u,min represents a minimum water storage of the upstream water reservoir, w.sub.l,t represents a water storage of a downstream water reservoir at the time point t, w.sub.l,t+1 represents a water storage of the downstream water reservoir at the time point t+1, w.sub.l,max represents a maximum water storage of the downstream water reservoir, w.sub.l,min represents a minimum water storage of the downstream water reservoir, p.sub.ch.t represents an incoming power of the pumped storage power station at the time point t, p.sub.dis.t represents an outgoing power of the pumped storage power station at the time point t, B represents a Boolean function.

(35) (1-2-6) a flexible direct current constraint:
p.sub.z=p.sub.z.i+p.sub.z.o
p.sub.z+l.sub.z=0
p.sub.z≤S.sub.z
r≥|l.sub.z/S.sub.zl|
r≤1

(36) where p.sub.z.i, p.sub.z.o represent an incoming power and an outgoing power of a flexible direct current bus Z, respectively, p.sub.z represents a direct current power of the flexible direct current bus Z, l.sub.z represents a transmission power of a flexible direct current line connected to the flexible direct current bus Z, r represents a maximum load rate of the flexible direct current line, S.sub.z represents a capacity of a convertor station at the flexible direct current bus Z, S.sub.zl represents a capacity of the flexible direct current line connected to the flexible direct current bus Z.

(37) (2) Solving the scheduling model using CPLEX to obtain respective optimal solutions of P.sub.Gi, w.sub.i,0, p.sub.g,t, l.sub.z, and using the respective optimal solutions in a generating control of the traditional energy power generation set, a generating control of the renewable energy power generation set, a control of the pumped storage power station and a control of the flexible direction current, so as to acquire an optimal scheduling scheme of the power system.