Two-stage dispatch optimal model of virtual power plant considering pumped storage

When virtual power plant (VPP) participates in power grid dispatch, it not only faces the problem of market bidding but also has the security and stability problems of voltage, frequency, power flow, and so on. The optimal dispatch strategy of VPP, which participates in a hybrid market, is proposed. The two-stage optimal model is established. An economic dispatch optimal model based on robust control and stochastic linear programming is established to maximize the profit of VPP. Aiming to minimize the difference between the output power of each distribution energy resource and the optimal results of economic dispatch, a safety dispatch optimal model based on a particle swarm optimization algorithm is established. The simulation results with the measured data of the Ningxia power grid show that the two-stage optimal dispatch model is effective.


Introduction
With the acceleration of the construction of a new-type power system, the grid-connected proportion of multiple distributed energy resources (DER) is gradually increasing.It brings challenges to the security and stability operation of the power system, such as lack of supervision in participating markets, instability of voltage and frequency, and so on.Virtual power plant (VPP) technology can provide safe, reliable, and flexible active management for a high proportion of DER in the system [1].According to the different functions, it can be divided into commercial VPP(CVPP) and technical VPP (TVPP).TVPP assembles DER nearby, and CVPP organizes single or multiple TVPPs to participate in the electricity market.It gives full play to complementary technological advantages and scale benefits of DERs in new-type power systems [2][3].
Research on VPP participation in the electricity market has been carried out at home and abroad.In [4], a robust optimization strategy for day-ahead bidding is proposed considering demand response and the frequency regulation performance index of VPP.In [5][6], a day-ahead stochastic game and the realtime adaptive time scale optimization method for multiple virtual power plants considering network constraints are proposed.However, the bidding strategy of VPP is only for the day-ahead market in the above literature.The optimal dispatch strategy of VPP when participating in the hybrid market is not mentioned.
Therefore, a two-stage dispatch optimal model of VPP considering pumped storage in a hybrid market is proposed.An economic dispatch optimal model is established to maximize the profit of VPP, which uses robust control and stochastic linear programming to deal with uncertainties of the photovoltaic power station and electrovalence.Due to the results of economic dispatch are not met security requirements, a safety dispatch optimal model based on particle swarm optimization algorithm is established.Finally, the correctness and effectiveness of the above dispatch model are verified by the VPP model established with the measured data of the Ningxia power grid.

Dispatch Optimal Strategy of VPP in A Hybrid Market
The optimal dispatch strategy that participates in the hybrid market is as follows.Firstly, CVPP aggregates the state parameters of DER and establishes an objective economy function with maximum profit under the condition of environmental constraints and forward contract constraints.Then, TVPP establishes a security dispatch optimal scheme that corrects the economic dispatch from the CVPP scheme and submits it to the distribution system operator (DSO) for technical confirmation.Finally, TVPP will feed back the optimal dispatch scheme to CVPP after receiving the security confirmation from DSO. CVPP will transmit the generation plan to TVPP after receiving the verification and confirmation from the electricity market, and then TVPP will allocate the generation plan to each DER [7].

Economic dispatch objective function
In the process of economic dispatch, the optimal model established with the goal of maximum profit of CVPP is as follows: in Formula (1), K and T are the total number of scenes and the total number of periods, St and Zt are the profit and cost of VPP at t, respectively.In Formula (2), Ct and Dt are, respectively, the electric energy delivered according to the contract requirements and the electric energy delivered according to the day-ahead market plan at time t, and Lt is the electric energy that VPP needs to supply to the internal load.c is the electricity price of contract,  are respectively the deviations between actual VPP processing and bidding processing.
In Formula (3), Ot is electricity purchase quantity, ni is the total number of gas turbine units available for distribution, biis respectively the fixed cost and the action cost of unit i, Qt,i is the action sign position of gas turbine unit i at t, njis the number of segments after piecewise linearization of the quadratic cost function for the gas turbine i, mj is the generation cost slope of segment j for unit i, , , g i j t is the electricity generation in the j section of unit i at t.

Constraint condition
in Formula (4), PV ks G is the output of the photovoltaic power station under scenario k at time t, pump _ d ks G and pump _ c ts G are, respectively, the output power of the pumped storage turbine and pump scenario k at time t.
(2) Contract constraints ' t 1 1 in Formula (5), s is the allowable deviation coefficient of electric quantity stipulated in the medium and long-term contract,   is the actual contracted transmission quantity.In addition, it also includes the operational constraints of gas turbine and pumped storage, which no more details here.In the process of economic dispatch, the uncertainties of photovoltaic power stations and electrovalence are treated by robust control and stochastic linear programming [8].

Security
in Formula ( 7), gi,t, Ot, gin,t and gout,t are the optimal solutions of gas turbine i, electricity purchase quantity, the output power of pumped storage, and g are the optimal solutions for the above variables under the security dispatch model.A particle swarm optimization algorithm is used for security dispatch, which has the advantages of fewer parameters and fast convergence [9].

Constraint condition
(1) The constraint of the power flow ) in the formula, g, , i t P and g, , i t Q are the total active and reactive power of DG on node i at t; d, , i t P and d, , i t Q are the active and reactive power injected from node i at t; t i, V , , j t V , , i t  and j,t  are the voltage amplitude and voltage phase angle of node i and j; ij  is the phase angle of line admittance between node i and node j.
(2) Node voltage constraint In Formula ( 9), min i V and max i V are, respectively, the minimum and maximum voltage allowed by node i.In addition, the security constraint includes apparent power constraint of lines between nodes and capacity constraint of connecting points between the distribution network and main network.

Simulation Verification
The VPP simulation model includes a small photovoltaic power station in the Ningxia power grid, a pumped storage power station, and a gas turbine.The capacity of pumped storage is 40 MWh, the maximum storage power and generating power in a single period are 8 MW, and the storage power and generating efficiency are 87%.The maximum and minimum generation power of gas turbine are 2.5 MWh and 5.67 MWh.The climbing rate is 3 MW/h.The Start-stop cost is 30 €.The first-stage/secondstage slope is 35/40€/ MW, and the minimum start/stop time is 3/2 h.The active output power of the photovoltaic power station on a typical summer day is shown in Figure 1.Internal loads of VPP are measured by the Ningxia power grid shown in Figure 2. According to the electricity price of a typical summer day in the European Electricity Exchange Center, the contract electricity price in the mediumforward contract market is 45 €, and the deviation of the supply in a single period is ±10%.Three schemes are adopted for security dispatch.The initial scheme directly adopts the results of economic dispatch.Conditions of Scheme 1 and Scheme 2 are shown in Table 1.
Table 1.Conditions of security dispatch scheme Figure 5. Trading electric quantity of VPP From Figure 3 to Figure 5, the generation power of PV, the charge and discharge amount of the pumped storage power station, and the electric trading quantity with Scheme 1 and Scheme 2 are significantly reduced compared with the initial scheme.The reduction for generation power of each DER and trading electric quantity under Scheme 2 is larger by comparing with Scheme 1.In other words, the initial economic dispatch results are reduced to meet the requirements of the security constraint.The more stringent the security constraint is, the greater the reduction of the initial economic dispatch results will be.

Conclusion
Two-stage dispatch optimal model of a virtual power plant considering pumped storage in a hybrid market is proposed, and the main research content and conclusions are as follows: (1) The objective function of economic dispatch takes into account the deviation of electricity quantity in the medium-long term contract market, the bidding price in the day-ahead market, and the penalty of imbalance, so the economic dispatch optimal model can maximize the profit in the hybrid market.
(2) Security dispatch optimal model can correct the results of economic dispatch with considering the safety constraints.The more stringent the security constraint is, the greater the reduction of the initial economic dispatch results will be.
In the next step, the two-stage optimal model will be used in the practical engineering of the Ningxia power grid and verify the validity of the model in the hybrid market according to field tests.


are respectively electricity price of the day-ahead market and the power supply price of VPP to internal load under each scenario k. is the unbalance penalty under the scenario k at t,   , and - are respectively positive and negative price unbalance coefficients, tk   and tk