A Method for Calculating Nodal Electricity Price Considering Nonlinear Network Losses and Distributed Balancing Nodes

Abstract

The present invention provides a method for calculating nodal electricity prices considering non-linear network losses and distributed balancing nodes, belonging to the field of electricity markets. The method of the present invention includes: establishing an improved DC optimal power flow model considering non-linear network losses; using a correction method for distributed balancing nodes of the load weight type to correct the nodal electricity price model; then, using a relaxation method based on the second-order cone to process the corrected nodal voltage model, solving the model and calculating the nodal electricity price to ensure the optimality of the electricity price result; finally, substituting the nodal electricity price and system parameters into the proposed sufficient conditions for exact relaxation to verify the rationality of the electricity price calculation result. The method of the present invention scientifically measures nodal electricity prices, adapts to the actual needs of rapid clearing and accurate solution in the spot market, helps to improve the enthusiasm of electricity users to participate in the spot market, helps to improve the resource allocation efficiency of the electricity spot market, and has practical value for the pricing mechanism of the electricity spot market in China.

Description

Technical Field

[0001] The present invention belongs to the field of power markets, and particularly relates to a nodal price calculation method considering non-linear network losses and distributed balancing nodes. Background Art

[0002] Driven by the dual-carbon goal, the electricity spot market will play an important role in the accommodation of a high proportion of new energy. In the construction of the spot market, electricity price is called the "thermometer" of the market. Therefore, the pricing mechanism with nodal price as the core is the focus of research. However, at present, there are still problems in how to model the network loss part of the nodal price. The most accurate AC optimal power flow modeling method cannot meet the actual market demand in terms of convergence and calculation speed, while the classical model based on DC optimal power flow does not consider network losses. Although some improved models incorporate linear network losses into the model, they cannot meet the actual market demand in terms of calculation accuracy. Therefore, considering network losses non-linearly in the DC optimal power flow framework can best meet the requirements for the calculation speed and accuracy of nodal prices in the actual spot market pricing mechanism.

[0003] However, when considering network losses non-linearly in the DC optimal power flow framework, there are still three problems: First, the multi-solution of nodal prices. The traditional method uses a single balancing node. When the balancing node changes, different nodal price calculation results will appear. Since the balancing node lacks physical meaning and can be arbitrarily selected, it is impossible to determine which nodal price result is the most feasible, which will lead to disputes in terms of market fairness. Second, the non-convexity of the nodal price model. A non-convex model may be trapped in a local optimal solution rather than the global optimal solution during the solution process, resulting in higher nodal prices for each node and reducing the resource allocation efficiency of the spot market. Third, the unreasonable nodal price result. After the nodal price model is convexified, a relaxation gap may be generated, making the electricity price solution result infeasible and untrustworthy. Summary of the Invention

[0004] In order to overcome the above problems, the purpose of the present invention is to provide a nodal price calculation method considering non-linear network losses and distributed balancing nodes. This method not only ensures that the electricity price result does not change with the selection of the balancing node, making the nodal price less likely to cause disputes among electricity users, but also ensures that the electricity price model converges to the global optimal point, and verifies the rationality of the electricity price result through a posteriori sufficient conditions, which has practical value for improving the pricing mechanism of China's electricity spot market.

[0005] The technical solution of the present invention:

[0006] To achieve the above object, the present invention provides a nodal price calculation method considering non-linear network losses and distributed balancing nodes, including:

[0007] 1) Establish an improved DC optimal power flow model considering nonlinear network losses, and obtain a nodal price model. This model has a special structure and can implement a solution strategy based on second-order cone relaxation;

[0008] 2) Propose a distributed slack node method based on load weights to correct the nodal price model in step 1). The corrected nodal price model can avoid the problem of multiple solutions of nodal prices caused by the selection of slack nodes, thus avoiding disputes over market fairness;

[0009] 3) Use the solution strategy based on second-order cone relaxation to process the nodal price model corrected in step 2), and use the processed nodal price model to solve the model and calculate the nodal prices, which can ensure the global optimality of the price results;

[0010] 4) Obtain the nodal price calculation results in step 3) and system parameters, and substitute them into the sufficient conditions for exact relaxation to verify the rationality of the price calculation results.

[0011] Furthermore, the establishment of the improved DC optimal power flow model considering nonlinear network losses in step 1) includes:

[0012] Ⅰ. Under the framework of DC optimal power flow, model the network losses in a nonlinear manner, and its expression is:

[0013]

[0014] where \(P\) loss,Σ is the total network loss of the system, \(R\) k is the resistance of the \(k\)-th line, \(F\) k is the power flow of the \(k\)-th line, \(H\) k,i is the power transfer distribution factor of the \(i\)-th node to the \(k\)-th line, \(P\) i is the output of the \(i\)-th generator, \(D\) j is the load of the \(j\)-th load node, \(N\) l 、\(N\) g 、\(N\) d are the total numbers of lines, generators, and load nodes respectively;

[0015] Ⅱ. Incorporate the network losses constructed by Equation (1) as equivalent loads into the power balance equation of DC optimal power flow to obtain an improved DC optimal power flow model considering nonlinear network losses. This model aims to minimize the system generation cost and find the optimal solution under the constraints of power balance including nonlinear network losses, generator operation constraints, and secure transmission constraints:

[0016]

[0017] where \(P\) is the output of each generator, \(Q_0\), \(q_0\), \(r_0\) are the system generator cost coefficient matrices, \(N\)g where \(n\) is the number of generators, \(\mathbf{e}_1\) and \(\mathbf{e}_2\) are unit vectors, \(D\) is the load of each load node, \(R\) is the diagonal matrix composed of line resistances, \(C\) is the conversion matrix, \(H\) is the power transfer distribution factor matrix, and \(F\) max is the thermal limit of the transmission line, and \(P\) min , \(P\) max are the lower and upper limits of the output of each generator. \(P\) T , \(q_0\) T , are the transposes of the column vectors \(P\), \(q_0\), \(\mathbf{e}_1\), and \(\mathbf{e}_2\), respectively. The meanings of the expressions from top to bottom in Equation (2) are: the objective function of minimizing the system generation cost, the power balance constraint considering network losses, the secure transmission constraint, and the upper and lower limits constraint of generator output. By embedding the non-linear network loss expression based on line power flow and resistance: \((CP - D)\) T \(\varXi\) T \(R H (CP - D)\), the accuracy of the DC optimal power flow model is improved. Since the improved DC optimal power flow model is a single-constraint quadratic optimization problem and \(Q_0\) and \(R\) are positive definite matrices, it is easy to implement the solution strategy based on second-order cone relaxation.

[0018] Furthermore, the load weight type of distributed balancing node method in step 2) for correcting the node price model in step 1) includes:[[]]

[0019] a) Establish a load weight factor according to the load magnitude of each load node:[[]]

[0020]

[0021] where is the weight vector proportional to the node load magnitude,[[]] is the load weight factor of node \(i\), and \(D\) i is the load of node \(i\);[[]]

[0022] b) Use the load weight factor to correct the power transfer distribution factor matrix:[[]]

[0023]

[0024] where is the power transfer distribution factor matrix corrected by the distributed balancing node;[[]]

[0025] c) Substitute Equation (3) into Equation (4) to obtain

[0026] d) Replace the power transfer distribution factor matrix \(H\) in step 1) with Equation (4) to complete the correction of the load weight type of distributed balancing node.

[0027] Further, the node electricity price model in step 3) processed by the solution strategy based on second-order cone relaxation is based on the second-order cone relaxation method to handle the power balance constraint considering network losses in Equation (2), and relax it to:

[0028]

[0029] The inequality constraint in Equation (6) is a rotated second-order cone constraint, which convexifies the original non-convex node electricity price model and ensures that the node electricity price model converges to the global optimal solution.

[0030] Further, the node electricity price described in step 3) has the following expression:

[0031]

[0032] where LMP is the vector composed of the node electricity prices of each node, λ * 、 and are the dual multipliers corresponding to the power balance constraint, the upper and lower limits of the secure transmission constraint, P * is the optimal solution of the corrected model, represents the transpose of the matrix .

[0033] Further, substituting the sufficient conditions for exact relaxation in step 4) and verifying the rationality of the electricity price calculation results includes the following steps: ① Extract the congestion electricity price of each node according to the financial transmission right transaction. When the system does not carry out the financial transmission right transaction, extract the congestion electricity price part of each node's electricity price:

[0034]

[0035] where LMP CONGESTION is the vector composed of the node electricity prices of each node.

[0036] ② Substitute the electricity price solution result into the following three sufficient conditions. If any one of the three sufficient conditions is satisfied, it indicates that the solution result is reasonable.

[0037] Further, there are three forms of the sufficient conditions for exact relaxation in step 4): that is, the system is not congested; or the system is congested but the marginal unit bid is greater than the congestion electricity price; or the weighted sum of the node electricity prices weighted by the load is not zero. Substitute the node electricity price and system parameters in step 3) into the above sufficient conditions. If any one is satisfied, it indicates that the electricity price solution result is reasonable.

[0038] The beneficial effects of the present invention are reflected in:

[0039] (1) The present invention proposes a method for calculating nodal electricity prices considering network losses and distributed balancing nodes. In the framework of DC power flow, this method models network losses in a non-linear manner, incorporates the constructed network losses as equivalent loads into the power balance equation of the DC optimal power flow, and obtains an improved DC optimal power flow model considering non-linear network losses. By considering non-linear network losses, the calculation accuracy of the DC optimal power flow model is improved, enabling this method to effectively balance the accuracy of nodal electricity prices and the solution speed, and meet the actual needs of rapid clearing and accurate electricity price calculation in the electricity spot market.

[0040] (2) The present invention corrects the nodal electricity price model by establishing load weight factors, modifying the power transfer distribution factor matrix, etc., using the load weight type distributed balancing node method, so that the method of the present invention solves the market fairness disputes that may be caused by balancing nodes, scientifically provides a pricing mechanism for electricity users, avoids the multi-solution problem of electricity prices in the electricity spot market, is conducive to improving the enthusiasm of users to participate in the electricity spot market, and is conducive to providing correct economic signals for the trading electricity prices in the medium and long-term electricity market.

[0041] (3) In the present invention, a solution strategy based on second-order cone relaxation is used to handle the nodal electricity price model, enabling this method to ensure the lowest system generation cost through the convexification of the electricity price model. In addition, the present invention also verifies the rationality of the electricity price results scientifically by substituting the nodal electricity prices into the sufficient conditions for exact relaxation, which is conducive to improving the resource allocation efficiency of the electricity spot market and has practical value for improving the pricing mechanism of the electricity spot market in China. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a flow chart of the electricity price calculation method considering non-linear network losses and distributed balancing nodes;

[0043] Figure 2 It is a comparison chart of the solution time between the designed method of the present invention and the AC optimal power flow electricity price. DETAILED DESCRIPTION OF THE INVENTION

[0044] The present invention will be further described in detail below with reference to the drawings and embodiments: This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation manners and processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0045] I. The method for calculating nodal electricity prices considering non-linear network losses and distributed balancing nodes is implemented through the following steps:

[0046] (1) Improved DC optimal power flow model considering non-linear network losses

[0047] The system network loss is the thermal power dissipated on each line. Therefore, in the DC power flow framework, the network loss is modeled non-linearly, and its expression is:

[0048]

[0049] where \(P\) loss,Σ is the total network loss of the system, \(R_k\) k is the resistance of the \(k\)-th line, \(F_k\) k is the power flow of the \(k\)-th line, \(H_{ik}\) k,i is the power transfer distribution factor of the \(i\)-th node to the \(k\)-th line, \(P_i\) i is the output of the \(i\)-th generator, \(D_j\) j is the load of the \(j\)-th load node, \(N_l\) l 、\(N_g\) g 、\(N_d\) d are the total numbers of lines, generators, and load nodes respectively.

[0050] Taking the network loss constructed by Equation (1) as the equivalent load and incorporating it into the power balance equation of the DC optimal power flow, an improved DC optimal power flow model considering the non-linear network loss is obtained. This model aims to minimize the system generation cost and find the optimal solution under the constraints of power balance including network loss, generator operation constraints, and secure transmission constraints:

[0051]

[0052] where \(P\) is the output of each generator, \(Q_0\), \(q_0\), \(r_0\) are the system generator cost coefficient matrices, \(N_g\) g is the number of generators, \(e_1\), \(e_2\) are unit vectors, \(D\) is the load of each load node, \(R\) is the diagonal matrix composed of line resistances, \(C\) is the transformation matrix, \(H\) is the power transfer distribution factor matrix, \(F_{max}\) max is the thermal limit of the transmission line, \(P_{min}\) min 、\(P_{max}\) max are the lower and upper limits of the output of each generator; \(P^T\) T 、\(q_0^T\) T 、 are the transposes of the column vectors \(P\), \(q_0\), \(e_1\), \(e_2\) respectively. The meanings of the expressions from top to bottom in Equation (2) are: the system generation cost minimization objective function, the power balance constraint considering network loss, the secure transmission constraint, and the generator output upper and lower limit constraints.

[0053] By embedding the non-linear network loss expression based on line power flow and resistance: \((CP - D)\) T \(H\) TRH(CP-D) realizes the accuracy improvement of the DC optimal power flow model. Since the improved DC optimal power flow model is a single-constraint quadratic optimization problem and Q0 and R are positive definite matrices, it is easy to implement the solution strategy based on second-order cone relaxation. (2) Distributed balancing node method of load weight type

[0054] First, according to the load magnitudes of each load node, a load weight factor is established:

[0055]

[0056] where is the load weight factor of the i-th node.

[0057] Then, using the load weight factor, the power transfer distribution factor matrix is corrected:

[0058]

[0059] where is the power transfer distribution factor matrix corrected by the distributed balancing node, is the weight vector proportional to the load magnitude of the node, and its elements are determined by Equation (3).

[0060] Substitute Equation (4) into Model (2) to complete the correction of the distributed balancing node of the load weight type. So far, the part related to the selection of the balancing node is uniquely determined. The nodal price is determined by the derivative of the total system generation cost with respect to the nodal load, and its expression is:

[0061]

[0062] where λ * , and are the dual multipliers corresponding to the power balance constraint, the upper and lower limits of the secure transmission constraint, P * is the optimal solution of the corrected model, represents the transpose of the matrix .

[0063] (3) Convexification method of nodal price model based on second-order cone relaxation method

[0064] First, based on the second-order cone relaxation method, the power balance constraint of Model (2) is processed and relaxed to:

[0065]

[0066] The above inequality constraint is a rotated second-order cone constraint, which convexifies the original non-convex nodal price model and ensures that the nodal price model converges to the global optimal solution.

[0067] (4) Sufficient conditions for relaxation accuracy

[0068] After the electricity price model is convexified, a relaxation gap may be generated, making the minimum cost only the lower bound of the original model, and the electricity price solution result infeasible and untrustworthy. Therefore, it is necessary to verify the rationality of the electricity price result through sufficient conditions.

[0069] First, extract the congestion electricity price of each node according to the financial transmission right. When the system does not carry out financial transmission right transactions, extract the congestion electricity price part of the electricity price of each node:

[0070]

[0071] Substitute the electricity price solution result into the following three sufficient conditions. If any one of the sufficient conditions is met, it indicates that the solution result is reasonable.

[0072] 1) The system has no congestion

[0073] If the congestion electricity price of each node calculated by Equation (7) is zero, the calculation result of the nodal electricity price is reasonable. In actual situations, high-voltage transmission systems are likely to meet this sufficient condition.

[0074] 2) The system is congested, but the bid price of the marginal unit is greater than the congestion electricity price

[0075] This condition applies to the case where the system is congested, that is, when the congestion electricity price of the nodes provided by Equation (7) is not all zero.

[0076] First, extract the marginal units from the solution result of the convexified nodal electricity price model, satisfying that the output is not equal to its upper or lower limit:

[0077]

[0078] where G = {1, 2,..., N g}. Then obtain the bid prices of the above units according to the unit bid price list.

[0079] Finally, compare the bid prices of the above units with the congestion electricity price. If the bid price is greater than the congestion electricity price, the calculation result of the nodal electricity price is reasonable. In actual situations, medium- and low-voltage transmission and distribution networks are likely to meet this sufficient condition.

[0080] 3) The weighted sum of the nodal electricity prices weighted by the load is not zero

[0081] First, weight the electricity prices of each node according to the load weight factor to obtain the weighted sum of the nodal electricity prices:

[0082]

[0083] If the weighted sum of the nodal electricity prices obtained by Equation (9) is not zero, the calculation result of the nodal electricity price is reasonable. This sufficient condition applies to all congested and non-congested systems. The full process of the above steps is asFigure 1 as shown

[0084] II. Case Study Analysis

[0085] 1) Electricity price accuracy analysis

[0086] Taking the IEEE - 24 - bus power system in MATPOWER7.1 as an example, the electricity prices of each bus are calculated using the method designed by the present invention and compared with the electricity prices of the single - slack - bus method and the accurate electricity prices measured by the AC optimal power flow. The results are shown in Table 1

[0087] Table 1 Comparison of electricity prices of each bus

[0088]

[0089] It can be seen from Table 1 that the maximum fluctuation of the electricity price of the single - slack - bus method reaches 3.14% (bus 22). Compared with the single - slack - bus method, the electricity price calculated by the method designed by the present invention has no volatility and is close to the accurate electricity price. In the actual spot market, the electricity price does not fluctuate with the arbitrary selection of the slack bus, which is not likely to cause disputes over market fairness and is conducive to improving the enthusiasm of users to participate

[0090] The congestion electricity prices of each bus are measured again, and the congestion electricity prices of each bus are 0, indicating that the system is not congested, meeting the sufficient condition 1. Therefore, the electricity price results are reasonable

[0091] 2) Electricity price calculation speed analysis

[0092] The power systems of IEEE - 6 - bus, 9 - bus, 14 - bus, 24 - bus, 30 - bus, 39 - bus, 57 - bus, 118 - bus, 200 - bus, 500 - bus, 2000 - bus, 2383 - bus, 2736 - bus, 2746 - bus and 3120 - bus in MATPOWER7.1 are traversed. The systems are numbered from small to large, and the method designed by the present invention is compared with the AC optimal power flow with the best accuracy to measure the solution time (wherein, the thermal limits of the transmission lines in the cases of 14 - bus, 57 - bus and 118 - bus are not specified, so they are respectively set to 0.15, 0.10 and 0.05 times of the total system load size). The results are as Figure 2 shown Figure 2In [the case where] the system scale is small (200 nodes and below), the calculation speeds of the two types of methods are similar. However, when the system scale increases to 500 nodes and above, the solution time of the AC optimal power flow method increases rapidly with the system scale and reaches more than 20 seconds in the 3120-node system. However, the solution time of the design method of the present invention increases relatively slowly and remains at about 1 second even in the 3120-node system. Since the actual power system has a larger scale and more nodes, the AC optimal power flow method may not be able to meet the system requirements of the real-time market clearing once every 5 minutes in the calculation of nodal electricity prices in the actual spot market. In contrast, the design method of the present invention has a fast calculation speed and is more adaptable to the actual application requirements.

[0093] 3) Analysis of electricity price rationality

[0094] Traverse the power systems of IEEE-6 nodes, 9 nodes, 14 nodes, 24 nodes, 30 nodes, 39 nodes, 57 nodes, 118 nodes, 200 nodes, 500 nodes, 2000 nodes, 2383 nodes, 2736 nodes, 2746 nodes and 3120 nodes in MATPOWER7.1, and measure the cases where the system meets the sufficient conditions. The results are shown in Table 2.

[0095] Table 2 Cases where the system meets the sufficient conditions

[0096]

[0097] In the results of Table 2, the situation where sufficient condition 1 and sufficient condition 2 are simultaneously satisfied or not satisfied does not occur. This is because, on the one hand, sufficient condition 1 means the system is unblocked, while the premise of sufficient condition 2 is that the system is blocked. Since the system cannot be blocked and unblocked at the same time, they cannot be satisfied simultaneously. And the situation where both are not satisfied can only be the case where the system is blocked but the marginal unit bid is less than the congestion price, which does not occur in the test cases of MATPOWER7.1. The results of Table 2 show that the second-order cone relaxation strategy in the design of the present invention remains accurate for the test case systems, and its electricity price results are reasonable, indicating that the second-order cone relaxation strategy designed by the present invention is applicable to systems of different scales and different degrees of congestion and can meet the application requirements in the construction of the actual power spot market in China.

Claims

1. A method for calculating nodal electricity price considering nonlinear network losses and distributed balancing nodes, characterized in that, It includes the following steps: 1) Establish an improved DC optimal power flow model considering nonlinear network losses to obtain a nodal electricity price model, including: Ⅰ. Under the framework of DC optimal power flow, model network losses in a nonlinear manner, and its expression is: Among which P loss,Σ is the total network loss of the system, R k is the resistance of the k-th line, F k is the power flow of the k-th line, H k,i is the power transfer distribution factor of the i-th node to the k-th line, P i is the output of the i-th generator, D j is the load of the j-th load node, N l 、N g 、N d are the total numbers of lines, generators, and load nodes respectively; Ⅱ. Take the network losses constructed by Equation (1) as equivalent loads and incorporate them into the power balance equation of DC optimal power flow to obtain an improved DC optimal power flow model considering nonlinear network losses. This model aims to minimize the system generation cost. Under the constraints of power balance including nonlinear network losses, generator operation constraints, and secure transmission constraints, find the optimal solution through Equation (2): where P is the output of each generator, Q0, q0, r0 are the system generator cost coefficient matrices, N g is the number of generators, e1, e2 are unit vectors, D is the load of each load node, R is the diagonal matrix composed of line resistances, C is the conversion matrix, H is the power transfer distribution factor matrix, F max is the thermal limit of the transmission line, P min 、P max are the lower and upper limits of the output of each generator. The meanings of the expressions from top to bottom in Equation (2) are: the system generation cost minimization objective function, the power balance constraint considering network losses, the secure transmission constraint, and the generator output upper and lower limit constraints; 2) Use the distributed slack bus method with load weights to correct the nodal electricity price model in step 1), including: a) Establish a load weight factor according to the load magnitudes of each load bus: Among them, is a weight vector proportional to the node load magnitude, is the load weight factor of node i, and D i is the load of node i; b) Use the load weight factor to correct the power transfer distribution factor matrix: Among them, is the power transfer distribution factor matrix corrected by the distributed balancing node; c) Substitute Equation (3) into Equation (4) to obtain d) Replace the power transfer distribution factor matrix H in step 1) with Equation (4) to complete the distributed slack bus correction with load weights; 3) Use a solution strategy based on second-order cone relaxation to handle the corrected nodal electricity price model in step 2), solve the model and calculate the nodal electricity price. Using the solution strategy based on second-order cone relaxation to handle the nodal electricity price model in step 2) is based on the second-order cone relaxation method to handle the power balance constraint considering network losses in Equation (2), and relax it to: The inequality constraint in Equation (5) is a rotated second-order cone constraint, which convexifies the original non-convex nodal electricity price model and ensures that the nodal electricity price model converges to the global optimal solution; The expression of the said nodal electricity price is: where LMP is a vector composed of the nodal electricity prices of each node, and λ * , and are the dual multipliers corresponding to the power balance constraint, the upper and lower limits of the secure transmission constraint, and P * is the optimal solution of the corrected model; 4) Obtain the nodal electricity price calculation results and system parameters in step 3), substitute them into the sufficient conditions for exact relaxation, and verify the rationality of the electricity price calculation results, including the following steps: ① Extract the congestion price of each node according to the financial transmission right trading. When the system does not carry out financial transmission right trading, extract the congestion price part of each node's electricity price: ② Substitute the electricity price solution results into the following three sufficient conditions. If any one of the three sufficient conditions is met, it indicates that the solution results are reasonable. The three sufficient conditions are that the system has no congestion, the system has congestion but the bid of the marginal unit is greater than the congestion price, and the weighted sum of the nodal electricity prices weighted by loads is not zero.

2. The nodal electricity price calculation method considering non-linear network losses and distributed balancing nodes according to claim 1, characterized in that The specific meaning of the sufficient condition that the system has no congestion is that the congestion prices of all nodes calculated by Equation (7) are zero, then the system has no congestion and the nodal electricity price calculation results are reasonable.

3. A nodal electricity price calculation method considering non-linear network losses and distributed balancing nodes according to claim 1, characterized in that, The specific meaning of the system having congestion but the bid of the marginal unit being greater than the congestion price is that when the congestion prices of the nodes provided by Equation (7) are not all zero, First, extract the marginal unit from the solution results of the convexified nodal electricity price model, which satisfies that the output is not equal to its upper or lower limit as shown in Equation (8). Then, obtain the bid of the i-th unit through the bid table and obtain the node number j where the unit is located; obtain the congestion price of the unit through the j-th element in Equation (7). If the bid of the unit is greater than the congestion price, it means that the system has congestion but the bid of the marginal unit is greater than the congestion price. where G = {1, 2,..., N g}.

4. The nodal electricity price calculation method considering non-linear network losses and distributed balancing nodes according to claim 1, characterized in that The specific meaning of the weighted sum of the nodal electricity prices weighted by loads not being zero is: First, the electricity prices of each node are weighted by the load weight factor to obtain the weighted sum of the node electricity prices as shown in Equation (9): If the weighted sum of the node electricity prices obtained from Equation (9) is not zero, the calculation result of the node electricity price is reasonable.

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